LMFDB - Embedded newform 2001.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +0.561553 q^{5} -1.00000 q^{6} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +0.561553 q^{5} -1.00000 q^{6} -3.00000 q^{8} +1.00000 q^{9} +0.561553 q^{10} +0.561553 q^{11} +1.00000 q^{12} +0.561553 q^{13} -0.561553 q^{15} -1.00000 q^{16} +1.00000 q^{18} +3.12311 q^{19} -0.561553 q^{20} +0.561553 q^{22} +1.00000 q^{23} +3.00000 q^{24} -4.68466 q^{25} +0.561553 q^{26} -1.00000 q^{27} -1.00000 q^{29} -0.561553 q^{30} -6.56155 q^{31} +5.00000 q^{32} -0.561553 q^{33} -1.00000 q^{36} +6.56155 q^{37} +3.12311 q^{38} -0.561553 q^{39} -1.68466 q^{40} +3.43845 q^{41} +12.2462 q^{43} -0.561553 q^{44} +0.561553 q^{45} +1.00000 q^{46} -1.12311 q^{47} +1.00000 q^{48} -7.00000 q^{49} -4.68466 q^{50} -0.561553 q^{52} +12.2462 q^{53} -1.00000 q^{54} +0.315342 q^{55} -3.12311 q^{57} -1.00000 q^{58} +5.43845 q^{59} +0.561553 q^{60} +8.80776 q^{61} -6.56155 q^{62} +7.00000 q^{64} +0.315342 q^{65} -0.561553 q^{66} +10.5616 q^{67} -1.00000 q^{69} +14.5616 q^{71} -3.00000 q^{72} +3.12311 q^{73} +6.56155 q^{74} +4.68466 q^{75} -3.12311 q^{76} -0.561553 q^{78} -2.00000 q^{79} -0.561553 q^{80} +1.00000 q^{81} +3.43845 q^{82} +1.12311 q^{83} +12.2462 q^{86} +1.00000 q^{87} -1.68466 q^{88} -7.36932 q^{89} +0.561553 q^{90} -1.00000 q^{92} +6.56155 q^{93} -1.12311 q^{94} +1.75379 q^{95} -5.00000 q^{96} +11.3693 q^{97} -7.00000 q^{98} +0.561553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9} - 3 q^{10} - 3 q^{11} + 2 q^{12} - 3 q^{13} + 3 q^{15} - 2 q^{16} + 2 q^{18} - 2 q^{19} + 3 q^{20} - 3 q^{22} + 2 q^{23} + 6 q^{24} + 3 q^{25} - 3 q^{26} - 2 q^{27} - 2 q^{29} + 3 q^{30} - 9 q^{31} + 10 q^{32} + 3 q^{33} - 2 q^{36} + 9 q^{37} - 2 q^{38} + 3 q^{39} + 9 q^{40} + 11 q^{41} + 8 q^{43} + 3 q^{44} - 3 q^{45} + 2 q^{46} + 6 q^{47} + 2 q^{48} - 14 q^{49} + 3 q^{50} + 3 q^{52} + 8 q^{53} - 2 q^{54} + 13 q^{55} + 2 q^{57} - 2 q^{58} + 15 q^{59} - 3 q^{60} - 3 q^{61} - 9 q^{62} + 14 q^{64} + 13 q^{65} + 3 q^{66} + 17 q^{67} - 2 q^{69} + 25 q^{71} - 6 q^{72} - 2 q^{73} + 9 q^{74} - 3 q^{75} + 2 q^{76} + 3 q^{78} - 4 q^{79} + 3 q^{80} + 2 q^{81} + 11 q^{82} - 6 q^{83} + 8 q^{86} + 2 q^{87} + 9 q^{88} + 10 q^{89} - 3 q^{90} - 2 q^{92} + 9 q^{93} + 6 q^{94} + 20 q^{95} - 10 q^{96} - 2 q^{97} - 14 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9 - 3 * q^10 - 3 * q^11 + 2 * q^12 - 3 * q^13 + 3 * q^15 - 2 * q^16 + 2 * q^18 - 2 * q^19 + 3 * q^20 - 3 * q^22 + 2 * q^23 + 6 * q^24 + 3 * q^25 - 3 * q^26 - 2 * q^27 - 2 * q^29 + 3 * q^30 - 9 * q^31 + 10 * q^32 + 3 * q^33 - 2 * q^36 + 9 * q^37 - 2 * q^38 + 3 * q^39 + 9 * q^40 + 11 * q^41 + 8 * q^43 + 3 * q^44 - 3 * q^45 + 2 * q^46 + 6 * q^47 + 2 * q^48 - 14 * q^49 + 3 * q^50 + 3 * q^52 + 8 * q^53 - 2 * q^54 + 13 * q^55 + 2 * q^57 - 2 * q^58 + 15 * q^59 - 3 * q^60 - 3 * q^61 - 9 * q^62 + 14 * q^64 + 13 * q^65 + 3 * q^66 + 17 * q^67 - 2 * q^69 + 25 * q^71 - 6 * q^72 - 2 * q^73 + 9 * q^74 - 3 * q^75 + 2 * q^76 + 3 * q^78 - 4 * q^79 + 3 * q^80 + 2 * q^81 + 11 * q^82 - 6 * q^83 + 8 * q^86 + 2 * q^87 + 9 * q^88 + 10 * q^89 - 3 * q^90 - 2 * q^92 + 9 * q^93 + 6 * q^94 + 20 * q^95 - 10 * q^96 - 2 * q^97 - 14 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107	0.353553	−	0.935414i	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.00000	−0.500000
$5$	0.561553	0.251134	0.125567	−	0.992085i	$-0.459925\pi$
$5$	0.561553	0.251134	0.125567	+	0.992085i	$0.459925\pi$
$6$	−1.00000	−0.408248
$7$	0	0		−	1.00000i	$-0.5\pi$
$7$	0	0			1.00000i	$0.5\pi$
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	0.561553	0.177579
$11$	0.561553	0.169315	0.0846573	−	0.996410i	$-0.473020\pi$
$11$	0.561553	0.169315	0.0846573	+	0.996410i	$0.473020\pi$
$12$	1.00000	0.288675
$13$	0.561553	0.155747	0.0778734	−	0.996963i	$-0.475187\pi$
$13$	0.561553	0.155747	0.0778734	+	0.996963i	$0.475187\pi$
$14$	0	0
$15$	−0.561553	−0.144992
$16$	−1.00000	−0.250000
$17$	0	0		−	1.00000i	$-0.5\pi$
$17$	0	0			1.00000i	$0.5\pi$
$18$	1.00000	0.235702
$19$	3.12311	0.716490	0.358245	−	0.933628i	$-0.383375\pi$
$19$	3.12311	0.716490	0.358245	+	0.933628i	$0.383375\pi$
$20$	−0.561553	−0.125567
$21$	0	0
$22$	0.561553	0.119723
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.00000	0.612372
$25$	−4.68466	−0.936932
$26$	0.561553	0.110130
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.561553	−0.102525
$31$	−6.56155	−1.17849	−0.589245	−	0.807955i	$-0.700575\pi$
$31$	−6.56155	−1.17849	−0.589245	+	0.807955i	$0.700575\pi$
$32$	5.00000	0.883883
$33$	−0.561553	−0.0977538
$34$	0	0
$35$	0	0
$36$	−1.00000	−0.166667
$37$	6.56155	1.07871	0.539356	−	0.842078i	$-0.318668\pi$
$37$	6.56155	1.07871	0.539356	+	0.842078i	$0.318668\pi$
$38$	3.12311	0.506635
$39$	−0.561553	−0.0899204
$40$	−1.68466	−0.266368
$41$	3.43845	0.536995	0.268498	−	0.963280i	$-0.413473\pi$
$41$	3.43845	0.536995	0.268498	+	0.963280i	$0.413473\pi$
$42$	0	0
$43$	12.2462	1.86753	0.933765	−	0.357887i	$-0.116503\pi$
$43$	12.2462	1.86753	0.933765	+	0.357887i	$0.116503\pi$
$44$	−0.561553	−0.0846573
$45$	0.561553	0.0837114
$46$	1.00000	0.147442
$47$	−1.12311	−0.163822	−0.0819109	−	0.996640i	$-0.526102\pi$
$47$	−1.12311	−0.163822	−0.0819109	+	0.996640i	$0.526102\pi$
$48$	1.00000	0.144338
$49$	−7.00000	−1.00000
$50$	−4.68466	−0.662511
$51$	0	0
$52$	−0.561553	−0.0778734
$53$	12.2462	1.68215	0.841073	−	0.540921i	$-0.181924\pi$
$53$	12.2462	1.68215	0.841073	+	0.540921i	$0.181924\pi$
$54$	−1.00000	−0.136083
$55$	0.315342	0.0425206
$56$	0	0
$57$	−3.12311	−0.413665
