LMFDB - Embedded newform 343.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [343,2,Mod(1,343)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(343, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("343.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 343 = 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	343.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:	$2.73886878933$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1279733.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 10x^{3} + 10x^{2} - 11x - 1 $ x^6 - 2x^5 - 6x^4 + 10x^3 + 10x^2 - 11*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.0849355$ of defining polynomial
Character	$\chi$	$=$	343.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33192 q^{2} -2.95499 q^{3} +3.43783 q^{4} -1.95286 q^{5} +6.89078 q^{6} -3.35289 q^{8} +5.73194 q^{9} +O(q^{10})$	\(q-2.33192 q^{2} -2.95499 q^{3} +3.43783 q^{4} -1.95286 q^{5} +6.89078 q^{6} -3.35289 q^{8} +5.73194 q^{9} +4.55391 q^{10} +2.65101 q^{11} -10.1587 q^{12} +1.50061 q^{13} +5.77069 q^{15} +0.943005 q^{16} -2.09215 q^{17} -13.3664 q^{18} +6.38881 q^{19} -6.71361 q^{20} -6.18193 q^{22} -2.12424 q^{23} +9.90775 q^{24} -1.18632 q^{25} -3.49929 q^{26} -8.07285 q^{27} -7.42740 q^{29} -13.4568 q^{30} +0.0654672 q^{31} +4.50678 q^{32} -7.83370 q^{33} +4.87871 q^{34} +19.7054 q^{36} +0.537796 q^{37} -14.8982 q^{38} -4.43428 q^{39} +6.54774 q^{40} -11.8724 q^{41} -0.588754 q^{43} +9.11372 q^{44} -11.1937 q^{45} +4.95356 q^{46} -3.02880 q^{47} -2.78657 q^{48} +2.76640 q^{50} +6.18227 q^{51} +5.15883 q^{52} +1.04162 q^{53} +18.8252 q^{54} -5.17707 q^{55} -18.8788 q^{57} +17.3201 q^{58} +2.27140 q^{59} +19.8386 q^{60} +10.2767 q^{61} -0.152664 q^{62} -12.3954 q^{64} -2.93048 q^{65} +18.2675 q^{66} -0.221714 q^{67} -7.19245 q^{68} +6.27711 q^{69} +10.7708 q^{71} -19.2186 q^{72} -10.2207 q^{73} -1.25409 q^{74} +3.50556 q^{75} +21.9636 q^{76} +10.3404 q^{78} -13.2859 q^{79} -1.84156 q^{80} +6.65934 q^{81} +27.6855 q^{82} +11.8543 q^{83} +4.08568 q^{85} +1.37293 q^{86} +21.9479 q^{87} -8.88855 q^{88} -3.51020 q^{89} +26.1028 q^{90} -7.30279 q^{92} -0.193455 q^{93} +7.06291 q^{94} -12.4765 q^{95} -13.3175 q^{96} -14.6497 q^{97} +15.1954 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 5 q^{3} + 4 q^{4} - 11 q^{5} - q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 5 * q^3 + 4 * q^4 - 11 * q^5 - q^6 - 6 * q^8 + 9 * q^9	$ 6 q - 2 q^{2} - 5 q^{3} + 4 q^{4} - 11 q^{5} - q^{6} - 6 q^{8} + 9 q^{9} + 2 q^{10} - q^{11} - 7 q^{12} - 7 q^{13} - 5 q^{15} - 8 q^{16} - 26 q^{17} - 18 q^{18} + 3 q^{19} - 14 q^{20} - 6 q^{22} - 9 q^{23} + 9 q^{24} + 15 q^{25} - 8 q^{27} - 2 q^{29} + 13 q^{30} + 2 q^{31} + q^{32} - 18 q^{33} + 13 q^{34} + 23 q^{36} - 2 q^{37} - 5 q^{38} + 7 q^{39} + 24 q^{40} - 28 q^{41} + 5 q^{43} - 12 q^{44} - 3 q^{45} - 12 q^{46} - 18 q^{47} + 13 q^{48} + 5 q^{50} + 13 q^{51} + 14 q^{52} - q^{53} + 32 q^{54} + 22 q^{55} - 26 q^{57} + 24 q^{58} - 5 q^{59} + 21 q^{60} + 17 q^{61} + 6 q^{62} - 18 q^{64} - 14 q^{65} + 58 q^{66} - 22 q^{67} - 7 q^{68} + 20 q^{69} - 2 q^{71} - 18 q^{72} - 12 q^{73} + 23 q^{74} + 27 q^{75} + 49 q^{76} + 21 q^{78} - 2 q^{79} + 16 q^{80} - 30 q^{81} + 35 q^{82} - 7 q^{83} + 37 q^{85} + 3 q^{86} + 25 q^{87} + 14 q^{88} - 39 q^{89} + 47 q^{90} + 11 q^{92} - 22 q^{93} + 16 q^{94} - 11 q^{95} + 28 q^{96} - 35 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q - 2 * q^2 - 5 * q^3 + 4 * q^4 - 11 * q^5 - q^6 - 6 * q^8 + 9 * q^9 + 2 * q^10 - q^11 - 7 * q^12 - 7 * q^13 - 5 * q^15 - 8 * q^16 - 26 * q^17 - 18 * q^18 + 3 * q^19 - 14 * q^20 - 6 * q^22 - 9 * q^23 + 9 * q^24 + 15 * q^25 - 8 * q^27 - 2 * q^29 + 13 * q^30 + 2 * q^31 + q^32 - 18 * q^33 + 13 * q^34 + 23 * q^36 - 2 * q^37 - 5 * q^38 + 7 * q^39 + 24 * q^40 - 28 * q^41 + 5 * q^43 - 12 * q^44 - 3 * q^45 - 12 * q^46 - 18 * q^47 + 13 * q^48 + 5 * q^50 + 13 * q^51 + 14 * q^52 - q^53 + 32 * q^54 + 22 * q^55 - 26 * q^57 + 24 * q^58 - 5 * q^59 + 21 * q^60 + 17 * q^61 + 6 * q^62 - 18 * q^64 - 14 * q^65 + 58 * q^66 - 22 * q^67 - 7 * q^68 + 20 * q^69 - 2 * q^71 - 18 * q^72 - 12 * q^73 + 23 * q^74 + 27 * q^75 + 49 * q^76 + 21 * q^78 - 2 * q^79 + 16 * q^80 - 30 * q^81 + 35 * q^82 - 7 * q^83 + 37 * q^85 + 3 * q^86 + 25 * q^87 + 14 * q^88 - 39 * q^89 + 47 * q^90 + 11 * q^92 - 22 * q^93 + 16 * q^94 - 11 * q^95 + 28 * q^96 - 35 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.33192	−1.64891	−0.824456	−	0.565925i	$-0.808519\pi$
$2$	−2.33192	−1.64891	−0.824456	+	0.565925i	$0.808519\pi$
$3$	−2.95499	−1.70606	−0.853031	−	0.521860i	$-0.825238\pi$
$3$	−2.95499	−1.70606	−0.853031	+	0.521860i	$0.825238\pi$
$4$	3.43783	1.71891
$5$	−1.95286	−0.873348	−0.436674	−	0.899620i	$-0.643844\pi$
$5$	−1.95286	−0.873348	−0.436674	+	0.899620i	$0.643844\pi$
$6$	6.89078	2.81315
$7$	0	0
$7$	0	0
$8$	−3.35289	−1.18543
$9$	5.73194	1.91065
$10$	4.55391	1.44007
$11$	2.65101	0.799310	0.399655	−	0.916666i	$-0.369130\pi$
$11$	2.65101	0.799310	0.399655	+	0.916666i	$0.369130\pi$
$12$	−10.1587	−2.93257
$13$	1.50061	0.416194	0.208097	−	0.978108i	$-0.433273\pi$
$13$	1.50061	0.416194	0.208097	+	0.978108i	$0.433273\pi$
$14$	0	0
$15$	5.77069	1.48999
$16$	0.943005	0.235751
$17$	−2.09215	−0.507421	−0.253710	−	0.967280i	$-0.581651\pi$
$17$	−2.09215	−0.507421	−0.253710	+	0.967280i	$0.581651\pi$
$18$	−13.3664	−3.15049
$19$	6.38881	1.46569	0.732847	−	0.680394i	$-0.238191\pi$
$19$	6.38881	1.46569	0.732847	+	0.680394i	$0.238191\pi$
$20$	−6.71361	−1.50121
$21$	0	0
$22$	−6.18193	−1.31799
$23$	−2.12424	−0.442936	−0.221468	−	0.975168i	$-0.571085\pi$
$23$	−2.12424	−0.442936	−0.221468	+	0.975168i	$0.571085\pi$
$24$	9.90775	2.02241
$25$	−1.18632	−0.237264
$26$	−3.49929	−0.686268
$27$	−8.07285	−1.55362
$28$	0	0
$29$	−7.42740	−1.37923	−0.689617	−	0.724174i	$-0.742221\pi$
$29$	−7.42740	−1.37923	−0.689617	+	0.724174i	$0.742221\pi$
$30$	−13.4568	−2.45686
