LMFDB - Embedded newform 637.2.a.n.1.4

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:	$0$
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			1.4
Root			$1.90903$ 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)

$f(q)$	$=$	$q+0.264627 q^{2} +2.90903 q^{3} -1.92997 q^{4} -1.43515 q^{5} +0.769807 q^{6} -1.03998 q^{8} +5.46247 q^{9} +O(q^{10})$	\(q+0.264627 q^{2} +2.90903 q^{3} -1.92997 q^{4} -1.43515 q^{5} +0.769807 q^{6} -1.03998 q^{8} +5.46247 q^{9} -0.379780 q^{10} +5.50474 q^{11} -5.61435 q^{12} +1.00000 q^{13} -4.17491 q^{15} +3.58474 q^{16} +4.83072 q^{17} +1.44552 q^{18} +2.82036 q^{19} +2.76981 q^{20} +1.45670 q^{22} -5.99956 q^{23} -3.02532 q^{24} -2.94033 q^{25} +0.264627 q^{26} +7.16341 q^{27} +1.04188 q^{29} -1.10479 q^{30} +9.20895 q^{31} +3.02857 q^{32} +16.0135 q^{33} +1.27834 q^{34} -10.5424 q^{36} +0.612497 q^{37} +0.746342 q^{38} +2.90903 q^{39} +1.49252 q^{40} -10.6196 q^{41} -8.43685 q^{43} -10.6240 q^{44} -7.83949 q^{45} -1.58764 q^{46} +2.40922 q^{47} +10.4281 q^{48} -0.778091 q^{50} +14.0527 q^{51} -1.92997 q^{52} -1.82959 q^{53} +1.89563 q^{54} -7.90015 q^{55} +8.20452 q^{57} +0.275709 q^{58} -0.870914 q^{59} +8.05746 q^{60} -3.33253 q^{61} +2.43693 q^{62} -6.36804 q^{64} -1.43515 q^{65} +4.23759 q^{66} -6.62741 q^{67} -9.32316 q^{68} -17.4529 q^{69} -6.85856 q^{71} -5.68083 q^{72} +3.14147 q^{73} +0.162083 q^{74} -8.55353 q^{75} -5.44322 q^{76} +0.769807 q^{78} -17.5723 q^{79} -5.14465 q^{80} +4.45118 q^{81} -2.81022 q^{82} +11.4525 q^{83} -6.93283 q^{85} -2.23261 q^{86} +3.03086 q^{87} -5.72479 q^{88} -0.995318 q^{89} -2.07454 q^{90} +11.5790 q^{92} +26.7891 q^{93} +0.637545 q^{94} -4.04765 q^{95} +8.81020 q^{96} +13.5090 q^{97} +30.0695 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.264627	0.187119	0.0935596	−	0.995614i	$-0.470175\pi$
$2$	0.264627	0.187119	0.0935596	+	0.995614i	$0.470175\pi$
$3$	2.90903	1.67953	0.839765	−	0.542949i	$-0.182692\pi$
$3$	2.90903	1.67953	0.839765	+	0.542949i	$0.182692\pi$
$4$	−1.92997	−0.964986
$5$	−1.43515	−0.641820	−0.320910	−	0.947110i	$-0.603989\pi$
$5$	−1.43515	−0.641820	−0.320910	+	0.947110i	$0.603989\pi$
$6$	0.769807	0.314273
$7$	0	0
$7$	0	0
$8$	−1.03998	−0.367687
$9$	5.46247	1.82082
$10$	−0.379780	−0.120097
$11$	5.50474	1.65974	0.829871	−	0.557955i	$-0.188414\pi$
$11$	5.50474	1.65974	0.829871	+	0.557955i	$0.188414\pi$
$12$	−5.61435	−1.62072
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	−4.17491	−1.07796
$16$	3.58474	0.896185
$17$	4.83072	1.17162	0.585811	−	0.810448i	$-0.300776\pi$
$17$	4.83072	1.17162	0.585811	+	0.810448i	$0.300776\pi$
$18$	1.44552	0.340711
$19$	2.82036	0.647035	0.323518	−	0.946222i	$-0.395135\pi$
$19$	2.82036	0.647035	0.323518	+	0.946222i	$0.395135\pi$
$20$	2.76981	0.619348
$21$	0	0
$22$	1.45670	0.310570
$23$	−5.99956	−1.25100	−0.625498	−	0.780226i	$-0.715104\pi$
$23$	−5.99956	−1.25100	−0.625498	+	0.780226i	$0.715104\pi$
$24$	−3.02532	−0.617541
$25$	−2.94033	−0.588067
$26$	0.264627	0.0518975
$27$	7.16341	1.37860
$28$	0	0
$29$	1.04188	0.193472	0.0967361	−	0.995310i	$-0.469160\pi$
$29$	1.04188	0.193472	0.0967361	+	0.995310i	$0.469160\pi$
$30$	−1.10479	−0.201706
$31$	9.20895	1.65398	0.826988	−	0.562219i	$-0.190052\pi$
$31$	9.20895	1.65398	0.826988	+	0.562219i	$0.190052\pi$
$32$	3.02857	0.535380
$33$	16.0135	2.78759
$34$	1.27834	0.219233
$35$	0	0
$36$	−10.5424	−1.75707
$37$	0.612497	0.100694	0.0503470	−	0.998732i	$-0.483967\pi$
$37$	0.612497	0.100694	0.0503470	+	0.998732i	$0.483967\pi$
$38$	0.746342	0.121073
$39$	2.90903	0.465818
$40$	1.49252	0.235989
$41$	−10.6196	−1.65850	−0.829249	−	0.558879i	$-0.811232\pi$
$41$	−10.6196	−1.65850	−0.829249	+	0.558879i	$0.811232\pi$
$42$	0	0
$43$	−8.43685	−1.28661	−0.643304	−	0.765611i	$-0.722437\pi$
$43$	−8.43685	−1.28661	−0.643304	+	0.765611i	$0.722437\pi$
$44$	−10.6240	−1.60163
$45$	−7.83949	−1.16864
$46$	−1.58764	−0.234085
$47$	2.40922	0.351422	0.175711	−	0.984442i	$-0.443778\pi$
$47$	2.40922	0.351422	0.175711	+	0.984442i	$0.443778\pi$
$48$	10.4281	1.50517
$49$	0	0
$50$	−0.778091	−0.110039
$51$	14.0527	1.96778
$52$	−1.92997	−0.267639
$53$	−1.82959	−0.251313	−0.125657	−	0.992074i	$-0.540104\pi$
$53$	−1.82959	−0.251313	−0.125657	+	0.992074i	$0.540104\pi$
$54$	1.89563	0.257962
$55$	−7.90015	−1.06526
$56$	0	0
$57$	8.20452	1.08672
$58$	0.275709	0.0362024
$59$	−0.870914	−0.113383	−0.0566917	−	0.998392i	$-0.518055\pi$
$59$	−0.870914	−0.113383	−0.0566917	+	0.998392i	$0.518055\pi$
$60$	8.05746	1.04021
$61$	−3.33253	−0.426686	−0.213343	−	0.976977i	$-0.568435\pi$
$61$	−3.33253	−0.426686	−0.213343	+	0.976977i	$0.568435\pi$
$62$	2.43693	0.309491
$63$	0	0
$64$	−6.36804	−0.796005
$65$	−1.43515	−0.178009
$66$	4.23759	0.521611
$67$	−6.62741	−0.809667	−0.404833	−	0.914390i	$-0.632671\pi$
$67$	−6.62741	−0.809667	−0.404833	+	0.914390i	$0.632671\pi$
$68$	−9.32316	−1.13060
$69$	−17.4529	−2.10108
$70$	0	0
$71$	−6.85856	−0.813961	−0.406980	−	0.913437i	$-0.633418\pi$
$71$	−6.85856	−0.813961	−0.406980	+	0.913437i	$0.633418\pi$
$72$	−5.68083	−0.669493
$73$	3.14147	0.367682	0.183841	−	0.982956i	$-0.441147\pi$
$73$	3.14147	0.367682	0.183841	+	0.982956i	$0.441147\pi$
$74$	0.162083	0.0188418
$75$	−8.55353	−0.987676
$76$	−5.44322	−0.624380
$77$	0	0
$78$	0.769807	0.0871635
$79$	−17.5723	−1.97704	−0.988518	−	0.151101i	$-0.951718\pi$