$58$	−1.00000	−0.131306
$59$	5.43845	0.708026	0.354013	−	0.935241i	$-0.384817\pi$
$59$	5.43845	0.708026	0.354013	+	0.935241i	$0.384817\pi$
$60$	0.561553	0.0724962
$61$	8.80776	1.12772	0.563859	−	0.825871i	$-0.309316\pi$
$61$	8.80776	1.12772	0.563859	+	0.825871i	$0.309316\pi$
$62$	−6.56155	−0.833318
$63$	0	0
$64$	7.00000	0.875000
$65$	0.315342	0.0391133
$66$	−0.561553	−0.0691224
$67$	10.5616	1.29030	0.645150	−	0.764056i	$-0.276795\pi$
$67$	10.5616	1.29030	0.645150	+	0.764056i	$0.276795\pi$
$68$	0	0
$69$	−1.00000	−0.120386
$70$	0	0
$71$	14.5616	1.72814	0.864069	−	0.503373i	$-0.167908\pi$
$71$	14.5616	1.72814	0.864069	+	0.503373i	$0.167908\pi$
$72$	−3.00000	−0.353553
$73$	3.12311	0.365532	0.182766	−	0.983156i	$-0.441495\pi$
$73$	3.12311	0.365532	0.182766	+	0.983156i	$0.441495\pi$
$74$	6.56155	0.762765
$75$	4.68466	0.540938
$76$	−3.12311	−0.358245
$77$	0	0
$78$	−0.561553	−0.0635833
$79$	−2.00000	−0.225018	−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000	−0.225018	−0.112509	+	0.993651i	$0.535889\pi$
$80$	−0.561553	−0.0627835
$81$	1.00000	0.111111
$82$	3.43845	0.379713
$83$	1.12311	0.123277	0.0616384	−	0.998099i	$-0.480367\pi$
$83$	1.12311	0.123277	0.0616384	+	0.998099i	$0.480367\pi$
$84$	0	0
$85$	0	0
$86$	12.2462	1.32054
$87$	1.00000	0.107211
$88$	−1.68466	−0.179585
$89$	−7.36932	−0.781146	−0.390573	−	0.920572i	$-0.627723\pi$
$89$	−7.36932	−0.781146	−0.390573	+	0.920572i	$0.627723\pi$
$90$	0.561553	0.0591929
$91$	0	0
$92$	−1.00000	−0.104257
$93$	6.56155	0.680401
$94$	−1.12311	−0.115840
$95$	1.75379	0.179935
$96$	−5.00000	−0.510310
$97$	11.3693	1.15438	0.577190	−	0.816610i	$-0.304149\pi$
$97$	11.3693	1.15438	0.577190	+	0.816610i	$0.304149\pi$
$98$	−7.00000	−0.707107
$99$	0.561553	0.0564382
$100$	4.68466	0.468466
$101$	−3.43845	−0.342138	−0.171069	−	0.985259i	$-0.554722\pi$
$101$	−3.43845	−0.342138	−0.171069	+	0.985259i	$0.554722\pi$
$102$	0	0
$103$	−2.56155	−0.252397	−0.126199	−	0.992005i	$-0.540278\pi$
$103$	−2.56155	−0.252397	−0.126199	+	0.992005i	$0.540278\pi$
$104$	−1.68466	−0.165194
$105$	0	0
$106$	12.2462	1.18946
$107$	0	0		−	1.00000i	$-0.5\pi$
$107$	0	0			1.00000i	$0.5\pi$
$108$	1.00000	0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0.315342	0.0300666
$111$	−6.56155	−0.622795
$112$	0	0
$113$	−11.3693	−1.06954	−0.534768	−	0.844999i	$-0.679601\pi$
$113$	−11.3693	−1.06954	−0.534768	+	0.844999i	$0.679601\pi$
$114$	−3.12311	−0.292506
$115$	0.561553	0.0523651
$116$	1.00000	0.0928477
$117$	0.561553	0.0519156
$118$	5.43845	0.500650
$119$	0	0
$120$	1.68466	0.153788
$121$	−10.6847	−0.971333
$122$	8.80776	0.797417
$123$	−3.43845	−0.310034
$124$	6.56155	0.589245
$125$	−5.43845	−0.486430
$126$	0	0
$127$	−8.80776	−0.781563	−0.390781	−	0.920484i	$-0.627795\pi$
$127$	−8.80776	−0.781563	−0.390781	+	0.920484i	$0.627795\pi$
$128$	−3.00000	−0.265165
$129$	−12.2462	−1.07822
$130$	0.315342	0.0276573
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0.561553	0.0488769
$133$	0	0
$134$	10.5616	0.912379
$135$	−0.561553	−0.0483308
$136$	0	0
$137$	18.2462	1.55888	0.779440	−	0.626477i	$-0.215504\pi$
$137$	18.2462	1.55888	0.779440	+	0.626477i	$0.215504\pi$
$138$	−1.00000	−0.0851257
$139$	21.6155	1.83341	0.916703	−	0.399570i	$-0.130841\pi$
$139$	21.6155	1.83341	0.916703	+	0.399570i	$0.130841\pi$
$140$	0	0
$141$	1.12311	0.0945826
$142$	14.5616	1.22198
$143$	0.315342	0.0263702
$144$	−1.00000	−0.0833333
$145$	−0.561553	−0.0466344
$146$	3.12311	0.258470
$147$	7.00000	0.577350
$148$	−6.56155	−0.539356
$149$	11.9309	0.977415	0.488707	−	0.872448i	$-0.337469\pi$
$149$	11.9309	0.977415	0.488707	+	0.872448i	$0.337469\pi$
$150$	4.68466	0.382501
$151$	−10.2462	−0.833825	−0.416912	−	0.908947i	$-0.636888\pi$
$151$	−10.2462	−0.833825	−0.416912	+	0.908947i	$0.636888\pi$
$152$	−9.36932	−0.759952
$153$	0	0
$154$	0	0
$155$	−3.68466	−0.295959
$156$	0.561553	0.0449602
$157$	10.8769	0.868071	0.434035	−	0.900896i	$-0.357089\pi$
$157$	10.8769	0.868071	0.434035	+	0.900896i	$0.357089\pi$
$158$	−2.00000	−0.159111
$159$	−12.2462	−0.971188
$160$	2.80776	0.221973
$161$	0	0
$162$	1.00000	0.0785674
$163$	1.43845	0.112668	0.0563339	−	0.998412i	$-0.482059\pi$
$163$	1.43845	0.112668	0.0563339	+	0.998412i	$0.482059\pi$
$164$	−3.43845	−0.268498
$165$	−0.315342	−0.0245493
$166$	1.12311	0.0871699
$167$	21.9309	1.69706	0.848531	−	0.529146i	$-0.177488\pi$
$167$	21.9309	1.69706	0.848531	+	0.529146i	$0.177488\pi$
$168$	0	0
$169$	−12.6847	−0.975743
$170$	0	0
$171$	3.12311	0.238830
$172$	−12.2462	−0.933765
$173$	−22.4924	−1.71007	−0.855034	−	0.518573i	$-0.826464\pi$
$173$	−22.4924	−1.71007	−0.855034	+	0.518573i	$0.826464\pi$
$174$	1.00000	0.0758098
$175$	0	0
$176$	−0.561553	−0.0423286
$177$	−5.43845	−0.408779
$178$	−7.36932	−0.552354
$179$	16.4924	1.23270	0.616351	−	0.787472i	$-0.288610\pi$
$179$	16.4924	1.23270	0.616351	+	0.787472i	$0.288610\pi$
$180$	−0.561553	−0.0418557
$181$	−14.4924	−1.07721	−0.538607	−	0.842557i	$-0.681049\pi$
$181$	−14.4924	−1.07721	−0.538607	+	0.842557i	$0.681049\pi$
$182$	0	0
$183$	−8.80776	−0.651089
$184$	−3.00000	−0.221163
$185$	3.68466	0.270901
$186$	6.56155	0.481116
$187$	0	0
$188$	1.12311	0.0819109
$189$	0	0
$190$	1.75379	0.127233
$191$	−15.4384	−1.11709	−0.558543	−	0.829475i	$-0.688640\pi$
$191$	−15.4384	−1.11709	−0.558543	+	0.829475i	$0.688640\pi$
$192$	−7.00000	−0.505181
$193$	−15.1231	−1.08858	−0.544292	−	0.838896i	$-0.683202\pi$
$193$	−15.1231	−1.08858	−0.544292	+	0.838896i	$0.683202\pi$
$194$	11.3693	0.816269
$195$	−0.315342	−0.0225821
$196$	7.00000	0.500000
