LMFDB - Embedded newform 2842.2.a.t.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, 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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.974241.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 9x^{3} - 2x^{2} + 11x + 3 $ x^5 - x^4 - 9x^3 - 2x^2 + 11*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56579$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.23997 q^{3} +1.00000 q^{4} -2.71905 q^{5} +2.23997 q^{6} -1.00000 q^{8} +2.01749 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.23997 q^{3} +1.00000 q^{4} -2.71905 q^{5} +2.23997 q^{6} -1.00000 q^{8} +2.01749 q^{9} +2.71905 q^{10} +3.73654 q^{11} -2.23997 q^{12} -3.06235 q^{13} +6.09060 q^{15} +1.00000 q^{16} -5.82325 q^{17} -2.01749 q^{18} +1.54650 q^{19} -2.71905 q^{20} -3.73654 q^{22} +2.39504 q^{23} +2.23997 q^{24} +2.39324 q^{25} +3.06235 q^{26} +2.20081 q^{27} -1.00000 q^{29} -6.09060 q^{30} -3.41072 q^{31} -1.00000 q^{32} -8.36975 q^{33} +5.82325 q^{34} +2.01749 q^{36} +5.61572 q^{37} -1.54650 q^{38} +6.85959 q^{39} +2.71905 q^{40} +10.4429 q^{41} -4.28752 q^{43} +3.73654 q^{44} -5.48565 q^{45} -2.39504 q^{46} +6.28960 q^{47} -2.23997 q^{48} -2.39324 q^{50} +13.0439 q^{51} -3.06235 q^{52} -13.1511 q^{53} -2.20081 q^{54} -10.1598 q^{55} -3.46411 q^{57} +1.00000 q^{58} +13.6005 q^{59} +6.09060 q^{60} +7.29813 q^{61} +3.41072 q^{62} +1.00000 q^{64} +8.32669 q^{65} +8.36975 q^{66} +7.21410 q^{67} -5.82325 q^{68} -5.36483 q^{69} +1.10152 q^{71} -2.01749 q^{72} +11.6546 q^{73} -5.61572 q^{74} -5.36079 q^{75} +1.54650 q^{76} -6.85959 q^{78} +9.71233 q^{79} -2.71905 q^{80} -10.9822 q^{81} -10.4429 q^{82} -11.0457 q^{83} +15.8337 q^{85} +4.28752 q^{86} +2.23997 q^{87} -3.73654 q^{88} -16.1355 q^{89} +5.48565 q^{90} +2.39504 q^{92} +7.63993 q^{93} -6.28960 q^{94} -4.20500 q^{95} +2.23997 q^{96} -0.150581 q^{97} +7.53841 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9	$ 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 3 q^{12} - 8 q^{15} + 5 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} - q^{20} - 4 q^{22} + 9 q^{23} + 3 q^{24} - 9 q^{27} - 5 q^{29} + 8 q^{30} - 3 q^{31} - 5 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{36} + 10 q^{37} + 8 q^{38} - 26 q^{39} + q^{40} - 19 q^{41} + 3 q^{43} + 4 q^{44} + 14 q^{45} - 9 q^{46} - 36 q^{47} - 3 q^{48} + 31 q^{51} - 3 q^{53} + 9 q^{54} - 10 q^{55} - 18 q^{57} + 5 q^{58} + 5 q^{59} - 8 q^{60} - 3 q^{61} + 3 q^{62} + 5 q^{64} + 29 q^{65} + 7 q^{66} - 2 q^{67} - 10 q^{68} + 18 q^{69} + 2 q^{71} - 8 q^{72} + 2 q^{73} - 10 q^{74} - 22 q^{75} - 8 q^{76} + 26 q^{78} + 17 q^{79} - q^{80} - 7 q^{81} + 19 q^{82} - 30 q^{83} - 11 q^{85} - 3 q^{86} + 3 q^{87} - 4 q^{88} - 29 q^{89} - 14 q^{90} + 9 q^{92} + 37 q^{93} + 36 q^{94} - 17 q^{95} + 3 q^{96} + 40 q^{99}+O(q^{100}) $ 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 3 * q^12 - 8 * q^15 + 5 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 - q^20 - 4 * q^22 + 9 * q^23 + 3 * q^24 - 9 * q^27 - 5 * q^29 + 8 * q^30 - 3 * q^31 - 5 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^36 + 10 * q^37 + 8 * q^38 - 26 * q^39 + q^40 - 19 * q^41 + 3 * q^43 + 4 * q^44 + 14 * q^45 - 9 * q^46 - 36 * q^47 - 3 * q^48 + 31 * q^51 - 3 * q^53 + 9 * q^54 - 10 * q^55 - 18 * q^57 + 5 * q^58 + 5 * q^59 - 8 * q^60 - 3 * q^61 + 3 * q^62 + 5 * q^64 + 29 * q^65 + 7 * q^66 - 2 * q^67 - 10 * q^68 + 18 * q^69 + 2 * q^71 - 8 * q^72 + 2 * q^73 - 10 * q^74 - 22 * q^75 - 8 * q^76 + 26 * q^78 + 17 * q^79 - q^80 - 7 * q^81 + 19 * q^82 - 30 * q^83 - 11 * q^85 - 3 * q^86 + 3 * q^87 - 4 * q^88 - 29 * q^89 - 14 * q^90 + 9 * q^92 + 37 * q^93 + 36 * q^94 - 17 * q^95 + 3 * q^96 + 40 * 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
$2$	−1.00000	−0.707107
$3$	−2.23997	−1.29325	−0.646625	−	0.762808i	$-0.723820\pi$
$3$	−2.23997	−1.29325	−0.646625	+	0.762808i	$0.723820\pi$
$4$	1.00000	0.500000
$5$	−2.71905	−1.21600	−0.607998	−	0.793938i	$-0.708027\pi$
$5$	−2.71905	−1.21600	−0.607998	+	0.793938i	$0.708027\pi$
$6$	2.23997	0.914466
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	2.01749	0.672495
$10$	2.71905	0.859839
$11$	3.73654	1.12661	0.563304	−	0.826250i	$-0.309530\pi$
$11$	3.73654	1.12661	0.563304	+	0.826250i	$0.309530\pi$
$12$	−2.23997	−0.646625
$13$	−3.06235	−0.849343	−0.424672	−	0.905347i	$-0.639610\pi$
$13$	−3.06235	−0.849343	−0.424672	+	0.905347i	$0.639610\pi$
$14$	0	0
$15$	6.09060	1.57259
$16$	1.00000	0.250000
$17$	−5.82325	−1.41235	−0.706173	−	0.708040i	$-0.749580\pi$
$17$	−5.82325	−1.41235	−0.706173	+	0.708040i	$0.749580\pi$
$18$	−2.01749	−0.475526
$19$	1.54650	0.354791	0.177395	−	0.984140i	$-0.443233\pi$
$19$	1.54650	0.354791	0.177395	+	0.984140i	$0.443233\pi$
$20$	−2.71905	−0.607998
$21$	0	0
$22$	−3.73654	−0.796632
$23$	2.39504	0.499401	0.249700	−	0.968323i	$-0.419668\pi$
$23$	2.39504	0.499401	0.249700	+	0.968323i	$0.419668\pi$
$24$	2.23997	0.457233
$25$	2.39324	0.478647
$26$	3.06235	0.600577
$27$	2.20081	0.423545
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−6.09060	−1.11199
$31$	−3.41072	−0.612584	−0.306292	−	0.951938i	$-0.599088\pi$
$31$	−3.41072	−0.612584	−0.306292	+	0.951938i	$0.599088\pi$
$32$	−1.00000	−0.176777
$33$	−8.36975	−1.45699
$34$	5.82325	0.998679
$35$	0	0
$36$	2.01749	0.336248
$37$	5.61572	0.923219	0.461610	−	0.887083i	$-0.347272\pi$
$37$	5.61572	0.923219	0.461610	+	0.887083i	$0.347272\pi$
$38$	−1.54650	−0.250875
$39$	6.85959	1.09841
$40$	2.71905	0.429920
$41$	10.4429	1.63090	0.815451	−	0.578826i	$-0.196489\pi$
$41$	10.4429	1.63090	0.815451	+	0.578826i	$0.196489\pi$
$42$	0	0
$43$	−4.28752	−0.653841	−0.326920	−	0.945052i	$-0.606011\pi$
$43$	−4.28752	−0.653841	−0.326920	+	0.945052i	$0.606011\pi$