$79$	−17.5723	−1.97704	−0.988518	+	0.151101i	$0.951718\pi$
$80$	−5.14465	−0.575190
$81$	4.45118	0.494576
$82$	−2.81022	−0.310337
$83$	11.4525	1.25708	0.628538	−	0.777779i	$-0.283654\pi$
$83$	11.4525	1.25708	0.628538	+	0.777779i	$0.283654\pi$
$84$	0	0
$85$	−6.93283	−0.751971
$86$	−2.23261	−0.240749
$87$	3.03086	0.324943
$88$	−5.72479	−0.610265
$89$	−0.995318	−0.105503	−0.0527517	−	0.998608i	$-0.516799\pi$
$89$	−0.995318	−0.105503	−0.0527517	+	0.998608i	$0.516799\pi$
$90$	−2.07454	−0.218675
$91$	0	0
$92$	11.5790	1.20719
$93$	26.7891	2.77790
$94$	0.637545	0.0657577
$95$	−4.04765	−0.415280
$96$	8.81020	0.899188
$97$	13.5090	1.37163	0.685817	−	0.727774i	$-0.259445\pi$
$97$	13.5090	1.37163	0.685817	+	0.727774i	$0.259445\pi$
$98$	0	0
$99$	30.0695	3.02210
$100$	5.67477	0.567477
$101$	−1.00807	−0.100306	−0.0501532	−	0.998742i	$-0.515971\pi$
$101$	−1.00807	−0.100306	−0.0501532	+	0.998742i	$0.515971\pi$
$102$	3.71873	0.368209
$103$	−12.7754	−1.25880	−0.629401	−	0.777081i	$-0.716700\pi$
$103$	−12.7754	−1.25880	−0.629401	+	0.777081i	$0.716700\pi$
$104$	−1.03998	−0.101978
$105$	0	0
$106$	−0.484157	−0.0470255
$107$	−0.685495	−0.0662693	−0.0331347	−	0.999451i	$-0.510549\pi$
$107$	−0.685495	−0.0662693	−0.0331347	+	0.999451i	$0.510549\pi$
$108$	−13.8252	−1.33033
$109$	−2.90344	−0.278099	−0.139050	−	0.990285i	$-0.544405\pi$
$109$	−2.90344	−0.278099	−0.139050	+	0.990285i	$0.544405\pi$
$110$	−2.09059	−0.199330
$111$	1.78177	0.169119
$112$	0	0
$113$	12.0315	1.13183	0.565915	−	0.824464i	$-0.308523\pi$
$113$	12.0315	1.13183	0.565915	+	0.824464i	$0.308523\pi$
$114$	2.17113	0.203345
$115$	8.61029	0.802914
$116$	−2.01080	−0.186698
$117$	5.46247	0.505006
$118$	−0.230467	−0.0212162
$119$	0	0
$120$	4.34180	0.396350
$121$	19.3022	1.75474
$122$	−0.881875	−0.0798412
$123$	−30.8927	−2.78550
$124$	−17.7730	−1.59606
$125$	11.3956	1.01925
$126$	0	0
$127$	15.6659	1.39012	0.695062	−	0.718950i	$-0.255377\pi$
$127$	15.6659	1.39012	0.695062	+	0.718950i	$0.255377\pi$
$128$	−7.74229	−0.684328
$129$	−24.5431	−2.16090
$130$	−0.379780	−0.0333089
$131$	12.1273	1.05957	0.529784	−	0.848132i	$-0.322273\pi$
$131$	12.1273	1.05957	0.529784	+	0.848132i	$0.322273\pi$
$132$	−30.9056	−2.68998
$133$	0	0
$134$	−1.75379	−0.151504
$135$	−10.2806	−0.884813
$136$	−5.02383	−0.430790
$137$	15.9375	1.36163	0.680815	−	0.732456i	$-0.261626\pi$
$137$	15.9375	1.36163	0.680815	+	0.732456i	$0.261626\pi$
$138$	−4.61851	−0.393153
$139$	−6.64088	−0.563272	−0.281636	−	0.959521i	$-0.590877\pi$
$139$	−6.64088	−0.563272	−0.281636	+	0.959521i	$0.590877\pi$
$140$	0	0
$141$	7.00851	0.590223
$142$	−1.81496	−0.152308
$143$	5.50474	0.460330
$144$	19.5815	1.63180
$145$	−1.49526	−0.124174
$146$	0.831317	0.0688003
$147$	0	0
$148$	−1.18210	−0.0971683
$149$	−19.5502	−1.60162	−0.800809	−	0.598920i	$-0.795597\pi$
$149$	−19.5502	−1.60162	−0.800809	+	0.598920i	$0.795597\pi$
$150$	−2.26349	−0.184813
$151$	10.6880	0.869779	0.434890	−	0.900484i	$-0.356787\pi$
$151$	10.6880	0.869779	0.434890	+	0.900484i	$0.356787\pi$
$152$	−2.93311	−0.237906
$153$	26.3877	2.13332
$154$	0	0
$155$	−13.2163	−1.06156
$156$	−5.61435	−0.449508
$157$	−15.0734	−1.20299	−0.601496	−	0.798876i	$-0.705428\pi$
$157$	−15.0734	−1.20299	−0.601496	+	0.798876i	$0.705428\pi$
$158$	−4.65009	−0.369942
$159$	−5.32233	−0.422088
$160$	−4.34646	−0.343618
$161$	0	0
$162$	1.17790	0.0925447
$163$	−23.8135	−1.86521	−0.932607	−	0.360894i	$-0.882472\pi$
$163$	−23.8135	−1.86521	−0.932607	+	0.360894i	$0.882472\pi$
$164$	20.4955	1.60043
$165$	−22.9818	−1.78913
$166$	3.03064	0.235223
$167$	−7.12371	−0.551249	−0.275625	−	0.961265i	$-0.588885\pi$
$167$	−7.12371	−0.551249	−0.275625	+	0.961265i	$0.588885\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−1.83461	−0.140708
$171$	15.4061	1.17814
$172$	16.2829	1.24156
$173$	11.2367	0.854309	0.427155	−	0.904179i	$-0.359516\pi$
$173$	11.2367	0.854309	0.427155	+	0.904179i	$0.359516\pi$
$174$	0.802047	0.0608030
$175$	0	0
$176$	19.7331	1.48744
$177$	−2.53352	−0.190431
$178$	−0.263387	−0.0197417
$179$	−13.1945	−0.986204	−0.493102	−	0.869972i	$-0.664137\pi$
$179$	−13.1945	−0.986204	−0.493102	+	0.869972i	$0.664137\pi$
$180$	15.1300	1.12772
$181$	−13.7414	−1.02139	−0.510696	−	0.859761i	$-0.670612\pi$
$181$	−13.7414	−1.02139	−0.510696	+	0.859761i	$0.670612\pi$
$182$	0	0
$183$	−9.69443	−0.716633
$184$	6.23939	0.459974
$185$	−0.879028	−0.0646274
$186$	7.08912	0.519799
$187$	26.5919	1.94459
$188$	−4.64974	−0.339117
$189$	0	0
$190$	−1.07112	−0.0777069
$191$	−16.3307	−1.18165	−0.590824	−	0.806800i	$-0.701197\pi$
$191$	−16.3307	−1.18165	−0.590824	+	0.806800i	$0.701197\pi$
$192$	−18.5248	−1.33692
$193$	−14.0533	−1.01158	−0.505790	−	0.862656i	$-0.668799\pi$
$193$	−14.0533	−1.01158	−0.505790	+	0.862656i	$0.668799\pi$
$194$	3.57485	0.256659
$195$	−4.17491	−0.298971
$196$	0	0
$197$	−1.46898	−0.104660	−0.0523302	−	0.998630i	$-0.516665\pi$
$197$	−1.46898	−0.104660	−0.0523302	+	0.998630i	$0.516665\pi$
$198$	7.95719	0.565493
$199$	−13.3772	−0.948285	−0.474142	−	0.880448i	$-0.657242\pi$
$199$	−13.3772	−0.948285	−0.474142	+	0.880448i	$0.657242\pi$
$200$	3.05787	0.216224
$201$	−19.2794	−1.35986
$202$	−0.266761	−0.0187692
$203$	0	0
$204$	−27.1214	−1.89888
$205$	15.2407	1.06446
$206$	−3.38072	−0.235546
$207$	−32.7724	−2.27784
$208$	3.58474	0.248557
$209$	15.5254	1.07391
$210$	0	0
