LMFDB - Embedded newform 3549.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.473.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 5x - 1 $ x^3 - 5*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.201640$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.201640 q^{2} -1.00000 q^{3} -1.95934 q^{4} -3.75770 q^{5} +0.201640 q^{6} -1.00000 q^{7} +0.798360 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.201640 q^{2} -1.00000 q^{3} -1.95934 q^{4} -3.75770 q^{5} +0.201640 q^{6} -1.00000 q^{7} +0.798360 q^{8} +1.00000 q^{9} +0.757702 q^{10} -5.75770 q^{11} +1.95934 q^{12} +0.201640 q^{14} +3.75770 q^{15} +3.75770 q^{16} +4.20164 q^{17} -0.201640 q^{18} -1.40328 q^{19} +7.36262 q^{20} +1.00000 q^{21} +1.16098 q^{22} +0.959341 q^{23} -0.798360 q^{24} +9.12032 q^{25} -1.00000 q^{27} +1.95934 q^{28} +2.79836 q^{29} -0.757702 q^{30} -4.35442 q^{31} -2.35442 q^{32} +5.75770 q^{33} -0.847217 q^{34} +3.75770 q^{35} -1.95934 q^{36} +10.0797 q^{37} +0.282957 q^{38} -3.00000 q^{40} -2.80656 q^{41} -0.201640 q^{42} +0.959341 q^{43} +11.2813 q^{44} -3.75770 q^{45} -0.193441 q^{46} +6.67638 q^{47} -3.75770 q^{48} +1.00000 q^{49} -1.83902 q^{50} -4.20164 q^{51} -10.9187 q^{53} +0.201640 q^{54} +21.6357 q^{55} -0.798360 q^{56} +1.40328 q^{57} -0.564260 q^{58} +12.3934 q^{59} -7.36262 q^{60} +13.3220 q^{61} +0.878024 q^{62} -1.00000 q^{63} -7.04066 q^{64} -1.16098 q^{66} -7.60492 q^{67} -8.23245 q^{68} -0.959341 q^{69} -0.757702 q^{70} -3.63738 q^{71} +0.798360 q^{72} +7.95934 q^{73} -2.03246 q^{74} -9.12032 q^{75} +2.74950 q^{76} +5.75770 q^{77} +3.56426 q^{79} -14.1203 q^{80} +1.00000 q^{81} +0.565914 q^{82} -14.5643 q^{83} -1.95934 q^{84} -15.7885 q^{85} -0.193441 q^{86} -2.79836 q^{87} -4.59672 q^{88} +1.80656 q^{89} +0.757702 q^{90} -1.87968 q^{92} +4.35442 q^{93} -1.34622 q^{94} +5.27311 q^{95} +2.35442 q^{96} +16.2731 q^{97} -0.201640 q^{98} -5.75770 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 4 q^{4} - 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 4 * q^4 - 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 4 q^{4} - 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} - 8 q^{11} - 4 q^{12} + 2 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{19} + 11 q^{20} + 3 q^{21} - 7 q^{22} - 7 q^{23} - 3 q^{24} + 7 q^{25} - 3 q^{27} - 4 q^{28} + 9 q^{29} + 7 q^{30} - 5 q^{31} + q^{32} + 8 q^{33} - 10 q^{34} + 2 q^{35} + 4 q^{36} + 20 q^{38} - 9 q^{40} - 6 q^{41} - 7 q^{43} + 3 q^{44} - 2 q^{45} - 3 q^{46} - 9 q^{47} - 2 q^{48} + 3 q^{49} - 16 q^{50} - 12 q^{51} - 13 q^{53} + 26 q^{55} - 3 q^{56} + 3 q^{57} + 10 q^{58} - 11 q^{59} - 11 q^{60} + 19 q^{61} - 27 q^{62} - 3 q^{63} - 31 q^{64} + 7 q^{66} - 