LMFDB - Embedded newform 637.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(1,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("637.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.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:	$5.08647060876$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.4507648.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 5x^{4} + 8x^{3} + 7x^{2} - 6x - 1 $ x^6 - 2x^5 - 5x^4 + 8x^3 + 7x^2 - 6*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.146243$ of defining polynomial
Character	$\chi$	$=$	637.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.83237 q^{2} -0.853757 q^{3} +1.35758 q^{4} -2.62555 q^{5} -1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} +O(q^{10})$	\(q+1.83237 q^{2} -0.853757 q^{3} +1.35758 q^{4} -2.62555 q^{5} -1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} -4.81098 q^{10} +3.26469 q^{11} -1.15904 q^{12} -1.00000 q^{13} +2.24158 q^{15} -4.87214 q^{16} -4.53021 q^{17} -4.16149 q^{18} -4.06615 q^{19} -3.56440 q^{20} +5.98212 q^{22} -4.53266 q^{23} +1.00500 q^{24} +1.89352 q^{25} -1.83237 q^{26} +4.50024 q^{27} -1.42268 q^{29} +4.10741 q^{30} +2.80328 q^{31} -6.57326 q^{32} -2.78725 q^{33} -8.30102 q^{34} -3.08320 q^{36} -10.0503 q^{37} -7.45070 q^{38} +0.853757 q^{39} +3.09067 q^{40} +2.84271 q^{41} +9.72632 q^{43} +4.43208 q^{44} +5.96289 q^{45} -8.30551 q^{46} +9.44956 q^{47} +4.15962 q^{48} +3.46963 q^{50} +3.86770 q^{51} -1.35758 q^{52} +5.26439 q^{53} +8.24610 q^{54} -8.57161 q^{55} +3.47151 q^{57} -2.60687 q^{58} +2.56791 q^{59} +3.04313 q^{60} +11.1830 q^{61} +5.13664 q^{62} -2.30037 q^{64} +2.62555 q^{65} -5.10728 q^{66} -1.98172 q^{67} -6.15013 q^{68} +3.86979 q^{69} -11.7544 q^{71} +2.67342 q^{72} -12.1391 q^{73} -18.4159 q^{74} -1.61661 q^{75} -5.52013 q^{76} +1.56440 q^{78} +11.9089 q^{79} +12.7920 q^{80} +2.97118 q^{81} +5.20889 q^{82} -13.2233 q^{83} +11.8943 q^{85} +17.8222 q^{86} +1.21462 q^{87} -3.84303 q^{88} -10.6666 q^{89} +10.9262 q^{90} -6.15345 q^{92} -2.39332 q^{93} +17.3151 q^{94} +10.6759 q^{95} +5.61197 q^{96} +13.7422 q^{97} -7.41443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 8 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) $ 6 * q - 8 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^9	$ 6 q - 8 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} - 6 q^{13} + 12 q^{15} - 16 q^{17} - 4 q^{18} - 2 q^{19} - 16 q^{20} - 12 q^{22} - 6 q^{23} - 12 q^{24} - 4 q^{25} - 20 q^{27} - 6 q^{29} - 6 q^{31} - 20 q^{32} - 4 q^{33} - 24 q^{36} - 8 q^{38} + 8 q^{39} - 4 q^{40} + 8 q^{41} + 2 q^{43} - 4 q^{44} - 14 q^{45} + 8 q^{46} - 30 q^{47} + 8 q^{48} + 8 q^{50} - 4 q^{51} - 4 q^{52} - 14 q^{53} + 48 q^{54} + 8 q^{55} + 4 q^{57} - 8 q^{58} - 24 q^{59} + 12 q^{60} - 28 q^{62} - 20 q^{64} + 6 q^{65} + 4 q^{66} + 16 q^{67} - 28 q^{68} + 20 q^{69} + 8 q^{71} + 28 q^{72} + 6 q^{73} - 12 q^{74} - 12 q^{75} + 16 q^{76} + 4 q^{78} - 22 q^{79} + 28 q^{80} + 46 q^{81} + 40 q^{82} - 50 q^{83} - 8 q^{85} - 16 q^{86} + 16 q^{87} - 44 q^{88} - 26 q^{89} + 40 q^{90} + 20 q^{92} + 16 q^{93} + 32 q^{94} - 6 q^{95} + 20 q^{96} + 14 q^{97} + 12 q^{99}+O(q^{100}) $ 6 * q - 8 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 - 6 * q^13 + 12 * q^15 - 16 * q^17 - 4 * q^18 - 2 * q^19 - 16 * q^20 - 12 * q^22 - 6 * q^23 - 12 * q^24 - 4 * q^25 - 20 * q^27 - 6 * q^29 - 6 * q^31 - 20 * q^32 - 4 * q^33 - 24 * q^36 - 8 * q^38 + 8 * q^39 - 4 * q^40 + 8 * q^41 + 2 * q^43 - 4 * q^44 - 14 * q^45 + 8 * q^46 - 30 * q^47 + 8 * q^48 + 8 * q^50 - 4 * q^51 - 4 * q^52 - 14 * q^53 + 48 * q^54 + 8 * q^55 + 4 * q^57 - 8 * q^58 - 24 * q^59 + 12 * q^60 - 28 * q^62 - 20 * q^64 + 6 * q^65 + 4 * q^66 + 16 * q^67 - 28 * q^68 + 20 * q^69 + 8 * q^71 + 28 * q^72 + 6 * q^73 - 12 * q^74 - 12 * q^75 + 16 * q^76 + 4 * q^78 - 22 * q^79 + 28 * q^80 + 46 * q^81 + 40 * q^82 - 50 * q^83 - 8 * q^85 - 16 * q^86 + 16 * q^87 - 44 * q^88 - 26 * q^89 + 40 * q^90 + 20 * q^92 + 16 * q^93 + 32 * q^94 - 6 * q^95 + 20 * q^96 + 14 * 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 $

$2$	1.83237	1.29568	0.647841	−	0.761776i	$-0.275672\pi$
$2$	1.83237	1.29568	0.647841	+	0.761776i	$0.275672\pi$
$3$	−0.853757	−0.492917	−0.246458	−	0.969153i	$-0.579267\pi$
$3$	−0.853757	−0.492917	−0.246458	+	0.969153i	$0.579267\pi$
$4$	1.35758	0.678791
$5$	−2.62555	−1.17418	−0.587091	−	0.809521i	$-0.699727\pi$
$5$	−2.62555	−1.17418	−0.587091	+	0.809521i	$0.699727\pi$
$6$	−1.56440	−0.638663
$7$	0	0
$7$	0	0
$8$	−1.17715	−0.416185
$9$	−2.27110	−0.757033
$10$	−4.81098	−1.52137
$11$	3.26469	0.984341	0.492170	−	0.870499i	$-0.336204\pi$
$11$	3.26469	0.984341	0.492170	+	0.870499i	$0.336204\pi$
$12$	−1.15904	−0.334587
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0	0
$15$	2.24158	0.578775
$16$	−4.87214	−1.21803
$17$	−4.53021	−1.09874	−0.549369	−	0.835580i	$-0.685132\pi$
$17$	−4.53021	−1.09874	−0.549369	+	0.835580i	$0.685132\pi$
$18$	−4.16149	−0.980873
$19$	−4.06615	−0.932839	−0.466420	−	0.884564i	$-0.654456\pi$
$19$	−4.06615	−0.932839	−0.466420	+	0.884564i	$0.654456\pi$
$20$	−3.56440	−0.797024
$21$	0	0
$22$	5.98212	1.27539
$23$	−4.53266	−0.945125	−0.472562	−	0.881297i	$-0.656671\pi$
$23$	−4.53266	−0.945125	−0.472562	+	0.881297i	$0.656671\pi$
$24$	1.00500	0.205145
$25$	1.89352	0.378705
$26$	−1.83237	−0.359357
$27$	4.50024	0.866071
$28$	0	0
$29$	−1.42268	−0.264184	−0.132092	−	0.991237i	$-0.542169\pi$
$29$	−1.42268	−0.264184	−0.132092	+	0.991237i	$0.542169\pi$
$30$	4.10741	0.749907
$31$	2.80328	0.503484	0.251742	−	0.967794i	$-0.418997\pi$
$31$	2.80328	0.503484	0.251742	+	0.967794i	$0.418997\pi$
$32$	−6.57326	−1.16200
$33$	−2.78725	−0.485198
$34$	−8.30102	−1.42361
$35$	0	0
$36$	−3.08320	−0.513867
$37$	−10.0503	−1.65227	−0.826133	−	0.563475i	$-0.809464\pi$
$37$	−10.0503	−1.65227	−0.826133	+	0.563475i	$0.809464\pi$