$211$	3.47044	0.238915	0.119457	−	0.992839i	$-0.461885\pi$
$211$	3.47044	0.238915	0.119457	+	0.992839i	$0.461885\pi$
$212$	3.53105	0.242514
$213$	−19.9518	−1.36707
$214$	−0.181400	−0.0124003
$215$	12.1082	0.825771
$216$	−7.44977	−0.506893
$217$	0	0
$218$	−0.768328	−0.0520378
$219$	9.13865	0.617533
$220$	15.2471	1.02796
$221$	4.83072	0.324950
$222$	0.471505	0.0316453
$223$	−9.91318	−0.663836	−0.331918	−	0.943308i	$-0.607696\pi$
$223$	−9.91318	−0.663836	−0.331918	+	0.943308i	$0.607696\pi$
$224$	0	0
$225$	−16.0615	−1.07077
$226$	3.18386	0.211787
$227$	12.0727	0.801292	0.400646	−	0.916233i	$-0.368786\pi$
$227$	12.0727	0.801292	0.400646	+	0.916233i	$0.368786\pi$
$228$	−15.8345	−1.04867
$229$	4.05171	0.267745	0.133872	−	0.990999i	$-0.457259\pi$
$229$	4.05171	0.267745	0.133872	+	0.990999i	$0.457259\pi$
$230$	2.27851	0.150241
$231$	0	0
$232$	−1.08353	−0.0711372
$233$	12.5450	0.821850	0.410925	−	0.911669i	$-0.365206\pi$
$233$	12.5450	0.821850	0.410925	+	0.911669i	$0.365206\pi$
$234$	1.44552	0.0944963
$235$	−3.45761	−0.225549
$236$	1.68084	0.109413
$237$	−51.1184	−3.32049
$238$	0	0
$239$	13.3463	0.863299	0.431649	−	0.902042i	$-0.357932\pi$
$239$	13.3463	0.863299	0.431649	+	0.902042i	$0.357932\pi$
$240$	−14.9660	−0.966049
$241$	20.3854	1.31314	0.656568	−	0.754267i	$-0.272007\pi$
$241$	20.3854	1.31314	0.656568	+	0.754267i	$0.272007\pi$
$242$	5.10787	0.328346
$243$	−8.54160	−0.547944
$244$	6.43169	0.411747
$245$	0	0
$246$	−8.17502	−0.521221
$247$	2.82036	0.179455
$248$	−9.57708	−0.608145
$249$	33.3157	2.11130
$250$	3.01558	0.190722
$251$	17.1921	1.08515	0.542577	−	0.840006i	$-0.317449\pi$
$251$	17.1921	1.08515	0.542577	+	0.840006i	$0.317449\pi$
$252$	0	0
$253$	−33.0260	−2.07633
$254$	4.14561	0.260119
$255$	−20.1678	−1.26296
$256$	10.6873	0.667954
$257$	−7.64695	−0.477004	−0.238502	−	0.971142i	$-0.576656\pi$
$257$	−7.64695	−0.477004	−0.238502	+	0.971142i	$0.576656\pi$
$258$	−6.49475	−0.404345
$259$	0	0
$260$	2.76981	0.171776
$261$	5.69124	0.352279
$262$	3.20921	0.198266
$263$	−0.101037	−0.00623022	−0.00311511	−	0.999995i	$-0.500992\pi$
$263$	−0.101037	−0.00623022	−0.00311511	+	0.999995i	$0.500992\pi$
$264$	−16.6536	−1.02496
$265$	2.62574	0.161298
$266$	0	0
$267$	−2.89541	−0.177196
$268$	12.7907	0.781318
$269$	−7.56852	−0.461461	−0.230730	−	0.973018i	$-0.574111\pi$
$269$	−7.56852	−0.461461	−0.230730	+	0.973018i	$0.574111\pi$
$270$	−2.72052	−0.165565
$271$	−13.8554	−0.841653	−0.420826	−	0.907141i	$-0.638260\pi$
$271$	−13.8554	−0.841653	−0.420826	+	0.907141i	$0.638260\pi$
$272$	17.3169	1.04999
$273$	0	0
$274$	4.21748	0.254787
$275$	−16.1858	−0.976039
$276$	33.6837	2.02752
$277$	0.552935	0.0332226	0.0166113	−	0.999862i	$-0.494712\pi$
$277$	0.552935	0.0332226	0.0166113	+	0.999862i	$0.494712\pi$
$278$	−1.75735	−0.105399
$279$	50.3036	3.01160
$280$	0	0
$281$	1.14667	0.0684043	0.0342022	−	0.999415i	$-0.489111\pi$
$281$	1.14667	0.0684043	0.0342022	+	0.999415i	$0.489111\pi$
$282$	1.85464	0.110442
$283$	−4.05396	−0.240983	−0.120491	−	0.992714i	$-0.538447\pi$
$283$	−4.05396	−0.240983	−0.120491	+	0.992714i	$0.538447\pi$
$284$	13.2368	0.785461
$285$	−11.7747	−0.697476
$286$	1.45670	0.0861365
$287$	0	0
$288$	16.5435	0.974833
$289$	6.33588	0.372699
$290$	−0.395685	−0.0232354
$291$	39.2982	2.30370
$292$	−6.06296	−0.354808
$293$	15.0649	0.880102	0.440051	−	0.897973i	$-0.354960\pi$
$293$	15.0649	0.880102	0.440051	+	0.897973i	$0.354960\pi$
$294$	0	0
$295$	1.24990	0.0727718
$296$	−0.636982	−0.0370238
$297$	39.4327	2.28812
$298$	−5.17351	−0.299694
$299$	−5.99956	−0.346964
$300$	16.5081	0.953094
$301$	0	0
$302$	2.82834	0.162752
$303$	−2.93250	−0.168468
$304$	10.1103	0.579863
$305$	4.78269	0.273856
$306$	6.98288	0.399185
$307$	−19.9408	−1.13808	−0.569040	−	0.822310i	$-0.692685\pi$
$307$	−19.9408	−1.13808	−0.569040	+	0.822310i	$0.692685\pi$
$308$	0	0
$309$	−37.1642	−2.11420
$310$	−3.49737	−0.198637
$311$	−10.8956	−0.617833	−0.308916	−	0.951089i	$-0.599966\pi$
$311$	−10.8956	−0.617833	−0.308916	+	0.951089i	$0.599966\pi$
$312$	−3.02532	−0.171275
$313$	−0.0519190	−0.00293464	−0.00146732	−	0.999999i	$-0.500467\pi$
$313$	−0.0519190	−0.00293464	−0.00146732	+	0.999999i	$0.500467\pi$
$314$	−3.98883	−0.225103
$315$	0	0
$316$	33.9140	1.90781
$317$	16.1010	0.904321	0.452161	−	0.891937i	$-0.350653\pi$
$317$	16.1010	0.904321	0.452161	+	0.891937i	$0.350653\pi$
$318$	−1.40843	−0.0789808
$319$	5.73528	0.321114
$320$	9.13912	0.510892
$321$	−1.99413	−0.111301
$322$	0	0
$323$	13.6244	0.758081
$324$	−8.59066	−0.477259
$325$	−2.94033	−0.163100
$326$	−6.30167	−0.349017
$327$	−8.44621	−0.467077
$328$	11.0441	0.609808
$329$	0	0
$330$	−6.08159	−0.334781
$331$	30.7862	1.69216	0.846081	−	0.533054i	$-0.178956\pi$
$331$	30.7862	1.69216	0.846081	+	0.533054i	$0.178956\pi$
$332$	−22.1030	−1.21306
$333$	3.34575	0.183346
$334$	−1.88512	−0.103149
$335$	9.51135	0.519661
$336$	0	0
$337$	−2.41842	−0.131740	−0.0658700	−	0.997828i	$-0.520982\pi$
$337$	−2.41842	−0.131740	−0.0658700	+	0.997828i	$0.520982\pi$
$338$	0.264627	0.0143938
$339$	35.0001	1.90094
$340$	13.3802	0.725642
$341$	50.6929	2.74517
$342$	4.07687	0.220452
$343$	0	0
$344$	8.77411	0.473069
$345$	25.0476	1.34852
$346$	2.97353	0.159858
$347$	−0.492527	−0.0264403	−0.0132201	−	0.999913i	$-0.504208\pi$
$347$	−0.492527	−0.0264403	−0.0132201	+	0.999913i	$0.504208\pi$