$31$	0.0654672	0.0117582	0.00587912	−	0.999983i	$-0.498129\pi$
$31$	0.0654672	0.0117582	0.00587912	+	0.999983i	$0.498129\pi$
$32$	4.50678	0.796693
$33$	−7.83370	−1.36367
$34$	4.87871	0.836693
$35$	0	0
$36$	19.7054	3.28424
$37$	0.537796	0.0884130	0.0442065	−	0.999022i	$-0.485924\pi$
$37$	0.537796	0.0884130	0.0442065	+	0.999022i	$0.485924\pi$
$38$	−14.8982	−2.41680
$39$	−4.43428	−0.710053
$40$	6.54774	1.03529
$41$	−11.8724	−1.85416	−0.927082	−	0.374858i	$-0.877691\pi$
$41$	−11.8724	−1.85416	−0.927082	+	0.374858i	$0.877691\pi$
$42$	0	0
$43$	−0.588754	−0.0897842	−0.0448921	−	0.998992i	$-0.514294\pi$
$43$	−0.588754	−0.0897842	−0.0448921	+	0.998992i	$0.514294\pi$
$44$	9.11372	1.37394
$45$	−11.1937	−1.66866
$46$	4.95356	0.730362
$47$	−3.02880	−0.441796	−0.220898	−	0.975297i	$-0.570899\pi$
$47$	−3.02880	−0.441796	−0.220898	+	0.975297i	$0.570899\pi$
$48$	−2.78657	−0.402206
$49$	0	0
$50$	2.76640	0.391228
$51$	6.18227	0.865691
$52$	5.15883	0.715402
$53$	1.04162	0.143078	0.0715390	−	0.997438i	$-0.477209\pi$
$53$	1.04162	0.143078	0.0715390	+	0.997438i	$0.477209\pi$
$54$	18.8252	2.56179
$55$	−5.17707	−0.698075
$56$	0	0
$57$	−18.8788	−2.50056
$58$	17.3201	2.27424
$59$	2.27140	0.295711	0.147855	−	0.989009i	$-0.452763\pi$
$59$	2.27140	0.295711	0.147855	+	0.989009i	$0.452763\pi$
$60$	19.8386	2.56116
$61$	10.2767	1.31580	0.657898	−	0.753107i	$-0.271446\pi$
$61$	10.2767	1.31580	0.657898	+	0.753107i	$0.271446\pi$
$62$	−0.152664	−0.0193883
$63$	0	0
$64$	−12.3954	−1.54943
$65$	−2.93048	−0.363482
$66$	18.2675	2.24858
$67$	−0.221714	−0.0270867	−0.0135434	−	0.999908i	$-0.504311\pi$
$67$	−0.221714	−0.0270867	−0.0135434	+	0.999908i	$0.504311\pi$
$68$	−7.19245	−0.872213
$69$	6.27711	0.755676
$70$	0	0
$71$	10.7708	1.27826	0.639131	−	0.769098i	$-0.279294\pi$
$71$	10.7708	1.27826	0.639131	+	0.769098i	$0.279294\pi$
$72$	−19.2186	−2.26493
$73$	−10.2207	−1.19624	−0.598122	−	0.801405i	$-0.704086\pi$
$73$	−10.2207	−1.19624	−0.598122	+	0.801405i	$0.704086\pi$
$74$	−1.25409	−0.145785
$75$	3.50556	0.404787
$76$	21.9636	2.51940
$77$	0	0
$78$	10.3404	1.17081
$79$	−13.2859	−1.49478	−0.747392	−	0.664383i	$-0.768694\pi$
$79$	−13.2859	−1.49478	−0.747392	+	0.664383i	$0.768694\pi$
$80$	−1.84156	−0.205893
$81$	6.65934	0.739927
$82$	27.6855	3.05736
$83$	11.8543	1.30118	0.650592	−	0.759428i	$-0.274521\pi$
$83$	11.8543	1.30118	0.650592	+	0.759428i	$0.274521\pi$
$84$	0	0
$85$	4.08568	0.443155
$86$	1.37293	0.148046
$87$	21.9479	2.35306
$88$	−8.88855	−0.947523
$89$	−3.51020	−0.372080	−0.186040	−	0.982542i	$-0.559565\pi$
$89$	−3.51020	−0.372080	−0.186040	+	0.982542i	$0.559565\pi$
$90$	26.1028	2.75147
$91$	0	0
$92$	−7.30279	−0.761368
$93$	−0.193455	−0.0200603
$94$	7.06291	0.728484
$95$	−12.4765	−1.28006
$96$	−13.3175	−1.35921
$97$	−14.6497	−1.48746	−0.743728	−	0.668483i	$-0.766944\pi$
$97$	−14.6497	−1.48746	−0.743728	+	0.668483i	$0.766944\pi$
$98$	0	0
$99$	15.1954	1.52720
$100$	−4.07837	−0.407837
$101$	−0.324269	−0.0322659	−0.0161330	−	0.999870i	$-0.505136\pi$
$101$	−0.324269	−0.0322659	−0.0161330	+	0.999870i	$0.505136\pi$
$102$	−14.4165	−1.42745
$103$	−10.1971	−1.00475	−0.502377	−	0.864648i	$-0.667541\pi$
$103$	−10.1971	−1.00475	−0.502377	+	0.864648i	$0.667541\pi$
$104$	−5.03138	−0.493367
$105$	0	0
$106$	−2.42898	−0.235923
$107$	−15.3684	−1.48572	−0.742861	−	0.669446i	$-0.766532\pi$
$107$	−15.3684	−1.48572	−0.742861	+	0.669446i	$0.766532\pi$
$108$	−27.7531	−2.67054
$109$	−14.2387	−1.36382	−0.681911	−	0.731435i	$-0.738851\pi$
$109$	−14.2387	−1.36382	−0.681911	+	0.731435i	$0.738851\pi$
$110$	12.0725	1.15107
$111$	−1.58918	−0.150838
$112$	0	0
$113$	−8.22812	−0.774037	−0.387018	−	0.922072i	$-0.626495\pi$
$113$	−8.22812	−0.774037	−0.387018	+	0.922072i	$0.626495\pi$
$114$	44.0239	4.12321
$115$	4.14836	0.386837
$116$	−25.5341	−2.37078
$117$	8.60140	0.795200
$118$	−5.29670	−0.487601
$119$	0	0
$120$	−19.3485	−1.76627
$121$	−3.97214	−0.361104
$122$	−23.9644	−2.16963
$123$	35.0829	3.16332
$124$	0.225065	0.0202114
$125$	12.0810	1.08056
$126$	0	0
$127$	15.7450	1.39714	0.698572	−	0.715540i	$-0.253819\pi$
$127$	15.7450	1.39714	0.698572	+	0.715540i	$0.253819\pi$
$128$	19.8915	1.75818
$129$	1.73976	0.153177
$130$	6.83364	0.599350
$131$	−8.25951	−0.721636	−0.360818	−	0.932636i	$-0.617503\pi$
$131$	−8.25951	−0.721636	−0.360818	+	0.932636i	$0.617503\pi$
$132$	−26.9309	−2.34404
$133$	0	0
$134$	0.517019	0.0446636
$135$	15.7652	1.35685
$136$	7.01475	0.601510
$137$	0.0780530	0.00666851	0.00333426	−	0.999994i	$-0.498939\pi$
$137$	0.0780530	0.00666851	0.00333426	+	0.999994i	$0.498939\pi$
$138$	−14.6377	−1.24604
$139$	−15.6375	−1.32635	−0.663177	−	0.748463i	$-0.730792\pi$
$139$	−15.6375	−1.32635	−0.663177	+	0.748463i	$0.730792\pi$
$140$	0	0
$141$	8.95007	0.753732
$142$	−25.1166	−2.10774
$143$	3.97813	0.332668
$144$	5.40525	0.450437
$145$	14.5047	1.20455
$146$	23.8339	1.97250
$147$	0	0
$148$	1.84885	0.151974
$149$	−6.26566	−0.513303	−0.256652	−	0.966504i	$-0.582619\pi$
$149$	−6.26566	−0.513303	−0.256652	+	0.966504i	$0.582619\pi$
$150$	−8.17467	−0.667459
$151$	−16.3222	−1.32828	−0.664142	−	0.747606i	$-0.731203\pi$
$151$	−16.3222	−1.32828	−0.664142	+	0.747606i	$0.731203\pi$
$152$	−21.4210	−1.73747
$153$	−11.9921	−0.969502
$154$	0	0
$155$	−0.127848	−0.0102690
$156$	−15.2443	−1.22052
$157$	13.3664	1.06675	0.533376	−	0.845878i	$-0.320923\pi$
$157$	13.3664	1.06675	0.533376	+	0.845878i	$0.320923\pi$
$158$	30.9817	2.46477
$159$	−3.07798	−0.244100
$160$	−8.80113	−0.695790
$161$	0	0
$162$	−15.5290	−1.22008
$163$	−11.1164	−0.870700	−0.435350	−	0.900261i	$-0.643375\pi$
$163$	−11.1164	−0.870700	−0.435350	+	0.900261i	$0.643375\pi$
$164$	−40.8154	−3.18715
$165$	15.2982	1.19096
$166$	−27.6433	−2.14554
$167$	8.91212	0.689640	0.344820	−	0.938669i	$-0.387940\pi$
$167$	8.91212	0.689640	0.344820	+	0.938669i	$0.387940\pi$
$168$	0	0
$169$	−10.7482	−0.826783
$170$	−9.52747	−0.730723
$171$	36.6203	2.80042
$172$	−2.02404	−0.154331