$44$	3.73654	0.563304
$45$	−5.48565	−0.817752
$46$	−2.39504	−0.353130
$47$	6.28960	0.917433	0.458716	−	0.888583i	$-0.348309\pi$
$47$	6.28960	0.917433	0.458716	+	0.888583i	$0.348309\pi$
$48$	−2.23997	−0.323312
$49$	0	0
$50$	−2.39324	−0.338455
$51$	13.0439	1.82652
$52$	−3.06235	−0.424672
$53$	−13.1511	−1.80645	−0.903225	−	0.429168i	$-0.858807\pi$
$53$	−13.1511	−1.80645	−0.903225	+	0.429168i	$0.858807\pi$
$54$	−2.20081	−0.299492
$55$	−10.1598	−1.36995
$56$	0	0
$57$	−3.46411	−0.458833
$58$	1.00000	0.131306
$59$	13.6005	1.77063	0.885314	−	0.464993i	$-0.153943\pi$
$59$	13.6005	1.77063	0.885314	+	0.464993i	$0.153943\pi$
$60$	6.09060	0.786294
$61$	7.29813	0.934430	0.467215	−	0.884144i	$-0.345257\pi$
$61$	7.29813	0.934430	0.467215	+	0.884144i	$0.345257\pi$
$62$	3.41072	0.433162
$63$	0	0
$64$	1.00000	0.125000
$65$	8.32669	1.03280
$66$	8.36975	1.03024
$67$	7.21410	0.881342	0.440671	−	0.897669i	$-0.354741\pi$
$67$	7.21410	0.881342	0.440671	+	0.897669i	$0.354741\pi$
$68$	−5.82325	−0.706173
$69$	−5.36483	−0.645850
$70$	0	0
$71$	1.10152	0.130726	0.0653632	−	0.997862i	$-0.479179\pi$
$71$	1.10152	0.130726	0.0653632	+	0.997862i	$0.479179\pi$
$72$	−2.01749	−0.237763
$73$	11.6546	1.36407	0.682033	−	0.731321i	$-0.261096\pi$
$73$	11.6546	1.36407	0.682033	+	0.731321i	$0.261096\pi$
$74$	−5.61572	−0.652815
$75$	−5.36079	−0.619010
$76$	1.54650	0.177395
$77$	0	0
$78$	−6.85959	−0.776696
$79$	9.71233	1.09272	0.546361	−	0.837550i	$-0.316013\pi$
$79$	9.71233	1.09272	0.546361	+	0.837550i	$0.316013\pi$
$80$	−2.71905	−0.303999
$81$	−10.9822	−1.22025
$82$	−10.4429	−1.15322
$83$	−11.0457	−1.21243	−0.606214	−	0.795302i	$-0.707312\pi$
$83$	−11.0457	−1.21243	−0.606214	+	0.795302i	$0.707312\pi$
$84$	0	0
$85$	15.8337	1.71741
$86$	4.28752	0.462335
$87$	2.23997	0.240150
$88$	−3.73654	−0.398316
$89$	−16.1355	−1.71036	−0.855178	−	0.518334i	$-0.826552\pi$
$89$	−16.1355	−1.71036	−0.855178	+	0.518334i	$0.826552\pi$
$90$	5.48565	0.578238
$91$	0	0
$92$	2.39504	0.249700
$93$	7.63993	0.792224
$94$	−6.28960	−0.648723
$95$	−4.20500	−0.431424
$96$	2.23997	0.228616
$97$	−0.150581	−0.0152892	−0.00764460	−	0.999971i	$-0.502433\pi$
$97$	−0.150581	−0.0152892	−0.00764460	+	0.999971i	$0.502433\pi$
$98$	0	0
$99$	7.53841	0.757639
$100$	2.39324	0.239324
$101$	−7.95231	−0.791284	−0.395642	−	0.918405i	$-0.629478\pi$
$101$	−7.95231	−0.791284	−0.395642	+	0.918405i	$0.629478\pi$
$102$	−13.0439	−1.29154
$103$	5.82506	0.573960	0.286980	−	0.957937i	$-0.407349\pi$
$103$	5.82506	0.573960	0.286980	+	0.957937i	$0.407349\pi$
$104$	3.06235	0.300288
$105$	0	0
$106$	13.1511	1.27735
$107$	3.36079	0.324900	0.162450	−	0.986717i	$-0.448060\pi$
$107$	3.36079	0.324900	0.162450	+	0.986717i	$0.448060\pi$
$108$	2.20081	0.211773
$109$	11.3664	1.08871	0.544353	−	0.838856i	$-0.316775\pi$
$109$	11.3664	1.08871	0.544353	+	0.838856i	$0.316775\pi$
$110$	10.1598	0.968702
$111$	−12.5791	−1.19395
$112$	0	0
$113$	−7.69288	−0.723685	−0.361843	−	0.932239i	$-0.617852\pi$
$113$	−7.69288	−0.723685	−0.361843	+	0.932239i	$0.617852\pi$
$114$	3.46411	0.324444
$115$	−6.51224	−0.607270
$116$	−1.00000	−0.0928477
$117$	−6.17825	−0.571180
$118$	−13.6005	−1.25202
$119$	0	0
$120$	−6.09060	−0.555994
$121$	2.96170	0.269246
$122$	−7.29813	−0.660742
$123$	−23.3918	−2.10916
$124$	−3.41072	−0.306292
$125$	7.08792	0.633963
$126$	0	0
$127$	1.77872	0.157836	0.0789180	−	0.996881i	$-0.474853\pi$
$127$	1.77872	0.157836	0.0789180	+	0.996881i	$0.474853\pi$
$128$	−1.00000	−0.0883883
$129$	9.60394	0.845579
$130$	−8.32669	−0.730299
$131$	−19.3237	−1.68832	−0.844160	−	0.536092i	$-0.819900\pi$
$131$	−19.3237	−1.68832	−0.844160	+	0.536092i	$0.819900\pi$
$132$	−8.36975	−0.728493
$133$	0	0
$134$	−7.21410	−0.623203
$135$	−5.98410	−0.515030
$136$	5.82325	0.499340
$137$	−14.8982	−1.27284	−0.636418	−	0.771344i	$-0.719585\pi$
$137$	−14.8982	−1.27284	−0.636418	+	0.771344i	$0.719585\pi$
$138$	5.36483	0.456685
$139$	−4.77586	−0.405083	−0.202542	−	0.979274i	$-0.564920\pi$
$139$	−4.77586	−0.405083	−0.202542	+	0.979274i	$0.564920\pi$
$140$	0	0
$141$	−14.0886	−1.18647
$142$	−1.10152	−0.0924375
$143$	−11.4426	−0.956877
$144$	2.01749	0.168124
$145$	2.71905	0.225805
$146$	−11.6546	−0.964540
$147$	0	0
$148$	5.61572	0.461610
$149$	−2.76660	−0.226648	−0.113324	−	0.993558i	$-0.536150\pi$
$149$	−2.76660	−0.226648	−0.113324	+	0.993558i	$0.536150\pi$
$150$	5.36079	0.437706
$151$	0.545624	0.0444022	0.0222011	−	0.999754i	$-0.492933\pi$
$151$	0.545624	0.0444022	0.0222011	+	0.999754i	$0.492933\pi$
$152$	−1.54650	−0.125437
$153$	−11.7483	−0.949796
$154$	0	0
$155$	9.27392	0.744900
$156$	6.85959	0.549207
$157$	6.51542	0.519987	0.259993	−	0.965610i	$-0.416280\pi$
$157$	6.51542	0.519987	0.259993	+	0.965610i	$0.416280\pi$
$158$	−9.71233	−0.772672
$159$	29.4582	2.33619
$160$	2.71905	0.214960
$161$	0	0
$162$	10.9822	0.862844
$163$	−17.9840	−1.40861	−0.704306	−	0.709896i	$-0.748742\pi$
$163$	−17.9840	−1.40861	−0.704306	+	0.709896i	$0.748742\pi$
$164$	10.4429	0.815451
$165$	22.7578	1.77169
$166$	11.0457	0.857316
$167$	3.54619	0.274412	0.137206	−	0.990543i	$-0.456188\pi$
$167$	3.54619	0.274412	0.137206	+	0.990543i	$0.456188\pi$
$168$	0	0
$169$	−3.62200	−0.278616
$170$	−15.8337	−1.21439
$171$	3.12004	0.238595
$172$	−4.28752	−0.326920
$173$	−13.9940	−1.06394	−0.531972	−	0.846762i	$-0.678549\pi$
$173$	−13.9940	−1.06394	−0.531972	+	0.846762i	$0.678549\pi$
$174$	−2.23997	−0.169812
$175$	0	0
$176$	3.73654	0.281652
$177$	−30.4647	−2.28987
$178$	16.1355	1.20940
$179$	−9.07370	−0.678200	−0.339100	−	0.940750i	$-0.610123\pi$
$179$	−9.07370	−0.678200	−0.339100	+	0.940750i	$0.610123\pi$
$180$	−5.48565	−0.408876
$181$	6.40263	0.475904	0.237952	−	0.971277i	$-0.423524\pi$