$348$	−5.84948	−0.313565
$349$	−11.9442	−0.639356	−0.319678	−	0.947526i	$-0.603575\pi$
$349$	−11.9442	−0.639356	−0.319678	+	0.947526i	$0.603575\pi$
$350$	0	0
$351$	7.16341	0.382355
$352$	16.6715	0.888593
$353$	15.5299	0.826575	0.413288	−	0.910601i	$-0.364380\pi$
$353$	15.5299	0.826575	0.413288	+	0.910601i	$0.364380\pi$
$354$	−0.670436	−0.0356333
$355$	9.84308	0.522417
$356$	1.92094	0.101809
$357$	0	0
$358$	−3.49162	−0.184538
$359$	−8.50709	−0.448987	−0.224493	−	0.974476i	$-0.572073\pi$
$359$	−8.50709	−0.448987	−0.224493	+	0.974476i	$0.572073\pi$
$360$	8.15287	0.429694
$361$	−11.0456	−0.581345
$362$	−3.63635	−0.191122
$363$	56.1507	2.94715
$364$	0	0
$365$	−4.50850	−0.235985
$366$	−2.56540	−0.134096
$367$	5.19084	0.270960	0.135480	−	0.990780i	$-0.456742\pi$
$367$	5.19084	0.270960	0.135480	+	0.990780i	$0.456742\pi$
$368$	−21.5069	−1.12112
$369$	−58.0091	−3.01983
$370$	−0.232614	−0.0120930
$371$	0	0
$372$	−51.7023	−2.68064
$373$	−10.1427	−0.525169	−0.262585	−	0.964909i	$-0.584575\pi$
$373$	−10.1427	−0.525169	−0.262585	+	0.964909i	$0.584575\pi$
$374$	7.03692	0.363870
$375$	33.1502	1.71187
$376$	−2.50553	−0.129213
$377$	1.04188	0.0536595
$378$	0	0
$379$	−3.63670	−0.186805	−0.0934024	−	0.995628i	$-0.529774\pi$
$379$	−3.63670	−0.186805	−0.0934024	+	0.995628i	$0.529774\pi$
$380$	7.81186	0.400740
$381$	45.5726	2.33476
$382$	−4.32154	−0.221109
$383$	4.60281	0.235192	0.117596	−	0.993061i	$-0.462481\pi$
$383$	4.60281	0.235192	0.117596	+	0.993061i	$0.462481\pi$
$384$	−22.5226	−1.14935
$385$	0	0
$386$	−3.71888	−0.189286
$387$	−46.0861	−2.34269
$388$	−26.0721	−1.32361
$389$	19.6104	0.994286	0.497143	−	0.867669i	$-0.334382\pi$
$389$	19.6104	0.994286	0.497143	+	0.867669i	$0.334382\pi$
$390$	−1.10479	−0.0559433
$391$	−28.9822	−1.46569
$392$	0	0
$393$	35.2788	1.77958
$394$	−0.388731	−0.0195840
$395$	25.2189	1.26890
$396$	−58.0333	−2.91628
$397$	−19.8635	−0.996919	−0.498459	−	0.866913i	$-0.666101\pi$
$397$	−19.8635	−0.996919	−0.498459	+	0.866913i	$0.666101\pi$
$398$	−3.53996	−0.177442
$399$	0	0
$400$	−10.5403	−0.527017
$401$	−15.1117	−0.754644	−0.377322	−	0.926082i	$-0.623155\pi$
$401$	−15.1117	−0.754644	−0.377322	+	0.926082i	$0.623155\pi$
$402$	−5.10183	−0.254456
$403$	9.20895	0.458731
$404$	1.94554	0.0967943
$405$	−6.38813	−0.317429
$406$	0	0
$407$	3.37164	0.167126
$408$	−14.6145	−0.723525
$409$	−35.2443	−1.74272	−0.871360	−	0.490644i	$-0.836762\pi$
$409$	−35.2443	−1.74272	−0.871360	+	0.490644i	$0.836762\pi$
$410$	4.03310	0.199181
$411$	46.3626	2.28690
$412$	24.6563	1.21473
$413$	0	0
$414$	−8.67246	−0.426228
$415$	−16.4361	−0.806816
$416$	3.02857	0.148488
$417$	−19.3185	−0.946033
$418$	4.10842	0.200950
$419$	1.50468	0.0735084	0.0367542	−	0.999324i	$-0.488298\pi$
$419$	1.50468	0.0735084	0.0367542	+	0.999324i	$0.488298\pi$
$420$	0	0
$421$	−24.5079	−1.19444	−0.597221	−	0.802077i	$-0.703728\pi$
$421$	−24.5079	−1.19444	−0.597221	+	0.802077i	$0.703728\pi$
$422$	0.918370	0.0447056
$423$	13.1603	0.639877
$424$	1.90272	0.0924045
$425$	−14.2039	−0.688992
$426$	−5.27977	−0.255806
$427$	0	0
$428$	1.32299	0.0639490
$429$	16.0135	0.773138
$430$	3.20414	0.154518
$431$	41.0655	1.97805	0.989027	−	0.147732i	$-0.0471974\pi$
$431$	41.0655	1.97805	0.989027	+	0.147732i	$0.0471974\pi$
$432$	25.6790	1.23548
$433$	6.65603	0.319869	0.159934	−	0.987128i	$-0.448872\pi$
$433$	6.65603	0.319869	0.159934	+	0.987128i	$0.448872\pi$
$434$	0	0
$435$	−4.34975	−0.208555
$436$	5.60357	0.268362
$437$	−16.9209	−0.809438
$438$	2.41833	0.115552
$439$	8.22990	0.392792	0.196396	−	0.980525i	$-0.437076\pi$
$439$	8.22990	0.392792	0.196396	+	0.980525i	$0.437076\pi$
$440$	8.21596	0.391681
$441$	0	0
$442$	1.27834	0.0608043
$443$	17.6856	0.840266	0.420133	−	0.907463i	$-0.361983\pi$
$443$	17.6856	0.840266	0.420133	+	0.907463i	$0.361983\pi$
$444$	−3.43878	−0.163197
$445$	1.42843	0.0677143
$446$	−2.62329	−0.124216
$447$	−56.8723	−2.68997
$448$	0	0
$449$	−14.5250	−0.685477	−0.342738	−	0.939431i	$-0.611354\pi$
$449$	−14.5250	−0.685477	−0.342738	+	0.939431i	$0.611354\pi$
$450$	−4.25030	−0.200361
$451$	−58.4580	−2.75268
$452$	−23.2205	−1.09220
$453$	31.0918	1.46082
$454$	3.19475	0.149937
$455$	0	0
$456$	−8.53250	−0.399571
$457$	3.78919	0.177251	0.0886255	−	0.996065i	$-0.471753\pi$
$457$	3.78919	0.177251	0.0886255	+	0.996065i	$0.471753\pi$
$458$	1.07219	0.0501002
$459$	34.6045	1.61520
$460$	−16.6176	−0.774801
$461$	13.1107	0.610627	0.305314	−	0.952252i	$-0.401239\pi$
$461$	13.1107	0.610627	0.305314	+	0.952252i	$0.401239\pi$
$462$	0	0
$463$	15.3027	0.711176	0.355588	−	0.934643i	$-0.384281\pi$
$463$	15.3027	0.711176	0.355588	+	0.934643i	$0.384281\pi$
$464$	3.73487	0.173387
$465$	−38.4465	−1.78292
$466$	3.31974	0.153784
$467$	30.7738	1.42404	0.712022	−	0.702158i	$-0.247780\pi$
$467$	30.7738	1.42404	0.712022	+	0.702158i	$0.247780\pi$
$468$	−10.5424	−0.487324
$469$	0	0
$470$	−0.914975	−0.0422046
$471$	−43.8491	−2.02046
$472$	0.905729	0.0416896
$473$	−46.4427	−2.13544
$474$	−13.5273	−0.621328
$475$	−8.29280	−0.380500
$476$	0	0
$477$	−9.99407	−0.457597
$478$	3.53178	0.161540
$479$	−1.71740	−0.0784699	−0.0392350	−	0.999230i	$-0.512492\pi$
$479$	−1.71740	−0.0784699	−0.0392350	+	0.999230i	$0.512492\pi$
$480$	−12.6440	−0.577117
$481$	0.612497	0.0279275
$482$	5.39451	0.245713
$483$	0	0
$484$	−37.2527	−1.69330
$485$	−19.3875	−0.880342