$38$	−7.45070	−1.20866
$39$	0.853757	0.136711
$40$	3.09067	0.488677
$41$	2.84271	0.443956	0.221978	−	0.975052i	$-0.428749\pi$
$41$	2.84271	0.443956	0.221978	+	0.975052i	$0.428749\pi$
$42$	0	0
$43$	9.72632	1.48325	0.741625	−	0.670815i	$-0.234056\pi$
$43$	9.72632	1.48325	0.741625	+	0.670815i	$0.234056\pi$
$44$	4.43208	0.668161
$45$	5.96289	0.888895
$46$	−8.30551	−1.22458
$47$	9.44956	1.37836	0.689180	−	0.724590i	$-0.257971\pi$
$47$	9.44956	1.37836	0.689180	+	0.724590i	$0.257971\pi$
$48$	4.15962	0.600390
$49$	0	0
$50$	3.46963	0.490680
$51$	3.86770	0.541586
$52$	−1.35758	−0.188263
$53$	5.26439	0.723119	0.361559	−	0.932349i	$-0.382244\pi$
$53$	5.26439	0.723119	0.361559	+	0.932349i	$0.382244\pi$
$54$	8.24610	1.12215
$55$	−8.57161	−1.15580
$56$	0	0
$57$	3.47151	0.459812
$58$	−2.60687	−0.342299
$59$	2.56791	0.334313	0.167156	−	0.985930i	$-0.446542\pi$
$59$	2.56791	0.334313	0.167156	+	0.985930i	$0.446542\pi$
$60$	3.04313	0.392867
$61$	11.1830	1.43183	0.715917	−	0.698185i	$-0.246009\pi$
$61$	11.1830	1.43183	0.715917	+	0.698185i	$0.246009\pi$
$62$	5.13664	0.652354
$63$	0	0
$64$	−2.30037	−0.287546
$65$	2.62555	0.325660
$66$	−5.10728	−0.628662
$67$	−1.98172	−0.242106	−0.121053	−	0.992646i	$-0.538627\pi$
$67$	−1.98172	−0.242106	−0.121053	+	0.992646i	$0.538627\pi$
$68$	−6.15013	−0.745813
$69$	3.86979	0.465868
$70$	0	0
$71$	−11.7544	−1.39499	−0.697495	−	0.716590i	$-0.745702\pi$
$71$	−11.7544	−1.39499	−0.697495	+	0.716590i	$0.745702\pi$
$72$	2.67342	0.315066
$73$	−12.1391	−1.42078	−0.710388	−	0.703810i	$-0.751481\pi$
$73$	−12.1391	−1.42078	−0.710388	+	0.703810i	$0.751481\pi$
$74$	−18.4159	−2.14081
$75$	−1.61661	−0.186670
$76$	−5.52013	−0.633202
$77$	0	0
$78$	1.56440	0.177133
$79$	11.9089	1.33986	0.669928	−	0.742426i	$-0.266325\pi$
$79$	11.9089	1.33986	0.669928	+	0.742426i	$0.266325\pi$
$80$	12.7920	1.43019
$81$	2.97118	0.330132
$82$	5.20889	0.575226
$83$	−13.2233	−1.45145	−0.725723	−	0.687987i	$-0.758495\pi$
$83$	−13.2233	−1.45145	−0.725723	+	0.687987i	$0.758495\pi$
$84$	0	0
$85$	11.8943	1.29012
$86$	17.8222	1.92182
$87$	1.21462	0.130221
$88$	−3.84303	−0.409668
$89$	−10.6666	−1.13065	−0.565326	−	0.824867i	$-0.691250\pi$
$89$	−10.6666	−1.13065	−0.565326	+	0.824867i	$0.691250\pi$
$90$	10.9262	1.15172
$91$	0	0
$92$	−6.15345	−0.641542
$93$	−2.39332	−0.248176
$94$	17.3151	1.78592
$95$	10.6759	1.09532
$96$	5.61197	0.572769
$97$	13.7422	1.39531	0.697655	−	0.716433i	$-0.254227\pi$
$97$	13.7422	1.39531	0.697655	+	0.716433i	$0.254227\pi$
$98$	0	0
$99$	−7.41443	−0.745178
$100$	2.57061	0.257061
$101$	−5.89458	−0.586533	−0.293266	−	0.956031i	$-0.594742\pi$
$101$	−5.89458	−0.586533	−0.293266	+	0.956031i	$0.594742\pi$
$102$	7.08706	0.701723
$103$	−2.78737	−0.274647	−0.137324	−	0.990526i	$-0.543850\pi$
$103$	−2.78737	−0.274647	−0.137324	+	0.990526i	$0.543850\pi$
$104$	1.17715	0.115429
$105$	0	0
$106$	9.64630	0.936932
$107$	−17.6647	−1.70771	−0.853856	−	0.520509i	$-0.825742\pi$
$107$	−17.6647	−1.70771	−0.853856	+	0.520509i	$0.825742\pi$
$108$	6.10944	0.587881
$109$	−9.56450	−0.916113	−0.458057	−	0.888923i	$-0.651454\pi$
$109$	−9.56450	−0.916113	−0.458057	+	0.888923i	$0.651454\pi$
$110$	−15.7064	−1.49754
$111$	8.58055	0.814430
$112$	0	0
$113$	−17.6017	−1.65583	−0.827916	−	0.560852i	$-0.810474\pi$
$113$	−17.6017	−1.65583	−0.827916	+	0.560852i	$0.810474\pi$
$114$	6.36109	0.595770
$115$	11.9007	1.10975
$116$	−1.93140	−0.179326
$117$	2.27110	0.209963
$118$	4.70535	0.433163
$119$	0	0
$120$	−2.63868	−0.240877
$121$	−0.341808	−0.0310735
$122$	20.4914	1.85520
$123$	−2.42698	−0.218833
$124$	3.80568	0.341760
$125$	8.15622	0.729514
$126$	0	0
$127$	−1.59482	−0.141517	−0.0707586	−	0.997493i	$-0.522542\pi$
$127$	−1.59482	−0.141517	−0.0707586	+	0.997493i	$0.522542\pi$
$128$	8.93138	0.789430
$129$	−8.30391	−0.731119
$130$	4.81098	0.421951
$131$	−4.30279	−0.375937	−0.187968	−	0.982175i	$-0.560190\pi$
$131$	−4.30279	−0.375937	−0.187968	+	0.982175i	$0.560190\pi$
$132$	−3.78392	−0.329348
$133$	0	0
$134$	−3.63125	−0.313692
$135$	−11.8156	−1.01693
$136$	5.33273	0.457278
$137$	9.82234	0.839179	0.419590	−	0.907714i	$-0.362174\pi$
$137$	9.82234	0.839179	0.419590	+	0.907714i	$0.362174\pi$
$138$	7.09089	0.603617
$139$	−10.0811	−0.855070	−0.427535	−	0.903999i	$-0.640618\pi$
$139$	−10.0811	−0.855070	−0.427535	+	0.903999i	$0.640618\pi$
$140$	0	0
$141$	−8.06763	−0.679417
$142$	−21.5384	−1.80746
$143$	−3.26469	−0.273007
$144$	11.0651	0.922092
$145$	3.73531	0.310201
$146$	−22.2434	−1.84087
$147$	0	0
$148$	−13.6442	−1.12154
$149$	−13.8124	−1.13155	−0.565777	−	0.824558i	$-0.691424\pi$
$149$	−13.8124	−1.13155	−0.565777	+	0.824558i	$0.691424\pi$
$150$	−2.96223	−0.241865
$151$	21.2123	1.72623	0.863117	−	0.505004i	$-0.168509\pi$
$151$	21.2123	1.72623	0.863117	+	0.505004i	$0.168509\pi$
$152$	4.78647	0.388234
$153$	10.2886	0.831780
$154$	0	0
$155$	−7.36015	−0.591182
$156$	1.15904	0.0927978
$157$	−23.5155	−1.87674	−0.938372	−	0.345627i	$-0.887666\pi$
$157$	−23.5155	−1.87674	−0.938372	+	0.345627i	$0.887666\pi$
$158$	21.8215	1.73603
$159$	−4.49451	−0.356438
$160$	17.2584	1.36440
$161$	0	0
$162$	5.44431	0.427745
$163$	7.83062	0.613341	0.306671	−	0.951816i	$-0.400785\pi$
$163$	7.83062	0.613341	0.306671	+	0.951816i	$0.400785\pi$
$164$	3.85920	0.301353
$165$	7.31807	0.569711
$166$	−24.2300	−1.88061
$167$	−12.7116	−0.983654	−0.491827	−	0.870693i	$-0.663671\pi$
$167$	−12.7116	−0.983654	−0.491827	+	0.870693i	$0.663671\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	21.7948	1.67158
$171$	9.23463	0.706190
$172$	13.2043	1.00682
$173$	−5.24907	−0.399079	−0.199540	−	0.979890i	$-0.563945\pi$
$173$	−5.24907	−0.399079	−0.199540	+	0.979890i	$0.563945\pi$
$174$	2.22563	0.168725
$175$	0	0
$176$	−15.9060	−1.19896
$177$	−2.19237	−0.164788
$178$	−19.5451	−1.46497
$179$	−10.5255	−0.786714	−0.393357	−	0.919386i	$-0.628686\pi$