$173$	−3.24509	−0.246720	−0.123360	−	0.992362i	$-0.539367\pi$
$173$	−3.24509	−0.246720	−0.123360	+	0.992362i	$0.539367\pi$
$174$	−51.1806	−3.87999
$175$	0	0
$176$	2.49992	0.188438
$177$	−6.71194	−0.504501
$178$	8.18548	0.613528
$179$	−4.04711	−0.302495	−0.151248	−	0.988496i	$-0.548329\pi$
$179$	−4.04711	−0.302495	−0.151248	+	0.988496i	$0.548329\pi$
$180$	−38.4820	−2.86828
$181$	−8.66577	−0.644121	−0.322061	−	0.946719i	$-0.604376\pi$
$181$	−8.66577	−0.644121	−0.322061	+	0.946719i	$0.604376\pi$
$182$	0	0
$183$	−30.3675	−2.24483
$184$	7.12236	0.525068
$185$	−1.05024	−0.0772153
$186$	0.451120	0.0330777
$187$	−5.54631	−0.405586
$188$	−10.4125	−0.759410
$189$	0	0
$190$	29.0941	2.11071
$191$	15.2165	1.10102	0.550512	−	0.834827i	$-0.314433\pi$
$191$	15.2165	1.10102	0.550512	+	0.834827i	$0.314433\pi$
$192$	36.6283	2.64342
$193$	10.2716	0.739364	0.369682	−	0.929158i	$-0.379467\pi$
$193$	10.2716	0.739364	0.369682	+	0.929158i	$0.379467\pi$
$194$	34.1619	2.45268
$195$	8.65954	0.620123
$196$	0	0
$197$	7.72522	0.550399	0.275200	−	0.961387i	$-0.411256\pi$
$197$	7.72522	0.550399	0.275200	+	0.961387i	$0.411256\pi$
$198$	−35.4345	−2.51822
$199$	14.7692	1.04696	0.523482	−	0.852037i	$-0.324633\pi$
$199$	14.7692	1.04696	0.523482	+	0.852037i	$0.324633\pi$
$200$	3.97761	0.281259
$201$	0.655163	0.0462116
$202$	0.756167	0.0532037
$203$	0	0
$204$	21.2536	1.48805
$205$	23.1853	1.61933
$206$	23.7789	1.65675
$207$	−12.1760	−0.846294
$208$	1.41508	0.0981182
$209$	16.9368	1.17154
$210$	0	0
$211$	−4.88834	−0.336527	−0.168264	−	0.985742i	$-0.553816\pi$
$211$	−4.88834	−0.336527	−0.168264	+	0.985742i	$0.553816\pi$
$212$	3.58092	0.245939
$213$	−31.8276	−2.18079
$214$	35.8379	2.44983
$215$	1.14976	0.0784128
$216$	27.0674	1.84170
$217$	0	0
$218$	33.2035	2.24883
$219$	30.2021	2.04087
$220$	−17.7979	−1.19993
$221$	−3.13950	−0.211185
$222$	3.70583	0.248719
$223$	−1.74696	−0.116985	−0.0584925	−	0.998288i	$-0.518629\pi$
$223$	−1.74696	−0.116985	−0.0584925	+	0.998288i	$0.518629\pi$
$224$	0	0
$225$	−6.79992	−0.453328
$226$	19.1873	1.27632
$227$	−23.6939	−1.57262	−0.786311	−	0.617831i	$-0.788012\pi$
$227$	−23.6939	−1.57262	−0.786311	+	0.617831i	$0.788012\pi$
$228$	−64.9022	−4.29825
$229$	−13.1910	−0.871685	−0.435843	−	0.900023i	$-0.643550\pi$
$229$	−13.1910	−0.871685	−0.435843	+	0.900023i	$0.643550\pi$
$230$	−9.67363	−0.637860
$231$	0	0
$232$	24.9033	1.63498
$233$	21.2901	1.39476	0.697379	−	0.716703i	$-0.254349\pi$
$233$	21.2901	1.39476	0.697379	+	0.716703i	$0.254349\pi$
$234$	−20.0577	−1.31122
$235$	5.91484	0.385842
$236$	7.80867	0.508301
$237$	39.2598	2.55020
$238$	0	0
$239$	−11.2612	−0.728429	−0.364215	−	0.931315i	$-0.618663\pi$
$239$	−11.2612	−0.728429	−0.364215	+	0.931315i	$0.618663\pi$
$240$	5.44178	0.351266
$241$	−9.26049	−0.596521	−0.298260	−	0.954485i	$-0.596406\pi$
$241$	−9.26049	−0.596521	−0.298260	+	0.954485i	$0.596406\pi$
$242$	9.26269	0.595428
$243$	4.54030	0.291260
$244$	35.3295	2.26174
$245$	0	0
$246$	−81.8104	−5.21604
$247$	9.58710	0.610013
$248$	−0.219504	−0.0139385
$249$	−35.0294	−2.21990
$250$	−28.1720	−1.78175
$251$	19.8599	1.25355	0.626773	−	0.779202i	$-0.284375\pi$
$251$	19.8599	1.25355	0.626773	+	0.779202i	$0.284375\pi$
$252$	0	0
$253$	−5.63140	−0.354043
$254$	−36.7160	−2.30377
$255$	−12.0731	−0.756049
$256$	−21.5945	−1.34966
$257$	−25.1574	−1.56927	−0.784637	−	0.619955i	$-0.787151\pi$
$257$	−25.1574	−1.56927	−0.784637	+	0.619955i	$0.787151\pi$
$258$	−4.05698	−0.252576
$259$	0	0
$260$	−10.0745	−0.624794
$261$	−42.5735	−2.63523
$262$	19.2605	1.18992
$263$	−10.3286	−0.636887	−0.318444	−	0.947942i	$-0.603160\pi$
$263$	−10.3286	−0.636887	−0.318444	+	0.947942i	$0.603160\pi$
$264$	26.2656	1.61653
$265$	−2.03415	−0.124957
$266$	0	0
$267$	10.3726	0.634792
$268$	−0.762215	−0.0465597
$269$	0.448329	0.0273351	0.0136676	−	0.999907i	$-0.495649\pi$
$269$	0.448329	0.0273351	0.0136676	+	0.999907i	$0.495649\pi$
$270$	−36.7631	−2.23733
$271$	23.9630	1.45565	0.727825	−	0.685763i	$-0.240531\pi$
$271$	23.9630	1.45565	0.727825	+	0.685763i	$0.240531\pi$
$272$	−1.97291	−0.119625
$273$	0	0
$274$	−0.182013	−0.0109958
$275$	−3.14495	−0.189648
$276$	21.5796	1.29894
$277$	15.1757	0.911822	0.455911	−	0.890025i	$-0.349314\pi$
$277$	15.1757	0.911822	0.455911	+	0.890025i	$0.349314\pi$
$278$	36.4653	2.18704
$279$	0.375254	0.0224659
$280$	0	0
$281$	10.0320	0.598460	0.299230	−	0.954181i	$-0.403270\pi$
$281$	10.0320	0.598460	0.299230	+	0.954181i	$0.403270\pi$
$282$	−20.8708	−1.24284
$283$	2.10305	0.125014	0.0625068	−	0.998045i	$-0.480090\pi$
$283$	2.10305	0.125014	0.0625068	+	0.998045i	$0.480090\pi$
$284$	37.0282	2.19722
$285$	36.8678	2.18386
$286$	−9.27666	−0.548540
$287$	0	0
$288$	25.8326	1.52220
$289$	−12.6229	−0.742524
$290$	−33.8238	−1.98620
$291$	43.2898	2.53769
$292$	−35.1371	−2.05624
$293$	−18.6487	−1.08947	−0.544735	−	0.838608i	$-0.683370\pi$
$293$	−18.6487	−1.08947	−0.544735	+	0.838608i	$0.683370\pi$
$294$	0	0
$295$	−4.43573	−0.258258
$296$	−1.80317	−0.104807
$297$	−21.4012	−1.24183
$298$	14.6110	0.846392
$299$	−3.18766	−0.184347
$300$	12.0515	0.695795
$301$	0	0
$302$	38.0620	2.19022
$303$	0.958209	0.0550477
$304$	6.02468	0.345539
$305$	−20.0690	−1.14915
$306$	27.9645	1.59862
$307$	−9.72652	−0.555122	−0.277561	−	0.960708i	$-0.589526\pi$
$307$	−9.72652	−0.555122	−0.277561	+	0.960708i	$0.589526\pi$
$308$	0	0
$309$	30.1324	1.71417
$310$	0.298132	0.0169327
$311$	27.8427	1.57881	0.789406	−	0.613871i	$-0.210389\pi$
$311$	27.8427	1.57881	0.789406	+	0.613871i	$0.210389\pi$
$312$	14.8677	0.841715
$313$	−20.2150	−1.14262	−0.571311	−	0.820734i	$-0.693565\pi$
$313$	−20.2150	−1.14262	−0.571311	+	0.820734i	$0.693565\pi$
$314$	−31.1692	−1.75898
$315$	0	0
$316$	−45.6748	−2.56941
$317$	11.8535	0.665760	0.332880	−	0.942969i	$-0.391980\pi$
$317$	11.8535	0.665760	0.332880	+	0.942969i	$0.391980\pi$
$318$	7.17759	0.402499
$319$	−19.6901	−1.10244
$320$	24.2066	1.35319
$321$	45.4135	2.53473
$322$	0	0