$486$	−2.26033	−0.102531
$487$	22.6805	1.02775	0.513877	−	0.857864i	$-0.328209\pi$
$487$	22.6805	1.02775	0.513877	+	0.857864i	$0.328209\pi$
$488$	3.46575	0.156887
$489$	−69.2741	−3.13268
$490$	0	0
$491$	−13.1366	−0.592846	−0.296423	−	0.955057i	$-0.595794\pi$
$491$	−13.1366	−0.592846	−0.296423	+	0.955057i	$0.595794\pi$
$492$	59.6220	2.68797
$493$	5.03303	0.226676
$494$	0.746342	0.0335795
$495$	−43.1543	−1.93964
$496$	33.0117	1.48227
$497$	0	0
$498$	8.81622	0.395064
$499$	14.0395	0.628495	0.314248	−	0.949341i	$-0.398248\pi$
$499$	14.0395	0.628495	0.314248	+	0.949341i	$0.398248\pi$
$500$	−21.9932	−0.983566
$501$	−20.7231	−0.925840
$502$	4.54948	0.203053
$503$	0.367865	0.0164023	0.00820114	−	0.999966i	$-0.497389\pi$
$503$	0.367865	0.0164023	0.00820114	+	0.999966i	$0.497389\pi$
$504$	0	0
$505$	1.44673	0.0643786
$506$	−8.73957	−0.388521
$507$	2.90903	0.129195
$508$	−30.2348	−1.34145
$509$	41.2319	1.82757	0.913787	−	0.406194i	$-0.133144\pi$
$509$	41.2319	1.82757	0.913787	+	0.406194i	$0.133144\pi$
$510$	−5.33694	−0.236324
$511$	0	0
$512$	18.3127	0.809315
$513$	20.2034	0.892002
$514$	−2.02359	−0.0892566
$515$	18.3347	0.807925
$516$	47.3675	2.08524
$517$	13.2622	0.583269
$518$	0	0
$519$	32.6879	1.43484
$520$	1.49252	0.0654515
$521$	1.04099	0.0456065	0.0228032	−	0.999740i	$-0.492741\pi$
$521$	1.04099	0.0456065	0.0228032	+	0.999740i	$0.492741\pi$
$522$	1.50605	0.0659182
$523$	−20.0209	−0.875451	−0.437726	−	0.899109i	$-0.644216\pi$
$523$	−20.0209	−0.875451	−0.437726	+	0.899109i	$0.644216\pi$
$524$	−23.4054	−1.02247
$525$	0	0
$526$	−0.0267371	−0.00116579
$527$	44.4859	1.93784
$528$	57.4042	2.49820
$529$	12.9947	0.564989
$530$	0.694840	0.0301819
$531$	−4.75735	−0.206451
$532$	0	0
$533$	−10.6196	−0.459985
$534$	−0.766203	−0.0331568
$535$	0.983791	0.0425330
$536$	6.89234	0.297704
$537$	−38.3833	−1.65636
$538$	−2.00283	−0.0863481
$539$	0	0
$540$	19.8413	0.853832
$541$	−9.78749	−0.420797	−0.210399	−	0.977616i	$-0.567476\pi$
$541$	−9.78749	−0.420797	−0.210399	+	0.977616i	$0.567476\pi$
$542$	−3.66649	−0.157489
$543$	−39.9743	−1.71546
$544$	14.6302	0.627263
$545$	4.16689	0.178490
$546$	0	0
$547$	−2.56174	−0.109532	−0.0547660	−	0.998499i	$-0.517441\pi$
$547$	−2.56174	−0.109532	−0.0547660	+	0.998499i	$0.517441\pi$
$548$	−30.7589	−1.31395
$549$	−18.2038	−0.776921
$550$	−4.28319	−0.182636
$551$	2.93848	0.125183
$552$	18.1506	0.772541
$553$	0	0
$554$	0.146321	0.00621660
$555$	−2.55712	−0.108544
$556$	12.8167	0.543550
$557$	−27.4442	−1.16285	−0.581424	−	0.813601i	$-0.697504\pi$
$557$	−27.4442	−1.16285	−0.581424	+	0.813601i	$0.697504\pi$
$558$	13.3117	0.563528
$559$	−8.43685	−0.356841
$560$	0	0
$561$	77.3567	3.26600
$562$	0.303438	0.0127998
$563$	0.162708	0.00685734	0.00342867	−	0.999994i	$-0.498909\pi$
$563$	0.162708	0.00685734	0.00342867	+	0.999994i	$0.498909\pi$
$564$	−13.5262	−0.569557
$565$	−17.2671	−0.726431
$566$	−1.07278	−0.0450925
$567$	0	0
$568$	7.13273	0.299283
$569$	−12.3901	−0.519419	−0.259709	−	0.965687i	$-0.583627\pi$
$569$	−12.3901	−0.519419	−0.259709	+	0.965687i	$0.583627\pi$
$570$	−3.11591	−0.130511
$571$	−21.8122	−0.912810	−0.456405	−	0.889772i	$-0.650863\pi$
$571$	−21.8122	−0.912810	−0.456405	+	0.889772i	$0.650863\pi$
$572$	−10.6240	−0.444212
$573$	−47.5066	−1.98462
$574$	0	0
$575$	17.6407	0.735669
$576$	−34.7852	−1.44939
$577$	6.06583	0.252524	0.126262	−	0.991997i	$-0.459702\pi$
$577$	6.06583	0.252524	0.126262	+	0.991997i	$0.459702\pi$
$578$	1.67664	0.0697391
$579$	−40.8816	−1.69898
$580$	2.88581	0.119827
$581$	0	0
$582$	10.3993	0.431067
$583$	−10.0714	−0.417115
$584$	−3.26705	−0.135192
$585$	−7.83949	−0.324123
$586$	3.98658	0.164684
$587$	20.5820	0.849510	0.424755	−	0.905308i	$-0.360360\pi$
$587$	20.5820	0.849510	0.424755	+	0.905308i	$0.360360\pi$
$588$	0	0
$589$	25.9726	1.07018
$590$	0.330756	0.0136170
$591$	−4.27331	−0.175781
$592$	2.19564	0.0902404
$593$	−24.0397	−0.987190	−0.493595	−	0.869692i	$-0.664318\pi$
$593$	−24.0397	−0.987190	−0.493595	+	0.869692i	$0.664318\pi$
$594$	10.4349	0.428151
$595$	0	0
$596$	37.7314	1.54554
$597$	−38.9147	−1.59267
$598$	−1.58764	−0.0649236
$599$	32.2523	1.31779	0.658896	−	0.752234i	$-0.271024\pi$
$599$	32.2523	1.31779	0.658896	+	0.752234i	$0.271024\pi$
$600$	8.89546	0.363156
$601$	5.21454	0.212705	0.106353	−	0.994328i	$-0.466083\pi$
$601$	5.21454	0.212705	0.106353	+	0.994328i	$0.466083\pi$
$602$	0	0
$603$	−36.2020	−1.47426
$604$	−20.6276	−0.839325
$605$	−27.7016	−1.12623
$606$	−0.776017	−0.0315235
$607$	9.07048	0.368160	0.184080	−	0.982911i	$-0.441070\pi$
$607$	9.07048	0.368160	0.184080	+	0.982911i	$0.441070\pi$
$608$	8.54165	0.346410
$609$	0	0
$610$	1.26563	0.0512437
$611$	2.40922	0.0974668
$612$	−50.9275	−2.05862
$613$	20.0920	0.811507	0.405754	−	0.913983i	$-0.367009\pi$
$613$	20.0920	0.811507	0.405754	+	0.913983i	$0.367009\pi$
$614$	−5.27686	−0.212957
$615$	44.3357	1.78779
$616$	0	0
$617$	−12.9556	−0.521572	−0.260786	−	0.965397i	$-0.583982\pi$
$617$	−12.9556	−0.521572	−0.260786	+	0.965397i	$0.583982\pi$
$618$	−9.83463	−0.395607
$619$	−44.3644	−1.78316	−0.891578	−	0.452866i	$-0.850402\pi$
$619$	−44.3644	−1.78316	−0.891578	+	0.452866i	$0.850402\pi$
$620$	25.5070	1.02439
$621$	−42.9773	−1.72462
$622$	−2.88327	−0.115608
$623$	0	0
$624$	10.4281	0.417459
$625$	−1.65276	−0.0661105
$626$	−0.0137392	−0.000549127 0
$627$	45.1638	1.80367