$181$	6.40263	0.475904	0.237952	+	0.971277i	$0.423524\pi$
$182$	0	0
$183$	−16.3476	−1.20845
$184$	−2.39504	−0.176565
$185$	−15.2694	−1.12263
$186$	−7.63993	−0.560187
$187$	−21.7588	−1.59116
$188$	6.28960	0.458716
$189$	0	0
$190$	4.20500	0.305063
$191$	5.69469	0.412053	0.206027	−	0.978546i	$-0.433947\pi$
$191$	5.69469	0.412053	0.206027	+	0.978546i	$0.433947\pi$
$192$	−2.23997	−0.161656
$193$	13.2457	0.953444	0.476722	−	0.879054i	$-0.341825\pi$
$193$	13.2457	0.953444	0.476722	+	0.879054i	$0.341825\pi$
$194$	0.150581	0.0108111
$195$	−18.6516	−1.33567
$196$	0	0
$197$	−21.4736	−1.52993	−0.764967	−	0.644070i	$-0.777245\pi$
$197$	−21.4736	−1.52993	−0.764967	+	0.644070i	$0.777245\pi$
$198$	−7.53841	−0.535731
$199$	16.4049	1.16291	0.581455	−	0.813578i	$-0.302483\pi$
$199$	16.4049	1.16291	0.581455	+	0.813578i	$0.302483\pi$
$200$	−2.39324	−0.169227
$201$	−16.1594	−1.13980
$202$	7.95231	0.559522
$203$	0	0
$204$	13.0439	0.913258
$205$	−28.3947	−1.98317
$206$	−5.82506	−0.405851
$207$	4.83196	0.335845
$208$	−3.06235	−0.212336
$209$	5.77854	0.399710
$210$	0	0
$211$	−4.59793	−0.316535	−0.158267	−	0.987396i	$-0.550591\pi$
$211$	−4.59793	−0.316535	−0.158267	+	0.987396i	$0.550591\pi$
$212$	−13.1511	−0.903225
$213$	−2.46738	−0.169062
$214$	−3.36079	−0.229739
$215$	11.6580	0.795068
$216$	−2.20081	−0.149746
$217$	0	0
$218$	−11.3664	−0.769831
$219$	−26.1060	−1.76408
$220$	−10.1598	−0.684976
$221$	17.8328	1.19957
$222$	12.5791	0.844253
$223$	−10.9821	−0.735414	−0.367707	−	0.929942i	$-0.619857\pi$
$223$	−10.9821	−0.735414	−0.367707	+	0.929942i	$0.619857\pi$
$224$	0	0
$225$	4.82832	0.321888
$226$	7.69288	0.511723
$227$	−19.3050	−1.28132	−0.640659	−	0.767825i	$-0.721339\pi$
$227$	−19.3050	−1.28132	−0.640659	+	0.767825i	$0.721339\pi$
$228$	−3.46411	−0.229417
$229$	−16.3205	−1.07849	−0.539246	−	0.842148i	$-0.681291\pi$
$229$	−16.3205	−1.07849	−0.539246	+	0.842148i	$0.681291\pi$
$230$	6.51224	0.429404
$231$	0	0
$232$	1.00000	0.0656532
$233$	25.7283	1.68552	0.842758	−	0.538293i	$-0.180931\pi$
$233$	25.7283	1.68552	0.842758	+	0.538293i	$0.180931\pi$
$234$	6.17825	0.403885
$235$	−17.1017	−1.11560
$236$	13.6005	0.885314
$237$	−21.7554	−1.41316
$238$	0	0
$239$	−6.65670	−0.430586	−0.215293	−	0.976549i	$-0.569071\pi$
$239$	−6.65670	−0.430586	−0.215293	+	0.976549i	$0.569071\pi$
$240$	6.09060	0.393147
$241$	22.4835	1.44829	0.724146	−	0.689647i	$-0.242234\pi$
$241$	22.4835	1.44829	0.724146	+	0.689647i	$0.242234\pi$
$242$	−2.96170	−0.190386
$243$	17.9974	1.15454
$244$	7.29813	0.467215
$245$	0	0
$246$	23.3918	1.49140
$247$	−4.73592	−0.301339
$248$	3.41072	0.216581
$249$	24.7422	1.56797
$250$	−7.08792	−0.448280
$251$	−15.5233	−0.979822	−0.489911	−	0.871772i	$-0.662971\pi$
$251$	−15.5233	−0.979822	−0.489911	+	0.871772i	$0.662971\pi$
$252$	0	0
$253$	8.94916	0.562629
$254$	−1.77872	−0.111607
$255$	−35.4671	−2.22104
$256$	1.00000	0.0625000
$257$	−9.90087	−0.617599	−0.308800	−	0.951127i	$-0.599927\pi$
$257$	−9.90087	−0.617599	−0.308800	+	0.951127i	$0.599927\pi$
$258$	−9.60394	−0.597915
$259$	0	0
$260$	8.32669	0.516399
$261$	−2.01749	−0.124879
$262$	19.3237	1.19382
$263$	−15.5973	−0.961770	−0.480885	−	0.876784i	$-0.659685\pi$
$263$	−15.5973	−0.961770	−0.480885	+	0.876784i	$0.659685\pi$
$264$	8.36975	0.515122
$265$	35.7586	2.19664
$266$	0	0
$267$	36.1430	2.21192
$268$	7.21410	0.440671
$269$	−23.6586	−1.44249	−0.721246	−	0.692679i	$-0.756430\pi$
$269$	−23.6586	−1.44249	−0.721246	+	0.692679i	$0.756430\pi$
$270$	5.98410	0.364181
$271$	4.38281	0.266237	0.133118	−	0.991100i	$-0.457501\pi$
$271$	4.38281	0.266237	0.133118	+	0.991100i	$0.457501\pi$
$272$	−5.82325	−0.353086
$273$	0	0
$274$	14.8982	0.900032
$275$	8.94241	0.539248
$276$	−5.36483	−0.322925
$277$	−19.9768	−1.20029	−0.600144	−	0.799892i	$-0.704890\pi$
$277$	−19.9768	−1.20029	−0.600144	+	0.799892i	$0.704890\pi$
$278$	4.77586	0.286437
$279$	−6.88108	−0.411960
$280$	0	0
$281$	23.8812	1.42464	0.712318	−	0.701857i	$-0.247646\pi$
$281$	23.8812	1.42464	0.712318	+	0.701857i	$0.247646\pi$
$282$	14.0886	0.838961
$283$	−8.09033	−0.480920	−0.240460	−	0.970659i	$-0.577298\pi$
$283$	−8.09033	−0.480920	−0.240460	+	0.970659i	$0.577298\pi$
$284$	1.10152	0.0653632
$285$	9.41910	0.557939
$286$	11.4426	0.676614
$287$	0	0
$288$	−2.01749	−0.118882
$289$	16.9102	0.994720
$290$	−2.71905	−0.159668
$291$	0.337298	0.0197728
$292$	11.6546	0.682033
$293$	27.1934	1.58866	0.794328	−	0.607489i	$-0.207823\pi$
$293$	27.1934	1.58866	0.794328	+	0.607489i	$0.207823\pi$
$294$	0	0
$295$	−36.9803	−2.15308
$296$	−5.61572	−0.326407
$297$	8.22339	0.477170
$298$	2.76660	0.160265
$299$	−7.33446	−0.424163
$300$	−5.36079	−0.309505
$301$	0	0
$302$	−0.545624	−0.0313971
$303$	17.8130	1.02333
$304$	1.54650	0.0886977
$305$	−19.8440	−1.13626
$306$	11.7483	0.671607
$307$	−23.3267	−1.33133	−0.665663	−	0.746252i	$-0.731851\pi$
$307$	−23.3267	−1.33133	−0.665663	+	0.746252i	$0.731851\pi$
$308$	0	0
$309$	−13.0480	−0.742274
$310$	−9.27392	−0.526724
$311$	−8.08033	−0.458194	−0.229097	−	0.973404i	$-0.573577\pi$
$311$	−8.08033	−0.458194	−0.229097	+	0.973404i	$0.573577\pi$
$312$	−6.85959	−0.388348
$313$	2.88845	0.163265	0.0816325	−	0.996662i	$-0.473987\pi$
$313$	2.88845	0.163265	0.0816325	+	0.996662i	$0.473987\pi$
$314$	−6.51542	−0.367686
$315$	0	0
$316$	9.71233	0.546361
$317$	15.7422	0.884169	0.442084	−	0.896974i	$-0.354239\pi$
$317$	15.7422	0.884169	0.442084	+	0.896974i	$0.354239\pi$
$318$	−29.4582	−1.65194
$319$	−3.73654	−0.209206
$320$	−2.71905	−0.152000
$321$	−7.52808	−0.420176
$322$	0	0
$323$	−9.00564	−0.501087
$324$	−10.9822	−0.610123
$325$	−7.32893	−0.406536
$326$	17.9840	0.996039
$327$	−25.4605	−1.40797
$328$	−10.4429	−0.576611
$329$	0	0
$330$	−22.7578	−1.25277