$179$	−10.5255	−0.786714	−0.393357	+	0.919386i	$0.628686\pi$
$180$	8.09510	0.603373
$181$	18.8177	1.39871	0.699356	−	0.714774i	$-0.253470\pi$
$181$	18.8177	1.39871	0.699356	+	0.714774i	$0.253470\pi$
$182$	0	0
$183$	−9.54755	−0.705775
$184$	5.33562	0.393347
$185$	26.3877	1.94006
$186$	−4.38545	−0.321557
$187$	−14.7897	−1.08153
$188$	12.8285	0.935618
$189$	0	0
$190$	19.5622	1.41919
$191$	14.9144	1.07917	0.539585	−	0.841931i	$-0.318581\pi$
$191$	14.9144	1.07917	0.539585	+	0.841931i	$0.318581\pi$
$192$	1.96396	0.141737
$193$	−0.0531356	−0.00382479	−0.00191239	−	0.999998i	$-0.500609\pi$
$193$	−0.0531356	−0.00382479	−0.00191239	+	0.999998i	$0.500609\pi$
$194$	25.1808	1.80788
$195$	−2.24158	−0.160523
$196$	0	0
$197$	10.0478	0.715875	0.357938	−	0.933745i	$-0.383480\pi$
$197$	10.0478	0.715875	0.357938	+	0.933745i	$0.383480\pi$
$198$	−13.5860	−0.965514
$199$	−23.2914	−1.65109	−0.825543	−	0.564340i	$-0.809131\pi$
$199$	−23.2914	−1.65109	−0.825543	+	0.564340i	$0.809131\pi$
$200$	−2.22896	−0.157611
$201$	1.69191	0.119338
$202$	−10.8011	−0.759959
$203$	0	0
$204$	5.25072	0.367624
$205$	−7.46367	−0.521285
$206$	−5.10749	−0.355855
$207$	10.2941	0.715491
$208$	4.87214	0.337822
$209$	−13.2747	−0.918232
$210$	0	0
$211$	−2.47457	−0.170356	−0.0851780	−	0.996366i	$-0.527146\pi$
$211$	−2.47457	−0.170356	−0.0851780	+	0.996366i	$0.527146\pi$
$212$	7.14683	0.490846
$213$	10.0354	0.687614
$214$	−32.3683	−2.21265
$215$	−25.5369	−1.74161
$216$	−5.29745	−0.360446
$217$	0	0
$218$	−17.5257	−1.18699
$219$	10.3639	0.700325
$220$	−11.6367	−0.784543
$221$	4.53021	0.304735
$222$	15.7227	1.05524
$223$	−6.17027	−0.413192	−0.206596	−	0.978426i	$-0.566239\pi$
$223$	−6.17027	−0.413192	−0.206596	+	0.978426i	$0.566239\pi$
$224$	0	0
$225$	−4.30038	−0.286692
$226$	−32.2529	−2.14543
$227$	−11.5939	−0.769513	−0.384757	−	0.923018i	$-0.625715\pi$
$227$	−11.5939	−0.769513	−0.384757	+	0.923018i	$0.625715\pi$
$228$	4.71285	0.312116
$229$	10.2382	0.676558	0.338279	−	0.941046i	$-0.390155\pi$
$229$	10.2382	0.676558	0.338279	+	0.941046i	$0.390155\pi$
$230$	21.8065	1.43788
$231$	0	0
$232$	1.67470	0.109950
$233$	21.4822	1.40735	0.703673	−	0.710524i	$-0.251542\pi$
$233$	21.4822	1.40735	0.703673	+	0.710524i	$0.251542\pi$
$234$	4.16149	0.272045
$235$	−24.8103	−1.61845
$236$	3.48614	0.226928
$237$	−10.1673	−0.660437
$238$	0	0
$239$	1.08591	0.0702414	0.0351207	−	0.999383i	$-0.488818\pi$
$239$	1.08591	0.0702414	0.0351207	+	0.999383i	$0.488818\pi$
$240$	−10.9213	−0.704967
$241$	19.9830	1.28722	0.643608	−	0.765355i	$-0.277437\pi$
$241$	19.9830	1.28722	0.643608	+	0.765355i	$0.277437\pi$
$242$	−0.626319	−0.0402613
$243$	−16.0374	−1.02880
$244$	15.1818	0.971915
$245$	0	0
$246$	−4.44713	−0.283538
$247$	4.06615	0.258723
$248$	−3.29988	−0.209542
$249$	11.2895	0.715443
$250$	14.9452	0.945218
$251$	−20.1497	−1.27184	−0.635920	−	0.771755i	$-0.719379\pi$
$251$	−20.1497	−1.27184	−0.635920	+	0.771755i	$0.719379\pi$
$252$	0	0
$253$	−14.7977	−0.930325
$254$	−2.92230	−0.183361
$255$	−10.1548	−0.635921
$256$	20.9663	1.31040
$257$	15.0174	0.936759	0.468379	−	0.883527i	$-0.344838\pi$
$257$	15.0174	0.936759	0.468379	+	0.883527i	$0.344838\pi$
$258$	−15.2158	−0.947297
$259$	0	0
$260$	3.56440	0.221055
$261$	3.23104	0.199996
$262$	−7.88431	−0.487094
$263$	−21.1662	−1.30516	−0.652582	−	0.757718i	$-0.726314\pi$
$263$	−21.1662	−1.30516	−0.652582	+	0.757718i	$0.726314\pi$
$264$	3.28101	0.201932
$265$	−13.8219	−0.849074
$266$	0	0
$267$	9.10665	0.557318
$268$	−2.69035	−0.164339
$269$	4.10480	0.250274	0.125137	−	0.992139i	$-0.460063\pi$
$269$	4.10480	0.250274	0.125137	+	0.992139i	$0.460063\pi$
$270$	−21.6506	−1.31761
$271$	−3.43244	−0.208506	−0.104253	−	0.994551i	$-0.533245\pi$
$271$	−3.43244	−0.208506	−0.104253	+	0.994551i	$0.533245\pi$
$272$	22.0718	1.33830
$273$	0	0
$274$	17.9982	1.08731
$275$	6.18176	0.372774
$276$	5.25355	0.316227
$277$	−0.361012	−0.0216911	−0.0108455	−	0.999941i	$-0.503452\pi$
$277$	−0.361012	−0.0216911	−0.0108455	+	0.999941i	$0.503452\pi$
$278$	−18.4724	−1.10790
$279$	−6.36652	−0.381154
$280$	0	0
$281$	18.5213	1.10489	0.552445	−	0.833550i	$-0.313695\pi$
$281$	18.5213	1.10489	0.552445	+	0.833550i	$0.313695\pi$
$282$	−14.7829	−0.880308
$283$	1.61158	0.0957983	0.0478991	−	0.998852i	$-0.484747\pi$
$283$	1.61158	0.0957983	0.0478991	+	0.998852i	$0.484747\pi$
$284$	−15.9575	−0.946906
$285$	−9.11462	−0.539904
$286$	−5.98212	−0.353730
$287$	0	0
$288$	14.9285	0.879671
$289$	3.52281	0.207224
$290$	6.84447	0.401921
$291$	−11.7325	−0.687772
$292$	−16.4798	−0.964410
$293$	4.41671	0.258027	0.129013	−	0.991643i	$-0.458819\pi$
$293$	4.41671	0.258027	0.129013	+	0.991643i	$0.458819\pi$
$294$	0	0
$295$	−6.74217	−0.392544
$296$	11.8308	0.687649
$297$	14.6919	0.852509
$298$	−25.3094	−1.46613
$299$	4.53266	0.262130
$300$	−2.19468	−0.126710
$301$	0	0
$302$	38.8688	2.23665
$303$	5.03254	0.289112
$304$	19.8108	1.13623
$305$	−29.3615	−1.68123
$306$	18.8524	1.07772
$307$	5.78353	0.330083	0.165042	−	0.986287i	$-0.447224\pi$
$307$	5.78353	0.330083	0.165042	+	0.986287i	$0.447224\pi$
$308$	0	0
$309$	2.37973	0.135378
$310$	−13.4865	−0.765983
$311$	−14.2895	−0.810284	−0.405142	−	0.914254i	$-0.632778\pi$
$311$	−14.2895	−0.810284	−0.405142	+	0.914254i	$0.632778\pi$
$312$	−1.00500	−0.0568969
$313$	−2.73725	−0.154718	−0.0773592	−	0.997003i	$-0.524649\pi$
$313$	−2.73725	−0.154718	−0.0773592	+	0.997003i	$0.524649\pi$
$314$	−43.0892	−2.43166
$315$	0	0
$316$	16.1673	0.909481
$317$	10.6512	0.598231	0.299116	−	0.954217i	$-0.403308\pi$
$317$	10.6512	0.598231	0.299116	+	0.954217i	$0.403308\pi$
$318$	−8.23560	−0.461830
$319$	−4.64460	−0.260047
$320$	6.03975	0.337632
$321$	15.0814	0.841761
$322$	0	0
$323$	18.4205	1.02495
$324$	4.03362	0.224090
$325$	−1.89352	−0.105034
$326$	14.3486	0.794695
$327$	8.16576	0.451568
$328$	−3.34629	−0.184768