$628$	29.0913	1.16087
$629$	2.95880	0.117975
$630$	0	0
$631$	6.61717	0.263426	0.131713	−	0.991288i	$-0.457952\pi$
$631$	6.61717	0.263426	0.131713	+	0.991288i	$0.457952\pi$
$632$	18.2747	0.726930
$633$	10.0956	0.401265
$634$	4.26075	0.169216
$635$	−22.4830	−0.892210
$636$	10.2719	0.407309
$637$	0	0
$638$	1.51771	0.0600866
$639$	−37.4647	−1.48208
$640$	11.1114	0.439216
$641$	18.9567	0.748744	0.374372	−	0.927279i	$-0.377858\pi$
$641$	18.9567	0.748744	0.374372	+	0.927279i	$0.377858\pi$
$642$	−0.527699	−0.0208266
$643$	13.4019	0.528517	0.264259	−	0.964452i	$-0.414873\pi$
$643$	13.4019	0.528517	0.264259	+	0.964452i	$0.414873\pi$
$644$	0	0
$645$	35.2231	1.38691
$646$	3.60537	0.141851
$647$	42.7588	1.68102	0.840511	−	0.541794i	$-0.182255\pi$
$647$	42.7588	1.68102	0.840511	+	0.541794i	$0.182255\pi$
$648$	−4.62912	−0.181849
$649$	−4.79416	−0.188187
$650$	−0.778091	−0.0305192
$651$	0	0
$652$	45.9593	1.79991
$653$	10.9852	0.429884	0.214942	−	0.976627i	$-0.431044\pi$
$653$	10.9852	0.429884	0.214942	+	0.976627i	$0.431044\pi$
$654$	−2.23509	−0.0873990
$655$	−17.4046	−0.680052
$656$	−38.0684	−1.48632
$657$	17.1602	0.669483
$658$	0	0
$659$	−17.7614	−0.691884	−0.345942	−	0.938256i	$-0.612441\pi$
$659$	−17.7614	−0.691884	−0.345942	+	0.938256i	$0.612441\pi$
$660$	44.3542	1.72649
$661$	8.18255	0.318264	0.159132	−	0.987257i	$-0.449130\pi$
$661$	8.18255	0.318264	0.159132	+	0.987257i	$0.449130\pi$
$662$	8.14685	0.316636
$663$	14.0527	0.545763
$664$	−11.9103	−0.462210
$665$	0	0
$666$	0.885374	0.0343076
$667$	−6.25082	−0.242033
$668$	13.7486	0.531948
$669$	−28.8378	−1.11493
$670$	2.51696	0.0972385
$671$	−18.3447	−0.708189
$672$	0	0
$673$	9.30129	0.358539	0.179269	−	0.983800i	$-0.442627\pi$
$673$	9.30129	0.358539	0.179269	+	0.983800i	$0.442627\pi$
$674$	−0.639979	−0.0246511
$675$	−21.0628	−0.810708
$676$	−1.92997	−0.0742297
$677$	−41.1552	−1.58172	−0.790862	−	0.611994i	$-0.790367\pi$
$677$	−41.1552	−1.58172	−0.790862	+	0.611994i	$0.790367\pi$
$678$	9.26195	0.355703
$679$	0	0
$680$	7.20997	0.276490
$681$	35.1198	1.34579
$682$	13.4147	0.513675
$683$	39.2842	1.50317	0.751583	−	0.659638i	$-0.229291\pi$
$683$	39.2842	1.50317	0.751583	+	0.659638i	$0.229291\pi$
$684$	−29.7334	−1.13689
$685$	−22.8727	−0.873921
$686$	0	0
$687$	11.7866	0.449685
$688$	−30.2439	−1.15304
$689$	−1.82959	−0.0697017
$690$	6.62827	0.252334
$691$	−3.03355	−0.115402	−0.0577009	−	0.998334i	$-0.518377\pi$
$691$	−3.03355	−0.115402	−0.0577009	+	0.998334i	$0.518377\pi$
$692$	−21.6865	−0.824397
$693$	0	0
$694$	−0.130336	−0.00494748
$695$	9.53069	0.361520
$696$	−3.15202	−0.119477
$697$	−51.3002	−1.94313
$698$	−3.16074	−0.119636
$699$	36.4938	1.38032
$700$	0	0
$701$	−26.2320	−0.990767	−0.495384	−	0.868674i	$-0.664972\pi$
$701$	−26.2320	−0.990767	−0.495384	+	0.868674i	$0.664972\pi$
$702$	1.89563	0.0715459
$703$	1.72746	0.0651525
$704$	−35.0544	−1.32116
$705$	−10.0583	−0.378817
$706$	4.10963	0.154668
$707$	0	0
$708$	4.88962	0.183763
$709$	−7.87770	−0.295853	−0.147927	−	0.988998i	$-0.547260\pi$
$709$	−7.87770	−0.295853	−0.147927	+	0.988998i	$0.547260\pi$
$710$	2.60474	0.0977542
$711$	−95.9881	−3.59984
$712$	1.03511	0.0387922
$713$	−55.2497	−2.06912
$714$	0	0
$715$	−7.90015	−0.295449
$716$	25.4650	0.951673
$717$	38.8247	1.44994
$718$	−2.25120	−0.0840141
$719$	45.6656	1.70304	0.851519	−	0.524323i	$-0.175682\pi$
$719$	45.6656	1.70304	0.851519	+	0.524323i	$0.175682\pi$
$720$	−28.1025	−1.04732
$721$	0	0
$722$	−2.92295	−0.108781
$723$	59.3017	2.20545
$724$	26.5206	0.985630
$725$	−3.06348	−0.113775
$726$	14.8590	0.551468
$727$	37.5947	1.39431	0.697155	−	0.716921i	$-0.254449\pi$
$727$	37.5947	1.39431	0.697155	+	0.716921i	$0.254449\pi$
$728$	0	0
$729$	−38.2013	−1.41486
$730$	−1.19307	−0.0441574
$731$	−40.7561	−1.50742
$732$	18.7100	0.691541
$733$	53.1810	1.96429	0.982143	−	0.188138i	$-0.0602451\pi$
$733$	53.1810	1.96429	0.982143	+	0.188138i	$0.0602451\pi$
$734$	1.37363	0.0507018
$735$	0	0
$736$	−18.1701	−0.669758
$737$	−36.4822	−1.34384
$738$	−15.3508	−0.565069
$739$	41.9633	1.54364	0.771822	−	0.635839i	$-0.219346\pi$
$739$	41.9633	1.54364	0.771822	+	0.635839i	$0.219346\pi$
$740$	1.69650	0.0623646
$741$	8.20452	0.301401
$742$	0	0
$743$	−38.5424	−1.41398	−0.706991	−	0.707222i	$-0.749948\pi$
$743$	−38.5424	−1.41398	−0.706991	+	0.707222i	$0.749948\pi$
$744$	−27.8600	−1.02140
$745$	28.0576	1.02795
$746$	−2.68403	−0.0982693
$747$	62.5590	2.28891
$748$	−51.3216	−1.87650
$749$	0	0
$750$	8.77242	0.320323
$751$	36.2434	1.32254	0.661270	−	0.750148i	$-0.270018\pi$
$751$	36.2434	1.32254	0.661270	+	0.750148i	$0.270018\pi$
$752$	8.63644	0.314939
$753$	50.0123	1.82255
$754$	0.275709	0.0100407
$755$	−15.3390	−0.558242
$756$	0	0
$757$	19.4752	0.707837	0.353919	−	0.935276i	$-0.384849\pi$
$757$	19.4752	0.707837	0.353919	+	0.935276i	$0.384849\pi$
$758$	−0.962368	−0.0349548
$759$	−96.0738	−3.48726
$760$	4.20946	0.152693
$761$	−51.9059	−1.88159	−0.940793	−	0.338981i	$-0.889918\pi$
$761$	−51.9059	−1.88159	−0.940793	+	0.338981i	$0.889918\pi$
$762$	12.0597	0.436878
$763$	0	0
$764$	31.5178	1.14028
$765$	−37.8704	−1.36921
$766$	1.21803	0.0440090
$767$	−0.870914	−0.0314469
$768$	31.0896	1.12185
$769$	−7.31376	−0.263741	−0.131870	−	0.991267i	$-0.542098\pi$
$769$	−7.31376	−0.263741	−0.131870	+	0.991267i	$0.542098\pi$
$770$	0	0
$771$	−22.2452	−0.801142