$197$	−4.24621	−0.302530	−0.151265	−	0.988493i	$-0.548335\pi$
$197$	−4.24621	−0.302530	−0.151265	+	0.988493i	$0.548335\pi$
$198$	0.561553	0.0399078
$199$	15.6847	1.11186	0.555928	−	0.831230i	$-0.312363\pi$
$199$	15.6847	1.11186	0.555928	+	0.831230i	$0.312363\pi$
$200$	14.0540	0.993766
$201$	−10.5616	−0.744954
$202$	−3.43845	−0.241928
$203$	0	0
$204$	0	0
$205$	1.93087	0.134858
$206$	−2.56155	−0.178472
$207$	1.00000	0.0695048
$208$	−0.561553	−0.0389367
$209$	1.75379	0.121312
$210$	0	0
$211$	−24.1771	−1.66442	−0.832209	−	0.554461i	$-0.812924\pi$
$211$	−24.1771	−1.66442	−0.832209	+	0.554461i	$0.812924\pi$
$212$	−12.2462	−0.841073
$213$	−14.5616	−0.997741
$214$	0	0
$215$	6.87689	0.469000
$216$	3.00000	0.204124
$217$	0	0
$218$	2.00000	0.135457
$219$	−3.12311	−0.211040
$220$	−0.315342	−0.0212603
$221$	0	0
$222$	−6.56155	−0.440383
$223$	4.49242	0.300835	0.150417	−	0.988623i	$-0.451938\pi$
$223$	4.49242	0.300835	0.150417	+	0.988623i	$0.451938\pi$
$224$	0	0
$225$	−4.68466	−0.312311
$226$	−11.3693	−0.756276
$227$	−4.63068	−0.307349	−0.153675	−	0.988122i	$-0.549111\pi$
$227$	−4.63068	−0.307349	−0.153675	+	0.988122i	$0.549111\pi$
$228$	3.12311	0.206833
$229$	20.8078	1.37502	0.687508	−	0.726177i	$-0.258705\pi$
$229$	20.8078	1.37502	0.687508	+	0.726177i	$0.258705\pi$
$230$	0.561553	0.0370277
$231$	0	0
$232$	3.00000	0.196960
$233$	0.876894	0.0574473	0.0287236	−	0.999587i	$-0.490856\pi$
$233$	0.876894	0.0574473	0.0287236	+	0.999587i	$0.490856\pi$
$234$	0.561553	0.0367099
$235$	−0.630683	−0.0411412
$236$	−5.43845	−0.354013
$237$	2.00000	0.129914
$238$	0	0
$239$	14.5616	0.941909	0.470954	−	0.882158i	$-0.343910\pi$
$239$	14.5616	0.941909	0.470954	+	0.882158i	$0.343910\pi$
$240$	0.561553	0.0362481
$241$	23.6155	1.52121	0.760605	−	0.649215i	$-0.224902\pi$
$241$	23.6155	1.52121	0.760605	+	0.649215i	$0.224902\pi$
$242$	−10.6847	−0.686836
$243$	−1.00000	−0.0641500
$244$	−8.80776	−0.563859
$245$	−3.93087	−0.251134
$246$	−3.43845	−0.219227
$247$	1.75379	0.111591
$248$	19.6847	1.24998
$249$	−1.12311	−0.0711739
$250$	−5.43845	−0.343958
$251$	−1.68466	−0.106335	−0.0531673	−	0.998586i	$-0.516932\pi$
$251$	−1.68466	−0.106335	−0.0531673	+	0.998586i	$0.516932\pi$
$252$	0	0
$253$	0.561553	0.0353045
$254$	−8.80776	−0.552648
$255$	0	0
$256$	−17.0000	−1.06250
$257$	12.2462	0.763898	0.381949	−	0.924183i	$-0.375253\pi$
$257$	12.2462	0.763898	0.381949	+	0.924183i	$0.375253\pi$
$258$	−12.2462	−0.762416
$259$	0	0
$260$	−0.315342	−0.0195567
$261$	−1.00000	−0.0618984
$262$	−4.00000	−0.247121
$263$	1.36932	0.0844357	0.0422178	−	0.999108i	$-0.486558\pi$
$263$	1.36932	0.0844357	0.0422178	+	0.999108i	$0.486558\pi$
$264$	1.68466	0.103684
$265$	6.87689	0.422444
$266$	0	0
$267$	7.36932	0.450995
$268$	−10.5616	−0.645150
$269$	23.9309	1.45909	0.729545	−	0.683932i	$-0.239732\pi$
$269$	23.9309	1.45909	0.729545	+	0.683932i	$0.239732\pi$
$270$	−0.561553	−0.0341750
$271$	−9.43845	−0.573345	−0.286672	−	0.958029i	$-0.592549\pi$
$271$	−9.43845	−0.573345	−0.286672	+	0.958029i	$0.592549\pi$
$272$	0	0
$273$	0	0
$274$	18.2462	1.10229
$275$	−2.63068	−0.158636
$276$	1.00000	0.0601929
$277$	−15.9309	−0.957193	−0.478597	−	0.878035i	$-0.658854\pi$
$277$	−15.9309	−0.957193	−0.478597	+	0.878035i	$0.658854\pi$
$278$	21.6155	1.29641
$279$	−6.56155	−0.392830
$280$	0	0
$281$	12.2462	0.730548	0.365274	−	0.930900i	$-0.380975\pi$
$281$	12.2462	0.730548	0.365274	+	0.930900i	$0.380975\pi$
$282$	1.12311	0.0668800
$283$	−11.6847	−0.694581	−0.347290	−	0.937758i	$-0.612898\pi$
$283$	−11.6847	−0.694581	−0.347290	+	0.937758i	$0.612898\pi$
$284$	−14.5616	−0.864069
$285$	−1.75379	−0.103885
$286$	0.315342	0.0186465
$287$	0	0
$288$	5.00000	0.294628
$289$	−17.0000	−1.00000
$290$	−0.561553	−0.0329755
$291$	−11.3693	−0.666481
$292$	−3.12311	−0.182766
$293$	−16.0000	−0.934730	−0.467365	−	0.884064i	$-0.654797\pi$
$293$	−16.0000	−0.934730	−0.467365	+	0.884064i	$0.654797\pi$
$294$	7.00000	0.408248
$295$	3.05398	0.177809
$296$	−19.6847	−1.14415
$297$	−0.561553	−0.0325846
$298$	11.9309	0.691137
$299$	0.561553	0.0324754
$300$	−4.68466	−0.270469
$301$	0	0
$302$	−10.2462	−0.589603
$303$	3.43845	0.197534
$304$	−3.12311	−0.179122
$305$	4.94602	0.283209
$306$	0	0
$307$	−19.6847	−1.12346	−0.561731	−	0.827320i	$-0.689865\pi$
$307$	−19.6847	−1.12346	−0.561731	+	0.827320i	$0.689865\pi$
$308$	0	0
$309$	2.56155	0.145722
$310$	−3.68466	−0.209275
$311$	25.1231	1.42460	0.712300	−	0.701875i	$-0.247653\pi$
$311$	25.1231	1.42460	0.712300	+	0.701875i	$0.247653\pi$
$312$	1.68466	0.0953750
$313$	−20.2462	−1.14438	−0.572192	−	0.820120i	$-0.693907\pi$
$313$	−20.2462	−1.14438	−0.572192	+	0.820120i	$0.693907\pi$
$314$	10.8769	0.613819
$315$	0	0
$316$	2.00000	0.112509
$317$	−19.9309	−1.11943	−0.559715	−	0.828685i	$-0.689089\pi$
$317$	−19.9309	−1.11943	−0.559715	+	0.828685i	$0.689089\pi$
$318$	−12.2462	−0.686733
$319$	−0.561553	−0.0314409
$320$	3.93087	0.219742
$321$	0	0
$322$	0	0
$323$	0	0
$324$	−1.00000	−0.0555556
$325$	−2.63068	−0.145924
$326$	1.43845	0.0796682
$327$	−2.00000	−0.110600
$328$	−10.3153	−0.569569
$329$	0	0
$330$	−0.315342	−0.0173590
$331$	20.0000	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$332$	−1.12311	−0.0616384
$333$	6.56155	0.359571
$334$	21.9309	1.20000
$335$	5.93087	0.324038
$336$	0	0
$337$	−3.19224	−0.173892	−0.0869461	−	0.996213i	$-0.527711\pi$
$337$	−3.19224	−0.173892	−0.0869461	+	0.996213i	$0.527711\pi$
$338$	−12.6847	−0.689954
$339$	11.3693	0.617497
$340$	0	0
$341$	−3.68466	−0.199535
$342$	3.12311	0.168878
$343$	0	0
$344$	−36.7386	−1.98081
$345$	−0.561553	−0.0302330