$329$	0	0
$330$	13.4094	0.738164
$331$	−3.41626	−0.187774	−0.0938872	−	0.995583i	$-0.529929\pi$
$331$	−3.41626	−0.187774	−0.0938872	+	0.995583i	$0.529929\pi$
$332$	−17.9517	−0.985228
$333$	22.8253	1.25082
$334$	−23.2924	−1.27450
$335$	5.20312	0.284277
$336$	0	0
$337$	24.9606	1.35969	0.679844	−	0.733357i	$-0.262047\pi$
$337$	24.9606	1.35969	0.679844	+	0.733357i	$0.262047\pi$
$338$	1.83237	0.0996678
$339$	15.0276	0.816188
$340$	16.1475	0.875720
$341$	9.15183	0.495599
$342$	16.9213	0.914997
$343$	0	0
$344$	−11.4493	−0.617306
$345$	−10.1603	−0.547014
$346$	−9.61824	−0.517080
$347$	−19.1833	−1.02981	−0.514907	−	0.857246i	$-0.672173\pi$
$347$	−19.1833	−1.02981	−0.514907	+	0.857246i	$0.672173\pi$
$348$	1.64895	0.0883928
$349$	3.94421	0.211129	0.105564	−	0.994412i	$-0.466335\pi$
$349$	3.94421	0.211129	0.105564	+	0.994412i	$0.466335\pi$
$350$	0	0
$351$	−4.50024	−0.240205
$352$	−21.4596	−1.14380
$353$	−28.0232	−1.49152	−0.745762	−	0.666212i	$-0.767914\pi$
$353$	−28.0232	−1.49152	−0.745762	+	0.666212i	$0.767914\pi$
$354$	−4.01723	−0.213513
$355$	30.8618	1.63797
$356$	−14.4807	−0.767476
$357$	0	0
$358$	−19.2866	−1.01933
$359$	33.2232	1.75345	0.876726	−	0.480989i	$-0.159722\pi$
$359$	33.2232	1.75345	0.876726	+	0.480989i	$0.159722\pi$
$360$	−7.01921	−0.369945
$361$	−2.46641	−0.129811
$362$	34.4811	1.81228
$363$	0.291821	0.0153166
$364$	0	0
$365$	31.8719	1.66825
$366$	−17.4947	−0.914460
$367$	28.3091	1.47772	0.738862	−	0.673857i	$-0.235363\pi$
$367$	28.3091	1.47772	0.738862	+	0.673857i	$0.235363\pi$
$368$	22.0837	1.15119
$369$	−6.45606	−0.336089
$370$	48.3520	2.51370
$371$	0	0
$372$	−3.24912	−0.168459
$373$	−12.9515	−0.670602	−0.335301	−	0.942111i	$-0.608838\pi$
$373$	−12.9515	−0.670602	−0.335301	+	0.942111i	$0.608838\pi$
$374$	−27.1003	−1.40132
$375$	−6.96343	−0.359590
$376$	−11.1235	−0.573653
$377$	1.42268	0.0732716
$378$	0	0
$379$	0.168981	0.00867995	0.00433997	−	0.999991i	$-0.498619\pi$
$379$	0.168981	0.00867995	0.00433997	+	0.999991i	$0.498619\pi$
$380$	14.4934	0.743495
$381$	1.36159	0.0697562
$382$	27.3288	1.39826
$383$	−10.1933	−0.520854	−0.260427	−	0.965494i	$-0.583863\pi$
$383$	−10.1933	−0.520854	−0.260427	+	0.965494i	$0.583863\pi$
$384$	−7.62523	−0.389124
$385$	0	0
$386$	−0.0973641	−0.00495570
$387$	−22.0894	−1.12287
$388$	18.6562	0.947124
$389$	−28.6665	−1.45345	−0.726723	−	0.686930i	$-0.758958\pi$
$389$	−28.6665	−1.45345	−0.726723	+	0.686930i	$0.758958\pi$
$390$	−4.10741	−0.207987
$391$	20.5339	1.03844
$392$	0	0
$393$	3.67354	0.185306
$394$	18.4113	0.927547
$395$	−31.2674	−1.57323
$396$	−10.0657	−0.505820
$397$	28.6411	1.43746	0.718728	−	0.695292i	$-0.244725\pi$
$397$	28.6411	1.43746	0.718728	+	0.695292i	$0.244725\pi$
$398$	−42.6785	−2.13928
$399$	0	0
$400$	−9.22550	−0.461275
$401$	−14.2963	−0.713922	−0.356961	−	0.934119i	$-0.616187\pi$
$401$	−14.2963	−0.713922	−0.356961	+	0.934119i	$0.616187\pi$
$402$	3.10021	0.154624
$403$	−2.80328	−0.139641
$404$	−8.00237	−0.398133
$405$	−7.80100	−0.387635
$406$	0	0
$407$	−32.8112	−1.62639
$408$	−4.55286	−0.225400
$409$	−25.6988	−1.27072	−0.635362	−	0.772215i	$-0.719149\pi$
$409$	−25.6988	−1.27072	−0.635362	+	0.772215i	$0.719149\pi$
$410$	−13.6762	−0.675420
$411$	−8.38590	−0.413646
$412$	−3.78408	−0.186428
$413$	0	0
$414$	18.8626	0.927048
$415$	34.7185	1.70426
$416$	6.57326	0.322281
$417$	8.60684	0.421479
$418$	−24.3242	−1.18974
$419$	−18.7999	−0.918433	−0.459216	−	0.888324i	$-0.651870\pi$
$419$	−18.7999	−0.918433	−0.459216	+	0.888324i	$0.651870\pi$
$420$	0	0
$421$	−18.0283	−0.878645	−0.439322	−	0.898329i	$-0.644781\pi$
$421$	−18.0283	−0.878645	−0.439322	+	0.898329i	$0.644781\pi$
$422$	−4.53432	−0.220727
$423$	−21.4609	−1.04346
$424$	−6.19697	−0.300951
$425$	−8.57806	−0.416097
$426$	18.3886	0.890929
$427$	0	0
$428$	−23.9813	−1.15918
$429$	2.78725	0.134570
$430$	−46.7931	−2.25657
$431$	20.5583	0.990256	0.495128	−	0.868820i	$-0.335121\pi$
$431$	20.5583	0.990256	0.495128	+	0.868820i	$0.335121\pi$
$432$	−21.9258	−1.05490
$433$	−18.9235	−0.909404	−0.454702	−	0.890644i	$-0.650254\pi$
$433$	−18.9235	−0.909404	−0.454702	+	0.890644i	$0.650254\pi$
$434$	0	0
$435$	−3.18905	−0.152903
$436$	−12.9846	−0.621849
$437$	18.4305	0.881650
$438$	18.9904	0.907398
$439$	14.6550	0.699445	0.349723	−	0.936853i	$-0.386276\pi$
$439$	14.6550	0.699445	0.349723	+	0.936853i	$0.386276\pi$
$440$	10.0901	0.481025
$441$	0	0
$442$	8.30102	0.394839
$443$	−11.9592	−0.568201	−0.284100	−	0.958795i	$-0.591695\pi$
$443$	−11.9592	−0.568201	−0.284100	+	0.958795i	$0.591695\pi$
$444$	11.6488	0.552827
$445$	28.0056	1.32759
$446$	−11.3062	−0.535365
$447$	11.7924	0.557762
$448$	0	0
$449$	−2.32245	−0.109603	−0.0548015	−	0.998497i	$-0.517453\pi$
$449$	−2.32245	−0.109603	−0.0548015	+	0.998497i	$0.517453\pi$
$450$	−7.87988	−0.371461
$451$	9.28055	0.437004
$452$	−23.8958	−1.12396
$453$	−18.1102	−0.850890
$454$	−21.2443	−0.997044
$455$	0	0
$456$	−4.08648	−0.191367
$457$	−18.5805	−0.869157	−0.434579	−	0.900634i	$-0.643103\pi$
$457$	−18.5805	−0.869157	−0.434579	+	0.900634i	$0.643103\pi$
$458$	18.7601	0.876604
$459$	−20.3870	−0.951585
$460$	16.1562	0.753287
$461$	−27.8926	−1.29909	−0.649543	−	0.760325i	$-0.725040\pi$
$461$	−27.8926	−1.29909	−0.649543	+	0.760325i	$0.725040\pi$
$462$	0	0
$463$	−3.66462	−0.170309	−0.0851547	−	0.996368i	$-0.527138\pi$
$463$	−3.66462	−0.170309	−0.0851547	+	0.996368i	$0.527138\pi$
$464$	6.93147	0.321786
$465$	6.28378	0.291403
$466$	39.3634	1.82347
$467$	−38.7532	−1.79328	−0.896641	−	0.442757i	$-0.854000\pi$
$467$	−38.7532	−1.79328	−0.896641	+	0.442757i	$0.854000\pi$
$468$	3.08320	0.142521
$469$	0	0
$470$	−45.4617	−2.09699
$471$	20.0766	0.925079
$472$	−3.02281	−0.139136
$473$	31.7534	1.46002
$474$	−18.6303	−0.855716
$475$	−7.69935	−0.353270
$476$	0	0
$477$	−11.9559	−0.547425
$478$	1.98978	0.0910105
$479$	6.03430	0.275714	0.137857	−	0.990452i	$-0.455979\pi$