$772$	27.1225	0.976161
$773$	−14.1844	−0.510178	−0.255089	−	0.966918i	$-0.582105\pi$
$773$	−14.1844	−0.510178	−0.255089	+	0.966918i	$0.582105\pi$
$774$	−12.1956	−0.438362
$775$	−27.0774	−0.972649
$776$	−14.0491	−0.504332
$777$	0	0
$778$	5.18943	0.186050
$779$	−29.9510	−1.07311
$780$	8.05746	0.288503
$781$	−37.7546	−1.35097
$782$	−7.66946	−0.274259
$783$	7.46341	0.266721
$784$	0	0
$785$	21.6327	0.772104
$786$	9.33569	0.332993
$787$	31.2777	1.11493	0.557465	−	0.830201i	$-0.311774\pi$
$787$	31.2777	1.11493	0.557465	+	0.830201i	$0.311774\pi$
$788$	2.83509	0.100996
$789$	−0.293921	−0.0104639
$790$	6.67360	0.237436
$791$	0	0
$792$	−31.2715	−1.11119
$793$	−3.33253	−0.118342
$794$	−5.25640	−0.186543
$795$	7.63836	0.270905
$796$	25.8176	0.915082
$797$	20.2422	0.717017	0.358509	−	0.933526i	$-0.383285\pi$
$797$	20.2422	0.717017	0.358509	+	0.933526i	$0.383285\pi$
$798$	0	0
$799$	11.6383	0.411733
$800$	−8.90500	−0.314839
$801$	−5.43689	−0.192103
$802$	−3.99897	−0.141208
$803$	17.2930	0.610257
$804$	37.2086	1.31225
$805$	0	0
$806$	2.43693	0.0858373
$807$	−22.0171	−0.775037
$808$	1.04836	0.0368813
$809$	7.88265	0.277139	0.138570	−	0.990353i	$-0.455750\pi$
$809$	7.88265	0.277139	0.138570	+	0.990353i	$0.455750\pi$
$810$	−1.69047	−0.0593970
$811$	−5.99962	−0.210675	−0.105338	−	0.994437i	$-0.533592\pi$
$811$	−5.99962	−0.210675	−0.105338	+	0.994437i	$0.533592\pi$
$812$	0	0
$813$	−40.3057	−1.41358
$814$	0.892226	0.0312725
$815$	34.1760	1.19713
$816$	50.3754	1.76349
$817$	−23.7950	−0.832480
$818$	−9.32659	−0.326096
$819$	0	0
$820$	−29.4142	−1.02719
$821$	−19.1692	−0.669011	−0.334505	−	0.942394i	$-0.608569\pi$
$821$	−19.1692	−0.669011	−0.334505	+	0.942394i	$0.608569\pi$
$822$	12.2688	0.427923
$823$	−30.3735	−1.05875	−0.529376	−	0.848387i	$-0.677574\pi$
$823$	−30.3735	−1.05875	−0.529376	+	0.848387i	$0.677574\pi$
$824$	13.2861	0.462845
$825$	−47.0850	−1.63929
$826$	0	0
$827$	−14.6870	−0.510717	−0.255359	−	0.966846i	$-0.582193\pi$
$827$	−14.6870	−0.510717	−0.255359	+	0.966846i	$0.582193\pi$
$828$	63.2499	2.19809
$829$	−34.9985	−1.21555	−0.607774	−	0.794110i	$-0.707938\pi$
$829$	−34.9985	−1.21555	−0.607774	+	0.794110i	$0.707938\pi$
$830$	−4.34943	−0.150971
$831$	1.60851	0.0557985
$832$	−6.36804	−0.220772
$833$	0	0
$834$	−5.11220	−0.177021
$835$	10.2236	0.353803
$836$	−29.9635	−1.03631
$837$	65.9675	2.28017
$838$	0.398178	0.0137548
$839$	27.6333	0.954008	0.477004	−	0.878901i	$-0.341723\pi$
$839$	27.6333	0.954008	0.477004	+	0.878901i	$0.341723\pi$
$840$	0	0
$841$	−27.9145	−0.962568
$842$	−6.48544	−0.223503
$843$	3.33569	0.114887
$844$	−6.69785	−0.230550
$845$	−1.43515	−0.0493708
$846$	3.48257	0.119733
$847$	0	0
$848$	−6.55859	−0.225223
$849$	−11.7931	−0.404738
$850$	−3.75874	−0.128924
$851$	−3.67472	−0.125968
$852$	38.5064	1.31921
$853$	32.6336	1.11735	0.558676	−	0.829386i	$-0.311310\pi$
$853$	32.6336	1.11735	0.558676	+	0.829386i	$0.311310\pi$
$854$	0	0
$855$	−22.1102	−0.756152
$856$	0.712898	0.0243664
$857$	−18.8742	−0.644730	−0.322365	−	0.946616i	$-0.604478\pi$
$857$	−18.8742	−0.644730	−0.322365	+	0.946616i	$0.604478\pi$
$858$	4.23759	0.144669
$859$	15.8242	0.539915	0.269957	−	0.962872i	$-0.412990\pi$
$859$	15.8242	0.539915	0.269957	+	0.962872i	$0.412990\pi$
$860$	−23.3684	−0.796857
$861$	0	0
$862$	10.8670	0.370132
$863$	52.3212	1.78104	0.890518	−	0.454948i	$-0.150342\pi$
$863$	52.3212	1.78104	0.890518	+	0.454948i	$0.150342\pi$
$864$	21.6949	0.738075
$865$	−16.1264	−0.548313
$866$	1.76136	0.0598536
$867$	18.4313	0.625959
$868$	0	0
$869$	−96.7309	−3.28137
$870$	−1.15106	−0.0390246
$871$	−6.62741	−0.224561
$872$	3.01951	0.102253
$873$	73.7927	2.49750
$874$	−4.47773	−0.151461
$875$	0	0
$876$	−17.6373	−0.595911
$877$	−54.0162	−1.82400	−0.911999	−	0.410193i	$-0.865461\pi$
$877$	−54.0162	−1.82400	−0.911999	+	0.410193i	$0.865461\pi$
$878$	2.17785	0.0734989
$879$	43.8243	1.47816
$880$	−28.3200	−0.954667
$881$	−42.0823	−1.41779	−0.708895	−	0.705314i	$-0.750806\pi$
$881$	−42.0823	−1.41779	−0.708895	+	0.705314i	$0.750806\pi$
$882$	0	0
$883$	36.5314	1.22938	0.614689	−	0.788769i	$-0.289281\pi$
$883$	36.5314	1.22938	0.614689	+	0.788769i	$0.289281\pi$
$884$	−9.32316	−0.313572
$885$	3.63599	0.122222
$886$	4.68007	0.157230
$887$	−11.4648	−0.384950	−0.192475	−	0.981302i	$-0.561651\pi$
$887$	−11.4648	−0.384950	−0.192475	+	0.981302i	$0.561651\pi$
$888$	−1.85300	−0.0621827
$889$	0	0
$890$	0.378001	0.0126706
$891$	24.5026	0.820869
$892$	19.1322	0.640592
$893$	6.79488	0.227382
$894$	−15.0499	−0.503345
$895$	18.9361	0.632965
$896$	0	0
$897$	−17.4529	−0.582736
$898$	−3.84370	−0.128266
$899$	9.59462	0.319999
$900$	30.9982	1.03327
$901$	−8.83823	−0.294444
$902$	−15.4695	−0.515079
$903$	0	0
$904$	−12.5125	−0.416159
$905$	19.7211	0.655550
$906$	8.22772	0.273348
$907$	−5.04665	−0.167571	−0.0837856	−	0.996484i	$-0.526701\pi$
$907$	−5.04665	−0.167571	−0.0837856	+	0.996484i	$0.526701\pi$
$908$	−23.2999	−0.773236
$909$	−5.50653	−0.182640
$910$	0	0
$911$	47.5236	1.57453	0.787263	−	0.616618i	$-0.211497\pi$
$911$	47.5236	1.57453	0.787263	+	0.616618i	$0.211497\pi$
$912$	29.4111	0.973898
$913$	63.0431	2.08642
$914$	1.00272	0.0331671
$915$	13.9130	0.459950
$916$	−7.81969	−0.258370
$917$	0	0
$918$	9.15726	0.302235
$919$	−45.6698	−1.50651	−0.753254	−	0.657730i	$-0.771517\pi$
$919$	−45.6698	−1.50651	−0.753254	+	0.657730i	$0.771517\pi$