$346$	−22.4924	−1.20920
$347$	−8.49242	−0.455897	−0.227949	−	0.973673i	$-0.573202\pi$
$347$	−8.49242	−0.455897	−0.227949	+	0.973673i	$0.573202\pi$
$348$	−1.00000	−0.0536056
$349$	−31.3002	−1.67546	−0.837730	−	0.546084i	$-0.816118\pi$
$349$	−31.3002	−1.67546	−0.837730	+	0.546084i	$0.816118\pi$
$350$	0	0
$351$	−0.561553	−0.0299735
$352$	2.80776	0.149654
$353$	−22.4924	−1.19715	−0.598575	−	0.801066i	$-0.704266\pi$
$353$	−22.4924	−1.19715	−0.598575	+	0.801066i	$0.704266\pi$
$354$	−5.43845	−0.289050
$355$	8.17708	0.433994
$356$	7.36932	0.390573
$357$	0	0
$358$	16.4924	0.871652
$359$	3.12311	0.164831	0.0824156	−	0.996598i	$-0.473737\pi$
$359$	3.12311	0.164831	0.0824156	+	0.996598i	$0.473737\pi$
$360$	−1.68466	−0.0887893
$361$	−9.24621	−0.486643
$362$	−14.4924	−0.761705
$363$	10.6847	0.560799
$364$	0	0
$365$	1.75379	0.0917975
$366$	−8.80776	−0.460389
$367$	−24.7386	−1.29135	−0.645673	−	0.763614i	$-0.723423\pi$
$367$	−24.7386	−1.29135	−0.645673	+	0.763614i	$0.723423\pi$
$368$	−1.00000	−0.0521286
$369$	3.43845	0.178998
$370$	3.68466	0.191556
$371$	0	0
$372$	−6.56155	−0.340201
$373$	−30.4924	−1.57884	−0.789419	−	0.613855i	$-0.789618\pi$
$373$	−30.4924	−1.57884	−0.789419	+	0.613855i	$0.789618\pi$
$374$	0	0
$375$	5.43845	0.280840
$376$	3.36932	0.173759
$377$	−0.561553	−0.0289214
$378$	0	0
$379$	30.0000	1.54100	0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000	1.54100	0.770498	+	0.637442i	$0.220007\pi$
$380$	−1.75379	−0.0899675
$381$	8.80776	0.451235
$382$	−15.4384	−0.789900
$383$	17.1231	0.874950	0.437475	−	0.899231i	$-0.355873\pi$
$383$	17.1231	0.874950	0.437475	+	0.899231i	$0.355873\pi$
$384$	3.00000	0.153093
$385$	0	0
$386$	−15.1231	−0.769746
$387$	12.2462	0.622510
$388$	−11.3693	−0.577190
$389$	21.7538	1.10296	0.551480	−	0.834188i	$-0.314063\pi$
$389$	21.7538	1.10296	0.551480	+	0.834188i	$0.314063\pi$
$390$	−0.315342	−0.0159679
$391$	0	0
$392$	21.0000	1.06066
$393$	4.00000	0.201773
$394$	−4.24621	−0.213921
$395$	−1.12311	−0.0565096
$396$	−0.561553	−0.0282191
$397$	−32.2462	−1.61839	−0.809195	−	0.587540i	$-0.800097\pi$
$397$	−32.2462	−1.61839	−0.809195	+	0.587540i	$0.800097\pi$
$398$	15.6847	0.786201
$399$	0	0
$400$	4.68466	0.234233
$401$	−22.8078	−1.13897	−0.569483	−	0.822003i	$-0.692856\pi$
$401$	−22.8078	−1.13897	−0.569483	+	0.822003i	$0.692856\pi$
$402$	−10.5616	−0.526762
$403$	−3.68466	−0.183546
$404$	3.43845	0.171069
$405$	0.561553	0.0279038
$406$	0	0
$407$	3.68466	0.182642
$408$	0	0
$409$	3.75379	0.185613	0.0928065	−	0.995684i	$-0.470416\pi$
$409$	3.75379	0.185613	0.0928065	+	0.995684i	$0.470416\pi$
$410$	1.93087	0.0953589
$411$	−18.2462	−0.900019
$412$	2.56155	0.126199
$413$	0	0
$414$	1.00000	0.0491473
$415$	0.630683	0.0309590
$416$	2.80776	0.137662
$417$	−21.6155	−1.05852
$418$	1.75379	0.0857806
$419$	14.8769	0.726784	0.363392	−	0.931636i	$-0.381619\pi$
$419$	14.8769	0.726784	0.363392	+	0.931636i	$0.381619\pi$
$420$	0	0
$421$	−0.807764	−0.0393680	−0.0196840	−	0.999806i	$-0.506266\pi$
$421$	−0.807764	−0.0393680	−0.0196840	+	0.999806i	$0.506266\pi$
$422$	−24.1771	−1.17692
$423$	−1.12311	−0.0546073
$424$	−36.7386	−1.78419
$425$	0	0
$426$	−14.5616	−0.705510
$427$	0	0
$428$	0	0
$429$	−0.315342	−0.0152248
$430$	6.87689	0.331633
$431$	29.1231	1.40281	0.701405	−	0.712763i	$-0.252556\pi$
$431$	29.1231	1.40281	0.701405	+	0.712763i	$0.252556\pi$
$432$	1.00000	0.0481125
$433$	−29.1231	−1.39957	−0.699784	−	0.714355i	$-0.746720\pi$
$433$	−29.1231	−1.39957	−0.699784	+	0.714355i	$0.746720\pi$
$434$	0	0
$435$	0.561553	0.0269244
$436$	−2.00000	−0.0957826
$437$	3.12311	0.149398
$438$	−3.12311	−0.149228
$439$	−27.8617	−1.32977	−0.664884	−	0.746947i	$-0.731519\pi$
$439$	−27.8617	−1.32977	−0.664884	+	0.746947i	$0.731519\pi$
$440$	−0.946025	−0.0451000
$441$	−7.00000	−0.333333
$442$	0	0
$443$	13.1231	0.623498	0.311749	−	0.950165i	$-0.399085\pi$
$443$	13.1231	0.623498	0.311749	+	0.950165i	$0.399085\pi$
$444$	6.56155	0.311398
$445$	−4.13826	−0.196172
$446$	4.49242	0.212722
$447$	−11.9309	−0.564311
$448$	0	0
$449$	29.6847	1.40091	0.700453	−	0.713699i	$-0.252981\pi$
$449$	29.6847	1.40091	0.700453	+	0.713699i	$0.252981\pi$
$450$	−4.68466	−0.220837
$451$	1.93087	0.0909211
$452$	11.3693	0.534768
$453$	10.2462	0.481409
$454$	−4.63068	−0.217329
$455$	0	0
$456$	9.36932	0.438758
$457$	7.12311	0.333205	0.166602	−	0.986024i	$-0.446720\pi$
$457$	7.12311	0.333205	0.166602	+	0.986024i	$0.446720\pi$
$458$	20.8078	0.972283
$459$	0	0
$460$	−0.561553	−0.0261825
$461$	15.3002	0.712601	0.356300	−	0.934371i	$-0.384038\pi$
$461$	15.3002	0.712601	0.356300	+	0.934371i	$0.384038\pi$
$462$	0	0
$463$	−12.4924	−0.580572	−0.290286	−	0.956940i	$-0.593750\pi$
$463$	−12.4924	−0.580572	−0.290286	+	0.956940i	$0.593750\pi$
$464$	1.00000	0.0464238
$465$	3.68466	0.170872
$466$	0.876894	0.0406213
$467$	−36.4233	−1.68547	−0.842734	−	0.538329i	$-0.819056\pi$
$467$	−36.4233	−1.68547	−0.842734	+	0.538329i	$0.819056\pi$
$468$	−0.561553	−0.0259578
$469$	0	0
$470$	−0.630683	−0.0290912
$471$	−10.8769	−0.501181
$472$	−16.3153	−0.750974
$473$	6.87689	0.316200
$474$	2.00000	0.0918630
$475$	−14.6307	−0.671302
$476$	0	0
$477$	12.2462	0.560715
$478$	14.5616	0.666030
$479$	33.6847	1.53909	0.769546	−	0.638592i	$-0.220483\pi$
$479$	33.6847	1.53909	0.769546	+	0.638592i	$0.220483\pi$
$480$	−2.80776	−0.128156
$481$	3.68466	0.168006
$482$	23.6155	1.07566
$483$	0	0
$484$	10.6847	0.485666
$485$	6.38447	0.289904
$486$	−1.00000	−0.0453609
$487$	38.7386	1.75542	0.877708	−	0.479197i	$-0.159072\pi$
$487$	38.7386	1.75542	0.877708	+	0.479197i	$0.159072\pi$