$323$	−13.3663	−0.743723
$324$	22.8937	1.27187
$325$	−1.78020	−0.0987479
$326$	25.9224	1.43571
$327$	42.0752	2.32677
$328$	39.8070	2.19798
$329$	0	0
$330$	−35.6740	−1.96379
$331$	12.6856	0.697261	0.348631	−	0.937260i	$-0.386647\pi$
$331$	12.6856	0.697261	0.348631	+	0.937260i	$0.386647\pi$
$332$	40.7532	2.23662
$333$	3.08261	0.168926
$334$	−20.7823	−1.13716
$335$	0.432978	0.0236561
$336$	0	0
$337$	28.8310	1.57053	0.785264	−	0.619162i	$-0.212527\pi$
$337$	28.8310	1.57053	0.785264	+	0.619162i	$0.212527\pi$
$338$	25.0638	1.36329
$339$	24.3140	1.32055
$340$	14.0459	0.761745
$341$	0.173554	0.00939848
$342$	−85.3954	−4.61766
$343$	0	0
$344$	1.97403	0.106433
$345$	−12.2583	−0.659967
$346$	7.56728	0.406819
$347$	15.5749	0.836103	0.418052	−	0.908423i	$-0.362713\pi$
$347$	15.5749	0.836103	0.418052	+	0.908423i	$0.362713\pi$
$348$	75.4530	4.04471
$349$	−9.08484	−0.486300	−0.243150	−	0.969989i	$-0.578181\pi$
$349$	−9.08484	−0.486300	−0.243150	+	0.969989i	$0.578181\pi$
$350$	0	0
$351$	−12.1142	−0.646608
$352$	11.9475	0.636805
$353$	−22.9922	−1.22375	−0.611876	−	0.790954i	$-0.709585\pi$
$353$	−22.9922	−1.22375	−0.611876	+	0.790954i	$0.709585\pi$
$354$	15.6517	0.831877
$355$	−21.0340	−1.11637
$356$	−12.0674	−0.639573
$357$	0	0
$358$	9.43751	0.498788
$359$	−14.1163	−0.745030	−0.372515	−	0.928026i	$-0.621504\pi$
$359$	−14.1163	−0.745030	−0.372515	+	0.928026i	$0.621504\pi$
$360$	37.5313	1.97807
$361$	21.8169	1.14826
$362$	20.2078	1.06210
$363$	11.7376	0.616065
$364$	0	0
$365$	19.9597	1.04474
$366$	70.8145	3.70153
$367$	−13.1892	−0.688469	−0.344235	−	0.938884i	$-0.611862\pi$
$367$	−13.1892	−0.688469	−0.344235	+	0.938884i	$0.611862\pi$
$368$	−2.00317	−0.104423
$369$	−68.0522	−3.54265
$370$	2.44907	0.127321
$371$	0	0
$372$	−0.665063	−0.0344819
$373$	9.15428	0.473991	0.236995	−	0.971511i	$-0.423837\pi$
$373$	9.15428	0.473991	0.236995	+	0.971511i	$0.423837\pi$
$374$	12.9335	0.668777
$375$	−35.6993	−1.84351
$376$	10.1553	0.523717
$377$	−11.1456	−0.574029
$378$	0	0
$379$	3.07480	0.157942	0.0789710	−	0.996877i	$-0.474837\pi$
$379$	3.07480	0.157942	0.0789710	+	0.996877i	$0.474837\pi$
$380$	−42.8920	−2.20031
$381$	−46.5263	−2.38361
$382$	−35.4835	−1.81549
$383$	−1.09321	−0.0558605	−0.0279303	−	0.999610i	$-0.508892\pi$
$383$	−1.09321	−0.0558605	−0.0279303	+	0.999610i	$0.508892\pi$
$384$	−58.7792	−2.99956
$385$	0	0
$386$	−23.9524	−1.21915
$387$	−3.37471	−0.171546
$388$	−50.3633	−2.55681
$389$	−11.8335	−0.599981	−0.299991	−	0.953942i	$-0.596984\pi$
$389$	−11.8335	−0.599981	−0.299991	+	0.953942i	$0.596984\pi$
$390$	−20.1933	−1.02253
$391$	4.44424	0.224755
$392$	0	0
$393$	24.4067	1.23116
$394$	−18.0146	−0.907561
$395$	25.9456	1.30547
$396$	52.2393	2.62512
$397$	28.2609	1.41838	0.709188	−	0.705020i	$-0.249062\pi$
$397$	28.2609	1.41838	0.709188	+	0.705020i	$0.249062\pi$
$398$	−34.4406	−1.72635
$399$	0	0
$400$	−1.11871	−0.0559353
$401$	−6.66256	−0.332713	−0.166356	−	0.986066i	$-0.553200\pi$
$401$	−6.66256	−0.332713	−0.166356	+	0.986066i	$0.553200\pi$
$402$	−1.52778	−0.0761989
$403$	0.0982406	0.00489371
$404$	−1.11478	−0.0554623
$405$	−13.0048	−0.646213
$406$	0	0
$407$	1.42570	0.0706694
$408$	−20.7285	−1.02621
$409$	−11.7556	−0.581276	−0.290638	−	0.956833i	$-0.593868\pi$
$409$	−11.7556	−0.581276	−0.290638	+	0.956833i	$0.593868\pi$
$410$	−54.0661	−2.67013
$411$	−0.230645	−0.0113769
$412$	−35.0560	−1.72709
$413$	0	0
$414$	28.3935	1.39546
$415$	−23.1499	−1.13639
$416$	6.76291	0.331579
$417$	46.2085	2.26284
$418$	−39.4952	−1.93177
$419$	−6.77442	−0.330952	−0.165476	−	0.986214i	$-0.552916\pi$
$419$	−6.77442	−0.330952	−0.165476	+	0.986214i	$0.552916\pi$
$420$	0	0
$421$	−1.52728	−0.0744351	−0.0372175	−	0.999307i	$-0.511849\pi$
$421$	−1.52728	−0.0744351	−0.0372175	+	0.999307i	$0.511849\pi$
$422$	11.3992	0.554904
$423$	−17.3609	−0.844117
$424$	−3.49245	−0.169608
$425$	2.48196	0.120393
$426$	74.2193	3.59594
$427$	0	0
$428$	−52.8340	−2.55383
$429$	−11.7553	−0.567552
$430$	−2.68114	−0.129296
$431$	3.78461	0.182298	0.0911491	−	0.995837i	$-0.470946\pi$
$431$	3.78461	0.182298	0.0911491	+	0.995837i	$0.470946\pi$
$432$	−7.61274	−0.366268
$433$	−3.53219	−0.169746	−0.0848730	−	0.996392i	$-0.527048\pi$
$433$	−3.53219	−0.169746	−0.0848730	+	0.996392i	$0.527048\pi$
$434$	0	0
$435$	−42.8612	−2.05504
$436$	−48.9503	−2.34429
$437$	−13.5714	−0.649208
$438$	−70.4287	−3.36521
$439$	−11.4480	−0.546381	−0.273190	−	0.961960i	$-0.588079\pi$
$439$	−11.4480	−0.546381	−0.273190	+	0.961960i	$0.588079\pi$
$440$	17.3581	0.827517
$441$	0	0
$442$	7.32104	0.348226
$443$	−13.5209	−0.642400	−0.321200	−	0.947011i	$-0.604086\pi$
$443$	−13.5209	−0.642400	−0.321200	+	0.947011i	$0.604086\pi$
$444$	−5.46332	−0.259278
$445$	6.85494	0.324955
$446$	4.07376	0.192898
$447$	18.5150	0.875727
$448$	0	0
$449$	−18.0667	−0.852621	−0.426310	−	0.904577i	$-0.640187\pi$
$449$	−18.0667	−0.852621	−0.426310	+	0.904577i	$0.640187\pi$
$450$	15.8568	0.747499
$451$	−31.4740	−1.48205
$452$	−28.2869	−1.33050
$453$	48.2320	2.26614
$454$	55.2523	2.59312
$455$	0	0
$456$	63.2987	2.96424
$457$	27.8916	1.30471	0.652357	−	0.757912i	$-0.273780\pi$
$457$	27.8916	1.30471	0.652357	+	0.757912i	$0.273780\pi$
$458$	30.7603	1.43733
$459$	16.8896	0.788340
$460$	14.2614	0.664939
$461$	−27.9948	−1.30385	−0.651925	−	0.758284i	$-0.726038\pi$
$461$	−27.9948	−1.30385	−0.651925	+	0.758284i	$0.726038\pi$
$462$	0	0
$463$	−37.3527	−1.73593	−0.867964	−	0.496627i	$-0.834572\pi$
$463$	−37.3527	−1.73593	−0.867964	+	0.496627i	$0.834572\pi$
$464$	−7.00408	−0.325156
$465$	0.377790	0.0175196
$466$	−49.6466	−2.29983
$467$	28.8663	1.33577	0.667886	−	0.744264i	$-0.267199\pi$
$467$	28.8663	1.33577	0.667886	+	0.744264i	$0.267199\pi$
$468$	29.5701	1.36688
$469$	0	0
$470$	−13.7929	−0.636220
$471$	−39.4974	−1.81995
$472$	−7.61575	−0.350543
$473$	−1.56079	−0.0717654
$474$	−91.5504	−4.20505
$475$	−7.57918	−0.347757
$476$	0	0
$477$	5.97052	0.273372
$478$	26.2603	1.20112
