LMFDB - Embedded newform 637.2.a.n.1.6

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			1.6
Root			$0.758419$ 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)

$f(q)$	$=$	$q+2.18322 q^{2} +1.75842 q^{3} +2.76645 q^{4} +2.11065 q^{5} +3.83901 q^{6} +1.67333 q^{8} +0.0920365 q^{9} +O(q^{10})$	\(q+2.18322 q^{2} +1.75842 q^{3} +2.76645 q^{4} +2.11065 q^{5} +3.83901 q^{6} +1.67333 q^{8} +0.0920365 q^{9} +4.60802 q^{10} -5.76889 q^{11} +4.86457 q^{12} +1.00000 q^{13} +3.71141 q^{15} -1.87966 q^{16} +1.64082 q^{17} +0.200936 q^{18} -2.67077 q^{19} +5.83901 q^{20} -12.5948 q^{22} +6.42469 q^{23} +2.94241 q^{24} -0.545141 q^{25} +2.18322 q^{26} -5.11342 q^{27} -6.04973 q^{29} +8.10283 q^{30} +5.12202 q^{31} -7.45036 q^{32} -10.1441 q^{33} +3.58227 q^{34} +0.254614 q^{36} +5.74772 q^{37} -5.83087 q^{38} +1.75842 q^{39} +3.53181 q^{40} -7.14100 q^{41} -4.47061 q^{43} -15.9593 q^{44} +0.194257 q^{45} +14.0265 q^{46} +11.7910 q^{47} -3.30523 q^{48} -1.19016 q^{50} +2.88525 q^{51} +2.76645 q^{52} +3.44959 q^{53} -11.1637 q^{54} -12.1761 q^{55} -4.69633 q^{57} -13.2079 q^{58} +13.1805 q^{59} +10.2674 q^{60} +6.24666 q^{61} +11.1825 q^{62} -12.5065 q^{64} +2.11065 q^{65} -22.1469 q^{66} +7.74216 q^{67} +4.53925 q^{68} +11.2973 q^{69} +13.6372 q^{71} +0.154007 q^{72} -15.5041 q^{73} +12.5485 q^{74} -0.958586 q^{75} -7.38854 q^{76} +3.83901 q^{78} +1.12214 q^{79} -3.96731 q^{80} -9.26764 q^{81} -15.5904 q^{82} +4.96925 q^{83} +3.46321 q^{85} -9.76032 q^{86} -10.6380 q^{87} -9.65324 q^{88} +1.14630 q^{89} +0.424106 q^{90} +17.7736 q^{92} +9.00665 q^{93} +25.7423 q^{94} -5.63707 q^{95} -13.1009 q^{96} -6.97223 q^{97} -0.530949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.18322	1.54377	0.771885	−	0.635762i	$-0.219314\pi$
$2$	2.18322	1.54377	0.771885	+	0.635762i	$0.219314\pi$
$3$	1.75842	1.01522	0.507612	−	0.861586i	$-0.330528\pi$
$3$	1.75842	1.01522	0.507612	+	0.861586i	$0.330528\pi$
$4$	2.76645	1.38322
$5$	2.11065	0.943913	0.471957	−	0.881622i	$-0.343548\pi$
$5$	2.11065	0.943913	0.471957	+	0.881622i	$0.343548\pi$
$6$	3.83901	1.56727
$7$	0	0
$7$	0	0
$8$	1.67333	0.591610
$9$	0.0920365	0.0306788
$10$	4.60802	1.45718
$11$	−5.76889	−1.73939	−0.869694	−	0.493592i	$-0.835684\pi$
$11$	−5.76889	−1.73939	−0.869694	+	0.493592i	$0.835684\pi$
$12$	4.86457	1.40428
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	3.71141	0.958283
$16$	−1.87966	−0.469915
$17$	1.64082	0.397958	0.198979	−	0.980004i	$-0.436237\pi$
$17$	1.64082	0.397958	0.198979	+	0.980004i	$0.436237\pi$
$18$	0.200936	0.0473611
$19$	−2.67077	−0.612716	−0.306358	−	0.951916i	$-0.599110\pi$
$19$	−2.67077	−0.612716	−0.306358	+	0.951916i	$0.599110\pi$
$20$	5.83901	1.30564
$21$	0	0
$22$	−12.5948	−2.68521
$23$	6.42469	1.33964	0.669820	−	0.742523i	$-0.266371\pi$
$23$	6.42469	1.33964	0.669820	+	0.742523i	$0.266371\pi$
$24$	2.94241	0.600616
$25$	−0.545141	−0.109028
$26$	2.18322	0.428165
$27$	−5.11342	−0.984078
$28$	0	0
$29$	−6.04973	−1.12341	−0.561704	−	0.827338i	$-0.689854\pi$
$29$	−6.04973	−1.12341	−0.561704	+	0.827338i	$0.689854\pi$
$30$	8.10283	1.47937
$31$	5.12202	0.919942	0.459971	−	0.887934i	$-0.347860\pi$
$31$	5.12202	0.919942	0.459971	+	0.887934i	$0.347860\pi$
$32$	−7.45036	−1.31705
$33$	−10.1441	−1.76587
$34$	3.58227	0.614355
$35$	0	0
$36$	0.254614	0.0424357
$37$	5.74772	0.944919	0.472460	−	0.881352i	$-0.343366\pi$
$37$	5.74772	0.944919	0.472460	+	0.881352i	$0.343366\pi$
$38$	−5.83087	−0.945892
$39$	1.75842	0.281572
$40$	3.53181	0.558428
$41$	−7.14100	−1.11524	−0.557619	−	0.830097i	$-0.688285\pi$
$41$	−7.14100	−1.11524	−0.557619	+	0.830097i	$0.688285\pi$
$42$	0	0
$43$	−4.47061	−0.681761	−0.340881	−	0.940107i	$-0.610725\pi$
$43$	−4.47061	−0.681761	−0.340881	+	0.940107i	$0.610725\pi$
$44$	−15.9593	−2.40596
$45$	0.194257	0.0289582
$46$	14.0265	2.06810
$47$	11.7910	1.71989	0.859947	−	0.510384i	$-0.170497\pi$
$47$	11.7910	1.71989	0.859947	+	0.510384i	$0.170497\pi$
$48$	−3.30523	−0.477069
$49$	0	0
$50$	−1.19016	−0.168314
$51$	2.88525	0.404016
$52$	2.76645	0.383637
$53$	3.44959	0.473838	0.236919	−	0.971529i	$-0.423862\pi$
$53$	3.44959	0.473838	0.236919	+	0.971529i	$0.423862\pi$
$54$	−11.1637	−1.51919
$55$	−12.1761	−1.64183
$56$	0	0
$57$	−4.69633	−0.622044
$58$	−13.2079	−1.73428
$59$	13.1805	1.71596	0.857981	−	0.513682i	$-0.171719\pi$
$59$	13.1805	1.71596	0.857981	+	0.513682i	$0.171719\pi$
$60$	10.2674	1.32552
$61$	6.24666	0.799803	0.399901	−	0.916558i	$-0.369044\pi$
$61$	6.24666	0.799803	0.399901	+	0.916558i	$0.369044\pi$
$62$	11.1825	1.42018
$63$	0	0
$64$	−12.5065	−1.56331
$65$	2.11065	0.261794
$66$	−22.1469	−2.72609
$67$	7.74216	0.945856	0.472928	−	0.881101i	$-0.343197\pi$
$67$	7.74216	0.945856	0.472928	+	0.881101i	$0.343197\pi$
$68$	4.53925	0.550465
$69$	11.2973	1.36003
$70$	0	0
$71$	13.6372	1.61844	0.809221	−	0.587504i	$-0.199889\pi$
$71$	13.6372	1.61844	0.809221	+	0.587504i	$0.199889\pi$
$72$	0.154007	0.0181499
$73$	−15.5041	−1.81462	−0.907308	−	0.420467i	$-0.861866\pi$
$73$	−15.5041	−1.81462	−0.907308	+	0.420467i	$0.861866\pi$
$74$	12.5485	1.45874
$75$	−0.958586	−0.110688
$76$	−7.38854	−0.847524
$77$	0	0
$78$	3.83901	0.434683
$79$	1.12214	0.126251	0.0631254	−	0.998006i	$-0.479893\pi$
$79$	1.12214	0.126251	0.0631254	+	0.998006i	$0.479893\pi$
$80$	−3.96731	−0.443559