$488$	−26.4233	−1.19613
$489$	−1.43845	−0.0650488
$490$	−3.93087	−0.177579
$491$	−27.3693	−1.23516	−0.617580	−	0.786508i	$-0.711887\pi$
$491$	−27.3693	−1.23516	−0.617580	+	0.786508i	$0.711887\pi$
$492$	3.43845	0.155017
$493$	0	0
$494$	1.75379	0.0789067
$495$	0.315342	0.0141735
$496$	6.56155	0.294622
$497$	0	0
$498$	−1.12311	−0.0503276
$499$	−19.3693	−0.867090	−0.433545	−	0.901132i	$-0.642737\pi$
$499$	−19.3693	−0.867090	−0.433545	+	0.901132i	$0.642737\pi$
$500$	5.43845	0.243215
$501$	−21.9309	−0.979799
$502$	−1.68466	−0.0751900
$503$	41.3693	1.84457	0.922283	−	0.386514i	$-0.126321\pi$
$503$	41.3693	1.84457	0.922283	+	0.386514i	$0.126321\pi$
$504$	0	0
$505$	−1.93087	−0.0859226
$506$	0.561553	0.0249641
$507$	12.6847	0.563345
$508$	8.80776	0.390781
$509$	−10.0000	−0.443242	−0.221621	−	0.975133i	$-0.571135\pi$
$509$	−10.0000	−0.443242	−0.221621	+	0.975133i	$0.571135\pi$
$510$	0	0
$511$	0	0
$512$	−11.0000	−0.486136
$513$	−3.12311	−0.137888
$514$	12.2462	0.540157
$515$	−1.43845	−0.0633856
$516$	12.2462	0.539109
$517$	−0.630683	−0.0277374
$518$	0	0
$519$	22.4924	0.987308
$520$	−0.946025	−0.0414859
$521$	−11.7538	−0.514943	−0.257471	−	0.966286i	$-0.582889\pi$
$521$	−11.7538	−0.514943	−0.257471	+	0.966286i	$0.582889\pi$
$522$	−1.00000	−0.0437688
$523$	12.8078	0.560044	0.280022	−	0.959994i	$-0.409658\pi$
$523$	12.8078	0.560044	0.280022	+	0.959994i	$0.409658\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	1.36932	0.0597051
$527$	0	0
$528$	0.561553	0.0244384
$529$	1.00000	0.0434783
$530$	6.87689	0.298713
$531$	5.43845	0.236009
$532$	0	0
$533$	1.93087	0.0836353
$534$	7.36932	0.318902
$535$	0	0
$536$	−31.6847	−1.36857
$537$	−16.4924	−0.711701
$538$	23.9309	1.03173
$539$	−3.93087	−0.169315
$540$	0.561553	0.0241654
$541$	12.2462	0.526506	0.263253	−	0.964727i	$-0.415205\pi$
$541$	12.2462	0.526506	0.263253	+	0.964727i	$0.415205\pi$
$542$	−9.43845	−0.405416
$543$	14.4924	0.621929
$544$	0	0
$545$	1.12311	0.0481086
$546$	0	0
$547$	25.7538	1.10115	0.550576	−	0.834785i	$-0.314408\pi$
$547$	25.7538	1.10115	0.550576	+	0.834785i	$0.314408\pi$
$548$	−18.2462	−0.779440
$549$	8.80776	0.375906
$550$	−2.63068	−0.112173
$551$	−3.12311	−0.133049
$552$	3.00000	0.127688
$553$	0	0
$554$	−15.9309	−0.676838
$555$	−3.68466	−0.156405
$556$	−21.6155	−0.916703
$557$	42.1771	1.78710	0.893550	−	0.448963i	$-0.148207\pi$
$557$	42.1771	1.78710	0.893550	+	0.448963i	$0.148207\pi$
$558$	−6.56155	−0.277773
$559$	6.87689	0.290862
$560$	0	0
$561$	0	0
$562$	12.2462	0.516575
$563$	43.9309	1.85147	0.925733	−	0.378178i	$-0.123449\pi$
$563$	43.9309	1.85147	0.925733	+	0.378178i	$0.123449\pi$
$564$	−1.12311	−0.0472913
$565$	−6.38447	−0.268597
$566$	−11.6847	−0.491143
$567$	0	0
$568$	−43.6847	−1.83297
$569$	18.7386	0.785564	0.392782	−	0.919632i	$-0.371513\pi$
$569$	18.7386	0.785564	0.392782	+	0.919632i	$0.371513\pi$
$570$	−1.75379	−0.0734581
$571$	32.1771	1.34657	0.673284	−	0.739384i	$-0.264883\pi$
$571$	32.1771	1.34657	0.673284	+	0.739384i	$0.264883\pi$
$572$	−0.315342	−0.0131851
$573$	15.4384	0.644950
$574$	0	0
$575$	−4.68466	−0.195364
$576$	7.00000	0.291667
$577$	3.12311	0.130017	0.0650083	−	0.997885i	$-0.479293\pi$
$577$	3.12311	0.130017	0.0650083	+	0.997885i	$0.479293\pi$
$578$	−17.0000	−0.707107
$579$	15.1231	0.628495
$580$	0.561553	0.0233172
$581$	0	0
$582$	−11.3693	−0.471273
$583$	6.87689	0.284812
$584$	−9.36932	−0.387705
$585$	0.315342	0.0130378
$586$	−16.0000	−0.660954
$587$	−47.2311	−1.94943	−0.974717	−	0.223442i	$-0.928271\pi$
$587$	−47.2311	−1.94943	−0.974717	+	0.223442i	$0.928271\pi$
$588$	−7.00000	−0.288675
$589$	−20.4924	−0.844376
$590$	3.05398	0.125730
$591$	4.24621	0.174666
$592$	−6.56155	−0.269678
$593$	29.3693	1.20605	0.603027	−	0.797721i	$-0.293961\pi$
$593$	29.3693	1.20605	0.603027	+	0.797721i	$0.293961\pi$
$594$	−0.561553	−0.0230408
$595$	0	0
$596$	−11.9309	−0.488707
$597$	−15.6847	−0.641930
$598$	0.561553	0.0229636
$599$	−44.9848	−1.83803	−0.919015	−	0.394221i	$-0.871014\pi$
$599$	−44.9848	−1.83803	−0.919015	+	0.394221i	$0.871014\pi$
$600$	−14.0540	−0.573751
$601$	−4.24621	−0.173207	−0.0866033	−	0.996243i	$-0.527601\pi$
$601$	−4.24621	−0.173207	−0.0866033	+	0.996243i	$0.527601\pi$
$602$	0	0
$603$	10.5616	0.430100
$604$	10.2462	0.416912
$605$	−6.00000	−0.243935
$606$	3.43845	0.139677
$607$	47.2311	1.91705	0.958525	−	0.285009i	$-0.0919967\pi$
$607$	47.2311	1.91705	0.958525	+	0.285009i	$0.0919967\pi$
$608$	15.6155	0.633293
$609$	0	0
$610$	4.94602	0.200259
$611$	−0.630683	−0.0255147
$612$	0	0
$613$	22.4924	0.908460	0.454230	−	0.890884i	$-0.349914\pi$
$613$	22.4924	0.908460	0.454230	+	0.890884i	$0.349914\pi$
$614$	−19.6847	−0.794408
$615$	−1.93087	−0.0778602
$616$	0	0
$617$	2.38447	0.0959952	0.0479976	−	0.998847i	$-0.484716\pi$
$617$	2.38447	0.0959952	0.0479976	+	0.998847i	$0.484716\pi$
$618$	2.56155	0.103041
$619$	8.24621	0.331443	0.165722	−	0.986173i	$-0.447005\pi$
$619$	8.24621	0.331443	0.165722	+	0.986173i	$0.447005\pi$
$620$	3.68466	0.147979
$621$	−1.00000	−0.0401286
$622$	25.1231	1.00734
$623$	0	0
$624$	0.561553	0.0224801
$625$	20.3693	0.814773
$626$	−20.2462	−0.809201
$627$	−1.75379	−0.0700396
$628$	−10.8769	−0.434035
$629$	0	0
$630$	0	0
$631$	34.5616	1.37587	0.687937	−	0.725771i	$-0.258517\pi$
$631$	34.5616	1.37587	0.687937	+	0.725771i	$0.258517\pi$
$632$	6.00000	0.238667
$633$	24.1771	0.960953
$634$	−19.9309	−0.791556
$635$	−4.94602	−0.196277
$636$	12.2462	0.485594
$637$	−3.93087	−0.155747
$638$	−0.561553	−0.0222321
$639$	14.5616	0.576046
$640$	−1.68466	−0.0665920