21 q^{67} + 13 q^{68} + 7 q^{69} + 7 q^{70} - 22 q^{71} + 3 q^{72} + 14 q^{73} - 19 q^{74} - 7 q^{75} + 2 q^{76} + 8 q^{77} - q^{79} - 22 q^{80} + 3 q^{81} + 40 q^{82} - 32 q^{83} + 4 q^{84} - q^{85} - 3 q^{86} - 9 q^{87} - 15 q^{88} + 3 q^{89} - 7 q^{90} - 26 q^{92} + 5 q^{93} + q^{94} - 12 q^{95} - q^{96} + 21 q^{97} - 8 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 4 * q^4 - 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 - 8 * q^11 - 4 * q^12 + 2 * q^15 + 2 * q^16 + 12 * q^17 - 3 * q^19 + 11 * q^20 + 3 * q^21 - 7 * q^22 - 7 * q^23 - 3 * q^24 + 7 * q^25 - 3 * q^27 - 4 * q^28 + 9 * q^29 + 7 * q^30 - 5 * q^31 + q^32 + 8 * q^33 - 10 * q^34 + 2 * q^35 + 4 * q^36 + 20 * q^38 - 9 * q^40 - 6 * q^41 - 7 * q^43 + 3 * q^44 - 2 * q^45 - 3 * q^46 - 9 * q^47 - 2 * q^48 + 3 * q^49 - 16 * q^50 - 12 * q^51 - 13 * q^53 + 26 * q^55 - 3 * q^56 + 3 * q^57 + 10 * q^58 - 11 * q^59 - 11 * q^60 + 19 * q^61 - 27 * q^62 - 3 * q^63 - 31 * q^64 + 7 * q^66 - 21 * q^67 + 13 * q^68 + 7 * q^69 + 7 * q^70 - 22 * q^71 + 3 * q^72 + 14 * q^73 - 19 * q^74 - 7 * q^75 + 2 * q^76 + 8 * q^77 - q^79 - 22 * q^80 + 3 * q^81 + 40 * q^82 - 32 * q^83 + 4 * q^84 - q^85 - 3 * q^86 - 9 * q^87 - 15 * q^88 + 3 * q^89 - 7 * q^90 - 26 * q^92 + 5 * q^93 + q^94 - 12 * q^95 - q^96 + 21 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.201640	−0.142581	−0.0712904	−	0.997456i	$-0.522712\pi$
$2$	−0.201640	−0.142581	−0.0712904	+	0.997456i	$0.522712\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.95934	−0.979671
$5$	−3.75770	−1.68050	−0.840248	−	0.542203i	$-0.817590\pi$
$5$	−3.75770	−1.68050	−0.840248	+	0.542203i	$0.817590\pi$
$6$	0.201640	0.0823191
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	0.798360	0.282263
$9$	1.00000	0.333333
$10$	0.757702	0.239606
$11$	−5.75770	−1.73601	−0.868006	−	0.496553i	$-0.834599\pi$
$11$	−5.75770	−1.73601	−0.868006	+	0.496553i	$0.834599\pi$
$12$	1.95934	0.565613
$13$	0	0
$13$	0	0
$14$	0.201640	0.0538905
$15$	3.75770	0.970234
$16$	3.75770	0.939425
$17$	4.20164	1.01905	0.509524	−	0.860457i	$-0.329822\pi$
$17$	4.20164	1.01905	0.509524	+	0.860457i	$0.329822\pi$
$18$	−0.201640	−0.0475269
$19$	−1.40328	−0.321934	−0.160967	−	0.986960i	$-0.551461\pi$
$19$	−1.40328	−0.321934	−0.160967	+	0.986960i	$0.551461\pi$
$20$	7.36262	1.64633
$21$	1.00000	0.218218
$22$	1.16098	0.247522
$23$	0.959341	0.200037	0.100018	−	0.994986i	$-0.468110\pi$
$23$	0.959341	0.200037	0.100018	+	0.994986i	$0.468110\pi$
$24$	−0.798360	−0.162965
$25$	9.12032	1.82406
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.95934	0.370281
$29$	2.79836	0.519642	0.259821	−	0.965657i	$-0.416336\pi$
$29$	2.79836	0.519642	0.259821	+	0.965657i	$0.416336\pi$