$81$	−9.26764	−1.02974
$82$	−15.5904	−1.72167
$83$	4.96925	0.545446	0.272723	−	0.962093i	$-0.412076\pi$
$83$	4.96925	0.545446	0.272723	+	0.962093i	$0.412076\pi$
$84$	0	0
$85$	3.46321	0.375638
$86$	−9.76032	−1.05248
$87$	−10.6380	−1.14051
$88$	−9.65324	−1.02904
$89$	1.14630	0.121507	0.0607535	−	0.998153i	$-0.480650\pi$
$89$	1.14630	0.121507	0.0607535	+	0.998153i	$0.480650\pi$
$90$	0.424106	0.0447047
$91$	0	0
$92$	17.7736	1.85302
$93$	9.00665	0.933946
$94$	25.7423	2.65512
$95$	−5.63707	−0.578351
$96$	−13.1009	−1.33710
$97$	−6.97223	−0.707923	−0.353961	−	0.935260i	$-0.615166\pi$
$97$	−6.97223	−0.707923	−0.353961	+	0.935260i	$0.615166\pi$
$98$	0	0
$99$	−0.530949	−0.0533624
$100$	−1.50810	−0.150810
$101$	−6.49919	−0.646694	−0.323347	−	0.946280i	$-0.604808\pi$
$101$	−6.49919	−0.646694	−0.323347	+	0.946280i	$0.604808\pi$
$102$	6.29914	0.623708
$103$	−0.578048	−0.0569568	−0.0284784	−	0.999594i	$-0.509066\pi$
$103$	−0.578048	−0.0569568	−0.0284784	+	0.999594i	$0.509066\pi$
$104$	1.67333	0.164083
$105$	0	0
$106$	7.53122	0.731497
$107$	−16.2573	−1.57165	−0.785824	−	0.618450i	$-0.787761\pi$
$107$	−16.2573	−1.57165	−0.785824	+	0.618450i	$0.787761\pi$
$108$	−14.1460	−1.36120
$109$	1.78191	0.170676	0.0853378	−	0.996352i	$-0.472803\pi$
$109$	1.78191	0.170676	0.0853378	+	0.996352i	$0.472803\pi$
$110$	−26.5832	−2.53461
$111$	10.1069	0.959304
$112$	0	0
$113$	−7.52215	−0.707624	−0.353812	−	0.935316i	$-0.615115\pi$
$113$	−7.52215	−0.707624	−0.353812	+	0.935316i	$0.615115\pi$
$114$	−10.2531	−0.960292
$115$	13.5603	1.26450
$116$	−16.7363	−1.55392
$117$	0.0920365	0.00850878
$118$	28.7760	2.64905
$119$	0	0
$120$	6.21040	0.566930
$121$	22.2801	2.02547
$122$	13.6378	1.23471
$123$	−12.5569	−1.13222
$124$	14.1698	1.27249
$125$	−11.7039	−1.04683
$126$	0	0
$127$	−19.3056	−1.71310	−0.856549	−	0.516067i	$-0.827396\pi$
$127$	−19.3056	−1.71310	−0.856549	+	0.516067i	$0.827396\pi$
$128$	−12.4036	−1.09634
$129$	−7.86120	−0.692140
$130$	4.60802	0.404150
$131$	9.69703	0.847234	0.423617	−	0.905842i	$-0.360760\pi$
$131$	9.69703	0.847234	0.423617	+	0.905842i	$0.360760\pi$
$132$	−28.0632	−2.44259
$133$	0	0
$134$	16.9028	1.46018
$135$	−10.7927	−0.928884
$136$	2.74563	0.235436
$137$	−15.4493	−1.31993	−0.659963	−	0.751298i	$-0.729428\pi$
$137$	−15.4493	−1.31993	−0.659963	+	0.751298i	$0.729428\pi$
$138$	24.6645	2.09958
$139$	3.84912	0.326478	0.163239	−	0.986587i	$-0.447806\pi$
$139$	3.84912	0.326478	0.163239	+	0.986587i	$0.447806\pi$
$140$	0	0
$141$	20.7335	1.74608
$142$	29.7731	2.49850
$143$	−5.76889	−0.482419
$144$	−0.172997	−0.0144164
$145$	−12.7689	−1.06040
$146$	−33.8488	−2.80135
$147$	0	0
$148$	15.9008	1.30704
$149$	−1.04028	−0.0852231	−0.0426115	−	0.999092i	$-0.513568\pi$
$149$	−1.04028	−0.0852231	−0.0426115	+	0.999092i	$0.513568\pi$
$150$	−2.09280	−0.170877
$151$	−4.34336	−0.353458	−0.176729	−	0.984260i	$-0.556552\pi$
$151$	−4.34336	−0.353458	−0.176729	+	0.984260i	$0.556552\pi$
$152$	−4.46906	−0.362489
$153$	0.151016	0.0122089
$154$	0	0
$155$	10.8108	0.868345
$156$	4.86457	0.389478
$157$	0.336000	0.0268157	0.0134079	−	0.999910i	$-0.495732\pi$
$157$	0.336000	0.0268157	0.0134079	+	0.999910i	$0.495732\pi$
$158$	2.44988	0.194902
$159$	6.06583	0.481052
$160$	−15.7251	−1.24318
$161$	0	0
$162$	−20.2333	−1.58968
$163$	6.79919	0.532553	0.266277	−	0.963897i	$-0.414207\pi$
$163$	6.79919	0.532553	0.266277	+	0.963897i	$0.414207\pi$
$164$	−19.7552	−1.54262
$165$	−21.4107	−1.66682
$166$	10.8490	0.842043
$167$	0.668649	0.0517416	0.0258708	−	0.999665i	$-0.491764\pi$
$167$	0.668649	0.0517416	0.0258708	+	0.999665i	$0.491764\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	7.56094	0.579898
$171$	−0.245808	−0.0187974
$172$	−12.3677	−0.943029
$173$	25.1178	1.90967	0.954837	−	0.297131i	$-0.0960298\pi$
$173$	25.1178	1.90967	0.954837	+	0.297131i	$0.0960298\pi$
$174$	−23.2250	−1.76068
$175$	0	0
$176$	10.8436	0.817364
$177$	23.1769	1.74208
$178$	2.50262	0.187579
$179$	−1.89527	−0.141659	−0.0708294	−	0.997488i	$-0.522565\pi$
$179$	−1.89527	−0.141659	−0.0708294	+	0.997488i	$0.522565\pi$
$180$	0.537403	0.0400556
$181$	11.3595	0.844347	0.422174	−	0.906515i	$-0.361267\pi$
$181$	11.3595	0.844347	0.422174	+	0.906515i	$0.361267\pi$
$182$	0	0
$183$	10.9842	0.811978
$184$	10.7506	0.792544
$185$	12.1314	0.891922
$186$	19.6635	1.44180
$187$	−9.46573	−0.692203
$188$	32.6192	2.37900
$189$	0	0
$190$	−12.3070	−0.892840
$191$	−23.4407	−1.69611	−0.848055	−	0.529909i	$-0.822226\pi$
$191$	−23.4407	−1.69611	−0.848055	+	0.529909i	$0.822226\pi$
$192$	−21.9916	−1.58711
$193$	−1.85210	−0.133317	−0.0666584	−	0.997776i	$-0.521234\pi$
$193$	−1.85210	−0.133317	−0.0666584	+	0.997776i	$0.521234\pi$
$194$	−15.2219	−1.09287
$195$	3.71141	0.265780
$196$	0	0
$197$	−9.87082	−0.703267	−0.351634	−	0.936138i	$-0.614374\pi$
$197$	−9.87082	−0.703267	−0.351634	+	0.936138i	$0.614374\pi$
$198$	−1.15918	−0.0823792
$199$	12.2492	0.868324	0.434162	−	0.900835i	$-0.357044\pi$
$199$	12.2492	0.868324	0.434162	+	0.900835i	$0.357044\pi$
$200$	−0.912199	−0.0645022
$201$	13.6140	0.960255
$202$	−14.1892	−0.998347
$203$	0	0
$204$	7.98190	0.558845
$205$	−15.0722	−1.05269
$206$	−1.26201	−0.0879281
$207$	0.591306	0.0410986
$208$	−1.87966	−0.130331
$209$	15.4074	1.06575
$210$	0	0
$211$	−0.739899	−0.0509368	−0.0254684	−	0.999676i	$-0.508108\pi$