$479$	6.03430	0.275714	0.137857	+	0.990452i	$0.455979\pi$
$480$	−14.7345	−0.672535
$481$	10.0503	0.458256
$482$	36.6162	1.66782
$483$	0	0
$484$	−0.464032	−0.0210924
$485$	−36.0809	−1.63835
$486$	−29.3864	−1.33300
$487$	−3.80249	−0.172307	−0.0861537	−	0.996282i	$-0.527458\pi$
$487$	−3.80249	−0.172307	−0.0861537	+	0.996282i	$0.527458\pi$
$488$	−13.1640	−0.595908
$489$	−6.68545	−0.302326
$490$	0	0
$491$	−0.381464	−0.0172152	−0.00860761	−	0.999963i	$-0.502740\pi$
$491$	−0.381464	−0.0172152	−0.00860761	+	0.999963i	$0.502740\pi$
$492$	−3.29482	−0.148542
$493$	6.44502	0.290269
$494$	7.45070	0.335223
$495$	19.4670	0.874975
$496$	−13.6580	−0.613260
$497$	0	0
$498$	20.6865	0.926986
$499$	34.5739	1.54774	0.773871	−	0.633343i	$-0.218318\pi$
$499$	34.5739	1.54774	0.773871	+	0.633343i	$0.218318\pi$
$500$	11.0727	0.495187
$501$	10.8526	0.484860
$502$	−36.9218	−1.64790
$503$	2.41090	0.107497	0.0537485	−	0.998555i	$-0.482883\pi$
$503$	2.41090	0.107497	0.0537485	+	0.998555i	$0.482883\pi$
$504$	0	0
$505$	15.4765	0.688696
$506$	−27.1149	−1.20540
$507$	−0.853757	−0.0379167
$508$	−2.16509	−0.0960605
$509$	21.9153	0.971380	0.485690	−	0.874131i	$-0.338568\pi$
$509$	21.9153	0.971380	0.485690	+	0.874131i	$0.338568\pi$
$510$	−18.6074	−0.823951
$511$	0	0
$512$	20.5553	0.908426
$513$	−18.2987	−0.807905
$514$	27.5174	1.21374
$515$	7.31837	0.322486
$516$	−11.2732	−0.496276
$517$	30.8499	1.35678
$518$	0	0
$519$	4.48143	0.196713
$520$	−3.09067	−0.135535
$521$	30.1450	1.32068	0.660338	−	0.750968i	$-0.270413\pi$
$521$	30.1450	1.32068	0.660338	+	0.750968i	$0.270413\pi$
$522$	5.92046	0.259131
$523$	18.0993	0.791428	0.395714	−	0.918374i	$-0.370497\pi$
$523$	18.0993	0.791428	0.395714	+	0.918374i	$0.370497\pi$
$524$	−5.84139	−0.255182
$525$	0	0
$526$	−38.7843	−1.69108
$527$	−12.6994	−0.553196
$528$	13.5799	0.590988
$529$	−2.45500	−0.106739
$530$	−25.3269	−1.10013
$531$	−5.83197	−0.253086
$532$	0	0
$533$	−2.84271	−0.123131
$534$	16.6868	0.722106
$535$	46.3796	2.00517
$536$	2.33278	0.100761
$537$	8.98623	0.387784
$538$	7.52151	0.324275
$539$	0	0
$540$	−16.0406	−0.690280
$541$	4.08890	0.175795	0.0878977	−	0.996130i	$-0.471985\pi$
$541$	4.08890	0.175795	0.0878977	+	0.996130i	$0.471985\pi$
$542$	−6.28950	−0.270157
$543$	−16.0658	−0.689449
$544$	29.7782	1.27673
$545$	25.1121	1.07568
$546$	0	0
$547$	−40.4264	−1.72851	−0.864255	−	0.503055i	$-0.832209\pi$
$547$	−40.4264	−1.72851	−0.864255	+	0.503055i	$0.832209\pi$
$548$	13.3346	0.569627
$549$	−25.3977	−1.08395
$550$	11.3273	0.482997
$551$	5.78482	0.246442
$552$	−4.55532	−0.193887
$553$	0	0
$554$	−0.661507	−0.0281047
$555$	−22.5287	−0.956289
$556$	−13.6859	−0.580413
$557$	19.7690	0.837640	0.418820	−	0.908069i	$-0.362444\pi$
$557$	19.7690	0.837640	0.418820	+	0.908069i	$0.362444\pi$
$558$	−11.6658	−0.493854
$559$	−9.72632	−0.411379
$560$	0	0
$561$	12.6268	0.533105
$562$	33.9379	1.43158
$563$	−8.22392	−0.346597	−0.173298	−	0.984869i	$-0.555443\pi$
$563$	−8.22392	−0.346597	−0.173298	+	0.984869i	$0.555443\pi$
$564$	−10.9525	−0.461182
$565$	46.2143	1.94425
$566$	2.95300	0.124124
$567$	0	0
$568$	13.8367	0.580574
$569$	14.5770	0.611099	0.305550	−	0.952176i	$-0.401160\pi$
$569$	14.5770	0.611099	0.305550	+	0.952176i	$0.401160\pi$
$570$	−16.7014	−0.699543
$571$	−2.58822	−0.108314	−0.0541568	−	0.998532i	$-0.517247\pi$
$571$	−2.58822	−0.108314	−0.0541568	+	0.998532i	$0.517247\pi$
$572$	−4.43208	−0.185315
$573$	−12.7333	−0.531942
$574$	0	0
$575$	−8.58269	−0.357923
$576$	5.22437	0.217682
$577$	23.8937	0.994707	0.497353	−	0.867548i	$-0.334305\pi$
$577$	23.8937	0.994707	0.497353	+	0.867548i	$0.334305\pi$
$578$	6.45509	0.268496
$579$	0.0453649	0.00188530
$580$	5.07099	0.210561
$581$	0	0
$582$	−21.4983	−0.891134
$583$	17.1866	0.711795
$584$	14.2896	0.591306
$585$	−5.96289	−0.246535
$586$	8.09304	0.334320
$587$	−28.5759	−1.17945	−0.589726	−	0.807604i	$-0.700764\pi$
$587$	−28.5759	−1.17945	−0.589726	+	0.807604i	$0.700764\pi$
$588$	0	0
$589$	−11.3986	−0.469669
$590$	−12.3541	−0.508612
$591$	−8.57837	−0.352867
$592$	48.9666	2.01252
$593$	19.9575	0.819556	0.409778	−	0.912185i	$-0.365606\pi$
$593$	19.9575	0.819556	0.409778	+	0.912185i	$0.365606\pi$
$594$	26.9210	1.10458
$595$	0	0
$596$	−18.7514	−0.768088
$597$	19.8852	0.813848
$598$	8.30551	0.339638
$599$	1.17716	0.0480973	0.0240486	−	0.999711i	$-0.492344\pi$
$599$	1.17716	0.0480973	0.0240486	+	0.999711i	$0.492344\pi$
$600$	1.90299	0.0776892
$601$	30.9250	1.26146	0.630729	−	0.776003i	$-0.282756\pi$
$601$	30.9250	1.26146	0.630729	+	0.776003i	$0.282756\pi$
$602$	0	0
$603$	4.50069	0.183282
$604$	28.7974	1.17175
$605$	0.897435	0.0364859
$606$	9.22148	0.374597
$607$	−2.40708	−0.0977005	−0.0488503	−	0.998806i	$-0.515556\pi$
$607$	−2.40708	−0.0977005	−0.0488503	+	0.998806i	$0.515556\pi$
$608$	26.7279	1.08396
$609$	0	0
$610$	−53.8011	−2.17834
$611$	−9.44956	−0.382288
$612$	13.9675	0.564605
$613$	−27.7742	−1.12179	−0.560895	−	0.827887i	$-0.689543\pi$
$613$	−27.7742	−1.12179	−0.560895	+	0.827887i	$0.689543\pi$
$614$	10.5976	0.427683
$615$	6.37216	0.256950
$616$	0	0
$617$	26.2125	1.05527	0.527637	−	0.849470i	$-0.323078\pi$
$617$	26.2125	1.05527	0.527637	+	0.849470i	$0.323078\pi$
$618$	4.36055	0.175407
$619$	17.2357	0.692763	0.346381	−	0.938094i	$-0.387410\pi$
$619$	17.2357	0.692763	0.346381	+	0.938094i	$0.387410\pi$
$620$	−9.99200	−0.401288
$621$	−20.3980	−0.818546
$622$	−26.1837	−1.04987
$623$	0	0
$624$	−4.15962	−0.166518
$625$	−30.8822	−1.23529
$626$	−5.01565	−0.200466
$627$	11.3334	0.452612
$628$	−31.9242	−1.27392
$629$	45.5302	1.81541
$630$	0	0
$631$	39.2125	1.56103	0.780513	−	0.625140i	$-0.214958\pi$
$631$	39.2125	1.56103	0.780513	+	0.625140i	$0.214958\pi$
$632$	−14.0185	−0.557628
$633$	2.11268	0.0839714
$634$	19.5170	0.775117
$635$	4.18728	0.166167
$636$	−6.10166	−0.241946
$637$	0	0
$638$	−8.51062	−0.336939