$30$	−0.757702	−0.138337
$31$	−4.35442	−0.782077	−0.391039	−	0.920374i	$-0.627884\pi$
$31$	−4.35442	−0.782077	−0.391039	+	0.920374i	$0.627884\pi$
$32$	−2.35442	−0.416207
$33$	5.75770	1.00229
$34$	−0.847217	−0.145297
$35$	3.75770	0.635168
$36$	−1.95934	−0.326557
$37$	10.0797	1.65709	0.828543	−	0.559925i	$-0.189170\pi$
$37$	10.0797	1.65709	0.828543	+	0.559925i	$0.189170\pi$
$38$	0.282957	0.0459017
$39$	0	0
$40$	−3.00000	−0.474342
$41$	−2.80656	−0.438311	−0.219155	−	0.975690i	$-0.570330\pi$
$41$	−2.80656	−0.438311	−0.219155	+	0.975690i	$0.570330\pi$
$42$	−0.201640	−0.0311137
$43$	0.959341	0.146298	0.0731491	−	0.997321i	$-0.476695\pi$
$43$	0.959341	0.146298	0.0731491	+	0.997321i	$0.476695\pi$
$44$	11.2813	1.70072
$45$	−3.75770	−0.560165
$46$	−0.193441	−0.0285214
$47$	6.67638	0.973851	0.486925	−	0.873444i	$-0.338118\pi$
$47$	6.67638	0.973851	0.486925	+	0.873444i	$0.338118\pi$
$48$	−3.75770	−0.542378
$49$	1.00000	0.142857
$50$	−1.83902	−0.260077
$51$	−4.20164	−0.588347
$52$	0	0
$53$	−10.9187	−1.49980	−0.749898	−	0.661553i	$-0.769898\pi$
$53$	−10.9187	−1.49980	−0.749898	+	0.661553i	$0.769898\pi$
$54$	0.201640	0.0274397
$55$	21.6357	2.91736
$56$	−0.798360	−0.106685
$57$	1.40328	0.185869
$58$	−0.564260	−0.0740910
$59$	12.3934	1.61349	0.806743	−	0.590902i	$-0.201228\pi$
$59$	12.3934	1.61349	0.806743	+	0.590902i	$0.201228\pi$
$60$	−7.36262	−0.950510
$61$	13.3220	1.70570	0.852851	−	0.522154i	$-0.174871\pi$
$61$	13.3220	1.70570	0.852851	+	0.522154i	$0.174871\pi$
$62$	0.878024	0.111509
$63$	−1.00000	−0.125988
$64$	−7.04066	−0.880082
$65$	0	0
$66$	−1.16098	−0.142907
$67$	−7.60492	−0.929089	−0.464544	−	0.885550i	$-0.653782\pi$
$67$	−7.60492	−0.929089	−0.464544	+	0.885550i	$0.653782\pi$
$68$	−8.23245	−0.998331
$69$	−0.959341	−0.115491
$70$	−0.757702	−0.0905627
$71$	−3.63738	−0.431677	−0.215839	−	0.976429i	$-0.569249\pi$
$71$	−3.63738	−0.431677	−0.215839	+	0.976429i	$0.569249\pi$
$72$	0.798360	0.0940877
$73$	7.95934	0.931570	0.465785	−	0.884898i	$-0.345772\pi$
$73$	7.95934	0.931570	0.465785	+	0.884898i	$0.345772\pi$
$74$	−2.03246	−0.236269
$75$	−9.12032	−1.05312
$76$	2.74950	0.315390
$77$	5.75770	0.656151
$78$	0	0
$79$	3.56426	0.401011	0.200505	−	0.979693i	$-0.435742\pi$
$79$	3.56426	0.401011	0.200505	+	0.979693i	$0.435742\pi$
$80$	−14.1203	−1.57870
$81$	1.00000	0.111111
$82$	0.565914	0.0624947
$83$	−14.5643	−1.59864	−0.799318	−	0.600909i	$-0.794806\pi$
$83$	−14.5643	−1.59864	−0.799318	+	0.600909i	$0.794806\pi$
$84$	−1.95934	−0.213782
$85$	−15.7885	−1.71250
$86$	−0.193441	−0.0208593
$87$	−2.79836	−0.300016
$88$	−4.59672	−0.490012
$89$	1.80656	0.191495	0.0957474	−	0.995406i	$-0.469476\pi$
$89$	1.80656	0.191495	0.0957474	+	0.995406i	$0.469476\pi$