$331$	−26.5752	−1.46070	−0.730351	−	0.683072i	$-0.760644\pi$
$331$	−26.5752	−1.46070	−0.730351	+	0.683072i	$0.760644\pi$
$332$	−11.0457	−0.606214
$333$	11.3296	0.620861
$334$	−3.54619	−0.194039
$335$	−19.6155	−1.07171
$336$	0	0
$337$	−9.93373	−0.541125	−0.270562	−	0.962702i	$-0.587210\pi$
$337$	−9.93373	−0.541125	−0.270562	+	0.962702i	$0.587210\pi$
$338$	3.62200	0.197011
$339$	17.2319	0.935906
$340$	15.8337	0.858704
$341$	−12.7443	−0.690142
$342$	−3.12004	−0.168712
$343$	0	0
$344$	4.28752	0.231168
$345$	14.5873	0.785351
$346$	13.9940	0.752322
$347$	23.2676	1.24907	0.624536	−	0.780996i	$-0.285288\pi$
$347$	23.2676	1.24907	0.624536	+	0.780996i	$0.285288\pi$
$348$	2.23997	0.120075
$349$	8.50775	0.455410	0.227705	−	0.973730i	$-0.426878\pi$
$349$	8.50775	0.455410	0.227705	+	0.973730i	$0.426878\pi$
$350$	0	0
$351$	−6.73964	−0.359735
$352$	−3.73654	−0.199158
$353$	−12.6307	−0.672264	−0.336132	−	0.941815i	$-0.609119\pi$
$353$	−12.6307	−0.672264	−0.336132	+	0.941815i	$0.609119\pi$
$354$	30.4647	1.61918
$355$	−2.99509	−0.158963
$356$	−16.1355	−0.855178
$357$	0	0
$358$	9.07370	0.479560
$359$	3.07392	0.162235	0.0811176	−	0.996705i	$-0.474151\pi$
$359$	3.07392	0.162235	0.0811176	+	0.996705i	$0.474151\pi$
$360$	5.48565	0.289119
$361$	−16.6083	−0.874124
$362$	−6.40263	−0.336515
$363$	−6.63414	−0.348202
$364$	0	0
$365$	−31.6894	−1.65870
$366$	16.3476	0.854504
$367$	−15.8201	−0.825804	−0.412902	−	0.910775i	$-0.635485\pi$
$367$	−15.8201	−0.825804	−0.412902	+	0.910775i	$0.635485\pi$
$368$	2.39504	0.124850
$369$	21.0683	1.09677
$370$	15.2694	0.793820
$371$	0	0
$372$	7.63993	0.396112
$373$	−31.8524	−1.64926	−0.824628	−	0.565676i	$-0.808615\pi$
$373$	−31.8524	−1.64926	−0.824628	+	0.565676i	$0.808615\pi$
$374$	21.7588	1.12512
$375$	−15.8768	−0.819873
$376$	−6.28960	−0.324362
$377$	3.06235	0.157719
$378$	0	0
$379$	−6.27914	−0.322538	−0.161269	−	0.986910i	$-0.551559\pi$
$379$	−6.27914	−0.322538	−0.161269	+	0.986910i	$0.551559\pi$
$380$	−4.20500	−0.215712
$381$	−3.98429	−0.204121
$382$	−5.69469	−0.291366
$383$	−11.1323	−0.568835	−0.284417	−	0.958701i	$-0.591800\pi$
$383$	−11.1323	−0.568835	−0.284417	+	0.958701i	$0.591800\pi$
$384$	2.23997	0.114308
$385$	0	0
$386$	−13.2457	−0.674187
$387$	−8.65001	−0.439705
$388$	−0.150581	−0.00764460
$389$	16.0578	0.814162	0.407081	−	0.913392i	$-0.366547\pi$
$389$	16.0578	0.814162	0.407081	+	0.913392i	$0.366547\pi$
$390$	18.6516	0.944459
$391$	−13.9469	−0.705327
$392$	0	0
$393$	43.2846	2.18342
$394$	21.4736	1.08183
$395$	−26.4083	−1.32875
$396$	7.53841	0.378819
$397$	19.8183	0.994652	0.497326	−	0.867564i	$-0.334315\pi$
$397$	19.8183	0.994652	0.497326	+	0.867564i	$0.334315\pi$
$398$	−16.4049	−0.822302
$399$	0	0
$400$	2.39324	0.119662
$401$	−24.9435	−1.24562	−0.622809	−	0.782374i	$-0.714008\pi$
$401$	−24.9435	−1.24562	−0.622809	+	0.782374i	$0.714008\pi$
$402$	16.1594	0.805957
$403$	10.4448	0.520294
$404$	−7.95231	−0.395642
$405$	29.8612	1.48381
$406$	0	0
$407$	20.9834	1.04011
$408$	−13.0439	−0.645771
$409$	−1.38964	−0.0687131	−0.0343565	−	0.999410i	$-0.510938\pi$
$409$	−1.38964	−0.0687131	−0.0343565	+	0.999410i	$0.510938\pi$
$410$	28.3947	1.40231
$411$	33.3715	1.64610
$412$	5.82506	0.286980
$413$	0	0
$414$	−4.83196	−0.237478
$415$	30.0339	1.47431
$416$	3.06235	0.150144
$417$	10.6978	0.523874
$418$	−5.77854	−0.282638
$419$	−32.6594	−1.59551	−0.797757	−	0.602979i	$-0.793980\pi$
$419$	−32.6594	−1.59551	−0.797757	+	0.602979i	$0.793980\pi$
$420$	0	0
$421$	−7.73040	−0.376757	−0.188378	−	0.982097i	$-0.560323\pi$
$421$	−7.73040	−0.376757	−0.188378	+	0.982097i	$0.560323\pi$
$422$	4.59793	0.223824
$423$	12.6892	0.616969
$424$	13.1511	0.638676
$425$	−13.9364	−0.676015
$426$	2.46738	0.119545
$427$	0	0
$428$	3.36079	0.162450
$429$	25.6311	1.23748
$430$	−11.6580	−0.562198
$431$	−11.1194	−0.535605	−0.267802	−	0.963474i	$-0.586297\pi$
$431$	−11.1194	−0.535605	−0.267802	+	0.963474i	$0.586297\pi$
$432$	2.20081	0.105886
$433$	38.4668	1.84860	0.924298	−	0.381672i	$-0.124652\pi$
$433$	38.4668	1.84860	0.924298	+	0.381672i	$0.124652\pi$
$434$	0	0
$435$	−6.09060	−0.292022
$436$	11.3664	0.544353
$437$	3.70393	0.177183
$438$	26.1060	1.24739
$439$	−5.79361	−0.276514	−0.138257	−	0.990396i	$-0.544150\pi$
$439$	−5.79361	−0.276514	−0.138257	+	0.990396i	$0.544150\pi$
$440$	10.1598	0.484351
$441$	0	0
$442$	−17.8328	−0.848222
$443$	−21.4284	−1.01809	−0.509047	−	0.860739i	$-0.670002\pi$
$443$	−21.4284	−1.01809	−0.509047	+	0.860739i	$0.670002\pi$
$444$	−12.5791	−0.596977
$445$	43.8732	2.07979
$446$	10.9821	0.520016
$447$	6.19710	0.293113
$448$	0	0
$449$	−6.54830	−0.309034	−0.154517	−	0.987990i	$-0.549382\pi$
$449$	−6.54830	−0.309034	−0.154517	+	0.987990i	$0.549382\pi$
$450$	−4.82832	−0.227609
$451$	39.0201	1.83739
$452$	−7.69288	−0.361843
$453$	−1.22218	−0.0574232
$454$	19.3050	0.906029
$455$	0	0
$456$	3.46411	0.162222
$457$	42.6826	1.99661	0.998305	−	0.0582059i	$-0.0185380\pi$
$457$	42.6826	1.99661	0.998305	+	0.0582059i	$0.0185380\pi$
$458$	16.3205	0.762609
$459$	−12.8158	−0.598192
$460$	−6.51224	−0.303635
$461$	11.4742	0.534408	0.267204	−	0.963640i	$-0.413900\pi$
$461$	11.4742	0.534408	0.267204	+	0.963640i	$0.413900\pi$
$462$	0	0
$463$	−4.64684	−0.215957	−0.107978	−	0.994153i	$-0.534438\pi$
$463$	−4.64684	−0.215957	−0.107978	+	0.994153i	$0.534438\pi$
$464$	−1.00000	−0.0464238
$465$	−20.7734	−0.963341
$466$	−25.7283	−1.19184
$467$	−33.7438	−1.56148	−0.780739	−	0.624857i	$-0.785157\pi$
$467$	−33.7438	−1.56148	−0.780739	+	0.624857i	$0.785157\pi$
$468$	−6.17825	−0.285590
$469$	0	0
$470$	17.1017	0.788845
$471$	−14.5944	−0.672473
$472$	−13.6005	−0.626012
$473$	−16.0205	−0.736622
$474$	21.7554	0.999257
$475$	3.70113	0.169820
$476$	0	0
$477$	−26.5323	−1.21483
$478$	6.65670	0.304470