$639$	26.6954	1.05605
$640$	−23.4498	−0.926935
$641$	−22.8735	−0.903451	−0.451725	−	0.892157i	$-0.649191\pi$
$641$	−22.8735	−0.903451	−0.451725	+	0.892157i	$0.649191\pi$
$642$	27.6347	1.09065
$643$	46.7072	1.84195	0.920976	−	0.389620i	$-0.127394\pi$
$643$	46.7072	1.84195	0.920976	+	0.389620i	$0.127394\pi$
$644$	0	0
$645$	21.8024	0.858467
$646$	33.7532	1.32800
$647$	−5.93075	−0.233162	−0.116581	−	0.993181i	$-0.537193\pi$
$647$	−5.93075	−0.233162	−0.116581	+	0.993181i	$0.537193\pi$
$648$	−3.49753	−0.137396
$649$	8.38341	0.329078
$650$	−3.46963	−0.136090
$651$	0	0
$652$	10.6307	0.416330
$653$	−18.8046	−0.735881	−0.367940	−	0.929849i	$-0.619937\pi$
$653$	−18.8046	−0.735881	−0.367940	+	0.929849i	$0.619937\pi$
$654$	14.9627	0.585088
$655$	11.2972	0.441419
$656$	−13.8500	−0.540754
$657$	27.5691	1.07557
$658$	0	0
$659$	23.1086	0.900184	0.450092	−	0.892982i	$-0.351391\pi$
$659$	23.1086	0.900184	0.450092	+	0.892982i	$0.351391\pi$
$660$	9.93488	0.386715
$661$	33.9087	1.31889	0.659447	−	0.751751i	$-0.270790\pi$
$661$	33.9087	1.31889	0.659447	+	0.751751i	$0.270790\pi$
$662$	−6.25985	−0.243296
$663$	−3.86770	−0.150209
$664$	15.5658	0.604071
$665$	0	0
$666$	41.8244	1.62066
$667$	6.44851	0.249687
$668$	−17.2570	−0.667695
$669$	5.26792	0.203669
$670$	9.53404	0.368332
$671$	36.5090	1.40941
$672$	0	0
$673$	6.00430	0.231449	0.115724	−	0.993281i	$-0.463081\pi$
$673$	6.00430	0.231449	0.115724	+	0.993281i	$0.463081\pi$
$674$	45.7370	1.76172
$675$	8.52130	0.327985
$676$	1.35758	0.0522147
$677$	−20.2075	−0.776637	−0.388318	−	0.921525i	$-0.626944\pi$
$677$	−20.2075	−0.776637	−0.388318	+	0.921525i	$0.626944\pi$
$678$	27.5361	1.05752
$679$	0	0
$680$	−14.0014	−0.536928
$681$	9.89837	0.379306
$682$	16.7695	0.642139
$683$	−31.6508	−1.21108	−0.605541	−	0.795814i	$-0.707043\pi$
$683$	−31.6508	−1.21108	−0.605541	+	0.795814i	$0.707043\pi$
$684$	12.5368	0.479355
$685$	−25.7891	−0.985350
$686$	0	0
$687$	−8.74092	−0.333487
$688$	−47.3879	−1.80665
$689$	−5.26439	−0.200557
$690$	−18.6175	−0.708756
$691$	−9.69199	−0.368701	−0.184350	−	0.982861i	$-0.559018\pi$
$691$	−9.69199	−0.368701	−0.184350	+	0.982861i	$0.559018\pi$
$692$	−7.12604	−0.270891
$693$	0	0
$694$	−35.1509	−1.33431
$695$	26.4685	1.00401
$696$	−1.42979	−0.0541960
$697$	−12.8781	−0.487791
$698$	7.22725	0.273556
$699$	−18.3406	−0.693705
$700$	0	0
$701$	−5.10365	−0.192762	−0.0963811	−	0.995345i	$-0.530727\pi$
$701$	−5.10365	−0.192762	−0.0963811	+	0.995345i	$0.530727\pi$
$702$	−8.24610	−0.311229
$703$	40.8662	1.54130
$704$	−7.51000	−0.283044
$705$	21.1820	0.797760
$706$	−51.3489	−1.93254
$707$	0	0
$708$	−2.97632	−0.111857
$709$	26.1445	0.981878	0.490939	−	0.871194i	$-0.336654\pi$
$709$	26.1445	0.981878	0.490939	+	0.871194i	$0.336654\pi$
$710$	56.5502	2.12229
$711$	−27.0463	−1.01431
$712$	12.5561	0.470561
$713$	−12.7063	−0.475855
$714$	0	0
$715$	8.57161	0.320560
$716$	−14.2892	−0.534014
$717$	−0.927100	−0.0346232
$718$	60.8772	2.27192
$719$	8.72884	0.325531	0.162765	−	0.986665i	$-0.447959\pi$
$719$	8.72884	0.325531	0.162765	+	0.986665i	$0.447959\pi$
$720$	−29.0520	−1.08270
$721$	0	0
$722$	−4.51937	−0.168193
$723$	−17.0606	−0.634491
$724$	25.5466	0.949432
$725$	−2.69387	−0.100048
$726$	0.534725	0.0198455
$727$	21.8712	0.811158	0.405579	−	0.914060i	$-0.367070\pi$
$727$	21.8712	0.811158	0.405579	+	0.914060i	$0.367070\pi$
$728$	0	0
$729$	4.77848	0.176981
$730$	58.4011	2.16152
$731$	−44.0623	−1.62970
$732$	−12.9616	−0.479074
$733$	35.5640	1.31359	0.656793	−	0.754071i	$-0.271912\pi$
$733$	35.5640	1.31359	0.656793	+	0.754071i	$0.271912\pi$
$734$	51.8728	1.91466
$735$	0	0
$736$	29.7943	1.09823
$737$	−6.46971	−0.238315
$738$	−11.8299	−0.435465
$739$	−36.4894	−1.34228	−0.671142	−	0.741329i	$-0.734196\pi$
$739$	−36.4894	−1.34228	−0.671142	+	0.741329i	$0.734196\pi$
$740$	35.8234	1.31690
$741$	−3.47151	−0.127529
$742$	0	0
$743$	12.4588	0.457071	0.228535	−	0.973536i	$-0.426606\pi$
$743$	12.4588	0.457071	0.228535	+	0.973536i	$0.426606\pi$
$744$	2.81729	0.103287
$745$	36.2651	1.32865
$746$	−23.7319	−0.868886
$747$	30.0314	1.09879
$748$	−20.0783	−0.734134
$749$	0	0
$750$	−12.7596	−0.465914
$751$	−18.9424	−0.691217	−0.345608	−	0.938379i	$-0.612327\pi$
$751$	−18.9424	−0.691217	−0.345608	+	0.938379i	$0.612327\pi$
$752$	−46.0395	−1.67889
$753$	17.2030	0.626912
$754$	2.60687	0.0949366
$755$	−55.6940	−2.02691
$756$	0	0
$757$	−25.0956	−0.912114	−0.456057	−	0.889951i	$-0.650739\pi$
$757$	−25.0956	−0.912114	−0.456057	+	0.889951i	$0.650739\pi$
$758$	0.309635	0.0112464
$759$	12.6337	0.458573
$760$	−12.5671	−0.455857
$761$	−28.0617	−1.01723	−0.508617	−	0.860993i	$-0.669843\pi$
$761$	−28.0617	−1.01723	−0.508617	+	0.860993i	$0.669843\pi$
$762$	2.49493	0.0903818
$763$	0	0
$764$	20.2476	0.732531
$765$	−27.0131	−0.976662
$766$	−18.6779	−0.674861
$767$	−2.56791	−0.0927217
$768$	−17.9002	−0.645917
$769$	23.2636	0.838907	0.419454	−	0.907777i	$-0.362222\pi$
$769$	23.2636	0.838907	0.419454	+	0.907777i	$0.362222\pi$
$770$	0	0
$771$	−12.8212	−0.461744
$772$	−0.0721359	−0.00259623
$773$	−45.8118	−1.64774	−0.823869	−	0.566781i	$-0.808189\pi$
$773$	−45.8118	−1.64774	−0.823869	+	0.566781i	$0.808189\pi$
$774$	−40.4760	−1.45488
$775$	5.30807	0.190672
$776$	−16.1766	−0.580708
$777$	0	0
$778$	−52.5276	−1.88320
$779$	−11.5589	−0.414140
$780$	−3.04313	−0.108962
$781$	−38.3744	−1.37315
$782$	37.6257	1.34549
$783$	−6.40238	−0.228803
$784$	0	0
$785$	61.7413	2.20364
$786$	6.73129	0.240097
$787$	−31.2715	−1.11471	−0.557355	−	0.830274i	$-0.688184\pi$
$787$	−31.2715	−1.11471	−0.557355	+	0.830274i	$0.688184\pi$
$788$	13.6407	0.485929
$789$	18.0708	0.643338
$790$	−57.2935	−2.03841
$791$	0	0
$792$	8.72789	0.310132
$793$	−11.1830	−0.397119
$794$	52.4811	1.86248
$795$	11.8006	0.418523
$796$	−31.6200	−1.12074
$797$	11.6121	0.411323	0.205661	−	0.978623i	$-0.434065\pi$