$90$	0.757702	0.0798688
$91$	0	0
$92$	−1.87968	−0.195970
$93$	4.35442	0.451533
$94$	−1.34622	−0.138852
$95$	5.27311	0.541009
$96$	2.35442	0.240297
$97$	16.2731	1.65228	0.826142	−	0.563462i	$-0.190531\pi$
$97$	16.2731	1.65228	0.826142	+	0.563462i	$0.190531\pi$
$98$	−0.201640	−0.0203687
$99$	−5.75770	−0.578671
$100$	−17.8698	−1.78698
$101$	−2.16918	−0.215841	−0.107921	−	0.994160i	$-0.534419\pi$
$101$	−2.16918	−0.215841	−0.107921	+	0.994160i	$0.534419\pi$
$102$	0.847217	0.0838870
$103$	−8.43409	−0.831035	−0.415518	−	0.909585i	$-0.636400\pi$
$103$	−8.43409	−0.831035	−0.415518	+	0.909585i	$0.636400\pi$
$104$	0	0
$105$	−3.75770	−0.366714
$106$	2.20164	0.213842
$107$	−7.47474	−0.722611	−0.361305	−	0.932448i	$-0.617669\pi$
$107$	−7.47474	−0.722611	−0.361305	+	0.932448i	$0.617669\pi$
$108$	1.95934	0.188538
$109$	−9.52360	−0.912196	−0.456098	−	0.889930i	$-0.650753\pi$
$109$	−9.52360	−0.912196	−0.456098	+	0.889930i	$0.650753\pi$
$110$	−4.36262	−0.415960
$111$	−10.0797	−0.956719
$112$	−3.75770	−0.355069
$113$	−9.86983	−0.928475	−0.464238	−	0.885711i	$-0.653672\pi$
$113$	−9.86983	−0.928475	−0.464238	+	0.885711i	$0.653672\pi$
$114$	−0.282957	−0.0265013
$115$	−3.60492	−0.336160
$116$	−5.48294	−0.509079
$117$	0	0
$118$	−2.49901	−0.230052
$119$	−4.20164	−0.385164
$120$	3.00000	0.273861
$121$	22.1511	2.01374
$122$	−2.68624	−0.243200
$123$	2.80656	0.253059
$124$	8.53180	0.766178
$125$	−15.4829	−1.38484
$126$	0.201640	0.0179635
$127$	−6.96754	−0.618269	−0.309135	−	0.951018i	$-0.600039\pi$
$127$	−6.96754	−0.618269	−0.309135	+	0.951018i	$0.600039\pi$
$128$	6.12852	0.541690
$129$	−0.959341	−0.0844653
$130$	0	0
$131$	−9.75770	−0.852534	−0.426267	−	0.904597i	$-0.640172\pi$
$131$	−9.75770	−0.852534	−0.426267	+	0.904597i	$0.640172\pi$
$132$	−11.2813	−0.981911
$133$	1.40328	0.121680
$134$	1.53345	0.132470
$135$	3.75770	0.323411
$136$	3.35442	0.287639
$137$	3.32196	0.283814	0.141907	−	0.989880i	$-0.454677\pi$
$137$	3.32196	0.283814	0.141907	+	0.989880i	$0.454677\pi$
$138$	0.193441	0.0164668
$139$	0.798360	0.0677160	0.0338580	−	0.999427i	$-0.489221\pi$
$139$	0.798360	0.0677160	0.0338580	+	0.999427i	$0.489221\pi$
$140$	−7.36262	−0.622255
$141$	−6.67638	−0.562253
$142$	0.733440	0.0615489
$143$	0	0
$144$	3.75770	0.313142
$145$	−10.5154	−0.873257
$146$	−1.60492	−0.132824
$147$	−1.00000	−0.0824786
$148$	−19.7495	−1.62340
$149$	19.5138	1.59863	0.799314	−	0.600913i	$-0.205196\pi$
$149$	19.5138	1.59863	0.799314	+	0.600913i	$0.205196\pi$
$150$	1.83902	0.150155
$151$	−9.11212	−0.741534	−0.370767	−	0.928726i	$-0.620905\pi$
$151$	−9.11212	−0.741534	−0.370767	+	0.928726i	$0.620905\pi$
$152$	−1.12032	−0.0908702
$153$	4.20164	0.339682
$154$	−1.16098	−0.0935545
$155$	16.3626	1.31428