$479$	19.3626	0.884699	0.442350	−	0.896843i	$-0.354145\pi$
$479$	19.3626	0.884699	0.442350	+	0.896843i	$0.354145\pi$
$480$	−6.09060	−0.277997
$481$	−17.1973	−0.784130
$482$	−22.4835	−1.02410
$483$	0	0
$484$	2.96170	0.134623
$485$	0.409438	0.0185916
$486$	−17.9974	−0.816381
$487$	16.0717	0.728279	0.364140	−	0.931344i	$-0.381363\pi$
$487$	16.0717	0.728279	0.364140	+	0.931344i	$0.381363\pi$
$488$	−7.29813	−0.330371
$489$	40.2836	1.82169
$490$	0	0
$491$	−41.0445	−1.85231	−0.926157	−	0.377139i	$-0.876908\pi$
$491$	−41.0445	−1.85231	−0.926157	+	0.377139i	$0.876908\pi$
$492$	−23.3918	−1.05458
$493$	5.82325	0.262266
$494$	4.73592	0.213079
$495$	−20.4973	−0.921286
$496$	−3.41072	−0.153146
$497$	0	0
$498$	−24.7422	−1.10872
$499$	32.6858	1.46322	0.731608	−	0.681725i	$-0.238770\pi$
$499$	32.6858	1.46322	0.731608	+	0.681725i	$0.238770\pi$
$500$	7.08792	0.316982
$501$	−7.94338	−0.354884
$502$	15.5233	0.692839
$503$	33.5524	1.49603	0.748013	−	0.663684i	$-0.231008\pi$
$503$	33.5524	1.49603	0.748013	+	0.663684i	$0.231008\pi$
$504$	0	0
$505$	21.6227	0.962198
$506$	−8.94916	−0.397839
$507$	8.11320	0.360320
$508$	1.77872	0.0789180
$509$	35.3582	1.56723	0.783613	−	0.621249i	$-0.213375\pi$
$509$	35.3582	1.56723	0.783613	+	0.621249i	$0.213375\pi$
$510$	35.4671	1.57051
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	3.40354	0.150270
$514$	9.90087	0.436709
$515$	−15.8386	−0.697933
$516$	9.60394	0.422790
$517$	23.5013	1.03359
$518$	0	0
$519$	31.3462	1.37595
$520$	−8.32669	−0.365149
$521$	−2.31715	−0.101516	−0.0507580	−	0.998711i	$-0.516164\pi$
$521$	−2.31715	−0.101516	−0.0507580	+	0.998711i	$0.516164\pi$
$522$	2.01749	0.0883030
$523$	−13.9610	−0.610471	−0.305235	−	0.952277i	$-0.598735\pi$
$523$	−13.9610	−0.610471	−0.305235	+	0.952277i	$0.598735\pi$
$524$	−19.3237	−0.844160
$525$	0	0
$526$	15.5973	0.680074
$527$	19.8615	0.865180
$528$	−8.36975	−0.364246
$529$	−17.2638	−0.750599
$530$	−35.7586	−1.55326
$531$	27.4387	1.19074
$532$	0	0
$533$	−31.9797	−1.38520
$534$	−36.1430	−1.56406
$535$	−9.13815	−0.395077
$536$	−7.21410	−0.311601
$537$	20.3249	0.877082
$538$	23.6586	1.02000
$539$	0	0
$540$	−5.98410	−0.257515
$541$	37.2429	1.60120	0.800598	−	0.599201i	$-0.204515\pi$
$541$	37.2429	1.60120	0.800598	+	0.599201i	$0.204515\pi$
$542$	−4.38281	−0.188258
$543$	−14.3417	−0.615463
$544$	5.82325	0.249670
$545$	−30.9059	−1.32386
$546$	0	0
$547$	−27.4266	−1.17268	−0.586338	−	0.810067i	$-0.699431\pi$
$547$	−27.4266	−1.17268	−0.586338	+	0.810067i	$0.699431\pi$
$548$	−14.8982	−0.636418
$549$	14.7239	0.628400
$550$	−8.94241	−0.381306
$551$	−1.54650	−0.0658830
$552$	5.36483	0.228342
$553$	0	0
$554$	19.9768	0.848732
$555$	34.2032	1.45184
$556$	−4.77586	−0.202542
$557$	46.0764	1.95232	0.976160	−	0.217052i	$-0.0696440\pi$
$557$	46.0764	1.95232	0.976160	+	0.217052i	$0.0696440\pi$
$558$	6.88108	0.291299
$559$	13.1299	0.555335
$560$	0	0
$561$	48.7391	2.05777
$562$	−23.8812	−1.00737
$563$	−32.7219	−1.37906	−0.689532	−	0.724255i	$-0.742184\pi$
$563$	−32.7219	−1.37906	−0.689532	+	0.724255i	$0.742184\pi$
$564$	−14.0886	−0.593235
$565$	20.9173	0.879999
$566$	8.09033	0.340062
$567$	0	0
$568$	−1.10152	−0.0462187
$569$	2.30444	0.0966071	0.0483035	−	0.998833i	$-0.484619\pi$
$569$	2.30444	0.0966071	0.0483035	+	0.998833i	$0.484619\pi$
$570$	−9.41910	−0.394523
$571$	−12.2041	−0.510724	−0.255362	−	0.966846i	$-0.582195\pi$
$571$	−12.2041	−0.510724	−0.255362	+	0.966846i	$0.582195\pi$
$572$	−11.4426	−0.478439
$573$	−12.7560	−0.532888
$574$	0	0
$575$	5.73190	0.239037
$576$	2.01749	0.0840619
$577$	−13.9285	−0.579851	−0.289926	−	0.957049i	$-0.593631\pi$
$577$	−13.9285	−0.579851	−0.289926	+	0.957049i	$0.593631\pi$
$578$	−16.9102	−0.703373
$579$	−29.6700	−1.23304
$580$	2.71905	0.112902
$581$	0	0
$582$	−0.337298	−0.0139814
$583$	−49.1397	−2.03516
$584$	−11.6546	−0.482270
$585$	16.7990	0.694552
$586$	−27.1934	−1.12335
$587$	41.2970	1.70451	0.852255	−	0.523127i	$-0.175235\pi$
$587$	41.2970	1.70451	0.852255	+	0.523127i	$0.175235\pi$
$588$	0	0
$589$	−5.27467	−0.217339
$590$	36.9803	1.52246
$591$	48.1004	1.97859
$592$	5.61572	0.230805
$593$	−9.05037	−0.371654	−0.185827	−	0.982582i	$-0.559496\pi$
$593$	−9.05037	−0.371654	−0.185827	+	0.982582i	$0.559496\pi$
$594$	−8.22339	−0.337410
$595$	0	0
$596$	−2.76660	−0.113324
$597$	−36.7465	−1.50393
$598$	7.33446	0.299928
$599$	21.4813	0.877703	0.438851	−	0.898560i	$-0.355385\pi$
$599$	21.4813	0.877703	0.438851	+	0.898560i	$0.355385\pi$
$600$	5.36079	0.218853
$601$	−33.1647	−1.35282	−0.676408	−	0.736527i	$-0.736464\pi$
$601$	−33.1647	−1.35282	−0.676408	+	0.736527i	$0.736464\pi$
$602$	0	0
$603$	14.5543	0.592698
$604$	0.545624	0.0222011
$605$	−8.05303	−0.327402
$606$	−17.8130	−0.723602
$607$	−30.2177	−1.22650	−0.613250	−	0.789889i	$-0.710138\pi$
$607$	−30.2177	−1.22650	−0.613250	+	0.789889i	$0.710138\pi$
$608$	−1.54650	−0.0627187
$609$	0	0
$610$	19.8440	0.803459
$611$	−19.2610	−0.779216
$612$	−11.7483	−0.474898
$613$	−8.10701	−0.327439	−0.163720	−	0.986507i	$-0.552349\pi$
$613$	−8.10701	−0.327439	−0.163720	+	0.986507i	$0.552349\pi$
$614$	23.3267	0.941390
$615$	63.6034	2.56473
$616$	0	0
$617$	37.4293	1.50685	0.753424	−	0.657534i	$-0.228401\pi$
$617$	37.4293	1.50685	0.753424	+	0.657534i	$0.228401\pi$
$618$	13.0480	0.524867
$619$	17.7610	0.713877	0.356938	−	0.934128i	$-0.383821\pi$
$619$	17.7610	0.713877	0.356938	+	0.934128i	$0.383821\pi$
$620$	9.27392	0.372450
$621$	5.27102	0.211519
$622$	8.08033	0.323992
$623$	0	0
$624$	6.85959	0.274603
$625$	−31.2386	−1.24954
$626$	−2.88845	−0.115446
$627$	−12.9438	−0.516925
$628$	6.51542	0.259993
$629$	−32.7018	−1.30390
$630$	0	0
$631$	29.1472	1.16033	0.580166	−	0.814498i	$-0.302988\pi$
$631$	29.1472	1.16033	0.580166	+	0.814498i	$0.302988\pi$