$211$	−0.739899	−0.0509368	−0.0254684	+	0.999676i	$0.508108\pi$
$212$	9.54312	0.655424
$213$	23.9800	1.64308
$214$	−35.4932	−2.42626
$215$	−9.43591	−0.643523
$216$	−8.55641	−0.582190
$217$	0	0
$218$	3.89029	0.263484
$219$	−27.2627	−1.84224
$220$	−33.6847	−2.27102
$221$	1.64082	0.110374
$222$	22.0656	1.48094
$223$	8.30577	0.556196	0.278098	−	0.960553i	$-0.410296\pi$
$223$	8.30577	0.556196	0.278098	+	0.960553i	$0.410296\pi$
$224$	0	0
$225$	−0.0501729	−0.00334486
$226$	−16.4225	−1.09241
$227$	13.2917	0.882198	0.441099	−	0.897458i	$-0.354589\pi$
$227$	13.2917	0.882198	0.441099	+	0.897458i	$0.354589\pi$
$228$	−12.9921	−0.860426
$229$	17.9207	1.18423	0.592115	−	0.805853i	$-0.298293\pi$
$229$	17.9207	1.18423	0.592115	+	0.805853i	$0.298293\pi$
$230$	29.6051	1.95210
$231$	0	0
$232$	−10.1232	−0.664619
$233$	6.29968	0.412705	0.206353	−	0.978478i	$-0.433841\pi$
$233$	6.29968	0.412705	0.206353	+	0.978478i	$0.433841\pi$
$234$	0.200936	0.0131356
$235$	24.8867	1.62343
$236$	36.4633	2.37356
$237$	1.97320	0.128173
$238$	0	0
$239$	9.41783	0.609189	0.304594	−	0.952482i	$-0.401479\pi$
$239$	9.41783	0.609189	0.304594	+	0.952482i	$0.401479\pi$
$240$	−6.97619	−0.450311
$241$	−19.9493	−1.28505	−0.642524	−	0.766266i	$-0.722113\pi$
$241$	−19.9493	−1.28505	−0.642524	+	0.766266i	$0.722113\pi$
$242$	48.6424	3.12685
$243$	−0.956137	−0.0613362
$244$	17.2811	1.10631
$245$	0	0
$246$	−27.4144	−1.74788
$247$	−2.67077	−0.169937
$248$	8.57080	0.544246
$249$	8.73802	0.553750
$250$	−25.5521	−1.61606
$251$	1.22202	0.0771330	0.0385665	−	0.999256i	$-0.487721\pi$
$251$	1.22202	0.0771330	0.0385665	+	0.999256i	$0.487721\pi$
$252$	0	0
$253$	−37.0633	−2.33015
$254$	−42.1484	−2.64463
$255$	6.08977	0.381356
$256$	−2.06691	−0.129182
$257$	−22.4240	−1.39877	−0.699386	−	0.714745i	$-0.746543\pi$
$257$	−22.4240	−1.39877	−0.699386	+	0.714745i	$0.746543\pi$
$258$	−17.1627	−1.06850
$259$	0	0
$260$	5.83901	0.362120
$261$	−0.556797	−0.0344648
$262$	21.1707	1.30793
$263$	8.99048	0.554377	0.277188	−	0.960816i	$-0.410597\pi$
$263$	8.99048	0.554377	0.277188	+	0.960816i	$0.410597\pi$
$264$	−16.9744	−1.04470
$265$	7.28090	0.447262
$266$	0	0
$267$	2.01567	0.123357
$268$	21.4183	1.30833
$269$	−22.2054	−1.35389	−0.676945	−	0.736034i	$-0.736697\pi$
$269$	−22.2054	−1.35389	−0.676945	+	0.736034i	$0.736697\pi$
$270$	−23.5627	−1.43398
$271$	−10.8423	−0.658624	−0.329312	−	0.944221i	$-0.606817\pi$
$271$	−10.8423	−0.658624	−0.329312	+	0.944221i	$0.606817\pi$
$272$	−3.08419	−0.187006
$273$	0	0
$274$	−33.7293	−2.03766
$275$	3.14486	0.189642
$276$	31.2534	1.88123
$277$	5.88828	0.353792	0.176896	−	0.984230i	$-0.443394\pi$
$277$	5.88828	0.353792	0.176896	+	0.984230i	$0.443394\pi$
$278$	8.40347	0.504006
$279$	0.471413	0.0282227
$280$	0	0
$281$	26.9071	1.60514	0.802572	−	0.596556i	$-0.203465\pi$
$281$	26.9071	1.60514	0.802572	+	0.596556i	$0.203465\pi$
$282$	45.2658	2.69554
$283$	−3.49717	−0.207885	−0.103943	−	0.994583i	$-0.533146\pi$
$283$	−3.49717	−0.207885	−0.103943	+	0.994583i	$0.533146\pi$
$284$	37.7267	2.23867
$285$	−9.91232	−0.587155
$286$	−12.5948	−0.744744
$287$	0	0
$288$	−0.685705	−0.0404056
$289$	−14.3077	−0.841630
$290$	−27.8773	−1.63701
$291$	−12.2601	−0.718700
$292$	−42.8913	−2.51002
$293$	1.00509	0.0587179	0.0293589	−	0.999569i	$-0.490653\pi$
$293$	1.00509	0.0587179	0.0293589	+	0.999569i	$0.490653\pi$
$294$	0	0
$295$	27.8196	1.61972
$296$	9.61780	0.559024
$297$	29.4988	1.71169
$298$	−2.27116	−0.131565
$299$	6.42469	0.371549
$300$	−2.65188	−0.153106
$301$	0	0
$302$	−9.48252	−0.545657
$303$	−11.4283	−0.656539
$304$	5.02013	0.287924
$305$	13.1845	0.754944
$306$	0.329700	0.0188477
$307$	4.25772	0.243001	0.121501	−	0.992591i	$-0.461229\pi$
$307$	4.25772	0.243001	0.121501	+	0.992591i	$0.461229\pi$
$308$	0	0
$309$	−1.01645	−0.0578238
$310$	23.6024	1.34052
$311$	−6.94043	−0.393556	−0.196778	−	0.980448i	$-0.563048\pi$
$311$	−6.94043	−0.393556	−0.196778	+	0.980448i	$0.563048\pi$
$312$	2.94241	0.166581
$313$	−9.96299	−0.563142	−0.281571	−	0.959540i	$-0.590855\pi$
$313$	−9.96299	−0.563142	−0.281571	+	0.959540i	$0.590855\pi$
$314$	0.733563	0.0413973
$315$	0	0
$316$	3.10435	0.174633
$317$	3.75345	0.210815	0.105407	−	0.994429i	$-0.466385\pi$
$317$	3.75345	0.210815	0.105407	+	0.994429i	$0.466385\pi$
$318$	13.2430	0.742633
$319$	34.9003	1.95404
$320$	−26.3968	−1.47563
$321$	−28.5871	−1.59557
$322$	0	0
$323$	−4.38225	−0.243835
$324$	−25.6384	−1.42436
$325$	−0.545141	−0.0302390
$326$	14.8441	0.822140
$327$	3.13334	0.173274
$328$	−11.9492	−0.659785
$329$	0	0
$330$	−46.7444	−2.57319
$331$	−19.9812	−1.09827	−0.549134	−	0.835734i	$-0.685042\pi$
$331$	−19.9812	−1.09827	−0.549134	+	0.835734i	$0.685042\pi$
$332$	13.7472	0.754474
$333$	0.529000	0.0289890
$334$	1.45981	0.0798771
$335$	16.3410	0.892805
$336$	0	0
$337$	18.4887	1.00714	0.503571	−	0.863954i	$-0.332019\pi$
$337$	18.4887	1.00714	0.503571	+	0.863954i	$0.332019\pi$
$338$	2.18322	0.118751
$339$	−13.2271	−0.718397
$340$	9.58078	0.519591
$341$	−29.5484	−1.60013
$342$	−0.536653	−0.0290189
$343$	0	0
$344$	−7.48078	−0.403337
$345$	23.8447	1.28375
$346$	54.8377	2.94810
$347$	−0.796100	−0.0427369	−0.0213684	−	0.999772i	$-0.506802\pi$
$347$	−0.796100	−0.0427369	−0.0213684	+	0.999772i	$0.506802\pi$
$348$	−29.4294	−1.57758
$349$	−11.3725	−0.608754	−0.304377	−	0.952552i	$-0.598448\pi$