$156$	0	0
$157$	−1.62918	−0.130023	−0.0650114	−	0.997885i	$-0.520708\pi$
$157$	−1.62918	−0.130023	−0.0650114	+	0.997885i	$0.520708\pi$
$158$	−0.718696	−0.0571764
$159$	10.9187	0.865908
$160$	8.84722	0.699434
$161$	−0.959341	−0.0756067
$162$	−0.201640	−0.0158423
$163$	3.16263	0.247717	0.123858	−	0.992300i	$-0.460473\pi$
$163$	3.16263	0.247717	0.123858	+	0.992300i	$0.460473\pi$
$164$	5.49901	0.429400
$165$	−21.6357	−1.68434
$166$	2.93673	0.227935
$167$	−10.8374	−0.838621	−0.419310	−	0.907843i	$-0.637728\pi$
$167$	−10.8374	−0.838621	−0.419310	+	0.907843i	$0.637728\pi$
$168$	0.798360	0.0615948
$169$	0	0
$170$	3.18359	0.244170
$171$	−1.40328	−0.107311
$172$	−1.87968	−0.143324
$173$	8.87802	0.674984	0.337492	−	0.941328i	$-0.390421\pi$
$173$	8.87802	0.674984	0.337492	+	0.941328i	$0.390421\pi$
$174$	0.564260	0.0427765
$175$	−9.12032	−0.689432
$176$	−21.6357	−1.63085
$177$	−12.3934	−0.931547
$178$	−0.364274	−0.0273035
$179$	−5.10393	−0.381485	−0.190743	−	0.981640i	$-0.561090\pi$
$179$	−5.10393	−0.381485	−0.190743	+	0.981640i	$0.561090\pi$
$180$	7.36262	0.548777
$181$	11.2649	0.837314	0.418657	−	0.908144i	$-0.362501\pi$
$181$	11.2649	0.837314	0.418657	+	0.908144i	$0.362501\pi$
$182$	0	0
$183$	−13.3220	−0.984788
$184$	0.765900	0.0564629
$185$	−37.8764	−2.78473
$186$	−0.878024	−0.0643799
$187$	−24.1918	−1.76908
$188$	−13.0813	−0.954053
$189$	1.00000	0.0727393
$190$	−1.06327	−0.0771375
$191$	13.7495	0.994879	0.497440	−	0.867499i	$-0.334274\pi$
$191$	13.7495	0.994879	0.497440	+	0.867499i	$0.334274\pi$
$192$	7.04066	0.508116
$193$	−15.9088	−1.14514	−0.572571	−	0.819855i	$-0.694054\pi$
$193$	−15.9088	−1.14514	−0.572571	+	0.819855i	$0.694054\pi$
$194$	−3.28130	−0.235584
$195$	0	0
$196$	−1.95934	−0.139953
$197$	1.71870	0.122452	0.0612260	−	0.998124i	$-0.480499\pi$
$197$	1.71870	0.122452	0.0612260	+	0.998124i	$0.480499\pi$
$198$	1.16098	0.0825073
$199$	7.94294	0.563060	0.281530	−	0.959552i	$-0.409158\pi$
$199$	7.94294	0.563060	0.281530	+	0.959552i	$0.409158\pi$
$200$	7.28130	0.514866
$201$	7.60492	0.536410
$202$	0.437393	0.0307748
$203$	−2.79836	−0.196406
$204$	8.23245	0.576387
$205$	10.5462	0.736579
$206$	1.70065	0.118490
$207$	0.959341	0.0666788
$208$	0	0
$209$	8.07966	0.558882
$210$	0.757702	0.0522864
$211$	25.2000	1.73484	0.867419	−	0.497578i	$-0.165777\pi$
$211$	25.2000	1.73484	0.867419	+	0.497578i	$0.165777\pi$
$212$	21.3934	1.46931
$213$	3.63738	0.249229
$214$	1.50721	0.103030
$215$	−3.60492	−0.245853
$216$	−0.798360	−0.0543215
$217$	4.35442	0.295597
$218$	1.92034	0.130062
$219$	−7.95934	−0.537842
$220$	−42.3918	−2.85805
$221$	0	0
$222$	2.03246	0.136410
$223$	4.67804	0.313265	0.156632	−	0.987657i	$-0.449936\pi$