$797$	11.6121	0.411323	0.205661	+	0.978623i	$0.434065\pi$
$798$	0	0
$799$	−42.8085	−1.51446
$800$	−12.4466	−0.440054
$801$	24.2248	0.855941
$802$	−26.1961	−0.925016
$803$	−39.6304	−1.39853
$804$	2.29691	0.0810056
$805$	0	0
$806$	−5.13664	−0.180931
$807$	−3.50450	−0.123364
$808$	6.93880	0.244106
$809$	7.30665	0.256888	0.128444	−	0.991717i	$-0.459002\pi$
$809$	7.30665	0.256888	0.128444	+	0.991717i	$0.459002\pi$
$810$	−14.2943	−0.502251
$811$	15.9662	0.560651	0.280325	−	0.959905i	$-0.409558\pi$
$811$	15.9662	0.560651	0.280325	+	0.959905i	$0.409558\pi$
$812$	0	0
$813$	2.93047	0.102776
$814$	−60.1223	−2.10729
$815$	−20.5597	−0.720175
$816$	−18.8440	−0.659671
$817$	−39.5487	−1.38363
$818$	−47.0897	−1.64645
$819$	0	0
$820$	−10.1325	−0.353844
$821$	1.12788	0.0393634	0.0196817	−	0.999806i	$-0.493735\pi$
$821$	1.12788	0.0393634	0.0196817	+	0.999806i	$0.493735\pi$
$822$	−15.3661	−0.535953
$823$	22.4044	0.780968	0.390484	−	0.920610i	$-0.372308\pi$
$823$	22.4044	0.780968	0.390484	+	0.920610i	$0.372308\pi$
$824$	3.28115	0.114304
$825$	−5.27772	−0.183747
$826$	0	0
$827$	−6.32296	−0.219871	−0.109935	−	0.993939i	$-0.535064\pi$
$827$	−6.32296	−0.219871	−0.109935	+	0.993939i	$0.535064\pi$
$828$	13.9751	0.485668
$829$	44.3704	1.54105	0.770523	−	0.637412i	$-0.219995\pi$
$829$	44.3704	1.54105	0.770523	+	0.637412i	$0.219995\pi$
$830$	63.6171	2.20818
$831$	0.308216	0.0106919
$832$	2.30037	0.0797510
$833$	0	0
$834$	15.7709	0.546102
$835$	33.3750	1.15499
$836$	−18.0215	−0.623287
$837$	12.6154	0.436053
$838$	−34.4483	−1.19000
$839$	9.89476	0.341605	0.170803	−	0.985305i	$-0.445364\pi$
$839$	9.89476	0.341605	0.170803	+	0.985305i	$0.445364\pi$
$840$	0	0
$841$	−26.9760	−0.930207
$842$	−33.0345	−1.13844
$843$	−15.8127	−0.544619
$844$	−3.35942	−0.115636
$845$	−2.62555	−0.0903217
$846$	−39.3243	−1.35200
$847$	0	0
$848$	−25.6488	−0.880783
$849$	−1.37589	−0.0472206
$850$	−15.7182	−0.539129
$851$	45.5548	1.56160
$852$	13.6239	0.466746
$853$	−25.9407	−0.888193	−0.444097	−	0.895979i	$-0.646475\pi$
$853$	−25.9407	−0.888193	−0.444097	+	0.895979i	$0.646475\pi$
$854$	0	0
$855$	−24.2460	−0.829196
$856$	20.7940	0.710725
$857$	−10.0244	−0.342426	−0.171213	−	0.985234i	$-0.554769\pi$
$857$	−10.0244	−0.342426	−0.171213	+	0.985234i	$0.554769\pi$
$858$	5.10728	0.174360
$859$	−37.4378	−1.27736	−0.638680	−	0.769472i	$-0.720519\pi$
$859$	−37.4378	−1.27736	−0.638680	+	0.769472i	$0.720519\pi$
$860$	−34.6685	−1.18219
$861$	0	0
$862$	37.6703	1.28306
$863$	21.0026	0.714938	0.357469	−	0.933925i	$-0.383640\pi$
$863$	21.0026	0.714938	0.357469	+	0.933925i	$0.383640\pi$
$864$	−29.5812	−1.00637
$865$	13.7817	0.468592
$866$	−34.6748	−1.17830
$867$	−3.00762	−0.102144
$868$	0	0
$869$	38.8788	1.31887
$870$	−5.84352	−0.198114
$871$	1.98172	0.0671481
$872$	11.2588	0.381273
$873$	−31.2099	−1.05630
$874$	33.7715	1.14234
$875$	0	0
$876$	14.0698	0.475374
$877$	7.56302	0.255385	0.127692	−	0.991814i	$-0.459243\pi$
$877$	7.56302	0.255385	0.127692	+	0.991814i	$0.459243\pi$
$878$	26.8534	0.906258
$879$	−3.77080	−0.127186
$880$	41.7620	1.40780
$881$	34.3550	1.15745	0.578725	−	0.815522i	$-0.303550\pi$
$881$	34.3550	1.15745	0.578725	+	0.815522i	$0.303550\pi$
$882$	0	0
$883$	49.6697	1.67152	0.835759	−	0.549096i	$-0.185028\pi$
$883$	49.6697	1.67152	0.835759	+	0.549096i	$0.185028\pi$
$884$	6.15013	0.206851
$885$	5.75617	0.193492
$886$	−21.9138	−0.736207
$887$	48.0325	1.61277	0.806386	−	0.591389i	$-0.201420\pi$
$887$	48.0325	1.61277	0.806386	+	0.591389i	$0.201420\pi$
$888$	−10.1006	−0.338954
$889$	0	0
$890$	51.3166	1.72014
$891$	9.69999	0.324962
$892$	−8.37665	−0.280471
$893$	−38.4234	−1.28579
$894$	21.6081	0.722682
$895$	27.6353	0.923745
$896$	0	0
$897$	−3.86979	−0.129209
$898$	−4.25558	−0.142011
$899$	−3.98816	−0.133013
$900$	−5.83811	−0.194604
$901$	−23.8488	−0.794518
$902$	17.0054	0.566218
$903$	0	0
$904$	20.7199	0.689133
$905$	−49.4069	−1.64234
$906$	−33.1845	−1.10248
$907$	2.40195	0.0797556	0.0398778	−	0.999205i	$-0.487303\pi$
$907$	2.40195	0.0797556	0.0398778	+	0.999205i	$0.487303\pi$
$908$	−15.7396	−0.522338
$909$	13.3872	0.444024
$910$	0	0
$911$	−33.9555	−1.12500	−0.562499	−	0.826798i	$-0.690160\pi$
$911$	−33.9555	−1.12500	−0.562499	+	0.826798i	$0.690160\pi$
$912$	−16.9137	−0.560067
$913$	−43.1700	−1.42872
$914$	−34.0463	−1.12615
$915$	25.0676	0.828709
$916$	13.8992	0.459241
$917$	0	0
$918$	−37.3566	−1.23295
$919$	−9.37134	−0.309132	−0.154566	−	0.987982i	$-0.549398\pi$
$919$	−9.37134	−0.309132	−0.154566	+	0.987982i	$0.549398\pi$
$920$	−14.0089	−0.461861
$921$	−4.93773	−0.162704
$922$	−51.1095	−1.68320
$923$	11.7544	0.386901
$924$	0	0
$925$	−19.0306	−0.625721
$926$	−6.71494	−0.220667
$927$	6.33038	0.207917
$928$	9.35162	0.306982
$929$	43.4273	1.42480	0.712402	−	0.701771i	$-0.247607\pi$
$929$	43.4273	1.42480	0.712402	+	0.701771i	$0.247607\pi$
$930$	11.5142	0.377566
$931$	0	0
$932$	29.1639	0.955294
$933$	12.1998	0.399403
$934$	−71.0102	−2.32352
$935$	38.8312	1.26992
$936$	−2.67342	−0.0873835
$937$	−2.59416	−0.0847476	−0.0423738	−	0.999102i	$-0.513492\pi$
$937$	−2.59416	−0.0847476	−0.0423738	+	0.999102i	$0.513492\pi$
$938$	0	0
$939$	2.33695	0.0762633
$940$	−33.6820	−1.09859
$941$	−43.4060	−1.41499	−0.707497	−	0.706716i	$-0.750176\pi$
$941$	−43.4060	−1.41499	−0.707497	+	0.706716i	$0.750176\pi$
$942$	36.7877	1.19861
$943$	−12.8850	−0.419594
$944$	−12.5112	−0.407204
$945$	0	0
$946$	58.1840	1.89172
$947$	−7.50058	−0.243736	−0.121868	−	0.992546i	$-0.538888\pi$
$947$	−7.50058	−0.243736	−0.121868	+	0.992546i	$0.538888\pi$
$948$	−13.8029	−0.448299
$949$	12.1391	0.394052
$950$	−14.1081	−0.457726
$951$	−9.09355	−0.294878
$952$	0	0
$953$	−0.708439	−0.0229486	−0.0114743	−	0.999934i	$-0.503652\pi$
$953$	−0.708439	−0.0229486	−0.0114743	+	0.999934i	$0.503652\pi$
$954$	−21.9077	−0.709288
$955$	−39.1586	−1.26714
$956$	1.47421	0.0476792