$349$	−11.3725	−0.608754	−0.304377	+	0.952552i	$0.598448\pi$
$350$	0	0
$351$	−5.11342	−0.272934
$352$	42.9803	2.29086
$353$	24.1068	1.28307	0.641537	−	0.767092i	$-0.278297\pi$
$353$	24.1068	1.28307	0.641537	+	0.767092i	$0.278297\pi$
$354$	50.6003	2.68938
$355$	28.7835	1.52767
$356$	3.17117	0.168072
$357$	0	0
$358$	−4.13778	−0.218689
$359$	9.07182	0.478792	0.239396	−	0.970922i	$-0.423051\pi$
$359$	9.07182	0.478792	0.239396	+	0.970922i	$0.423051\pi$
$360$	0.325056	0.0171319
$361$	−11.8670	−0.624579
$362$	24.8003	1.30348
$363$	39.1778	2.05630
$364$	0	0
$365$	−32.7238	−1.71284
$366$	23.9810	1.25351
$367$	−31.5507	−1.64693	−0.823467	−	0.567364i	$-0.807963\pi$
$367$	−31.5507	−1.64693	−0.823467	+	0.567364i	$0.807963\pi$
$368$	−12.0762	−0.629517
$369$	−0.657233	−0.0342142
$370$	26.4856	1.37692
$371$	0	0
$372$	24.9164	1.29186
$373$	−16.0581	−0.831457	−0.415728	−	0.909489i	$-0.636473\pi$
$373$	−16.0581	−0.831457	−0.415728	+	0.909489i	$0.636473\pi$
$374$	−20.6658	−1.06860
$375$	−20.5803	−1.06276
$376$	19.7302	1.01751
$377$	−6.04973	−0.311577
$378$	0	0
$379$	−5.36895	−0.275785	−0.137892	−	0.990447i	$-0.544033\pi$
$379$	−5.36895	−0.275785	−0.137892	+	0.990447i	$0.544033\pi$
$380$	−15.5947	−0.799989
$381$	−33.9474	−1.73918
$382$	−51.1762	−2.61840
$383$	34.5075	1.76325	0.881625	−	0.471951i	$-0.156450\pi$
$383$	34.5075	1.76325	0.881625	+	0.471951i	$0.156450\pi$
$384$	−21.8108	−1.11303
$385$	0	0
$386$	−4.04353	−0.205810
$387$	−0.411459	−0.0209156
$388$	−19.2883	−0.979216
$389$	22.9210	1.16214	0.581070	−	0.813854i	$-0.302634\pi$
$389$	22.9210	1.16214	0.581070	+	0.813854i	$0.302634\pi$
$390$	8.10283	0.410303
$391$	10.5418	0.533120
$392$	0	0
$393$	17.0514	0.860131
$394$	−21.5502	−1.08568
$395$	2.36845	0.119170
$396$	−1.46884	−0.0738121
$397$	10.8294	0.543510	0.271755	−	0.962366i	$-0.412396\pi$
$397$	10.8294	0.543510	0.271755	+	0.962366i	$0.412396\pi$
$398$	26.7427	1.34049
$399$	0	0
$400$	1.02468	0.0512340
$401$	37.5415	1.87473	0.937367	−	0.348342i	$-0.113255\pi$
$401$	37.5415	1.87473	0.937367	+	0.348342i	$0.113255\pi$
$402$	29.7223	1.48241
$403$	5.12202	0.255146
$404$	−17.9797	−0.894523
$405$	−19.5608	−0.971983
$406$	0	0
$407$	−33.1580	−1.64358
$408$	4.82797	0.239020
$409$	−20.4727	−1.01231	−0.506155	−	0.862443i	$-0.668934\pi$
$409$	−20.4727	−1.01231	−0.506155	+	0.862443i	$0.668934\pi$
$410$	−32.9059	−1.62511
$411$	−27.1664	−1.34002
$412$	−1.59914	−0.0787840
$413$	0	0
$414$	1.29095	0.0634468
$415$	10.4884	0.514854
$416$	−7.45036	−0.365284
$417$	6.76836	0.331448
$418$	33.6377	1.64527
$419$	−15.4980	−0.757127	−0.378564	−	0.925575i	$-0.623582\pi$
$419$	−15.4980	−0.757127	−0.378564	+	0.925575i	$0.623582\pi$
$420$	0	0
$421$	17.9390	0.874293	0.437147	−	0.899390i	$-0.355989\pi$
$421$	17.9390	0.874293	0.437147	+	0.899390i	$0.355989\pi$
$422$	−1.61536	−0.0786346
$423$	1.08520	0.0527643
$424$	5.77229	0.280327
$425$	−0.894480	−0.0433886
$426$	52.3535	2.53654
$427$	0	0
$428$	−44.9749	−2.17394
$429$	−10.1441	−0.489763
$430$	−20.6007	−0.993452
$431$	21.4438	1.03291	0.516456	−	0.856313i	$-0.327251\pi$
$431$	21.4438	1.03291	0.516456	+	0.856313i	$0.327251\pi$
$432$	9.61149	0.462433
$433$	−14.9365	−0.717800	−0.358900	−	0.933376i	$-0.616848\pi$
$433$	−14.9365	−0.717800	−0.358900	+	0.933376i	$0.616848\pi$
$434$	0	0
$435$	−22.4531	−1.07654
$436$	4.92955	0.236083
$437$	−17.1589	−0.820819
$438$	−59.5204	−2.84400
$439$	−3.59323	−0.171495	−0.0857476	−	0.996317i	$-0.527328\pi$
$439$	−3.59323	−0.171495	−0.0857476	+	0.996317i	$0.527328\pi$
$440$	−20.3746	−0.971323
$441$	0	0
$442$	3.58227	0.170391
$443$	−13.6534	−0.648694	−0.324347	−	0.945938i	$-0.605145\pi$
$443$	−13.6534	−0.648694	−0.324347	+	0.945938i	$0.605145\pi$
$444$	27.9602	1.32693
$445$	2.41943	0.114692
$446$	18.1333	0.858638
$447$	−1.82925	−0.0865205
$448$	0	0
$449$	−8.72412	−0.411717	−0.205858	−	0.978582i	$-0.565999\pi$
$449$	−8.72412	−0.411717	−0.205858	+	0.978582i	$0.565999\pi$
$450$	−0.109538	−0.00516369
$451$	41.1957	1.93983
$452$	−20.8096	−0.978803
$453$	−7.63745	−0.358839
$454$	29.0186	1.36191
$455$	0	0
$456$	−7.85848	−0.368007
$457$	−30.4659	−1.42514	−0.712568	−	0.701603i	$-0.752468\pi$
$457$	−30.4659	−1.42514	−0.712568	+	0.701603i	$0.752468\pi$
$458$	39.1247	1.82818
$459$	−8.39021	−0.391621
$460$	37.5139	1.74909
$461$	5.22253	0.243237	0.121619	−	0.992577i	$-0.461191\pi$
$461$	5.22253	0.243237	0.121619	+	0.992577i	$0.461191\pi$
$462$	0	0
$463$	20.6220	0.958386	0.479193	−	0.877709i	$-0.340929\pi$
$463$	20.6220	0.958386	0.479193	+	0.877709i	$0.340929\pi$
$464$	11.3714	0.527906
$465$	19.0099	0.881564
$466$	13.7536	0.637122
$467$	1.67149	0.0773474	0.0386737	−	0.999252i	$-0.487687\pi$
$467$	1.67149	0.0773474	0.0386737	+	0.999252i	$0.487687\pi$
$468$	0.254614	0.0117696
$469$	0	0
$470$	54.3332	2.50620
$471$	0.590829	0.0272240
$472$	22.0553	1.01518
$473$	25.7905	1.18585
$474$	4.30792	0.197869
$475$	1.45595	0.0668034
$476$	0	0
$477$	0.317489	0.0145368
$478$	20.5612	0.940447
$479$	10.6439	0.486333	0.243166	−	0.969985i	$-0.421814\pi$
$479$	10.6439	0.486333	0.243166	+	0.969985i	$0.421814\pi$
$480$	−27.6514	−1.26211
$481$	5.74772	0.262073
$482$	−43.5537	−1.98382
$483$	0	0
$484$	61.6369	2.80168
$485$	−14.7160	−0.668217
$486$	−2.08746	−0.0946890
$487$	−31.8312	−1.44241	−0.721206	−	0.692721i	$-0.756412\pi$