$920$	−8.95449	−0.295221
$921$	−58.0084	−1.91144
$922$	3.46945	0.114260
$923$	−6.85856	−0.225752
$924$	0	0
$925$	−1.80095	−0.0592148
$926$	4.04950	0.133075
$927$	−69.7855	−2.29206
$928$	3.15540	0.103581
$929$	−44.4449	−1.45819	−0.729095	−	0.684412i	$-0.760059\pi$
$929$	−44.4449	−1.45819	−0.729095	+	0.684412i	$0.760059\pi$
$930$	−10.1740	−0.333618
$931$	0	0
$932$	−24.2115	−0.793074
$933$	−31.6957	−1.03767
$934$	8.14357	0.266466
$935$	−38.1634	−1.24808
$936$	−5.68083	−0.185684
$937$	46.9796	1.53476	0.767379	−	0.641194i	$-0.221561\pi$
$937$	46.9796	1.53476	0.767379	+	0.641194i	$0.221561\pi$
$938$	0	0
$939$	−0.151034	−0.00492881
$940$	6.67309	0.217652
$941$	35.5654	1.15940	0.579699	−	0.814830i	$-0.303170\pi$
$941$	35.5654	1.15940	0.579699	+	0.814830i	$0.303170\pi$
$942$	−11.6036	−0.378067
$943$	63.7128	2.07477
$944$	−3.12200	−0.101613
$945$	0	0
$946$	−12.2900	−0.399581
$947$	−22.3592	−0.726576	−0.363288	−	0.931677i	$-0.618346\pi$
$947$	−22.3592	−0.726576	−0.363288	+	0.931677i	$0.618346\pi$
$948$	98.6570	3.20423
$949$	3.14147	0.101977
$950$	−2.19450	−0.0711989
$951$	46.8383	1.51884
$952$	0	0
$953$	−46.7684	−1.51498	−0.757488	−	0.652849i	$-0.773574\pi$
$953$	−46.7684	−1.51498	−0.757488	+	0.652849i	$0.773574\pi$
$954$	−2.64470	−0.0856252
$955$	23.4371	0.758406
$956$	−25.7579	−0.833071
$957$	16.6841	0.539321
$958$	−0.454469	−0.0146832
$959$	0	0
$960$	26.5860	0.858059
$961$	53.8048	1.73564
$962$	0.162083	0.00522577
$963$	−3.74450	−0.120665
$964$	−39.3432	−1.26716
$965$	20.1687	0.649253
$966$	0	0
$967$	8.22976	0.264651	0.132326	−	0.991206i	$-0.457756\pi$
$967$	8.22976	0.264651	0.132326	+	0.991206i	$0.457756\pi$
$968$	−20.0738	−0.645196
$969$	39.6338	1.27322
$970$	−5.13046	−0.164729
$971$	−23.6326	−0.758407	−0.379204	−	0.925313i	$-0.623802\pi$
$971$	−23.6326	−0.758407	−0.379204	+	0.925313i	$0.623802\pi$
$972$	16.4850	0.528758
$973$	0	0
$974$	6.00187	0.192312
$975$	−8.55353	−0.273932
$976$	−11.9462	−0.382390
$977$	−26.6428	−0.852379	−0.426190	−	0.904634i	$-0.640144\pi$
$977$	−26.6428	−0.852379	−0.426190	+	0.904634i	$0.640144\pi$
$978$	−18.3318	−0.586185
$979$	−5.47897	−0.175109
$980$	0	0
$981$	−15.8600	−0.506370
$982$	−3.47629	−0.110933
$983$	43.6302	1.39159	0.695793	−	0.718242i	$-0.255053\pi$
$983$	43.6302	1.39159	0.695793	+	0.718242i	$0.255053\pi$
$984$	32.1276	1.02419
$985$	2.10821	0.0671732
$986$	1.33187	0.0424155
$987$	0	0
$988$	−5.44322	−0.173172
$989$	50.6174	1.60954
$990$	−11.4198	−0.362945
$991$	−7.60816	−0.241681	−0.120841	−	0.992672i	$-0.538559\pi$
$991$	−7.60816	−0.241681	−0.120841	+	0.992672i	$0.538559\pi$
$992$	27.8899	0.885506
$993$	89.5581	2.84204
$994$	0	0
$995$	19.1983	0.608628
$996$	−64.2984	−2.03737
$997$	19.4356	0.615532	0.307766	−	0.951462i	$-0.400419\pi$
$997$	19.4356	0.615532	0.307766	+	0.951462i	$0.400419\pi$
$998$	3.71523	0.117604
$999$	4.38757	0.138817

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.a.n.1.4	yes	6
3.2	odd	2		5733.2.a.br.1.3		6
7.2	even	3		637.2.e.n.508.3		12
7.3	odd	6		637.2.e.o.79.3		12
7.4	even	3		637.2.e.n.79.3		12
7.5	odd	6		637.2.e.o.508.3		12
7.6	odd	2		637.2.a.m.1.4	✓	6
13.12	even	2		8281.2.a.cd.1.3		6
21.20	even	2		5733.2.a.bu.1.3		6
91.90	odd	2		8281.2.a.cc.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.4	✓	6	7.6	odd	2
637.2.a.n.1.4	yes	6	1.1	even	1	trivial
637.2.e.n.79.3		12	7.4	even	3
637.2.e.n.508.3		12	7.2	even	3
637.2.e.o.79.3		12	7.3	odd	6
637.2.e.o.508.3		12	7.5	odd	6
5733.2.a.br.1.3		6	3.2	odd	2
5733.2.a.bu.1.3		6	21.20	even	2
8281.2.a.cc.1.3		6	91.90	odd	2
8281.2.a.cd.1.3		6	13.12	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.a (trivial)

\(f(q)\)	\(=\)	\(q+0.264627 q^{2} +2.90903 q^{3} -1.92997 q^{4} -1.43515 q^{5} +0.769807 q^{6} -1.03998 q^{8} +5.46247 q^{9} +O(q^{10})\)	\(q+0.264627 q^{2} +2.90903 q^{3} -1.92997 q^{4} -1.43515 q^{5} +0.769807 q^{6} -1.03998 q^{8} +5.46247 q^{9} -0.379780 q^{10} +5.50474 q^{11} -5.61435 q^{12} +1.00000 q^{13} -4.17491 q^{15} +3.58474 q^{16} +4.83072 q^{17} +1.44552 q^{18} +2.82036 q^{19} +2.76981 q^{20} +1.45670 q^{22} -5.99956 q^{23} -3.02532 q^{24} -2.94033 q^{25} +0.264627 q^{26} +7.16341 q^{27} +1.04188 q^{29} -1.10479 q^{30} +9.20895 q^{31} +3.02857 q^{32} +16.0135 q^{33} +1.27834 q^{34} -10.5424 q^{36} +0.612497 q^{37} +0.746342 q^{38} +2.90903 q^{39} +1.49252 q^{40} -10.6196 q^{41} -8.43685 q^{43} -10.6240 q^{44} -7.83949 q^{45} -1.58764 q^{46} +2.40922 q^{47} +10.4281 q^{48} -0.778091 q^{50} +14.0527 q^{51} -1.92997 q^{52} -1.82959 q^{53} +1.89563 q^{54} -7.90015 q^{55} +8.20452 q^{57} +0.275709 q^{58} -0.870914 q^{59} +8.05746 q^{60} -3.33253 q^{61} +2.43693 q^{62} -6.36804 q^{64} -1.43515 q^{65} +4.23759 q^{66} -6.62741 q^{67} -9.32316 q^{68} -17.4529 q^{69} -6.85856 q^{71} -5.68083 q^{72} +3.14147 q^{73} +0.162083 q^{74} -8.55353 q^{75} -5.44322 q^{76} +0.769807 q^{78} -17.5723 q^{79} -5.14465 q^{80} +4.45118 q^{81} -2.81022 q^{82} +11.4525 q^{83} -6.93283 q^{85} -2.23261 q^{86} +3.03086 q^{87} -5.72479 q^{88} -0.995318 q^{89} -2.07454 q^{90} +11.5790 q^{92} +26.7891 q^{93} +0.637545 q^{94} -4.04765 q^{95} +8.81020 q^{96} +13.5090 q^{97} +30.0695 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) 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

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