$632$	−9.71233	−0.386336
$633$	10.2993	0.409359
$634$	−15.7422	−0.625202
$635$	−4.83643	−0.191928
$636$	29.4582	1.16810
$637$	0	0
$638$	3.73654	0.147931
$639$	2.22230	0.0879128
$640$	2.71905	0.107480
$641$	10.1478	0.400814	0.200407	−	0.979713i	$-0.435773\pi$
$641$	10.1478	0.400814	0.200407	+	0.979713i	$0.435773\pi$
$642$	7.52808	0.297110
$643$	35.4624	1.39850	0.699251	−	0.714877i	$-0.253517\pi$
$643$	35.4624	1.39850	0.699251	+	0.714877i	$0.253517\pi$
$644$	0	0
$645$	−26.1136	−1.02822
$646$	9.00564	0.354322
$647$	21.4734	0.844206	0.422103	−	0.906548i	$-0.361292\pi$
$647$	21.4734	0.844206	0.422103	+	0.906548i	$0.361292\pi$
$648$	10.9822	0.431422
$649$	50.8186	1.99480
$650$	7.32893	0.287464
$651$	0	0
$652$	−17.9840	−0.704306
$653$	−45.6106	−1.78488	−0.892441	−	0.451164i	$-0.851009\pi$
$653$	−45.6106	−1.78488	−0.892441	+	0.451164i	$0.851009\pi$
$654$	25.4605	0.995584
$655$	52.5421	2.05299
$656$	10.4429	0.407725
$657$	23.5130	0.917328
$658$	0	0
$659$	−40.2055	−1.56618	−0.783092	−	0.621905i	$-0.786359\pi$
$659$	−40.2055	−1.56618	−0.783092	+	0.621905i	$0.786359\pi$
$660$	22.7578	0.885845
$661$	22.1018	0.859660	0.429830	−	0.902910i	$-0.358573\pi$
$661$	22.1018	0.859660	0.429830	+	0.902910i	$0.358573\pi$
$662$	26.5752	1.03287
$663$	−39.9451	−1.55134
$664$	11.0457	0.428658
$665$	0	0
$666$	−11.3296	−0.439015
$667$	−2.39504	−0.0927364
$668$	3.54619	0.137206
$669$	24.5996	0.951074
$670$	19.6155	0.757813
$671$	27.2697	1.05274
$672$	0	0
$673$	−35.6953	−1.37595	−0.687977	−	0.725733i	$-0.741501\pi$
$673$	−35.6953	−1.37595	−0.687977	+	0.725733i	$0.741501\pi$
$674$	9.93373	0.382633
$675$	5.26705	0.202729
$676$	−3.62200	−0.139308
$677$	−4.42937	−0.170235	−0.0851173	−	0.996371i	$-0.527126\pi$
$677$	−4.42937	−0.170235	−0.0851173	+	0.996371i	$0.527126\pi$
$678$	−17.2319	−0.661786
$679$	0	0
$680$	−15.8337	−0.607195
$681$	43.2427	1.65706
$682$	12.7443	0.488004
$683$	40.1374	1.53581	0.767907	−	0.640561i	$-0.221298\pi$
$683$	40.1374	1.53581	0.767907	+	0.640561i	$0.221298\pi$
$684$	3.12004	0.119298
$685$	40.5089	1.54777
$686$	0	0
$687$	36.5576	1.39476
$688$	−4.28752	−0.163460
$689$	40.2734	1.53430
$690$	−14.5873	−0.555327
$691$	19.7382	0.750876	0.375438	−	0.926848i	$-0.377492\pi$
$691$	19.7382	0.750876	0.375438	+	0.926848i	$0.377492\pi$
$692$	−13.9940	−0.531972
$693$	0	0
$694$	−23.2676	−0.883227
$695$	12.9858	0.492580
$696$	−2.23997	−0.0849060
$697$	−60.8114	−2.30340
$698$	−8.50775	−0.322023
$699$	−57.6307	−2.17979
$700$	0	0
$701$	−24.0203	−0.907235	−0.453617	−	0.891197i	$-0.649867\pi$
$701$	−24.0203	−0.907235	−0.453617	+	0.891197i	$0.649867\pi$
$702$	6.73964	0.254371
$703$	8.68470	0.327550
$704$	3.73654	0.140826
$705$	38.3075	1.44274
$706$	12.6307	0.475362
$707$	0	0
$708$	−30.4647	−1.14493
$709$	−26.8894	−1.00985	−0.504927	−	0.863162i	$-0.668480\pi$
$709$	−26.8894	−1.00985	−0.504927	+	0.863162i	$0.668480\pi$
$710$	2.99509	0.112404
$711$	19.5945	0.734851
$712$	16.1355	0.604702
$713$	−8.16882	−0.305925
$714$	0	0
$715$	31.1130	1.16356
$716$	−9.07370	−0.339100
$717$	14.9108	0.556855
$718$	−3.07392	−0.114718
$719$	49.9416	1.86251	0.931254	−	0.364372i	$-0.118716\pi$
$719$	49.9416	1.86251	0.931254	+	0.364372i	$0.118716\pi$
$720$	−5.48565	−0.204438
$721$	0	0
$722$	16.6083	0.618099
$723$	−50.3625	−1.87300
$724$	6.40263	0.237952
$725$	−2.39324	−0.0888825
$726$	6.63414	0.246216
$727$	13.8293	0.512900	0.256450	−	0.966558i	$-0.417447\pi$
$727$	13.8293	0.512900	0.256450	+	0.966558i	$0.417447\pi$
$728$	0	0
$729$	−7.36720	−0.272859
$730$	31.6894	1.17288
$731$	24.9673	0.923449
$732$	−16.3476	−0.604226
$733$	17.4188	0.643378	0.321689	−	0.946845i	$-0.395749\pi$
$733$	17.4188	0.643378	0.321689	+	0.946845i	$0.395749\pi$
$734$	15.8201	0.583932
$735$	0	0
$736$	−2.39504	−0.0882824
$737$	26.9557	0.992927
$738$	−21.0683	−0.775536
$739$	24.0419	0.884397	0.442198	−	0.896917i	$-0.354199\pi$
$739$	24.0419	0.884397	0.442198	+	0.896917i	$0.354199\pi$
$740$	−15.2694	−0.561316
$741$	10.6083	0.389707
$742$	0	0
$743$	−21.9992	−0.807073	−0.403537	−	0.914963i	$-0.632219\pi$
$743$	−21.9992	−0.807073	−0.403537	+	0.914963i	$0.632219\pi$
$744$	−7.63993	−0.280093
$745$	7.52251	0.275604
$746$	31.8524	1.16620
$747$	−22.2846	−0.815352
$748$	−21.7588	−0.795580
$749$	0	0
$750$	15.8768	0.579738
$751$	−15.7066	−0.573142	−0.286571	−	0.958059i	$-0.592515\pi$
$751$	−15.7066	−0.573142	−0.286571	+	0.958059i	$0.592515\pi$
$752$	6.28960	0.229358
$753$	34.7718	1.26715
$754$	−3.06235	−0.111524
$755$	−1.48358	−0.0539929
$756$	0	0
$757$	0.692620	0.0251737	0.0125869	−	0.999921i	$-0.495993\pi$
$757$	0.692620	0.0251737	0.0125869	+	0.999921i	$0.495993\pi$
$758$	6.27914	0.228069
$759$	−20.0459	−0.727620
$760$	4.20500	0.152531
$761$	−39.5300	−1.43296	−0.716481	−	0.697607i	$-0.754248\pi$
$761$	−39.5300	−1.43296	−0.716481	+	0.697607i	$0.754248\pi$
$762$	3.98429	0.144336
$763$	0	0
$764$	5.69469	0.206027
$765$	31.9443	1.15495
$766$	11.1323	0.402227
$767$	−41.6494	−1.50387
$768$	−2.23997	−0.0808281
$769$	−23.1479	−0.834735	−0.417368	−	0.908738i	$-0.637047\pi$
$769$	−23.1479	−0.834735	−0.417368	+	0.908738i	$0.637047\pi$
$770$	0	0
$771$	22.1777	0.798710
$772$	13.2457	0.476722
$773$	−28.3783	−1.02070	−0.510348	−	0.859968i	$-0.670483\pi$
$773$	−28.3783	−1.02070	−0.510348	+	0.859968i	$0.670483\pi$
$774$	8.65001	0.310918
$775$	−8.16266	−0.293211
$776$	0.150581	0.00540555
$777$	0	0
$778$	−16.0578	−0.575700
$779$	16.1499	0.578629
$780$	−18.6516	−0.667833
$781$	4.11587	0.147277
$782$	13.9469	0.498741
$783$	−2.20081	−0.0786504
$784$	0	0
$785$	−17.7157	−0.632302
$786$	−43.2846	−1.54391
$787$	0.550536	0.0196245	0.00981225	−	0.999952i	$-0.496877\pi$
$787$	0.550536	0.0196245	0.00981225	+	0.999952i	$0.496877\pi$