$487$	−31.8312	−1.44241	−0.721206	+	0.692721i	$0.756412\pi$
$488$	10.4527	0.473171
$489$	11.9558	0.540661
$490$	0	0
$491$	6.87077	0.310074	0.155037	−	0.987909i	$-0.450450\pi$
$491$	6.87077	0.310074	0.155037	+	0.987909i	$0.450450\pi$
$492$	−34.7379	−1.56611
$493$	−9.92654	−0.447069
$494$	−5.83087	−0.262343
$495$	−1.12065	−0.0503694
$496$	−9.62765	−0.432294
$497$	0	0
$498$	19.0770	0.854862
$499$	0.344335	0.0154145	0.00770727	−	0.999970i	$-0.497547\pi$
$499$	0.344335	0.0154145	0.00770727	+	0.999970i	$0.497547\pi$
$500$	−32.3782	−1.44800
$501$	1.17576	0.0525293
$502$	2.66793	0.119076
$503$	30.0808	1.34123	0.670617	−	0.741803i	$-0.266029\pi$
$503$	30.0808	1.34123	0.670617	+	0.741803i	$0.266029\pi$
$504$	0	0
$505$	−13.7175	−0.610423
$506$	−80.9174	−3.59722
$507$	1.75842	0.0780941
$508$	−53.4080	−2.36960
$509$	33.3105	1.47646	0.738232	−	0.674547i	$-0.235661\pi$
$509$	33.3105	1.47646	0.738232	+	0.674547i	$0.235661\pi$
$510$	13.2953	0.588726
$511$	0	0
$512$	20.2947	0.896908
$513$	13.6568	0.602960
$514$	−48.9565	−2.15938
$515$	−1.22006	−0.0537622
$516$	−21.7476	−0.957385
$517$	−68.0210	−2.99156
$518$	0	0
$519$	44.1677	1.93875
$520$	3.53181	0.154880
$521$	32.7726	1.43579	0.717897	−	0.696149i	$-0.245105\pi$
$521$	32.7726	1.43579	0.717897	+	0.696149i	$0.245105\pi$
$522$	−1.21561	−0.0532058
$523$	25.2616	1.10461	0.552307	−	0.833641i	$-0.313748\pi$
$523$	25.2616	1.10461	0.552307	+	0.833641i	$0.313748\pi$
$524$	26.8263	1.17191
$525$	0	0
$526$	19.6282	0.855830
$527$	8.40432	0.366098
$528$	19.0675	0.829807
$529$	18.2766	0.794636
$530$	15.8958	0.690469
$531$	1.21309	0.0526437
$532$	0	0
$533$	−7.14100	−0.309311
$534$	4.40065	0.190435
$535$	−34.3134	−1.48350
$536$	12.9552	0.559578
$537$	−3.33267	−0.143815
$538$	−48.4794	−2.09009
$539$	0	0
$540$	−29.8573	−1.28485
$541$	13.1630	0.565920	0.282960	−	0.959132i	$-0.408684\pi$
$541$	13.1630	0.565920	0.282960	+	0.959132i	$0.408684\pi$
$542$	−23.6712	−1.01676
$543$	19.9748	0.857201
$544$	−12.2247	−0.524130
$545$	3.76099	0.161103
$546$	0	0
$547$	−2.79349	−0.119441	−0.0597204	−	0.998215i	$-0.519021\pi$
$547$	−2.79349	−0.119441	−0.0597204	+	0.998215i	$0.519021\pi$
$548$	−42.7398	−1.82575
$549$	0.574921	0.0245370
$550$	6.86592	0.292764
$551$	16.1574	0.688330
$552$	18.9040	0.804610
$553$	0	0
$554$	12.8554	0.546174
$555$	21.3322	0.905500
$556$	10.6484	0.451592
$557$	−4.61284	−0.195452	−0.0977262	−	0.995213i	$-0.531157\pi$
$557$	−4.61284	−0.195452	−0.0977262	+	0.995213i	$0.531157\pi$
$558$	1.02920	0.0435694
$559$	−4.47061	−0.189087
$560$	0	0
$561$	−16.6447	−0.702740
$562$	58.7441	2.47797
$563$	40.2805	1.69762	0.848811	−	0.528697i	$-0.177319\pi$
$563$	40.2805	1.69762	0.848811	+	0.528697i	$0.177319\pi$
$564$	57.3582	2.41522
$565$	−15.8767	−0.667936
$566$	−7.63510	−0.320927
$567$	0	0
$568$	22.8195	0.957486
$569$	7.19869	0.301785	0.150892	−	0.988550i	$-0.451785\pi$
$569$	7.19869	0.301785	0.150892	+	0.988550i	$0.451785\pi$
$570$	−21.6408	−0.906432
$571$	11.3820	0.476323	0.238161	−	0.971226i	$-0.423455\pi$
$571$	11.3820	0.476323	0.238161	+	0.971226i	$0.423455\pi$
$572$	−15.9593	−0.667294
$573$	−41.2186	−1.72193
$574$	0	0
$575$	−3.50236	−0.146059
$576$	−1.15105	−0.0479604
$577$	−35.6257	−1.48312	−0.741560	−	0.670887i	$-0.765914\pi$
$577$	−35.6257	−1.48312	−0.741560	+	0.670887i	$0.765914\pi$
$578$	−31.2369	−1.29928
$579$	−3.25676	−0.135346
$580$	−35.3245	−1.46677
$581$	0	0
$582$	−26.7665	−1.10951
$583$	−19.9003	−0.824188
$584$	−25.9434	−1.07354
$585$	0.194257	0.00803155
$586$	2.19433	0.0906469
$587$	4.14755	0.171188	0.0855938	−	0.996330i	$-0.472721\pi$
$587$	4.14755	0.171188	0.0855938	+	0.996330i	$0.472721\pi$
$588$	0	0
$589$	−13.6797	−0.563663
$590$	60.7362	2.50047
$591$	−17.3570	−0.713973
$592$	−10.8038	−0.444032
$593$	−24.1313	−0.990953	−0.495476	−	0.868621i	$-0.665006\pi$
$593$	−24.1313	−0.990953	−0.495476	+	0.868621i	$0.665006\pi$
$594$	64.4023	2.64246
$595$	0	0
$596$	−2.87788	−0.117883
$597$	21.5393	0.881543
$598$	14.0265	0.573587
$599$	−48.5607	−1.98414	−0.992068	−	0.125703i	$-0.959881\pi$
$599$	−48.5607	−1.98414	−0.992068	+	0.125703i	$0.959881\pi$
$600$	−1.60403	−0.0654841
$601$	−33.2069	−1.35454	−0.677270	−	0.735735i	$-0.736837\pi$
$601$	−33.2069	−1.35454	−0.677270	+	0.735735i	$0.736837\pi$
$602$	0	0
$603$	0.712562	0.0290178
$604$	−12.0157	−0.488911
$605$	47.0257	1.91186
$606$	−24.9505	−1.01354
$607$	−21.7946	−0.884616	−0.442308	−	0.896863i	$-0.645840\pi$
$607$	−21.7946	−0.884616	−0.442308	+	0.896863i	$0.645840\pi$
$608$	19.8982	0.806978
$609$	0	0
$610$	28.7847	1.16546
$611$	11.7910	0.477013
$612$	0.417777	0.0168876
$613$	−22.7991	−0.920847	−0.460423	−	0.887700i	$-0.652302\pi$
$613$	−22.7991	−0.920847	−0.460423	+	0.887700i	$0.652302\pi$
$614$	9.29554	0.375138
$615$	−26.5032	−1.06871
$616$	0	0
$617$	−42.5433	−1.71273	−0.856364	−	0.516373i	$-0.827282\pi$
$617$	−42.5433	−1.71273	−0.856364	+	0.516373i	$0.827282\pi$
$618$	−2.21913	−0.0892667
$619$	−44.1285	−1.77367	−0.886836	−	0.462084i	$-0.847102\pi$
$619$	−44.1285	−1.77367	−0.886836	+	0.462084i	$0.847102\pi$
$620$	29.9075	1.20112
$621$	−32.8521	−1.31831
$622$	−15.1525	−0.607559
$623$	0	0
$624$	−3.30523	−0.132315
$625$	−21.9771	−0.879085
$626$	−21.7514	−0.869361
$627$	27.0926	1.08197
$628$	0.929528	0.0370922
$629$	9.43098	0.376038
$630$	0	0
$631$	9.09226	0.361957	0.180979	−	0.983487i	$-0.442074\pi$