$957$	3.96536	0.128182
$958$	11.0571	0.357238
$959$	0	0
$960$	−5.15648	−0.166425
$961$	−23.1416	−0.746504
$962$	18.4159	0.593754
$963$	40.1183	1.29279
$964$	27.1285	0.873750
$965$	0.139510	0.00449100
$966$	0	0
$967$	−16.9761	−0.545915	−0.272957	−	0.962026i	$-0.588002\pi$
$967$	−16.9761	−0.545915	−0.272957	+	0.962026i	$0.588002\pi$
$968$	0.402359	0.0129323
$969$	−15.7267	−0.505213
$970$	−66.1136	−2.12278
$971$	6.86359	0.220263	0.110132	−	0.993917i	$-0.464873\pi$
$971$	6.86359	0.220263	0.110132	+	0.993917i	$0.464873\pi$
$972$	−21.7721	−0.698339
$973$	0	0
$974$	−6.96757	−0.223255
$975$	1.61661	0.0517729
$976$	−54.4850	−1.74402
$977$	0.581913	0.0186171	0.00930853	−	0.999957i	$-0.497037\pi$
$977$	0.581913	0.0186171	0.00930853	+	0.999957i	$0.497037\pi$
$978$	−12.2502	−0.391719
$979$	−34.8230	−1.11295
$980$	0	0
$981$	21.7219	0.693528
$982$	−0.698983	−0.0223054
$983$	−34.7195	−1.10738	−0.553689	−	0.832723i	$-0.686780\pi$
$983$	−34.7195	−1.10738	−0.553689	+	0.832723i	$0.686780\pi$
$984$	2.85692	0.0910752
$985$	−26.3810	−0.840568
$986$	11.8097	0.376097
$987$	0	0
$988$	5.52013	0.175619
$989$	−44.0861	−1.40186
$990$	35.6707	1.13369
$991$	24.1688	0.767748	0.383874	−	0.923385i	$-0.374590\pi$
$991$	24.1688	0.767748	0.383874	+	0.923385i	$0.374590\pi$
$992$	−18.4267	−0.585047
$993$	2.91665	0.0925572
$994$	0	0
$995$	61.1528	1.93868
$996$	15.3264	0.485636
$997$	35.1852	1.11433	0.557163	−	0.830403i	$-0.311890\pi$
$997$	35.1852	1.11433	0.557163	+	0.830403i	$0.311890\pi$
$998$	63.3523	2.00538
$999$	−45.2289	−1.43098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.a.m.1.5	✓	6
3.2	odd	2		5733.2.a.bu.1.2		6
7.2	even	3		637.2.e.o.508.2		12
7.3	odd	6		637.2.e.n.79.2		12
7.4	even	3		637.2.e.o.79.2		12
7.5	odd	6		637.2.e.n.508.2		12
7.6	odd	2		637.2.a.n.1.5	yes	6
13.12	even	2		8281.2.a.cc.1.2		6
21.20	even	2		5733.2.a.br.1.2		6
91.90	odd	2		8281.2.a.cd.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.5	✓	6	1.1	even	1	trivial
637.2.a.n.1.5	yes	6	7.6	odd	2
637.2.e.n.79.2		12	7.3	odd	6
637.2.e.n.508.2		12	7.5	odd	6
637.2.e.o.79.2		12	7.4	even	3
637.2.e.o.508.2		12	7.2	even	3
5733.2.a.br.1.2		6	21.20	even	2
5733.2.a.bu.1.2		6	3.2	odd	2
8281.2.a.cc.1.2		6	13.12	even	2
8281.2.a.cd.1.2		6	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q+1.83237 q^{2} -0.853757 q^{3} +1.35758 q^{4} -2.62555 q^{5} -1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} +O(q^{10})\)	\(q+1.83237 q^{2} -0.853757 q^{3} +1.35758 q^{4} -2.62555 q^{5} -1.56440 q^{6} -1.17715 q^{8} -2.27110 q^{9} -4.81098 q^{10} +3.26469 q^{11} -1.15904 q^{12} -1.00000 q^{13} +2.24158 q^{15} -4.87214 q^{16} -4.53021 q^{17} -4.16149 q^{18} -4.06615 q^{19} -3.56440 q^{20} +5.98212 q^{22} -4.53266 q^{23} +1.00500 q^{24} +1.89352 q^{25} -1.83237 q^{26} +4.50024 q^{27} -1.42268 q^{29} +4.10741 q^{30} +2.80328 q^{31} -6.57326 q^{32} -2.78725 q^{33} -8.30102 q^{34} -3.08320 q^{36} -10.0503 q^{37} -7.45070 q^{38} +0.853757 q^{39} +3.09067 q^{40} +2.84271 q^{41} +9.72632 q^{43} +4.43208 q^{44} +5.96289 q^{45} -8.30551 q^{46} +9.44956 q^{47} +4.15962 q^{48} +3.46963 q^{50} +3.86770 q^{51} -1.35758 q^{52} +5.26439 q^{53} +8.24610 q^{54} -8.57161 q^{55} +3.47151 q^{57} -2.60687 q^{58} +2.56791 q^{59} +3.04313 q^{60} +11.1830 q^{61} +5.13664 q^{62} -2.30037 q^{64} +2.62555 q^{65} -5.10728 q^{66} -1.98172 q^{67} -6.15013 q^{68} +3.86979 q^{69} -11.7544 q^{71} +2.67342 q^{72} -12.1391 q^{73} -18.4159 q^{74} -1.61661 q^{75} -5.52013 q^{76} +1.56440 q^{78} +11.9089 q^{79} +12.7920 q^{80} +2.97118 q^{81} +5.20889 q^{82} -13.2233 q^{83} +11.8943 q^{85} +17.8222 q^{86} +1.21462 q^{87} -3.84303 q^{88} -10.6666 q^{89} +10.9262 q^{90} -6.15345 q^{92} -2.39332 q^{93} +17.3151 q^{94} +10.6759 q^{95} +5.61197 q^{96} +13.7422 q^{97} -7.41443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 8 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{9}+O(q^{10}) \) 6 * q - 8 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^9	\( 6 q - 8 q^{3} + 4 q^{4} - 6 q^{5} - 4 q^{6} + 6 q^{9} - 4 q^{10} + 4 q^{11} + 4 q^{12} - 6 q^{13} + 12 q^{15} - 16 q^{17} - 4 q^{18} - 2 q^{19} - 16 q^{20} - 12 q^{22} - 6 q^{23} - 12 q^{24} - 4 q^{25} - 20 q^{27} - 6 q^{29} - 6 q^{31} - 20 q^{32} - 4 q^{33} - 24 q^{36} - 8 q^{38} + 8 q^{39} - 4 q^{40} + 8 q^{41} + 2 q^{43} - 4 q^{44} - 14 q^{45} + 8 q^{46} - 30 q^{47} + 8 q^{48} + 8 q^{50} - 4 q^{51} - 4 q^{52} - 14 q^{53} + 48 q^{54} + 8 q^{55} + 4 q^{57} - 8 q^{58} - 24 q^{59} + 12 q^{60} - 28 q^{62} - 20 q^{64} + 6 q^{65} + 4 q^{66} + 16 q^{67} - 28 q^{68} + 20 q^{69} + 8 q^{71} + 28 q^{72} + 6 q^{73} - 12 q^{74} - 12 q^{75} + 16 q^{76} + 4 q^{78} - 22 q^{79} + 28 q^{80} + 46 q^{81} + 40 q^{82} - 50 q^{83} - 8 q^{85} - 16 q^{86} + 16 q^{87} - 44 q^{88} - 26 q^{89} + 40 q^{90} + 20 q^{92} + 16 q^{93} + 32 q^{94} - 6 q^{95} + 20 q^{96} + 14 q^{97} + 12 q^{99}+O(q^{100}) \) 6 * q - 8 * q^3 + 4 * q^4 - 6 * q^5 - 4 * q^6 + 6 * q^9 - 4 * q^10 + 4 * q^11 + 4 * q^12 - 6 * q^13 + 12 * q^15 - 16 * q^17 - 4 * q^18 - 2 * q^19 - 16 * q^20 - 12 * q^22 - 6 * q^23 - 12 * q^24 - 4 * q^25 - 20 * q^27 - 6 * q^29 - 6 * q^31 - 20 * q^32 - 4 * q^33 - 24 * q^36 - 8 * q^38 + 8 * q^39 - 4 * q^40 + 8 * q^41 + 2 * q^43 - 4 * q^44 - 14 * q^45 + 8 * q^46 - 30 * q^47 + 8 * q^48 + 8 * q^50 - 4 * q^51 - 4 * q^52 - 14 * q^53 + 48 * q^54 + 8 * q^55 + 4 * q^57 - 8 * q^58 - 24 * q^59 + 12 * q^60 - 28 * q^62 - 20 * q^64 + 6 * q^65 + 4 * q^66 + 16 * q^67 - 28 * q^68 + 20 * q^69 + 8 * q^71 + 28 * q^72 + 6 * q^73 - 12 * q^74 - 12 * q^75 + 16 * q^76 + 4 * q^78 - 22 * q^79 + 28 * q^80 + 46 * q^81 + 40 * q^82 - 50 * q^83 - 8 * q^85 - 16 * q^86 + 16 * q^87 - 44 * q^88 - 26 * q^89 + 40 * q^90 + 20 * q^92 + 16 * q^93 + 32 * q^94 - 6 * q^95 + 20 * q^96 + 14 * q^97 + 12 * q^99

Introduction

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