$223$	4.67804	0.313265	0.156632	+	0.987657i	$0.449936\pi$
$224$	2.35442	0.157311
$225$	9.12032	0.608022
$226$	1.99015	0.132383
$227$	−15.7885	−1.04792	−0.523960	−	0.851743i	$-0.675546\pi$
$227$	−15.7885	−1.04792	−0.523960	+	0.851743i	$0.675546\pi$
$228$	−2.74950	−0.182090
$229$	−22.3770	−1.47872	−0.739358	−	0.673313i	$-0.764871\pi$
$229$	−22.3770	−1.47872	−0.739358	+	0.673313i	$0.764871\pi$
$230$	0.726895	0.0479300
$231$	−5.75770	−0.378829
$232$	2.23410	0.146676
$233$	7.64392	0.500770	0.250385	−	0.968146i	$-0.419443\pi$
$233$	7.64392	0.500770	0.250385	+	0.968146i	$0.419443\pi$
$234$	0	0
$235$	−25.0879	−1.63655
$236$	−24.2830	−1.58069
$237$	−3.56426	−0.231524
$238$	0.847217	0.0549169
$239$	−19.5967	−1.26761	−0.633803	−	0.773494i	$-0.718507\pi$
$239$	−19.5967	−1.26761	−0.633803	+	0.773494i	$0.718507\pi$
$240$	14.1203	0.911463
$241$	18.9006	1.21750	0.608748	−	0.793363i	$-0.291672\pi$
$241$	18.9006	1.21750	0.608748	+	0.793363i	$0.291672\pi$
$242$	−4.46655	−0.287120
$243$	−1.00000	−0.0641500
$244$	−26.1023	−1.67103
$245$	−3.75770	−0.240071
$246$	−0.565914	−0.0360813
$247$	0	0
$248$	−3.47640	−0.220751
$249$	14.5643	0.922973
$250$	3.12198	0.197451
$251$	−5.32362	−0.336024	−0.168012	−	0.985785i	$-0.553735\pi$
$251$	−5.32362	−0.336024	−0.168012	+	0.985785i	$0.553735\pi$
$252$	1.95934	0.123427
$253$	−5.52360	−0.347266
$254$	1.40493	0.0881533
$255$	15.7885	0.988715
$256$	12.8456	0.802848
$257$	−11.7967	−0.735858	−0.367929	−	0.929854i	$-0.619933\pi$
$257$	−11.7967	−0.735858	−0.367929	+	0.929854i	$0.619933\pi$
$258$	0.193441	0.0120431
$259$	−10.0797	−0.626320
$260$	0	0
$261$	2.79836	0.173214
$262$	1.96754	0.121555
$263$	14.1836	0.874598	0.437299	−	0.899316i	$-0.355935\pi$
$263$	14.1836	0.874598	0.437299	+	0.899316i	$0.355935\pi$
$264$	4.59672	0.282909
$265$	41.0292	2.52040
$266$	−0.282957	−0.0173492
$267$	−1.80656	−0.110560
$268$	14.9006	0.910201
$269$	−20.9983	−1.28029	−0.640146	−	0.768253i	$-0.721126\pi$
$269$	−20.9983	−1.28029	−0.640146	+	0.768253i	$0.721126\pi$
$270$	−0.757702	−0.0461123
$271$	11.0082	0.668700	0.334350	−	0.942449i	$-0.391483\pi$
$271$	11.0082	0.668700	0.334350	+	0.942449i	$0.391483\pi$
$272$	15.7885	0.957319
$273$	0	0
$274$	−0.669839	−0.0404665
$275$	−52.5121	−3.16660
$276$	1.87968	0.113143
$277$	−30.1757	−1.81308	−0.906542	−	0.422116i	$-0.861287\pi$
$277$	−30.1757	−1.81308	−0.906542	+	0.422116i	$0.861287\pi$
$278$	−0.160981	−0.00965501
$279$	−4.35442	−0.260692
$280$	3.00000	0.179284
$281$	7.48294	0.446395	0.223197	−	0.974773i	$-0.428351\pi$
$281$	7.48294	0.446395	0.223197	+	0.974773i	$0.428351\pi$
$282$	1.34622	0.0801665
$283$	2.07312	0.123234	0.0616171	−	0.998100i	$-0.480374\pi$
$283$	2.07312	0.123234	0.0616171	+	0.998100i	$0.480374\pi$