$631$	9.09226	0.361957	0.180979	+	0.983487i	$0.442074\pi$
$632$	1.87771	0.0746912
$633$	−1.30105	−0.0517122
$634$	8.19461	0.325449
$635$	−40.7475	−1.61701
$636$	16.7808	0.665402
$637$	0	0
$638$	76.1950	3.01659
$639$	1.25512	0.0496519
$640$	−26.1797	−1.03485
$641$	−22.6642	−0.895181	−0.447591	−	0.894239i	$-0.647718\pi$
$641$	−22.6642	−0.895181	−0.447591	+	0.894239i	$0.647718\pi$
$642$	−62.4119	−2.46320
$643$	24.3792	0.961422	0.480711	−	0.876879i	$-0.340379\pi$
$643$	24.3792	0.961422	0.480711	+	0.876879i	$0.340379\pi$
$644$	0	0
$645$	−16.5923	−0.653320
$646$	−9.56742	−0.376425
$647$	−37.0364	−1.45605	−0.728026	−	0.685549i	$-0.759562\pi$
$647$	−37.0364	−1.45605	−0.728026	+	0.685549i	$0.759562\pi$
$648$	−15.5078	−0.609203
$649$	−76.0372	−2.98472
$650$	−1.19016	−0.0466820
$651$	0	0
$652$	18.8096	0.736641
$653$	18.7341	0.733122	0.366561	−	0.930394i	$-0.380535\pi$
$653$	18.7341	0.733122	0.366561	+	0.930394i	$0.380535\pi$
$654$	6.84077	0.267495
$655$	20.4671	0.799715
$656$	13.4227	0.524067
$657$	−1.42694	−0.0556703
$658$	0	0
$659$	−28.5206	−1.11100	−0.555502	−	0.831515i	$-0.687474\pi$
$659$	−28.5206	−1.11100	−0.555502	+	0.831515i	$0.687474\pi$
$660$	−59.2317	−2.30559
$661$	−19.9758	−0.776968	−0.388484	−	0.921455i	$-0.627001\pi$
$661$	−19.9758	−0.776968	−0.388484	+	0.921455i	$0.627001\pi$
$662$	−43.6234	−1.69547
$663$	2.88525	0.112054
$664$	8.31517	0.322691
$665$	0	0
$666$	1.15492	0.0447524
$667$	−38.8677	−1.50496
$668$	1.84978	0.0715702
$669$	14.6050	0.564663
$670$	35.6760	1.37829
$671$	−36.0363	−1.39117
$672$	0	0
$673$	−4.18849	−0.161454	−0.0807272	−	0.996736i	$-0.525724\pi$
$673$	−4.18849	−0.161454	−0.0807272	+	0.996736i	$0.525724\pi$
$674$	40.3649	1.55480
$675$	2.78753	0.107292
$676$	2.76645	0.106402
$677$	−38.3396	−1.47351	−0.736755	−	0.676159i	$-0.763643\pi$
$677$	−38.3396	−1.47351	−0.736755	+	0.676159i	$0.763643\pi$
$678$	−28.8776	−1.10904
$679$	0	0
$680$	5.79507	0.222231
$681$	23.3723	0.895628
$682$	−64.5106	−2.47024
$683$	−2.61207	−0.0999482	−0.0499741	−	0.998751i	$-0.515914\pi$
$683$	−2.61207	−0.0999482	−0.0499741	+	0.998751i	$0.515914\pi$
$684$	−0.680016	−0.0260010
$685$	−32.6082	−1.24589
$686$	0	0
$687$	31.5120	1.20226
$688$	8.40322	0.320370
$689$	3.44959	0.131419
$690$	52.0582	1.98182
$691$	−40.9185	−1.55661	−0.778307	−	0.627884i	$-0.783921\pi$
$691$	−40.9185	−1.55661	−0.778307	+	0.627884i	$0.783921\pi$
$692$	69.4872	2.64151
$693$	0	0
$694$	−1.73806	−0.0659759
$695$	8.12415	0.308167
$696$	−17.8008	−0.674737
$697$	−11.7171	−0.443817
$698$	−24.8286	−0.939776
$699$	11.0775	0.418988
$700$	0	0
$701$	−0.762896	−0.0288142	−0.0144071	−	0.999896i	$-0.504586\pi$
$701$	−0.762896	−0.0288142	−0.0144071	+	0.999896i	$0.504586\pi$
$702$	−11.1637	−0.421347
$703$	−15.3508	−0.578967
$704$	72.1484	2.71920
$705$	43.7613	1.64814
$706$	52.6304	1.98077
$707$	0	0
$708$	64.1178	2.40969
$709$	2.65281	0.0996284	0.0498142	−	0.998759i	$-0.484137\pi$
$709$	2.65281	0.0996284	0.0498142	+	0.998759i	$0.484137\pi$
$710$	62.8407	2.35837
$711$	0.103278	0.00387323
$712$	1.91813	0.0718848
$713$	32.9074	1.23239
$714$	0	0
$715$	−12.1761	−0.455362
$716$	−5.24315	−0.195946
$717$	16.5605	0.618463
$718$	19.8058	0.739145
$719$	11.0443	0.411883	0.205942	−	0.978564i	$-0.433974\pi$
$719$	11.0443	0.411883	0.205942	+	0.978564i	$0.433974\pi$
$720$	−0.365138	−0.0136079
$721$	0	0
$722$	−25.9083	−0.964206
$723$	−35.0792	−1.30461
$724$	31.4255	1.16792
$725$	3.29796	0.122483
$726$	85.5338	3.17446
$727$	3.46566	0.128534	0.0642672	−	0.997933i	$-0.479529\pi$
$727$	3.46566	0.128534	0.0642672	+	0.997933i	$0.479529\pi$
$728$	0	0
$729$	26.1216	0.967468
$730$	−71.4432	−2.64423
$731$	−7.33547	−0.271312
$732$	30.3873	1.12315
$733$	−29.0332	−1.07236	−0.536182	−	0.844102i	$-0.680134\pi$
$733$	−29.0332	−1.07236	−0.536182	+	0.844102i	$0.680134\pi$
$734$	−68.8822	−2.54249
$735$	0	0
$736$	−47.8663	−1.76437
$737$	−44.6637	−1.64521
$738$	−1.43488	−0.0528188
$739$	47.5522	1.74924	0.874618	−	0.484813i	$-0.161112\pi$
$739$	47.5522	1.74924	0.874618	+	0.484813i	$0.161112\pi$
$740$	33.5610	1.23373
$741$	−4.69633	−0.172524
$742$	0	0
$743$	12.6122	0.462697	0.231349	−	0.972871i	$-0.425686\pi$
$743$	12.6122	0.462697	0.231349	+	0.972871i	$0.425686\pi$
$744$	15.0711	0.552532
$745$	−2.19567	−0.0804432
$746$	−35.0584	−1.28358
$747$	0.457353	0.0167337
$748$	−26.1864	−0.957471
$749$	0	0
$750$	−44.9313	−1.64066
$751$	−7.70781	−0.281262	−0.140631	−	0.990062i	$-0.544913\pi$
$751$	−7.70781	−0.281262	−0.140631	+	0.990062i	$0.544913\pi$
$752$	−22.1631	−0.808204
$753$	2.14882	0.0783073
$754$	−13.2079	−0.481003
$755$	−9.16734	−0.333633
$756$	0	0
$757$	2.39454	0.0870311	0.0435156	−	0.999053i	$-0.486144\pi$
$757$	2.39454	0.0870311	0.0435156	+	0.999053i	$0.486144\pi$
$758$	−11.7216	−0.425748
$759$	−65.1729	−2.36563
$760$	−9.43265	−0.342158
$761$	−41.3296	−1.49820	−0.749098	−	0.662459i	$-0.769513\pi$
$761$	−41.3296	−1.49820	−0.749098	+	0.662459i	$0.769513\pi$
$762$	−74.1146	−2.68489
$763$	0	0
$764$	−64.8475	−2.34610
$765$	0.318742	0.0115241
$766$	75.3374	2.72205
$767$	13.1805	0.475922
$768$	−3.63450	−0.131149
$769$	36.7414	1.32493	0.662464	−	0.749094i	$-0.269511\pi$
$769$	36.7414	1.32493	0.662464	+	0.749094i	$0.269511\pi$
$770$	0	0
$771$	−39.4308	−1.42007
$772$	−5.12373	−0.184407