$641$	10.7386	0.424151	0.212075	−	0.977253i	$-0.431978\pi$
$641$	10.7386	0.424151	0.212075	+	0.977253i	$0.431978\pi$
$642$	0	0
$643$	−16.4924	−0.650398	−0.325199	−	0.945646i	$-0.605431\pi$
$643$	−16.4924	−0.650398	−0.325199	+	0.945646i	$0.605431\pi$
$644$	0	0
$645$	−6.87689	−0.270777
$646$	0	0
$647$	12.3153	0.484166	0.242083	−	0.970256i	$-0.422169\pi$
$647$	12.3153	0.484166	0.242083	+	0.970256i	$0.422169\pi$
$648$	−3.00000	−0.117851
$649$	3.05398	0.119879
$650$	−2.63068	−0.103184
$651$	0	0
$652$	−1.43845	−0.0563339
$653$	39.4384	1.54335	0.771673	−	0.636020i	$-0.219420\pi$
$653$	39.4384	1.54335	0.771673	+	0.636020i	$0.219420\pi$
$654$	−2.00000	−0.0782062
$655$	−2.24621	−0.0877667
$656$	−3.43845	−0.134249
$657$	3.12311	0.121844
$658$	0	0
$659$	24.8769	0.969066	0.484533	−	0.874773i	$-0.338990\pi$
$659$	24.8769	0.969066	0.484533	+	0.874773i	$0.338990\pi$
$660$	0.315342	0.0122747
$661$	−23.6155	−0.918538	−0.459269	−	0.888297i	$-0.651889\pi$
$661$	−23.6155	−0.918538	−0.459269	+	0.888297i	$0.651889\pi$
$662$	20.0000	0.777322
$663$	0	0
$664$	−3.36932	−0.130755
$665$	0	0
$666$	6.56155	0.254255
$667$	−1.00000	−0.0387202
$668$	−21.9309	−0.848531
$669$	−4.49242	−0.173687
$670$	5.93087	0.229129
$671$	4.94602	0.190939
$672$	0	0
$673$	−30.0000	−1.15642	−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000	−1.15642	−0.578208	+	0.815890i	$0.696248\pi$
$674$	−3.19224	−0.122960
$675$	4.68466	0.180313
$676$	12.6847	0.487871
$677$	−29.7538	−1.14353	−0.571765	−	0.820417i	$-0.693741\pi$
$677$	−29.7538	−1.14353	−0.571765	+	0.820417i	$0.693741\pi$
$678$	11.3693	0.436636
$679$	0	0
$680$	0	0
$681$	4.63068	0.177448
$682$	−3.68466	−0.141093
$683$	5.43845	0.208096	0.104048	−	0.994572i	$-0.466820\pi$
$683$	5.43845	0.208096	0.104048	+	0.994572i	$0.466820\pi$
$684$	−3.12311	−0.119415
$685$	10.2462	0.391488
$686$	0	0
$687$	−20.8078	−0.793866
$688$	−12.2462	−0.466882
$689$	6.87689	0.261989
$690$	−0.561553	−0.0213780
$691$	−50.1080	−1.90620	−0.953098	−	0.302661i	$-0.902125\pi$
$691$	−50.1080	−1.90620	−0.953098	+	0.302661i	$0.902125\pi$
$692$	22.4924	0.855034
$693$	0	0
$694$	−8.49242	−0.322368
$695$	12.1383	0.460430
$696$	−3.00000	−0.113715
$697$	0	0
$698$	−31.3002	−1.18473
$699$	−0.876894	−0.0331672
$700$	0	0
$701$	−21.0540	−0.795198	−0.397599	−	0.917559i	$-0.630156\pi$
$701$	−21.0540	−0.795198	−0.397599	+	0.917559i	$0.630156\pi$
$702$	−0.561553	−0.0211944
$703$	20.4924	0.772886
$704$	3.93087	0.148150
$705$	0.630683	0.0237529
$706$	−22.4924	−0.846513
$707$	0	0
$708$	5.43845	0.204389
$709$	−7.12311	−0.267514	−0.133757	−	0.991014i	$-0.542704\pi$
$709$	−7.12311	−0.267514	−0.133757	+	0.991014i	$0.542704\pi$
$710$	8.17708	0.306880
$711$	−2.00000	−0.0750059
$712$	22.1080	0.828530
$713$	−6.56155	−0.245732
$714$	0	0
$715$	0.177081	0.00662245
$716$	−16.4924	−0.616351
$717$	−14.5616	−0.543811
$718$	3.12311	0.116553
$719$	−13.3002	−0.496013	−0.248007	−	0.968758i	$-0.579775\pi$
$719$	−13.3002	−0.496013	−0.248007	+	0.968758i	$0.579775\pi$
$720$	−0.561553	−0.0209278
$721$	0	0
$722$	−9.24621	−0.344108
$723$	−23.6155	−0.878271
$724$	14.4924	0.538607
$725$	4.68466	0.173984
$726$	10.6847	0.396545
$727$	0.738634	0.0273944	0.0136972	−	0.999906i	$-0.495640\pi$
$727$	0.738634	0.0273944	0.0136972	+	0.999906i	$0.495640\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	1.75379	0.0649106
$731$	0	0
$732$	8.80776	0.325544
$733$	−29.4384	−1.08733	−0.543667	−	0.839301i	$-0.682965\pi$
$733$	−29.4384	−1.08733	−0.543667	+	0.839301i	$0.682965\pi$
$734$	−24.7386	−0.913120
$735$	3.93087	0.144992
$736$	5.00000	0.184302
$737$	5.93087	0.218466
$738$	3.43845	0.126571
$739$	39.5464	1.45474	0.727369	−	0.686247i	$-0.240743\pi$
$739$	39.5464	1.45474	0.727369	+	0.686247i	$0.240743\pi$
$740$	−3.68466	−0.135451
$741$	−1.75379	−0.0644270
$742$	0	0
$743$	31.3002	1.14829	0.574146	−	0.818753i	$-0.305334\pi$
$743$	31.3002	1.14829	0.574146	+	0.818753i	$0.305334\pi$
$744$	−19.6847	−0.721675
$745$	6.69981	0.245462
$746$	−30.4924	−1.11641
$747$	1.12311	0.0410923
$748$	0	0
$749$	0	0
$750$	5.43845	0.198584
$751$	−37.8617	−1.38159	−0.690797	−	0.723049i	$-0.742740\pi$
$751$	−37.8617	−1.38159	−0.690797	+	0.723049i	$0.742740\pi$
$752$	1.12311	0.0409554
$753$	1.68466	0.0613924
$754$	−0.561553	−0.0204505
$755$	−5.75379	−0.209402
$756$	0	0
$757$	8.31534	0.302226	0.151113	−	0.988516i	$-0.451714\pi$
$757$	8.31534	0.302226	0.151113	+	0.988516i	$0.451714\pi$
$758$	30.0000	1.08965
$759$	−0.561553	−0.0203831
$760$	−5.26137	−0.190850
$761$	46.9848	1.70320	0.851600	−	0.524193i	$-0.175633\pi$
$761$	46.9848	1.70320	0.851600	+	0.524193i	$0.175633\pi$
$762$	8.80776	0.319072
$763$	0	0
$764$	15.4384	0.558543
$765$	0	0
$766$	17.1231	0.618683
$767$	3.05398	0.110273
$768$	17.0000	0.613435
$769$	−1.43845	−0.0518717	−0.0259359	−	0.999664i	$-0.508257\pi$
$769$	−1.43845	−0.0518717	−0.0259359	+	0.999664i	$0.508257\pi$
$770$	0	0
$771$	−12.2462	−0.441037
$772$	15.1231	0.544292
$773$	−44.0000	−1.58257	−0.791285	−	0.611448i	$-0.790588\pi$
$773$	−44.0000	−1.58257	−0.791285	+	0.611448i	$0.790588\pi$
$774$	12.2462	0.440181
$775$	30.7386	1.10416
$776$	−34.1080	−1.22440
$777$	0	0
$778$	21.7538	0.779911
$779$	10.7386	0.384751
$780$	0.315342	0.0112910
$781$	8.17708	0.292599
$782$	0	0
$783$	1.00000	0.0357371
$784$	7.00000	0.250000
$785$	6.10795	0.218002
$786$	4.00000	0.142675
$787$	−55.0540	−1.96246	−0.981231	−	0.192835i	$-0.938232\pi$
$787$	−55.0540	−1.96246	−0.981231	+	0.192835i	$0.938232\pi$
$788$	4.24621	0.151265
$789$	−1.36932	−0.0487490
$790$	−1.12311	−0.0399583
$791$	0	0