$788$	−21.4736	−0.764967
$789$	34.9375	1.24381
$790$	26.4083	0.939566
$791$	0	0
$792$	−7.53841	−0.267866
$793$	−22.3494	−0.793652
$794$	−19.8183	−0.703325
$795$	−80.0984	−2.84080
$796$	16.4049	0.581455
$797$	22.5817	0.799886	0.399943	−	0.916540i	$-0.369030\pi$
$797$	22.5817	0.799886	0.399943	+	0.916540i	$0.369030\pi$
$798$	0	0
$799$	−36.6259	−1.29573
$800$	−2.39324	−0.0846137
$801$	−32.5531	−1.15021
$802$	24.9435	0.880784
$803$	43.5478	1.53677
$804$	−16.1594	−0.569898
$805$	0	0
$806$	−10.4448	−0.367903
$807$	52.9947	1.86550
$808$	7.95231	0.279761
$809$	25.5640	0.898783	0.449391	−	0.893335i	$-0.351641\pi$
$809$	25.5640	0.898783	0.449391	+	0.893335i	$0.351641\pi$
$810$	−29.8612	−1.04921
$811$	−27.2412	−0.956567	−0.478284	−	0.878205i	$-0.658741\pi$
$811$	−27.2412	−0.956567	−0.478284	+	0.878205i	$0.658741\pi$
$812$	0	0
$813$	−9.81737	−0.344310
$814$	−20.9834	−0.735466
$815$	48.8993	1.71287
$816$	13.0439	0.456629
$817$	−6.63064	−0.231977
$818$	1.38964	0.0485875
$819$	0	0
$820$	−28.3947	−0.991585
$821$	−36.8974	−1.28773	−0.643864	−	0.765140i	$-0.722670\pi$
$821$	−36.8974	−1.28773	−0.643864	+	0.765140i	$0.722670\pi$
$822$	−33.3715	−1.16397
$823$	−17.7566	−0.618958	−0.309479	−	0.950906i	$-0.600155\pi$
$823$	−17.7566	−0.618958	−0.309479	+	0.950906i	$0.600155\pi$
$824$	−5.82506	−0.202925
$825$	−20.0308	−0.697382
$826$	0	0
$827$	11.9806	0.416605	0.208302	−	0.978064i	$-0.433206\pi$
$827$	11.9806	0.416605	0.208302	+	0.978064i	$0.433206\pi$
$828$	4.83196	0.167922
$829$	−30.8869	−1.07275	−0.536373	−	0.843981i	$-0.680206\pi$
$829$	−30.8869	−1.07275	−0.536373	+	0.843981i	$0.680206\pi$
$830$	−30.0339	−1.04249
$831$	44.7475	1.55227
$832$	−3.06235	−0.106168
$833$	0	0
$834$	−10.6978	−0.370435
$835$	−9.64227	−0.333685
$836$	5.77854	0.199855
$837$	−7.50634	−0.259457
$838$	32.6594	1.12820
$839$	−13.9289	−0.480879	−0.240440	−	0.970664i	$-0.577292\pi$
$839$	−13.9289	−0.480879	−0.240440	+	0.970664i	$0.577292\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	7.73040	0.266407
$843$	−53.4934	−1.84241
$844$	−4.59793	−0.158267
$845$	9.84841	0.338796
$846$	−12.6892	−0.436263
$847$	0	0
$848$	−13.1511	−0.451612
$849$	18.1221	0.621950
$850$	13.9364	0.478015
$851$	13.4499	0.461057
$852$	−2.46738	−0.0845309
$853$	−56.6325	−1.93906	−0.969530	−	0.244972i	$-0.921221\pi$
$853$	−56.6325	−1.93906	−0.969530	+	0.244972i	$0.921221\pi$
$854$	0	0
$855$	−8.48353	−0.290131
$856$	−3.36079	−0.114869
$857$	−9.46955	−0.323474	−0.161737	−	0.986834i	$-0.551710\pi$
$857$	−9.46955	−0.323474	−0.161737	+	0.986834i	$0.551710\pi$
$858$	−25.6311	−0.875032
$859$	51.0542	1.74195	0.870974	−	0.491330i	$-0.163489\pi$
$859$	51.0542	1.74195	0.870974	+	0.491330i	$0.163489\pi$
$860$	11.6580	0.397534
$861$	0	0
$862$	11.1194	0.378730
$863$	2.71152	0.0923012	0.0461506	−	0.998934i	$-0.485305\pi$
$863$	2.71152	0.0923012	0.0461506	+	0.998934i	$0.485305\pi$
$864$	−2.20081	−0.0748730
$865$	38.0504	1.29375
$866$	−38.4668	−1.30715
$867$	−37.8785	−1.28642
$868$	0	0
$869$	36.2905	1.23107
$870$	6.09060	0.206491
$871$	−22.0921	−0.748562
$872$	−11.3664	−0.384916
$873$	−0.303795	−0.0102819
$874$	−3.70393	−0.125287
$875$	0	0
$876$	−26.1060	−0.882039
$877$	−5.47882	−0.185007	−0.0925033	−	0.995712i	$-0.529487\pi$
$877$	−5.47882	−0.185007	−0.0925033	+	0.995712i	$0.529487\pi$
$878$	5.79361	0.195525
$879$	−60.9126	−2.05453
$880$	−10.1598	−0.342488
$881$	16.9157	0.569905	0.284952	−	0.958542i	$-0.408022\pi$
$881$	16.9157	0.569905	0.284952	+	0.958542i	$0.408022\pi$
$882$	0	0
$883$	8.53245	0.287140	0.143570	−	0.989640i	$-0.454142\pi$
$883$	8.53245	0.287140	0.143570	+	0.989640i	$0.454142\pi$
$884$	17.8328	0.599783
$885$	82.8350	2.78447
$886$	21.4284	0.719901
$887$	−49.1535	−1.65041	−0.825207	−	0.564830i	$-0.808942\pi$
$887$	−49.1535	−1.65041	−0.825207	+	0.564830i	$0.808942\pi$
$888$	12.5791	0.422126
$889$	0	0
$890$	−43.8732	−1.47063
$891$	−41.0354	−1.37474
$892$	−10.9821	−0.367707
$893$	9.72685	0.325497
$894$	−6.19710	−0.207262
$895$	24.6719	0.824689
$896$	0	0
$897$	16.4290	0.548549
$898$	6.54830	0.218520
$899$	3.41072	0.113754
$900$	4.82832	0.160944
$901$	76.5824	2.55133
$902$	−39.0201	−1.29923
$903$	0	0
$904$	7.69288	0.255861
$905$	−17.4091	−0.578698
$906$	1.22218	0.0406043
$907$	−11.8391	−0.393112	−0.196556	−	0.980493i	$-0.562976\pi$
$907$	−11.8391	−0.393112	−0.196556	+	0.980493i	$0.562976\pi$
$908$	−19.3050	−0.640659
$909$	−16.0437	−0.532135
$910$	0	0
$911$	34.1629	1.13187	0.565933	−	0.824451i	$-0.308516\pi$
$911$	34.1629	1.13187	0.565933	+	0.824451i	$0.308516\pi$
$912$	−3.46411	−0.114708
$913$	−41.2728	−1.36593
$914$	−42.6826	−1.41182
$915$	44.4500	1.46947
$916$	−16.3205	−0.539246
$917$	0	0
$918$	12.8158	0.422986
$919$	−13.2623	−0.437483	−0.218741	−	0.975783i	$-0.570195\pi$
$919$	−13.2623	−0.437483	−0.218741	+	0.975783i	$0.570195\pi$
$920$	6.51224	0.214702
$921$	52.2513	1.72174
$922$	−11.4742	−0.377884
$923$	−3.37324	−0.111032
$924$	0	0
$925$	13.4398	0.441896
$926$	4.64684	0.152705
$927$	11.7520	0.385985
$928$	1.00000	0.0328266
$929$	0.546408	0.0179271	0.00896353	−	0.999960i	$-0.497147\pi$
$929$	0.546408	0.0179271	0.00896353	+	0.999960i	$0.497147\pi$
$930$	20.7734	0.681185
$931$	0	0
$932$	25.7283	0.842758
$933$	18.0997	0.592559
$934$	33.7438	1.10413
$935$	59.1632	1.93484
$936$	6.17825	0.201942
$937$	−5.61521	−0.183441	−0.0917204	−	0.995785i	$-0.529237\pi$
$937$	−5.61521	−0.183441	−0.0917204	+	0.995785i	$0.529237\pi$
$938$	0	0
$939$	−6.47006	−0.211142
$940$	−17.1017	−0.557798
$941$	31.3818	1.02302	0.511509	−	0.859278i	$-0.329087\pi$
$941$	31.3818	1.02302	0.511509	+	0.859278i	$0.329087\pi$
$942$	14.5944	0.475510
$943$	25.0111	0.814474
$944$	13.6005	0.442657
$945$	0	0
$946$	16.0205	0.520871