$479$	−25.0973	−1.14672	−0.573362	−	0.819302i	$-0.694361\pi$
$479$	−25.0973	−1.14672	−0.573362	+	0.819302i	$0.694361\pi$
$480$	26.0072	1.18706
$481$	0.807021	0.0367970
$482$	21.5947	0.983611
$483$	0	0
$484$	−13.6555	−0.620706
$485$	28.6089	1.29907
$486$	−10.5876	−0.480263
$487$	−41.0234	−1.85895	−0.929474	−	0.368888i	$-0.879738\pi$
$487$	−41.0234	−1.85895	−0.929474	+	0.368888i	$0.879738\pi$
$488$	−34.4567	−1.55978
$489$	32.8487	1.48547
$490$	0	0
$491$	0.985019	0.0444533	0.0222266	−	0.999753i	$-0.492924\pi$
$491$	0.985019	0.0444533	0.0222266	+	0.999753i	$0.492924\pi$
$492$	120.609	5.43747
$493$	15.5392	0.699852
$494$	−22.3563	−1.00586
$495$	−29.6746	−1.33378
$496$	0.0617358	0.00277202
$497$	0	0
$498$	81.6856	3.66042
$499$	−9.68113	−0.433387	−0.216693	−	0.976240i	$-0.569527\pi$
$499$	−9.68113	−0.433387	−0.216693	+	0.976240i	$0.569527\pi$
$500$	41.5326	1.85739
$501$	−26.3352	−1.17657
$502$	−46.3116	−2.06699
$503$	12.4080	0.553243	0.276622	−	0.960979i	$-0.410785\pi$
$503$	12.4080	0.553243	0.276622	+	0.960979i	$0.410785\pi$
$504$	0	0
$505$	0.633252	0.0281794
$506$	13.1319	0.583786
$507$	31.7607	1.41054
$508$	54.1287	2.40157
$509$	−13.7199	−0.608122	−0.304061	−	0.952653i	$-0.598343\pi$
$509$	−13.7199	−0.608122	−0.304061	+	0.952653i	$0.598343\pi$
$510$	28.1535	1.24666
$511$	0	0
$512$	10.5735	0.467287
$513$	−51.5759	−2.27713
$514$	58.6649	2.58760
$515$	19.9136	0.877500
$516$	5.98100	0.263299
$517$	−8.02939	−0.353132
$518$	0	0
$519$	9.58920	0.420919
$520$	9.82560	0.430881
$521$	34.1034	1.49410	0.747049	−	0.664769i	$-0.231470\pi$
$521$	34.1034	1.49410	0.747049	+	0.664769i	$0.231470\pi$
$522$	99.2777	4.34527
$523$	−5.24558	−0.229373	−0.114687	−	0.993402i	$-0.536586\pi$
$523$	−5.24558	−0.229373	−0.114687	+	0.993402i	$0.536586\pi$
$524$	−28.3948	−1.24043
$525$	0	0
$526$	24.0854	1.05017
$527$	−0.136967	−0.00596638
$528$	−7.38722	−0.321487
$529$	−18.4876	−0.803808
$530$	4.74346	0.206043
$531$	13.0195	0.564999
$532$	0	0
$533$	−17.8159	−0.771692
$534$	−24.1880	−1.04672
$535$	30.0125	1.29755
$536$	0.743384	0.0321093
$537$	11.9592	0.516075
$538$	−1.04547	−0.0450732
$539$	0	0
$540$	54.1980	2.33231
$541$	43.6622	1.87719	0.938593	−	0.345027i	$-0.112130\pi$
$541$	43.6622	1.87719	0.938593	+	0.345027i	$0.112130\pi$
$542$	−55.8797	−2.40024
$543$	25.6072	1.09891
$544$	−9.42885	−0.404259
$545$	27.8063	1.19109
$546$	0	0
$547$	−36.2818	−1.55130	−0.775648	−	0.631166i	$-0.782577\pi$
$547$	−36.2818	−1.55130	−0.775648	+	0.631166i	$0.782577\pi$
$548$	0.268333	0.0114626
$549$	58.9055	2.51402
$550$	7.33375	0.312712
$551$	−47.4523	−2.02153
$552$	−21.0465	−0.895798
$553$	0	0
$554$	−35.3885	−1.50352
$555$	3.10345	0.131734
$556$	−53.7589	−2.27989
$557$	−7.19093	−0.304689	−0.152345	−	0.988327i	$-0.548682\pi$
$557$	−7.19093	−0.304689	−0.152345	+	0.988327i	$0.548682\pi$
$558$	−0.875061	−0.0370443
$559$	−0.883490	−0.0373676
$560$	0	0
$561$	16.3893	0.691956
$562$	−23.3938	−0.986808
$563$	−11.6990	−0.493053	−0.246527	−	0.969136i	$-0.579289\pi$
$563$	−11.6990	−0.493053	−0.246527	+	0.969136i	$0.579289\pi$
$564$	30.7688	1.29560
$565$	16.0684	0.676003
$566$	−4.90414	−0.206136
$567$	0	0
$568$	−36.1134	−1.51528
$569$	24.2886	1.01823	0.509115	−	0.860698i	$-0.329973\pi$
$569$	24.2886	1.01823	0.509115	+	0.860698i	$0.329973\pi$
$570$	−85.9726	−3.60100
$571$	1.58477	0.0663206	0.0331603	−	0.999450i	$-0.489443\pi$
$571$	1.58477	0.0663206	0.0331603	+	0.999450i	$0.489443\pi$
$572$	13.6761	0.571828
$573$	−44.9644	−1.87842
$574$	0	0
$575$	2.52004	0.105093
$576$	−71.0499	−2.96041
$577$	17.9000	0.745188	0.372594	−	0.927994i	$-0.378468\pi$
$577$	17.9000	0.745188	0.372594	+	0.927994i	$0.378468\pi$
$578$	29.4356	1.22436
$579$	−30.3523	−1.26140
$580$	49.8647	2.07052
$581$	0	0
$582$	−100.948	−4.18443
$583$	2.76135	0.114364
$584$	34.2690	1.41806
$585$	−16.7974	−0.694486
$586$	43.4873	1.79644
$587$	1.07134	0.0442189	0.0221094	−	0.999756i	$-0.492962\pi$
$587$	1.07134	0.0442189	0.0221094	+	0.999756i	$0.492962\pi$
$588$	0	0
$589$	0.418257	0.0172340
$590$	10.3437	0.425845
$591$	−22.8279	−0.939015
$592$	0.507144	0.0208435
$593$	5.21037	0.213964	0.106982	−	0.994261i	$-0.465881\pi$
$593$	5.21037	0.213964	0.106982	+	0.994261i	$0.465881\pi$
$594$	49.9058	2.04766
$595$	0	0
$596$	−21.5403	−0.882324
$597$	−43.6429	−1.78619
$598$	7.43335	0.303972
$599$	19.3597	0.791015	0.395508	−	0.918463i	$-0.370569\pi$
$599$	19.3597	0.791015	0.395508	+	0.918463i	$0.370569\pi$
$600$	−11.7538	−0.479846
$601$	15.0693	0.614689	0.307345	−	0.951598i	$-0.400560\pi$
$601$	15.0693	0.614689	0.307345	+	0.951598i	$0.400560\pi$
$602$	0	0
$603$	−1.27085	−0.0517532
$604$	−56.1130	−2.28321
$605$	7.75705	0.315369
$606$	−2.23446	−0.0907688
$607$	30.9662	1.25688	0.628440	−	0.777858i	$-0.283694\pi$
$607$	30.9662	1.25688	0.628440	+	0.777858i	$0.283694\pi$
$608$	28.7930	1.16771
$609$	0	0
$610$	46.7992	1.89484
$611$	−4.54505	−0.183873
$612$	−41.2267	−1.66649
$613$	3.75434	0.151636	0.0758182	−	0.997122i	$-0.475843\pi$
$613$	3.75434	0.151636	0.0758182	+	0.997122i	$0.475843\pi$
$614$	22.6814	0.915348
$615$	−68.5122	−2.76268
$616$	0	0
$617$	28.0758	1.13029	0.565145	−	0.824991i	$-0.308820\pi$
$617$	28.0758	1.13029	0.565145	+	0.824991i	$0.308820\pi$
$618$	−70.2663	−2.82652
$619$	19.3674	0.778441	0.389221	−	0.921145i	$-0.372744\pi$
$619$	19.3674	0.778441	0.389221	+	0.921145i	$0.372744\pi$
$620$	−0.439521	−0.0176516
$621$	17.1487	0.688154
$622$	−64.9267	−2.60332
$623$	0	0
$624$	−4.18154	−0.167396
$625$	−17.6610	−0.706442
$626$	47.1398	1.88408
$627$	−50.0480	−1.99873
$628$	45.9513	1.83366
$629$	−1.12515	−0.0448626
$630$	0	0
$631$	40.7248	1.62123	0.810615	−	0.585580i	$-0.199133\pi$
$631$	40.7248	1.62123	0.810615	+	0.585580i	$0.199133\pi$
$632$	44.5463	1.77196
$633$	14.4450	0.574136
$634$	−27.6414	−1.09778
$635$	−30.7479	−1.22019
$636$	−10.5816	−0.419587
$637$	0	0
$638$	45.9157	1.81782
$639$	61.7377	2.44231
$640$	−38.8455	−1.53550