$773$	−23.9672	−0.862040	−0.431020	−	0.902342i	$-0.641846\pi$
$773$	−23.9672	−0.862040	−0.431020	+	0.902342i	$0.641846\pi$
$774$	−0.898306	−0.0322889
$775$	−2.79222	−0.100300
$776$	−11.6668	−0.418814
$777$	0	0
$778$	50.0415	1.79408
$779$	19.0720	0.683324
$780$	10.2674	0.367633
$781$	−78.6718	−2.81510
$782$	23.0150	0.823015
$783$	30.9348	1.10552
$784$	0	0
$785$	0.709180	0.0253117
$786$	37.2270	1.32784
$787$	36.0134	1.28374	0.641870	−	0.766814i	$-0.278159\pi$
$787$	36.0134	1.28374	0.641870	+	0.766814i	$0.278159\pi$
$788$	−27.3071	−0.972776
$789$	15.8090	0.562816
$790$	5.17085	0.183971
$791$	0	0
$792$	−0.888450	−0.0315697
$793$	6.24666	0.221825
$794$	23.6429	0.839054
$795$	12.8029	0.454071
$796$	33.8868	1.20109
$797$	−18.8155	−0.666478	−0.333239	−	0.942842i	$-0.608142\pi$
$797$	−18.8155	−0.666478	−0.333239	+	0.942842i	$0.608142\pi$
$798$	0	0
$799$	19.3469	0.684445
$800$	4.06150	0.143596
$801$	0.105501	0.00372770
$802$	81.9614	2.89416
$803$	89.4414	3.15632
$804$	37.6623	1.32825
$805$	0	0
$806$	11.1825	0.393886
$807$	−39.0465	−1.37450
$808$	−10.8753	−0.382591
$809$	−47.3322	−1.66411	−0.832056	−	0.554692i	$-0.812836\pi$
$809$	−47.3322	−1.66411	−0.832056	+	0.554692i	$0.812836\pi$
$810$	−42.7055	−1.50052
$811$	19.2555	0.676153	0.338077	−	0.941119i	$-0.390224\pi$
$811$	19.2555	0.676153	0.338077	+	0.941119i	$0.390224\pi$
$812$	0	0
$813$	−19.0653	−0.668650
$814$	−72.3912	−2.53731
$815$	14.3507	0.502684
$816$	−5.42329	−0.189853
$817$	11.9400	0.417726
$818$	−44.6964	−1.56277
$819$	0	0
$820$	−41.6964	−1.45610
$821$	41.5165	1.44894	0.724468	−	0.689308i	$-0.242085\pi$
$821$	41.5165	1.44894	0.724468	+	0.689308i	$0.242085\pi$
$822$	−59.3102	−2.06868
$823$	24.5627	0.856201	0.428100	−	0.903731i	$-0.359183\pi$
$823$	24.5627	0.856201	0.428100	+	0.903731i	$0.359183\pi$
$824$	−0.967262	−0.0336962
$825$	5.52998	0.192529
$826$	0	0
$827$	−0.580957	−0.0202019	−0.0101009	−	0.999949i	$-0.503215\pi$
$827$	−0.580957	−0.0202019	−0.0101009	+	0.999949i	$0.503215\pi$
$828$	1.63582	0.0568486
$829$	14.6630	0.509268	0.254634	−	0.967038i	$-0.418045\pi$
$829$	14.6630	0.509268	0.254634	+	0.967038i	$0.418045\pi$
$830$	22.8984	0.794815
$831$	10.3541	0.359178
$832$	−12.5065	−0.433583
$833$	0	0
$834$	14.7768	0.511679
$835$	1.41129	0.0488396
$836$	42.6237	1.47417
$837$	−26.1910	−0.905294
$838$	−33.8356	−1.16883
$839$	25.6151	0.884332	0.442166	−	0.896933i	$-0.354210\pi$
$839$	25.6151	0.884332	0.442166	+	0.896933i	$0.354210\pi$
$840$	0	0
$841$	7.59929	0.262044
$842$	39.1648	1.34971
$843$	47.3140	1.62958
$844$	−2.04689	−0.0704569
$845$	2.11065	0.0726087
$846$	2.36924	0.0814560
$847$	0	0
$848$	−6.48406	−0.222664
$849$	−6.14949	−0.211050
$850$	−1.95285	−0.0669820
$851$	36.9273	1.26585
$852$	66.3394	2.27275
$853$	−0.587340	−0.0201101	−0.0100551	−	0.999949i	$-0.503201\pi$
$853$	−0.587340	−0.0201101	−0.0100551	+	0.999949i	$0.503201\pi$
$854$	0	0
$855$	−0.518816	−0.0177431
$856$	−27.2037	−0.929803
$857$	31.1680	1.06468	0.532340	−	0.846531i	$-0.321313\pi$
$857$	31.1680	1.06468	0.532340	+	0.846531i	$0.321313\pi$
$858$	−22.1469	−0.756082
$859$	−22.7944	−0.777735	−0.388867	−	0.921294i	$-0.627134\pi$
$859$	−22.7944	−0.777735	−0.388867	+	0.921294i	$0.627134\pi$
$860$	−26.1039	−0.890137
$861$	0	0
$862$	46.8166	1.59458
$863$	50.6249	1.72329	0.861646	−	0.507510i	$-0.169434\pi$
$863$	50.6249	1.72329	0.861646	+	0.507510i	$0.169434\pi$
$864$	38.0968	1.29608
$865$	53.0150	1.80257
$866$	−32.6096	−1.10812
$867$	−25.1589	−0.854442
$868$	0	0
$869$	−6.47352	−0.219599
$870$	−49.0200	−1.66193
$871$	7.74216	0.262333
$872$	2.98171	0.100973
$873$	−0.641700	−0.0217182
$874$	−37.4615	−1.26716
$875$	0	0
$876$	−75.4208	−2.54823
$877$	11.9495	0.403505	0.201753	−	0.979436i	$-0.435336\pi$
$877$	11.9495	0.403505	0.201753	+	0.979436i	$0.435336\pi$
$878$	−7.84480	−0.264749
$879$	1.76737	0.0596118
$880$	22.8870	0.771520
$881$	54.6400	1.84087	0.920434	−	0.390898i	$-0.127835\pi$
$881$	54.6400	1.84087	0.920434	+	0.390898i	$0.127835\pi$
$882$	0	0
$883$	−26.7256	−0.899388	−0.449694	−	0.893183i	$-0.648467\pi$
$883$	−26.7256	−0.899388	−0.449694	+	0.893183i	$0.648467\pi$
$884$	4.53925	0.152671
$885$	48.9185	1.64438
$886$	−29.8084	−1.00143
$887$	−5.82278	−0.195510	−0.0977549	−	0.995211i	$-0.531166\pi$
$887$	−5.82278	−0.195510	−0.0977549	+	0.995211i	$0.531166\pi$
$888$	16.9121	0.567534
$889$	0	0
$890$	5.28215	0.177058
$891$	53.4640	1.79111
$892$	22.9775	0.769343
$893$	−31.4910	−1.05381
$894$	−3.99365	−0.133568
$895$	−4.00025	−0.133714
$896$	0	0
$897$	11.2973	0.377206
$898$	−19.0467	−0.635595
$899$	−30.9868	−1.03347
$900$	−0.138801	−0.00462669
$901$	5.66017	0.188568
$902$	89.9392	2.99465
$903$	0	0
$904$	−12.5870	−0.418638
$905$	23.9760	0.796990
$906$	−16.6742	−0.553964
$907$	−54.4672	−1.80855	−0.904276	−	0.426948i	$-0.859589\pi$
$907$	−54.4672	−1.80855	−0.904276	+	0.426948i	$0.859589\pi$
$908$	36.7707	1.22028
$909$	−0.598163	−0.0198398
$910$	0	0
$911$	5.94815	0.197071	0.0985355	−	0.995134i	$-0.468584\pi$
$911$	5.94815	0.197071	0.0985355	+	0.995134i	$0.468584\pi$
$912$	8.82750	0.292308
$913$	−28.6671	−0.948742
$914$	−66.5138	−2.20008
$915$	23.1839	0.766437
$916$	49.5766	1.63806
$917$	0	0
$918$	−18.3177	−0.604573
$919$	13.6480	0.450207	0.225103	−	0.974335i	$-0.427728\pi$
$919$	13.6480	0.450207	0.225103	+	0.974335i	$0.427728\pi$
$920$	22.6908	0.748093