$792$	−1.68466	−0.0598617
$793$	4.94602	0.175638
$794$	−32.2462	−1.14438
$795$	−6.87689	−0.243898
$796$	−15.6847	−0.555928
$797$	−42.1080	−1.49154	−0.745770	−	0.666203i	$-0.767918\pi$
$797$	−42.1080	−1.49154	−0.745770	+	0.666203i	$0.767918\pi$
$798$	0	0
$799$	0	0
$800$	−23.4233	−0.828138
$801$	−7.36932	−0.260382
$802$	−22.8078	−0.805370
$803$	1.75379	0.0618899
$804$	10.5616	0.372477
$805$	0	0
$806$	−3.68466	−0.129787
$807$	−23.9309	−0.842407
$808$	10.3153	0.362892
$809$	51.3002	1.80362	0.901809	−	0.432134i	$-0.142239\pi$
$809$	51.3002	1.80362	0.901809	+	0.432134i	$0.142239\pi$
$810$	0.561553	0.0197310
$811$	−1.75379	−0.0615839	−0.0307919	−	0.999526i	$-0.509803\pi$
$811$	−1.75379	−0.0615839	−0.0307919	+	0.999526i	$0.509803\pi$
$812$	0	0
$813$	9.43845	0.331021
$814$	3.68466	0.129147
$815$	0.807764	0.0282947
$816$	0	0
$817$	38.2462	1.33807
$818$	3.75379	0.131248
$819$	0	0
$820$	−1.93087	−0.0674289
$821$	−21.3693	−0.745794	−0.372897	−	0.927873i	$-0.621636\pi$
$821$	−21.3693	−0.745794	−0.372897	+	0.927873i	$0.621636\pi$
$822$	−18.2462	−0.636410
$823$	−25.3002	−0.881909	−0.440955	−	0.897529i	$-0.645360\pi$
$823$	−25.3002	−0.881909	−0.440955	+	0.897529i	$0.645360\pi$
$824$	7.68466	0.267708
$825$	2.63068	0.0915886
$826$	0	0
$827$	3.93087	0.136690	0.0683449	−	0.997662i	$-0.478228\pi$
$827$	3.93087	0.136690	0.0683449	+	0.997662i	$0.478228\pi$
$828$	−1.00000	−0.0347524
$829$	50.3542	1.74887	0.874436	−	0.485141i	$-0.161232\pi$
$829$	50.3542	1.74887	0.874436	+	0.485141i	$0.161232\pi$
$830$	0.630683	0.0218913
$831$	15.9309	0.552636
$832$	3.93087	0.136278
$833$	0	0
$834$	−21.6155	−0.748485
$835$	12.3153	0.426190
$836$	−1.75379	−0.0606561
$837$	6.56155	0.226800
$838$	14.8769	0.513914
$839$	29.1922	1.00783	0.503914	−	0.863754i	$-0.331893\pi$
$839$	29.1922	1.00783	0.503914	+	0.863754i	$0.331893\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−0.807764	−0.0278374
$843$	−12.2462	−0.421782
$844$	24.1771	0.832209
$845$	−7.12311	−0.245042
$846$	−1.12311	−0.0386132
$847$	0	0
$848$	−12.2462	−0.420537
$849$	11.6847	0.401016
$850$	0	0
$851$	6.56155	0.224927
$852$	14.5616	0.498871
$853$	5.36932	0.183842	0.0919210	−	0.995766i	$-0.470699\pi$
$853$	5.36932	0.183842	0.0919210	+	0.995766i	$0.470699\pi$
$854$	0	0
$855$	1.75379	0.0599783
$856$	0	0
$857$	32.2462	1.10151	0.550755	−	0.834667i	$-0.314340\pi$
$857$	32.2462	1.10151	0.550755	+	0.834667i	$0.314340\pi$
$858$	−0.315342	−0.0107656
$859$	−52.9848	−1.80782	−0.903910	−	0.427723i	$-0.859316\pi$
$859$	−52.9848	−1.80782	−0.903910	+	0.427723i	$0.859316\pi$
$860$	−6.87689	−0.234500
$861$	0	0
$862$	29.1231	0.991937
$863$	5.93087	0.201889	0.100945	−	0.994892i	$-0.467814\pi$
$863$	5.93087	0.201889	0.100945	+	0.994892i	$0.467814\pi$
$864$	−5.00000	−0.170103
$865$	−12.6307	−0.429456
$866$	−29.1231	−0.989643
$867$	17.0000	0.577350
$868$	0	0
$869$	−1.12311	−0.0380987
$870$	0.561553	0.0190384
$871$	5.93087	0.200960
$872$	−6.00000	−0.203186
$873$	11.3693	0.384793
$874$	3.12311	0.105641
$875$	0	0
$876$	3.12311	0.105520
$877$	−49.2311	−1.66241	−0.831207	−	0.555963i	$-0.812350\pi$
$877$	−49.2311	−1.66241	−0.831207	+	0.555963i	$0.812350\pi$
$878$	−27.8617	−0.940288
$879$	16.0000	0.539667
$880$	−0.315342	−0.0106302
$881$	−38.1080	−1.28389	−0.641945	−	0.766751i	$-0.721872\pi$
$881$	−38.1080	−1.28389	−0.641945	+	0.766751i	$0.721872\pi$
$882$	−7.00000	−0.235702
$883$	5.26137	0.177059	0.0885295	−	0.996074i	$-0.471783\pi$
$883$	5.26137	0.177059	0.0885295	+	0.996074i	$0.471783\pi$
$884$	0	0
$885$	−3.05398	−0.102658
$886$	13.1231	0.440879
$887$	−28.4924	−0.956682	−0.478341	−	0.878174i	$-0.658762\pi$
$887$	−28.4924	−0.956682	−0.478341	+	0.878174i	$0.658762\pi$
$888$	19.6847	0.660574
$889$	0	0
$890$	−4.13826	−0.138715
$891$	0.561553	0.0188127
$892$	−4.49242	−0.150417
$893$	−3.50758	−0.117377
$894$	−11.9309	−0.399028
$895$	9.26137	0.309573
$896$	0	0
$897$	−0.561553	−0.0187497
$898$	29.6847	0.990590
$899$	6.56155	0.218840
$900$	4.68466	0.156155
$901$	0	0
$902$	1.93087	0.0642909
$903$	0	0
$904$	34.1080	1.13441
$905$	−8.13826	−0.270525
$906$	10.2462	0.340408
$907$	2.00000	0.0664089	0.0332045	−	0.999449i	$-0.489429\pi$
$907$	2.00000	0.0664089	0.0332045	+	0.999449i	$0.489429\pi$
$908$	4.63068	0.153675
$909$	−3.43845	−0.114046
$910$	0	0
$911$	−41.6847	−1.38107	−0.690537	−	0.723297i	$-0.742626\pi$
$911$	−41.6847	−1.38107	−0.690537	+	0.723297i	$0.742626\pi$
$912$	3.12311	0.103416
$913$	0.630683	0.0208726
$914$	7.12311	0.235611
$915$	−4.94602	−0.163511
$916$	−20.8078	−0.687508
$917$	0	0
$918$	0	0
$919$	−8.80776	−0.290541	−0.145271	−	0.989392i	$-0.546405\pi$
$919$	−8.80776	−0.290541	−0.145271	+	0.989392i	$0.546405\pi$
$920$	−1.68466	−0.0555415
$921$	19.6847	0.648632
$922$	15.3002	0.503885
$923$	8.17708	0.269152
$924$	0	0
$925$	−30.7386	−1.01068
$926$	−12.4924	−0.410526
$927$	−2.56155	−0.0841324
$928$	−5.00000	−0.164133
$929$	14.0000	0.459325	0.229663	−	0.973270i	$-0.426238\pi$
$929$	14.0000	0.459325	0.229663	+	0.973270i	$0.426238\pi$
$930$	3.68466	0.120825
$931$	−21.8617	−0.716490
$932$	−0.876894	−0.0287236
$933$	−25.1231	−0.822494
$934$	−36.4233	−1.19181
$935$	0	0
$936$	−1.68466	−0.0550648
$937$	−46.9848	−1.53493	−0.767464	−	0.641092i	$-0.778482\pi$
$937$	−46.9848	−1.53493	−0.767464	+	0.641092i	$0.778482\pi$
$938$	0	0
$939$	20.2462	0.660710
$940$	0.630683	0.0205706
$941$	25.5464	0.832789	0.416394	−	0.909184i	$-0.363294\pi$
$941$	25.5464	0.832789	0.416394	+	0.909184i	$0.363294\pi$
$942$	−10.8769	−0.354388
$943$	3.43845	0.111971
$944$	−5.43845	−0.177006
$945$	0	0