$947$	5.14014	0.167032	0.0835161	−	0.996506i	$-0.473385\pi$
$947$	5.14014	0.167032	0.0835161	+	0.996506i	$0.473385\pi$
$948$	−21.7554	−0.706582
$949$	−35.6904	−1.15856
$950$	−3.70113	−0.120081
$951$	−35.2621	−1.14345
$952$	0	0
$953$	−6.76575	−0.219164	−0.109582	−	0.993978i	$-0.534951\pi$
$953$	−6.76575	−0.219164	−0.109582	+	0.993978i	$0.534951\pi$
$954$	26.5323	0.859014
$955$	−15.4841	−0.501055
$956$	−6.65670	−0.215293
$957$	8.36975	0.270555
$958$	−19.3626	−0.625577
$959$	0	0
$960$	6.09060	0.196573
$961$	−19.3670	−0.624741
$962$	17.1973	0.554464
$963$	6.78034	0.218493
$964$	22.4835	0.724146
$965$	−36.0157	−1.15938
$966$	0	0
$967$	30.9728	0.996019	0.498010	−	0.867172i	$-0.334064\pi$
$967$	30.9728	0.996019	0.498010	+	0.867172i	$0.334064\pi$
$968$	−2.96170	−0.0951928
$969$	20.1724	0.648031
$970$	−0.409438	−0.0131463
$971$	−56.1546	−1.80209	−0.901043	−	0.433729i	$-0.857197\pi$
$971$	−56.1546	−1.80209	−0.901043	+	0.433729i	$0.857197\pi$
$972$	17.9974	0.577268
$973$	0	0
$974$	−16.0717	−0.514971
$975$	16.4166	0.525752
$976$	7.29813	0.233607
$977$	−3.65753	−0.117015	−0.0585073	−	0.998287i	$-0.518634\pi$
$977$	−3.65753	−0.117015	−0.0585073	+	0.998287i	$0.518634\pi$
$978$	−40.2836	−1.28813
$979$	−60.2908	−1.92690
$980$	0	0
$981$	22.9316	0.732150
$982$	41.0445	1.30978
$983$	6.15447	0.196297	0.0981486	−	0.995172i	$-0.468708\pi$
$983$	6.15447	0.196297	0.0981486	+	0.995172i	$0.468708\pi$
$984$	23.3918	0.745702
$985$	58.3879	1.86039
$986$	−5.82325	−0.185450
$987$	0	0
$988$	−4.73592	−0.150670
$989$	−10.2688	−0.326529
$990$	20.4973	0.651448
$991$	16.5280	0.525030	0.262515	−	0.964928i	$-0.415448\pi$
$991$	16.5280	0.525030	0.262515	+	0.964928i	$0.415448\pi$
$992$	3.41072	0.108291
$993$	59.5277	1.88905
$994$	0	0
$995$	−44.6057	−1.41410
$996$	24.7422	0.783986
$997$	−35.4374	−1.12232	−0.561158	−	0.827709i	$-0.689644\pi$
$997$	−35.4374	−1.12232	−0.561158	+	0.827709i	$0.689644\pi$
$998$	−32.6858	−1.03465
$999$	12.3591	0.391025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.t.1.2		5
7.2	even	3		406.2.e.d.291.4	yes	10
7.4	even	3		406.2.e.d.233.4	✓	10
7.6	odd	2		2842.2.a.u.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.d.233.4	✓	10	7.4	even	3
406.2.e.d.291.4	yes	10	7.2	even	3
2842.2.a.t.1.2		5	1.1	even	1	trivial
2842.2.a.u.1.4		5	7.6	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.23997 q^{3} +1.00000 q^{4} -2.71905 q^{5} +2.23997 q^{6} -1.00000 q^{8} +2.01749 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.23997 q^{3} +1.00000 q^{4} -2.71905 q^{5} +2.23997 q^{6} -1.00000 q^{8} +2.01749 q^{9} +2.71905 q^{10} +3.73654 q^{11} -2.23997 q^{12} -3.06235 q^{13} +6.09060 q^{15} +1.00000 q^{16} -5.82325 q^{17} -2.01749 q^{18} +1.54650 q^{19} -2.71905 q^{20} -3.73654 q^{22} +2.39504 q^{23} +2.23997 q^{24} +2.39324 q^{25} +3.06235 q^{26} +2.20081 q^{27} -1.00000 q^{29} -6.09060 q^{30} -3.41072 q^{31} -1.00000 q^{32} -8.36975 q^{33} +5.82325 q^{34} +2.01749 q^{36} +5.61572 q^{37} -1.54650 q^{38} +6.85959 q^{39} +2.71905 q^{40} +10.4429 q^{41} -4.28752 q^{43} +3.73654 q^{44} -5.48565 q^{45} -2.39504 q^{46} +6.28960 q^{47} -2.23997 q^{48} -2.39324 q^{50} +13.0439 q^{51} -3.06235 q^{52} -13.1511 q^{53} -2.20081 q^{54} -10.1598 q^{55} -3.46411 q^{57} +1.00000 q^{58} +13.6005 q^{59} +6.09060 q^{60} +7.29813 q^{61} +3.41072 q^{62} +1.00000 q^{64} +8.32669 q^{65} +8.36975 q^{66} +7.21410 q^{67} -5.82325 q^{68} -5.36483 q^{69} +1.10152 q^{71} -2.01749 q^{72} +11.6546 q^{73} -5.61572 q^{74} -5.36079 q^{75} +1.54650 q^{76} -6.85959 q^{78} +9.71233 q^{79} -2.71905 q^{80} -10.9822 q^{81} -10.4429 q^{82} -11.0457 q^{83} +15.8337 q^{85} +4.28752 q^{86} +2.23997 q^{87} -3.73654 q^{88} -16.1355 q^{89} +5.48565 q^{90} +2.39504 q^{92} +7.63993 q^{93} -6.28960 q^{94} -4.20500 q^{95} +2.23997 q^{96} -0.150581 q^{97} +7.53841 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9	\( 5 q - 5 q^{2} - 3 q^{3} + 5 q^{4} - q^{5} + 3 q^{6} - 5 q^{8} + 8 q^{9} + q^{10} + 4 q^{11} - 3 q^{12} - 8 q^{15} + 5 q^{16} - 10 q^{17} - 8 q^{18} - 8 q^{19} - q^{20} - 4 q^{22} + 9 q^{23} + 3 q^{24} - 9 q^{27} - 5 q^{29} + 8 q^{30} - 3 q^{31} - 5 q^{32} - 7 q^{33} + 10 q^{34} + 8 q^{36} + 10 q^{37} + 8 q^{38} - 26 q^{39} + q^{40} - 19 q^{41} + 3 q^{43} + 4 q^{44} + 14 q^{45} - 9 q^{46} - 36 q^{47} - 3 q^{48} + 31 q^{51} - 3 q^{53} + 9 q^{54} - 10 q^{55} - 18 q^{57} + 5 q^{58} + 5 q^{59} - 8 q^{60} - 3 q^{61} + 3 q^{62} + 5 q^{64} + 29 q^{65} + 7 q^{66} - 2 q^{67} - 10 q^{68} + 18 q^{69} + 2 q^{71} - 8 q^{72} + 2 q^{73} - 10 q^{74} - 22 q^{75} - 8 q^{76} + 26 q^{78} + 17 q^{79} - q^{80} - 7 q^{81} + 19 q^{82} - 30 q^{83} - 11 q^{85} - 3 q^{86} + 3 q^{87} - 4 q^{88} - 29 q^{89} - 14 q^{90} + 9 q^{92} + 37 q^{93} + 36 q^{94} - 17 q^{95} + 3 q^{96} + 40 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 - 3 * q^3 + 5 * q^4 - q^5 + 3 * q^6 - 5 * q^8 + 8 * q^9 + q^10 + 4 * q^11 - 3 * q^12 - 8 * q^15 + 5 * q^16 - 10 * q^17 - 8 * q^18 - 8 * q^19 - q^20 - 4 * q^22 + 9 * q^23 + 3 * q^24 - 9 * q^27 - 5 * q^29 + 8 * q^30 - 3 * q^31 - 5 * q^32 - 7 * q^33 + 10 * q^34 + 8 * q^36 + 10 * q^37 + 8 * q^38 - 26 * q^39 + q^40 - 19 * q^41 + 3 * q^43 + 4 * q^44 + 14 * q^45 - 9 * q^46 - 36 * q^47 - 3 * q^48 + 31 * q^51 - 3 * q^53 + 9 * q^54 - 10 * q^55 - 18 * q^57 + 5 * q^58 + 5 * q^59 - 8 * q^60 - 3 * q^61 + 3 * q^62 + 5 * q^64 + 29 * q^65 + 7 * q^66 - 2 * q^67 - 10 * q^68 + 18 * q^69 + 2 * q^71 - 8 * q^72 + 2 * q^73 - 10 * q^74 - 22 * q^75 - 8 * q^76 + 26 * q^78 + 17 * q^79 - q^80 - 7 * q^81 + 19 * q^82 - 30 * q^83 - 11 * q^85 - 3 * q^86 + 3 * q^87 - 4 * q^88 - 29 * q^89 - 14 * q^90 + 9 * q^92 + 37 * q^93 + 36 * q^94 - 17 * q^95 + 3 * q^96 + 40 * q^99

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