$641$	0.706513	0.0279056	0.0139528	−	0.999903i	$-0.495559\pi$
$641$	0.706513	0.0279056	0.0139528	+	0.999903i	$0.495559\pi$
$642$	−105.900	−4.17956
$643$	−16.5495	−0.652650	−0.326325	−	0.945258i	$-0.605810\pi$
$643$	−16.5495	−0.652650	−0.326325	+	0.945258i	$0.605810\pi$
$644$	0	0
$645$	−3.39752	−0.133777
$646$	31.1692	1.22634
$647$	11.7596	0.462317	0.231159	−	0.972916i	$-0.425748\pi$
$647$	11.7596	0.462317	0.231159	+	0.972916i	$0.425748\pi$
$648$	−22.3281	−0.877129
$649$	6.02150	0.236364
$650$	4.15128	0.162827
$651$	0	0
$652$	−38.2161	−1.49666
$653$	22.5877	0.883925	0.441962	−	0.897034i	$-0.354282\pi$
$653$	22.5877	0.883925	0.441962	+	0.897034i	$0.354282\pi$
$654$	−98.1159	−3.83664
$655$	16.1297	0.630239
$656$	−11.1958	−0.437121
$657$	−58.5846	−2.28560
$658$	0	0
$659$	18.0135	0.701705	0.350852	−	0.936431i	$-0.385892\pi$
$659$	18.0135	0.701705	0.350852	+	0.936431i	$0.385892\pi$
$660$	52.5924	2.04716
$661$	−37.6880	−1.46590	−0.732948	−	0.680285i	$-0.761856\pi$
$661$	−37.6880	−1.46590	−0.732948	+	0.680285i	$0.761856\pi$
$662$	−29.5816	−1.14972
$663$	9.27717	0.360295
$664$	−39.7463	−1.54246
$665$	0	0
$666$	−7.18839	−0.278545
$667$	15.7776	0.610912
$668$	30.6383	1.18543
$669$	5.16223	0.199584
$670$	−1.00967	−0.0390069
$671$	27.2436	1.05173
$672$	0	0
$673$	−18.7754	−0.723738	−0.361869	−	0.932229i	$-0.617861\pi$
$673$	−18.7754	−0.723738	−0.361869	+	0.932229i	$0.617861\pi$
$674$	−67.2316	−2.58966
$675$	9.57699	0.368619
$676$	−36.9504	−1.42117
$677$	3.85662	0.148222	0.0741110	−	0.997250i	$-0.476388\pi$
$677$	3.85662	0.148222	0.0741110	+	0.997250i	$0.476388\pi$
$678$	−56.6982	−2.17748
$679$	0	0
$680$	−13.6989	−0.525327
$681$	70.0153	2.68299
$682$	−0.404714	−0.0154973
$683$	40.0543	1.53264	0.766318	−	0.642461i	$-0.222087\pi$
$683$	40.0543	1.53264	0.766318	+	0.642461i	$0.222087\pi$
$684$	125.894	4.81369
$685$	−0.152427	−0.00582393
$686$	0	0
$687$	38.9792	1.48715
$688$	−0.555198	−0.0211667
$689$	1.56307	0.0595482
$690$	28.5854	1.08823
$691$	33.8236	1.28671	0.643356	−	0.765567i	$-0.277542\pi$
$691$	33.8236	1.28671	0.643356	+	0.765567i	$0.277542\pi$
$692$	−11.1561	−0.424090
$693$	0	0
$694$	−36.3193	−1.37866
$695$	30.5379	1.15837
$696$	−73.5889	−2.78938
$697$	24.8389	0.940842
$698$	21.1851	0.801867
$699$	−62.9118	−2.37954
$700$	0	0
$701$	41.0095	1.54891	0.774453	−	0.632631i	$-0.218025\pi$
$701$	41.0095	1.54891	0.774453	+	0.632631i	$0.218025\pi$
$702$	28.2493	1.06620
$703$	3.43587	0.129586
$704$	−32.8604	−1.23847
$705$	−17.4783	−0.658270
$706$	53.6159	2.01786
$707$	0	0
$708$	−23.0745	−0.867193
$709$	−24.8640	−0.933787	−0.466893	−	0.884314i	$-0.654627\pi$
$709$	−24.8640	−0.933787	−0.466893	+	0.884314i	$0.654627\pi$
$710$	49.0494	1.84079
$711$	−76.1542	−2.85601
$712$	11.7693	0.441073
$713$	−0.139068	−0.00520815
$714$	0	0
$715$	−7.76875	−0.290535
$716$	−13.9133	−0.519963
$717$	33.2768	1.24275
$718$	32.9180	1.22849
$719$	−20.1550	−0.751654	−0.375827	−	0.926690i	$-0.622641\pi$
$719$	−20.1550	−0.751654	−0.375827	+	0.926690i	$0.622641\pi$
$720$	−10.5557	−0.393388
$721$	0	0
$722$	−50.8752	−1.89338
$723$	27.3646	1.01770
$724$	−29.7914	−1.10719
$725$	8.81128	0.327243
$726$	−27.3711	−1.01584
$727$	−39.6430	−1.47028	−0.735138	−	0.677918i	$-0.762883\pi$
$727$	−39.6430	−1.47028	−0.735138	+	0.677918i	$0.762883\pi$
$728$	0	0
$729$	−33.3945	−1.23683
$730$	−46.5443	−1.72268
$731$	1.23176	0.0455584
$732$	−104.398	−3.85867
$733$	4.69321	0.173348	0.0866738	−	0.996237i	$-0.472376\pi$
$733$	4.69321	0.173348	0.0866738	+	0.996237i	$0.472376\pi$
$734$	30.7560	1.13523
$735$	0	0
$736$	−9.57350	−0.352884
$737$	−0.587767	−0.0216507
$738$	158.692	5.84153
$739$	24.4235	0.898433	0.449216	−	0.893423i	$-0.351703\pi$
$739$	24.4235	0.898433	0.449216	+	0.893423i	$0.351703\pi$
$740$	−3.61055	−0.132726
$741$	−28.3298	−1.04072
$742$	0	0
$743$	28.1516	1.03278	0.516391	−	0.856353i	$-0.327275\pi$
$743$	28.1516	1.03278	0.516391	+	0.856353i	$0.327275\pi$
$744$	0.648632	0.0237800
$745$	12.2360	0.448292
$746$	−21.3470	−0.781570
$747$	67.9484	2.48610
$748$	−19.0673	−0.697168
$749$	0	0
$750$	83.2478	3.03978
$751$	−28.7070	−1.04753	−0.523766	−	0.851862i	$-0.675474\pi$
$751$	−28.7070	−1.04753	−0.523766	+	0.851862i	$0.675474\pi$
$752$	−2.85618	−0.104154
$753$	−58.6858	−2.13863
$754$	25.9906	0.946524
$755$	31.8751	1.16005
$756$	0	0
$757$	−34.9823	−1.27145	−0.635726	−	0.771915i	$-0.719299\pi$
$757$	−34.9823	−1.27145	−0.635726	+	0.771915i	$0.719299\pi$
$758$	−7.17018	−0.260433
$759$	16.6407	0.604019
$760$	41.8323	1.51742
$761$	−47.2861	−1.71412	−0.857060	−	0.515216i	$-0.827712\pi$
$761$	−47.2861	−1.71412	−0.857060	+	0.515216i	$0.827712\pi$
$762$	108.495	3.93037
$763$	0	0
$764$	52.3116	1.89257
$765$	23.4189	0.846712
$766$	2.54928	0.0921091
$767$	3.40848	0.123073
$768$	63.8115	2.30260
$769$	41.8758	1.51008	0.755040	−	0.655678i	$-0.227617\pi$
$769$	41.8758	1.51008	0.755040	+	0.655678i	$0.227617\pi$
$770$	0	0
$771$	74.3397	2.67728
$772$	35.3119	1.27090
$773$	21.0942	0.758706	0.379353	−	0.925252i	$-0.376147\pi$
$773$	21.0942	0.758706	0.379353	+	0.925252i	$0.376147\pi$
$774$	7.86953	0.282864
$775$	−0.0776650	−0.00278981
$776$	49.1190	1.76327
$777$	0	0
$778$	27.5947	0.989317
$779$	−75.8508	−2.71764
$780$	29.7700	1.06594
$781$	28.5536	1.02173
$782$	−10.3636	−0.370601
$783$	59.9603	2.14281
$784$	0	0
$785$	−26.1027	−0.931646
$786$	−56.9144	−2.03007
$787$	−40.2501	−1.43476	−0.717380	−	0.696682i	$-0.754659\pi$
$787$	−40.2501	−1.43476	−0.717380	+	0.696682i	$0.754659\pi$
$788$	26.5580	0.946089
$789$	30.5208	1.08657
$790$	−60.5030	−2.15260
$791$	0	0
$792$	−50.9487	−1.81038
$793$	15.4213	0.547627
$794$	−65.9021	−2.33878
$795$	6.01088	0.213184
$796$	50.7741	1.79964
$797$	5.32667	0.188680	0.0943401	−	0.995540i	$-0.469926\pi$
$797$	5.32667	0.188680	0.0943401	+	0.995540i	$0.469926\pi$
$798$	0	0
$799$	6.33671	0.224177
$800$	−5.34648	−0.189027
$801$	−20.1202	−0.710914
$802$	15.5365	0.548614
$803$	−27.0952	−0.956170
$804$	2.25234	0.0794338