$946$	6.87689	0.223587
$947$	49.4773	1.60780	0.803898	−	0.594768i	$-0.202756\pi$
$947$	49.4773	1.60780	0.803898	+	0.594768i	$0.202756\pi$
$948$	−2.00000	−0.0649570
$949$	1.75379	0.0569304
$950$	−14.6307	−0.474682
$951$	19.9309	0.646303
$952$	0	0
$953$	−38.9848	−1.26284	−0.631422	−	0.775440i	$-0.717528\pi$
$953$	−38.9848	−1.26284	−0.631422	+	0.775440i	$0.717528\pi$
$954$	12.2462	0.396486
$955$	−8.66950	−0.280539
$956$	−14.5616	−0.470954
$957$	0.561553	0.0181524
$958$	33.6847	1.08830
$959$	0	0
$960$	−3.93087	−0.126868
$961$	12.0540	0.388838
$962$	3.68466	0.118798
$963$	0	0
$964$	−23.6155	−0.760605
$965$	−8.49242	−0.273381
$966$	0	0
$967$	54.2462	1.74444	0.872220	−	0.489113i	$-0.162680\pi$
$967$	54.2462	1.74444	0.872220	+	0.489113i	$0.162680\pi$
$968$	32.0540	1.03025
$969$	0	0
$970$	6.38447	0.204993
$971$	−2.80776	−0.0901054	−0.0450527	−	0.998985i	$-0.514346\pi$
$971$	−2.80776	−0.0901054	−0.0450527	+	0.998985i	$0.514346\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	38.7386	1.24127
$975$	2.63068	0.0842493
$976$	−8.80776	−0.281930
$977$	30.1771	0.965450	0.482725	−	0.875772i	$-0.339647\pi$
$977$	30.1771	0.965450	0.482725	+	0.875772i	$0.339647\pi$
$978$	−1.43845	−0.0459965
$979$	−4.13826	−0.132259
$980$	3.93087	0.125567
$981$	2.00000	0.0638551
$982$	−27.3693	−0.873390
$983$	−3.43845	−0.109669	−0.0548347	−	0.998495i	$-0.517463\pi$
$983$	−3.43845	−0.109669	−0.0548347	+	0.998495i	$0.517463\pi$
$984$	10.3153	0.328841
$985$	−2.38447	−0.0759756
$986$	0	0
$987$	0	0
$988$	−1.75379	−0.0557955
$989$	12.2462	0.389407
$990$	0.315342	0.0100222
$991$	−44.4924	−1.41335	−0.706674	−	0.707539i	$-0.749805\pi$
$991$	−44.4924	−1.41335	−0.706674	+	0.707539i	$0.749805\pi$
$992$	−32.8078	−1.04165
$993$	−20.0000	−0.634681
$994$	0	0
$995$	8.80776	0.279225
$996$	1.12311	0.0355870
$997$	24.7386	0.783480	0.391740	−	0.920076i	$-0.371873\pi$
$997$	24.7386	0.783480	0.391740	+	0.920076i	$0.371873\pi$
$998$	−19.3693	−0.613125
$999$	−6.56155	−0.207598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.f.1.2	✓	2
3.2	odd	2		6003.2.a.d.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.f.1.2	✓	2	1.1	even	1	trivial
6003.2.a.d.1.1		2	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +0.561553 q^{5} -1.00000 q^{6} -3.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} -1.00000 q^{4} +0.561553 q^{5} -1.00000 q^{6} -3.00000 q^{8} +1.00000 q^{9} +0.561553 q^{10} +0.561553 q^{11} +1.00000 q^{12} +0.561553 q^{13} -0.561553 q^{15} -1.00000 q^{16} +1.00000 q^{18} +3.12311 q^{19} -0.561553 q^{20} +0.561553 q^{22} +1.00000 q^{23} +3.00000 q^{24} -4.68466 q^{25} +0.561553 q^{26} -1.00000 q^{27} -1.00000 q^{29} -0.561553 q^{30} -6.56155 q^{31} +5.00000 q^{32} -0.561553 q^{33} -1.00000 q^{36} +6.56155 q^{37} +3.12311 q^{38} -0.561553 q^{39} -1.68466 q^{40} +3.43845 q^{41} +12.2462 q^{43} -0.561553 q^{44} +0.561553 q^{45} +1.00000 q^{46} -1.12311 q^{47} +1.00000 q^{48} -7.00000 q^{49} -4.68466 q^{50} -0.561553 q^{52} +12.2462 q^{53} -1.00000 q^{54} +0.315342 q^{55} -3.12311 q^{57} -1.00000 q^{58} +5.43845 q^{59} +0.561553 q^{60} +8.80776 q^{61} -6.56155 q^{62} +7.00000 q^{64} +0.315342 q^{65} -0.561553 q^{66} +10.5616 q^{67} -1.00000 q^{69} +14.5616 q^{71} -3.00000 q^{72} +3.12311 q^{73} +6.56155 q^{74} +4.68466 q^{75} -3.12311 q^{76} -0.561553 q^{78} -2.00000 q^{79} -0.561553 q^{80} +1.00000 q^{81} +3.43845 q^{82} +1.12311 q^{83} +12.2462 q^{86} +1.00000 q^{87} -1.68466 q^{88} -7.36932 q^{89} +0.561553 q^{90} -1.00000 q^{92} +6.56155 q^{93} -1.12311 q^{94} +1.75379 q^{95} -5.00000 q^{96} +11.3693 q^{97} -7.00000 q^{98} +0.561553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} - 2 q^{4} - 3 q^{5} - 2 q^{6} - 6 q^{8} + 2 q^{9} - 3 q^{10} - 3 q^{11} + 2 q^{12} - 3 q^{13} + 3 q^{15} - 2 q^{16} + 2 q^{18} - 2 q^{19} + 3 q^{20} - 3 q^{22} + 2 q^{23} + 6 q^{24} + 3 q^{25} - 3 q^{26} - 2 q^{27} - 2 q^{29} + 3 q^{30} - 9 q^{31} + 10 q^{32} + 3 q^{33} - 2 q^{36} + 9 q^{37} - 2 q^{38} + 3 q^{39} + 9 q^{40} + 11 q^{41} + 8 q^{43} + 3 q^{44} - 3 q^{45} + 2 q^{46} + 6 q^{47} + 2 q^{48} - 14 q^{49} + 3 q^{50} + 3 q^{52} + 8 q^{53} - 2 q^{54} + 13 q^{55} + 2 q^{57} - 2 q^{58} + 15 q^{59} - 3 q^{60} - 3 q^{61} - 9 q^{62} + 14 q^{64} + 13 q^{65} + 3 q^{66} + 17 q^{67} - 2 q^{69} + 25 q^{71} - 6 q^{72} - 2 q^{73} + 9 q^{74} - 3 q^{75} + 2 q^{76} + 3 q^{78} - 4 q^{79} + 3 q^{80} + 2 q^{81} + 11 q^{82} - 6 q^{83} + 8 q^{86} + 2 q^{87} + 9 q^{88} + 10 q^{89} - 3 q^{90} - 2 q^{92} + 9 q^{93} + 6 q^{94} + 20 q^{95} - 10 q^{96} - 2 q^{97} - 14 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 - 2 * q^4 - 3 * q^5 - 2 * q^6 - 6 * q^8 + 2 * q^9 - 3 * q^10 - 3 * q^11 + 2 * q^12 - 3 * q^13 + 3 * q^15 - 2 * q^16 + 2 * q^18 - 2 * q^19 + 3 * q^20 - 3 * q^22 + 2 * q^23 + 6 * q^24 + 3 * q^25 - 3 * q^26 - 2 * q^27 - 2 * q^29 + 3 * q^30 - 9 * q^31 + 10 * q^32 + 3 * q^33 - 2 * q^36 + 9 * q^37 - 2 * q^38 + 3 * q^39 + 9 * q^40 + 11 * q^41 + 8 * q^43 + 3 * q^44 - 3 * q^45 + 2 * q^46 + 6 * q^47 + 2 * q^48 - 14 * q^49 + 3 * q^50 + 3 * q^52 + 8 * q^53 - 2 * q^54 + 13 * q^55 + 2 * q^57 - 2 * q^58 + 15 * q^59 - 3 * q^60 - 3 * q^61 - 9 * q^62 + 14 * q^64 + 13 * q^65 + 3 * q^66 + 17 * q^67 - 2 * q^69 + 25 * q^71 - 6 * q^72 - 2 * q^73 + 9 * q^74 - 3 * q^75 + 2 * q^76 + 3 * q^78 - 4 * q^79 + 3 * q^80 + 2 * q^81 + 11 * q^82 - 6 * q^83 + 8 * q^86 + 2 * q^87 + 9 * q^88 + 10 * q^89 - 3 * q^90 - 2 * q^92 + 9 * q^93 + 6 * q^94 + 20 * q^95 - 10 * q^96 - 2 * q^97 - 14 * q^98 - 3 * q^99

Introduction

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