$921$	7.48686	0.246700
$922$	11.4019	0.375503
$923$	13.6372	0.448875
$924$	0	0
$925$	−3.13332	−0.103023
$926$	45.0224	1.47953
$927$	−0.0532015	−0.00174737
$928$	45.0727	1.47958
$929$	36.3062	1.19117	0.595585	−	0.803293i	$-0.296920\pi$
$929$	36.3062	1.19117	0.595585	+	0.803293i	$0.296920\pi$
$930$	41.5028	1.36093
$931$	0	0
$932$	17.4277	0.570864
$933$	−12.2042	−0.399547
$934$	3.64923	0.119406
$935$	−19.9789	−0.653379
$936$	0.154007	0.00503388
$937$	27.7384	0.906175	0.453087	−	0.891466i	$-0.350323\pi$
$937$	27.7384	0.906175	0.453087	+	0.891466i	$0.350323\pi$
$938$	0	0
$939$	−17.5191	−0.571715
$940$	68.8478	2.24557
$941$	−31.9163	−1.04044	−0.520222	−	0.854031i	$-0.674151\pi$
$941$	−31.9163	−1.04044	−0.520222	+	0.854031i	$0.674151\pi$
$942$	1.28991	0.0420275
$943$	−45.8787	−1.49402
$944$	−24.7750	−0.806356
$945$	0	0
$946$	56.3063	1.83067
$947$	23.1657	0.752785	0.376392	−	0.926460i	$-0.377164\pi$
$947$	23.1657	0.752785	0.376392	+	0.926460i	$0.377164\pi$
$948$	5.45874	0.177292
$949$	−15.5041	−0.503284
$950$	3.17865	0.103129
$951$	6.60014	0.214024
$952$	0	0
$953$	25.7340	0.833607	0.416803	−	0.908997i	$-0.363150\pi$
$953$	25.7340	0.833607	0.416803	+	0.908997i	$0.363150\pi$
$954$	0.693147	0.0224415
$955$	−49.4752	−1.60098
$956$	26.0539	0.842645
$957$	61.3693	1.98379
$958$	23.2380	0.750786
$959$	0	0
$960$	−46.4166	−1.49809
$961$	−4.76494	−0.153708
$962$	12.5485	0.404581
$963$	−1.49626	−0.0482164
$964$	−55.1887	−1.77751
$965$	−3.90913	−0.125839
$966$	0	0
$967$	16.2544	0.522706	0.261353	−	0.965243i	$-0.415831\pi$
$967$	16.2544	0.522706	0.261353	+	0.965243i	$0.415831\pi$
$968$	37.2819	1.19829
$969$	−7.70584	−0.247547
$970$	−32.1282	−1.03157
$971$	39.7465	1.27553	0.637763	−	0.770232i	$-0.279860\pi$
$971$	39.7465	1.27553	0.637763	+	0.770232i	$0.279860\pi$
$972$	−2.64510	−0.0848418
$973$	0	0
$974$	−69.4946	−2.22675
$975$	−0.958586	−0.0306993
$976$	−11.7416	−0.375839
$977$	−26.1884	−0.837842	−0.418921	−	0.908023i	$-0.637592\pi$
$977$	−26.1884	−0.837842	−0.418921	+	0.908023i	$0.637592\pi$
$978$	26.1022	0.834655
$979$	−6.61286	−0.211348
$980$	0	0
$981$	0.164000	0.00523613
$982$	15.0004	0.478682
$983$	12.2915	0.392039	0.196020	−	0.980600i	$-0.437198\pi$
$983$	12.2915	0.392039	0.196020	+	0.980600i	$0.437198\pi$
$984$	−21.0117	−0.669830
$985$	−20.8339	−0.663823
$986$	−21.6718	−0.690171
$987$	0	0
$988$	−7.38854	−0.235061
$989$	−28.7223	−0.913315
$990$	−2.44662	−0.0777588
$991$	11.4681	0.364298	0.182149	−	0.983271i	$-0.441695\pi$
$991$	11.4681	0.364298	0.182149	+	0.983271i	$0.441695\pi$
$992$	−38.1609	−1.21161
$993$	−35.1354	−1.11499
$994$	0	0
$995$	25.8539	0.819623
$996$	24.1733	0.765960
$997$	−5.30214	−0.167920	−0.0839602	−	0.996469i	$-0.526757\pi$
$997$	−5.30214	−0.167920	−0.0839602	+	0.996469i	$0.526757\pi$
$998$	0.751758	0.0237965
$999$	−29.3905	−0.929874

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.a.n.1.6	yes	6
3.2	odd	2		5733.2.a.br.1.1		6
7.2	even	3		637.2.e.n.508.1		12
7.3	odd	6		637.2.e.o.79.1		12
7.4	even	3		637.2.e.n.79.1		12
7.5	odd	6		637.2.e.o.508.1		12
7.6	odd	2		637.2.a.m.1.6	✓	6
13.12	even	2		8281.2.a.cd.1.1		6
21.20	even	2		5733.2.a.bu.1.1		6
91.90	odd	2		8281.2.a.cc.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.a.m.1.6	✓	6	7.6	odd	2
637.2.a.n.1.6	yes	6	1.1	even	1	trivial
637.2.e.n.79.1		12	7.4	even	3
637.2.e.n.508.1		12	7.2	even	3
637.2.e.o.79.1		12	7.3	odd	6
637.2.e.o.508.1		12	7.5	odd	6
5733.2.a.br.1.1		6	3.2	odd	2
5733.2.a.bu.1.1		6	21.20	even	2
8281.2.a.cc.1.1		6	91.90	odd	2
8281.2.a.cd.1.1		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)

\(f(q)\)	\(=\)	\(q+2.18322 q^{2} +1.75842 q^{3} +2.76645 q^{4} +2.11065 q^{5} +3.83901 q^{6} +1.67333 q^{8} +0.0920365 q^{9} +O(q^{10})\)	\(q+2.18322 q^{2} +1.75842 q^{3} +2.76645 q^{4} +2.11065 q^{5} +3.83901 q^{6} +1.67333 q^{8} +0.0920365 q^{9} +4.60802 q^{10} -5.76889 q^{11} +4.86457 q^{12} +1.00000 q^{13} +3.71141 q^{15} -1.87966 q^{16} +1.64082 q^{17} +0.200936 q^{18} -2.67077 q^{19} +5.83901 q^{20} -12.5948 q^{22} +6.42469 q^{23} +2.94241 q^{24} -0.545141 q^{25} +2.18322 q^{26} -5.11342 q^{27} -6.04973 q^{29} +8.10283 q^{30} +5.12202 q^{31} -7.45036 q^{32} -10.1441 q^{33} +3.58227 q^{34} +0.254614 q^{36} +5.74772 q^{37} -5.83087 q^{38} +1.75842 q^{39} +3.53181 q^{40} -7.14100 q^{41} -4.47061 q^{43} -15.9593 q^{44} +0.194257 q^{45} +14.0265 q^{46} +11.7910 q^{47} -3.30523 q^{48} -1.19016 q^{50} +2.88525 q^{51} +2.76645 q^{52} +3.44959 q^{53} -11.1637 q^{54} -12.1761 q^{55} -4.69633 q^{57} -13.2079 q^{58} +13.1805 q^{59} +10.2674 q^{60} +6.24666 q^{61} +11.1825 q^{62} -12.5065 q^{64} +2.11065 q^{65} -22.1469 q^{66} +7.74216 q^{67} +4.53925 q^{68} +11.2973 q^{69} +13.6372 q^{71} +0.154007 q^{72} -15.5041 q^{73} +12.5485 q^{74} -0.958586 q^{75} -7.38854 q^{76} +3.83901 q^{78} +1.12214 q^{79} -3.96731 q^{80} -9.26764 q^{81} -15.5904 q^{82} +4.96925 q^{83} +3.46321 q^{85} -9.76032 q^{86} -10.6380 q^{87} -9.65324 q^{88} +1.14630 q^{89} +0.424106 q^{90} +17.7736 q^{92} +9.00665 q^{93} +25.7423 q^{94} -5.63707 q^{95} -13.1009 q^{96} -6.97223 q^{97} -0.530949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 8 q^{3} + 4 q^{4} + 6 q^{5} + 4 q^{6} + 6 q^{9}+O(q^{10}) \) 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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