$805$	0	0
$806$	−0.229089	−0.00806930
$807$	−1.32481	−0.0466354
$808$	1.08724	0.0382489
$809$	38.3657	1.34887	0.674434	−	0.738335i	$-0.264388\pi$
$809$	38.3657	1.34887	0.674434	+	0.738335i	$0.264388\pi$
$810$	30.3261	1.06555
$811$	−33.5120	−1.17676	−0.588382	−	0.808583i	$-0.700235\pi$
$811$	−33.5120	−1.17676	−0.588382	+	0.808583i	$0.700235\pi$
$812$	0	0
$813$	−70.8104	−2.48343
$814$	−3.32462	−0.116528
$815$	21.7087	0.760424
$816$	5.82991	0.204088
$817$	−3.76144	−0.131596
$818$	27.4130	0.958473
$819$	0	0
$820$	79.7070	2.78349
$821$	−36.9875	−1.29087	−0.645437	−	0.763814i	$-0.723325\pi$
$821$	−36.9875	−1.29087	−0.645437	+	0.763814i	$0.723325\pi$
$822$	0.537846	0.0187595
$823$	8.10944	0.282677	0.141339	−	0.989961i	$-0.454859\pi$
$823$	8.10944	0.282677	0.141339	+	0.989961i	$0.454859\pi$
$824$	34.1899	1.19106
$825$	9.29328	0.323551
$826$	0	0
$827$	−47.9413	−1.66708	−0.833541	−	0.552458i	$-0.813690\pi$
$827$	−47.9413	−1.66708	−0.833541	+	0.552458i	$0.813690\pi$
$828$	−41.8592	−1.45471
$829$	−29.4695	−1.02352	−0.511758	−	0.859129i	$-0.671006\pi$
$829$	−29.4695	−1.02352	−0.511758	+	0.859129i	$0.671006\pi$
$830$	53.9837	1.87380
$831$	−44.8441	−1.55562
$832$	−18.6007	−0.644863
$833$	0	0
$834$	−107.754	−3.73123
$835$	−17.4042	−0.602296
$836$	58.2258	2.01378
$837$	−0.528507	−0.0182679
$838$	15.7974	0.545711
$839$	−42.6216	−1.47146	−0.735731	−	0.677274i	$-0.763161\pi$
$839$	−42.6216	−1.47146	−0.735731	+	0.677274i	$0.763161\pi$
$840$	0	0
$841$	26.1663	0.902287
$842$	3.56149	0.122737
$843$	−29.6445	−1.02101
$844$	−16.8053	−0.578461
$845$	20.9897	0.722069
$846$	40.4842	1.39188
$847$	0	0
$848$	0.982255	0.0337308
$849$	−6.21449	−0.213281
$850$	−5.78772	−0.198517
$851$	−1.14241	−0.0391613
$852$	−109.418	−3.74860
$853$	44.8312	1.53499	0.767496	−	0.641054i	$-0.221502\pi$
$853$	44.8312	1.53499	0.767496	+	0.641054i	$0.221502\pi$
$854$	0	0
$855$	−71.5145	−2.44574
$856$	51.5287	1.76121
$857$	−32.5489	−1.11185	−0.555924	−	0.831233i	$-0.687636\pi$
$857$	−32.5489	−1.11185	−0.555924	+	0.831233i	$0.687636\pi$
$858$	27.4124	0.935844
$859$	34.8831	1.19020	0.595099	−	0.803653i	$-0.297113\pi$
$859$	34.8831	1.19020	0.595099	+	0.803653i	$0.297113\pi$
$860$	3.95267	0.134785
$861$	0	0
$862$	−8.82539	−0.300594
$863$	−1.66021	−0.0565141	−0.0282571	−	0.999601i	$-0.508996\pi$
$863$	−1.66021	−0.0565141	−0.0282571	+	0.999601i	$0.508996\pi$
$864$	−36.3826	−1.23776
$865$	6.33722	0.215472
$866$	8.23676	0.279897
$867$	37.3005	1.26679
$868$	0	0
$869$	−35.2212	−1.19480
$870$	99.9487	3.38858
$871$	−0.332706	−0.0112733
$872$	47.7409	1.61671
$873$	−83.9714	−2.84200
$874$	31.6473	1.07049
$875$	0	0
$876$	103.830	3.50808
$877$	30.5981	1.03323	0.516613	−	0.856219i	$-0.327193\pi$
$877$	30.5981	1.03323	0.516613	+	0.856219i	$0.327193\pi$
$878$	26.6957	0.900935
$879$	55.1067	1.85870
$880$	−4.88200	−0.164572
$881$	−51.9678	−1.75084	−0.875419	−	0.483365i	$-0.839414\pi$
$881$	−51.9678	−1.75084	−0.875419	+	0.483365i	$0.839414\pi$
$882$	0	0
$883$	22.8041	0.767420	0.383710	−	0.923454i	$-0.374646\pi$
$883$	22.8041	0.767420	0.383710	+	0.923454i	$0.374646\pi$
$884$	−10.7931	−0.363010
$885$	13.1075	0.440604
$886$	31.5297	1.05926
$887$	14.9208	0.500993	0.250496	−	0.968118i	$-0.419406\pi$
$887$	14.9208	0.500993	0.250496	+	0.968118i	$0.419406\pi$
$888$	5.32834	0.178808
$889$	0	0
$890$	−15.9851	−0.535823
$891$	17.6540	0.591431
$892$	−6.00574	−0.201087
$893$	−19.3505	−0.647538
$894$	−43.1753	−1.44400
$895$	7.90346	0.264183
$896$	0	0
$897$	9.41949	0.314508
$898$	42.1300	1.40590
$899$	−0.486251	−0.0162174
$900$	−23.3770	−0.779232
$901$	−2.17923	−0.0726007
$902$	73.3947	2.44377
$903$	0	0
$904$	27.5880	0.917564
$905$	16.9231	0.562542
$906$	−112.473	−3.73666
$907$	−41.6207	−1.38199	−0.690996	−	0.722858i	$-0.742828\pi$
$907$	−41.6207	−1.38199	−0.690996	+	0.722858i	$0.742828\pi$
$908$	−81.4557	−2.70320
$909$	−1.85869	−0.0616488
$910$	0	0
$911$	21.8850	0.725083	0.362541	−	0.931968i	$-0.381909\pi$
$911$	21.8850	0.725083	0.362541	+	0.931968i	$0.381909\pi$
$912$	−17.8028	−0.589511
$913$	31.4260	1.04005
$914$	−65.0409	−2.15136
$915$	59.3036	1.96052
$916$	−45.3484	−1.49835
$917$	0	0
$918$	−39.3852	−1.29990
$919$	4.45638	0.147002	0.0735012	−	0.997295i	$-0.476583\pi$
$919$	4.45638	0.147002	0.0735012	+	0.997295i	$0.476583\pi$
$920$	−13.9090	−0.458566
$921$	28.7417	0.947072
$922$	65.2816	2.14993
$923$	16.1628	0.532005
$924$	0	0
$925$	−0.637998	−0.0209772
$926$	87.1034	2.86239
$927$	−58.4495	−1.91973
$928$	−33.4737	−1.09883
$929$	−18.0749	−0.593019	−0.296509	−	0.955030i	$-0.595823\pi$
$929$	−18.0749	−0.593019	−0.296509	+	0.955030i	$0.595823\pi$
$930$	−0.880975	−0.0288883
$931$	0	0
$932$	73.1916	2.39747
$933$	−82.2747	−2.69355
$934$	−67.3137	−2.20257
$935$	10.8312	0.354218
$936$	−28.8396	−0.942651
$937$	23.0218	0.752088	0.376044	−	0.926602i	$-0.377284\pi$
$937$	23.0218	0.752088	0.376044	+	0.926602i	$0.377284\pi$
$938$	0	0
$939$	59.7352	1.94938
$940$	20.3342	0.663229
$941$	11.2388	0.366373	0.183186	−	0.983078i	$-0.441359\pi$
$941$	11.2388	0.366373	0.183186	+	0.983078i	$0.441359\pi$
$942$	92.1047	3.00093
$943$	25.2200	0.821275
$944$	2.14194	0.0697141
$945$	0	0
$946$	3.63964	0.118335
$947$	8.60672	0.279681	0.139840	−	0.990174i	$-0.455341\pi$
$947$	8.60672	0.279681	0.139840	+	0.990174i	$0.455341\pi$
$948$	134.968	4.38357
$949$	−15.3373	−0.497870
$950$	17.6740	0.573420
$951$	−35.0270	−1.13583
$952$	0	0
$953$	−16.0513	−0.519951	−0.259976	−	0.965615i	$-0.583715\pi$
$953$	−16.0513	−0.519951	−0.259976	+	0.965615i	$0.583715\pi$
$954$	−13.9228	−0.450766
$955$	−29.7157	−0.961577
$956$	−38.7142	−1.25211
$957$	58.1841	1.88082
$958$	58.5247	1.89085
$959$	0	0
$960$	−71.5302	−2.30863
$961$	−30.9957	−0.999862
$962$	−1.88190	−0.0606750
$963$	−88.0909	−2.83869
$964$	−31.8360	−1.02537
$965$	−20.0590	−0.645721
$966$	0	0
$967$	15.6295	0.502610	0.251305	−	0.967908i	$-0.419140\pi$
$967$	15.6295	0.502610	0.251305	+	0.967908i	$0.419140\pi$
$968$	13.3182	0.428062
$969$	39.4974	1.26884
$970$	−66.7136	−2.14205
$971$	−5.03310	−0.161520	−0.0807600	−	0.996734i	$-0.525735\pi$
$971$	−5.03310	−0.161520	−0.0807600	+	0.996734i	$0.525735\pi$
$972$	15.6088	0.500651
$973$	0	0
$974$	95.6631	3.06524
$975$	5.26047	0.168470
$976$	9.69098	0.310201
$977$	17.0593	0.545776	0.272888	−	0.962046i	$-0.412021\pi$
$977$	17.0593	0.545776	0.272888	+	0.962046i	$0.412021\pi$
$978$	−76.6003	−2.44941
$979$	−9.30557	−0.297407
$980$	0	0
$981$	−81.6156	−2.60578
$982$	−2.29698	−0.0732996
$983$	−26.8870	−0.857561	−0.428781	−	0.903409i	$-0.641057\pi$
$983$	−26.8870	−0.857561	−0.428781	+	0.903409i	$0.641057\pi$
$984$	−117.629	−3.74988
$985$	−15.0863	−0.480690
$986$	−36.2362	−1.15400
$987$	0	0
$988$	32.9588	1.04856
$989$	1.25066	0.0397686
$990$	69.1987	2.19928
$991$	30.0379	0.954184	0.477092	−	0.878853i	$-0.341691\pi$
$991$	30.0379	0.954184	0.477092	+	0.878853i	$0.341691\pi$
$992$	0.295046	0.00936772
$993$	−37.4857	−1.18957
$994$	0	0
$995$	−28.8423	−0.914364
$996$	−120.425	−3.81582
$997$	42.6067	1.34937	0.674684	−	0.738107i	$-0.264280\pi$
$997$	42.6067	1.34937	0.674684	+	0.738107i	$0.264280\pi$
$998$	22.5756	0.714617
$999$	−4.34155	−0.137360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	343.2.a.c.1.1	✓	6
3.2	odd	2		3087.2.a.k.1.6		6
4.3	odd	2		5488.2.a.p.1.6		6
5.4	even	2		8575.2.a.o.1.6		6
7.2	even	3		343.2.c.e.18.6		12
7.3	odd	6		343.2.c.d.324.6		12
7.4	even	3		343.2.c.e.324.6		12
7.5	odd	6		343.2.c.d.18.6		12
7.6	odd	2		343.2.a.d.1.1	yes	6
21.20	even	2		3087.2.a.j.1.6		6
28.27	even	2		5488.2.a.h.1.1		6
35.34	odd	2		8575.2.a.n.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
343.2.a.c.1.1	✓	6	1.1	even	1	trivial
343.2.a.d.1.1	yes	6	7.6	odd	2
343.2.c.d.18.6		12	7.5	odd	6
343.2.c.d.324.6		12	7.3	odd	6
343.2.c.e.18.6		12	7.2	even	3
343.2.c.e.324.6		12	7.4	even	3
3087.2.a.j.1.6		6	21.20	even	2
3087.2.a.k.1.6		6	3.2	odd	2
5488.2.a.h.1.1		6	28.27	even	2
5488.2.a.p.1.6		6	4.3	odd	2
8575.2.a.n.1.6		6	35.34	odd	2
8575.2.a.o.1.6		6	5.4	even	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:	\( N \)	\(=\)	\( 343 = 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	343.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33192 q^{2} -2.95499 q^{3} +3.43783 q^{4} -1.95286 q^{5} +6.89078 q^{6} -3.35289 q^{8} +5.73194 q^{9} +O(q^{10})\)	\(q-2.33192 q^{2} -2.95499 q^{3} +3.43783 q^{4} -1.95286 q^{5} +6.89078 q^{6} -3.35289 q^{8} +5.73194 q^{9} +4.55391 q^{10} +2.65101 q^{11} -10.1587 q^{12} +1.50061 q^{13} +5.77069 q^{15} +0.943005 q^{16} -2.09215 q^{17} -13.3664 q^{18} +6.38881 q^{19} -6.71361 q^{20} -6.18193 q^{22} -2.12424 q^{23} +9.90775 q^{24} -1.18632 q^{25} -3.49929 q^{26} -8.07285 q^{27} -7.42740 q^{29} -13.4568 q^{30} +0.0654672 q^{31} +4.50678 q^{32} -7.83370 q^{33} +4.87871 q^{34} +19.7054 q^{36} +0.537796 q^{37} -14.8982 q^{38} -4.43428 q^{39} +6.54774 q^{40} -11.8724 q^{41} -0.588754 q^{43} +9.11372 q^{44} -11.1937 q^{45} +4.95356 q^{46} -3.02880 q^{47} -2.78657 q^{48} +2.76640 q^{50} +6.18227 q^{51} +5.15883 q^{52} +1.04162 q^{53} +18.8252 q^{54} -5.17707 q^{55} -18.8788 q^{57} +17.3201 q^{58} +2.27140 q^{59} +19.8386 q^{60} +10.2767 q^{61} -0.152664 q^{62} -12.3954 q^{64} -2.93048 q^{65} +18.2675 q^{66} -0.221714 q^{67} -7.19245 q^{68} +6.27711 q^{69} +10.7708 q^{71} -19.2186 q^{72} -10.2207 q^{73} -1.25409 q^{74} +3.50556 q^{75} +21.9636 q^{76} +10.3404 q^{78} -13.2859 q^{79} -1.84156 q^{80} +6.65934 q^{81} +27.6855 q^{82} +11.8543 q^{83} +4.08568 q^{85} +1.37293 q^{86} +21.9479 q^{87} -8.88855 q^{88} -3.51020 q^{89} +26.1028 q^{90} -7.30279 q^{92} -0.193455 q^{93} +7.06291 q^{94} -12.4765 q^{95} -13.3175 q^{96} -14.6497 q^{97} +15.1954 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 5 q^{3} + 4 q^{4} - 11 q^{5} - q^{6} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 5 * q^3 + 4 * q^4 - 11 * q^5 - q^6 - 6 * q^8 + 9 * q^9	\( 6 q - 2 q^{2} - 5 q^{3} + 4 q^{4} - 11 q^{5} - q^{6} - 6 q^{8} + 9 q^{9} + 2 q^{10} - q^{11} - 7 q^{12} - 7 q^{13} - 5 q^{15} - 8 q^{16} - 26 q^{17} - 18 q^{18} + 3 q^{19} - 14 q^{20} - 6 q^{22} - 9 q^{23} + 9 q^{24} + 15 q^{25} - 8 q^{27} - 2 q^{29} + 13 q^{30} + 2 q^{31} + q^{32} - 18 q^{33} + 13 q^{34} + 23 q^{36} - 2 q^{37} - 5 q^{38} + 7 q^{39} + 24 q^{40} - 28 q^{41} + 5 q^{43} - 12 q^{44} - 3 q^{45} - 12 q^{46} - 18 q^{47} + 13 q^{48} + 5 q^{50} + 13 q^{51} + 14 q^{52} - q^{53} + 32 q^{54} + 22 q^{55} - 26 q^{57} + 24 q^{58} - 5 q^{59} + 21 q^{60} + 17 q^{61} + 6 q^{62} - 18 q^{64} - 14 q^{65} + 58 q^{66} - 22 q^{67} - 7 q^{68} + 20 q^{69} - 2 q^{71} - 18 q^{72} - 12 q^{73} + 23 q^{74} + 27 q^{75} + 49 q^{76} + 21 q^{78} - 2 q^{79} + 16 q^{80} - 30 q^{81} + 35 q^{82} - 7 q^{83} + 37 q^{85} + 3 q^{86} + 25 q^{87} + 14 q^{88} - 39 q^{89} + 47 q^{90} + 11 q^{92} - 22 q^{93} + 16 q^{94} - 11 q^{95} + 28 q^{96} - 35 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 5 * q^3 + 4 * q^4 - 11 * q^5 - q^6 - 6 * q^8 + 9 * q^9 + 2 * q^10 - q^11 - 7 * q^12 - 7 * q^13 - 5 * q^15 - 8 * q^16 - 26 * q^17 - 18 * q^18 + 3 * q^19 - 14 * q^20 - 6 * q^22 - 9 * q^23 + 9 * q^24 + 15 * q^25 - 8 * q^27 - 2 * q^29 + 13 * q^30 + 2 * q^31 + q^32 - 18 * q^33 + 13 * q^34 + 23 * q^36 - 2 * q^37 - 5 * q^38 + 7 * q^39 + 24 * q^40 - 28 * q^41 + 5 * q^43 - 12 * q^44 - 3 * q^45 - 12 * q^46 - 18 * q^47 + 13 * q^48 + 5 * q^50 + 13 * q^51 + 14 * q^52 - q^53 + 32 * q^54 + 22 * q^55 - 26 * q^57 + 24 * q^58 - 5 * q^59 + 21 * q^60 + 17 * q^61 + 6 * q^62 - 18 * q^64 - 14 * q^65 + 58 * q^66 - 22 * q^67 - 7 * q^68 + 20 * q^69 - 2 * q^71 - 18 * q^72 - 12 * q^73 + 23 * q^74 + 27 * q^75 + 49 * q^76 + 21 * q^78 - 2 * q^79 + 16 * q^80 - 30 * q^81 + 35 * q^82 - 7 * q^83 + 37 * q^85 + 3 * q^86 + 25 * q^87 + 14 * q^88 - 39 * q^89 + 47 * q^90 + 11 * q^92 - 22 * q^93 + 16 * q^94 - 11 * q^95 + 28 * q^96 - 35 * q^97 + 12 * q^99

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