$284$	7.12687	0.422902
$285$	−5.27311	−0.312352
$286$	0	0
$287$	2.80656	0.165666
$288$	−2.35442	−0.138736
$289$	0.653776	0.0384574
$290$	2.12032	0.124510
$291$	−16.2731	−0.953946
$292$	−15.5951	−0.912632
$293$	−17.7741	−1.03837	−0.519187	−	0.854661i	$-0.673765\pi$
$293$	−17.7741	−1.03837	−0.519187	+	0.854661i	$0.673765\pi$
$294$	0.201640	0.0117599
$295$	−46.5708	−2.71146
$296$	8.04720	0.467734
$297$	5.75770	0.334096
$298$	−3.93475	−0.227934
$299$	0	0
$300$	17.8698	1.03171
$301$	−0.959341	−0.0552955
$302$	1.83737	0.105729
$303$	2.16918	0.124616
$304$	−5.27311	−0.302433
$305$	−50.0600	−2.86643
$306$	−0.847217	−0.0484322
$307$	3.84556	0.219478	0.109739	−	0.993960i	$-0.464999\pi$
$307$	3.84556	0.219478	0.109739	+	0.993960i	$0.464999\pi$
$308$	−11.2813	−0.642812
$309$	8.43409	0.479798
$310$	−3.29935	−0.187391
$311$	−2.52360	−0.143100	−0.0715502	−	0.997437i	$-0.522795\pi$
$311$	−2.52360	−0.143100	−0.0715502	+	0.997437i	$0.522795\pi$
$312$	0	0
$313$	29.2731	1.65461	0.827307	−	0.561750i	$-0.189872\pi$
$313$	29.2731	1.65461	0.827307	+	0.561750i	$0.189872\pi$
$314$	0.328507	0.0185388
$315$	3.75770	0.211723
$316$	−6.98360	−0.392858
$317$	−9.81476	−0.551252	−0.275626	−	0.961265i	$-0.588885\pi$
$317$	−9.81476	−0.551252	−0.275626	+	0.961265i	$0.588885\pi$
$318$	−2.20164	−0.123462
$319$	−16.1121	−0.902106
$320$	26.4567	1.47897
$321$	7.47474	0.417200
$322$	0.193441	0.0107801
$323$	−5.89607	−0.328066
$324$	−1.95934	−0.108852
$325$	0	0
$326$	−0.637713	−0.0353196
$327$	9.52360	0.526656
$328$	−2.24065	−0.123719
$329$	−6.67638	−0.368081
$330$	4.36262	0.240154
$331$	−34.7170	−1.90822	−0.954111	−	0.299454i	$-0.903195\pi$
$331$	−34.7170	−1.90822	−0.954111	+	0.299454i	$0.903195\pi$
$332$	28.5364	1.56614
$333$	10.0797	0.552362
$334$	2.18524	0.119571
$335$	28.5770	1.56133
$336$	3.75770	0.204999
$337$	5.46655	0.297782	0.148891	−	0.988854i	$-0.452430\pi$
$337$	5.46655	0.297782	0.148891	+	0.988854i	$0.452430\pi$
$338$	0	0
$339$	9.86983	0.536055
$340$	30.9351	1.67769
$341$	25.0715	1.35770
$342$	0.282957	0.0153006
$343$	−1.00000	−0.0539949
$344$	0.765900	0.0412946
$345$	3.60492	0.194082
$346$	−1.79016	−0.0962397
$347$	22.0698	1.18477	0.592385	−	0.805655i	$-0.298187\pi$
$347$	22.0698	1.18477	0.592385	+	0.805655i	$0.298187\pi$
$348$	5.48294	0.293917
$349$	13.3446	0.714319	0.357159	−	0.934044i	$-0.383745\pi$
$349$	13.3446	0.714319	0.357159	+	0.934044i	$0.383745\pi$
$350$	1.83902	0.0982997
$351$	0	0
$352$	13.5561	0.722541
$353$	27.3203	1.45411	0.727057	−	0.686577i	$-0.240888\pi$
$353$	27.3203	1.45411	0.727057	+	0.686577i	$0.240888\pi$
$354$	2.49901	0.132821
$355$	13.6682	0.725432
$356$	−3.53967	−0.187602
$357$	4.20164	0.222374
$358$	1.02915	0.0543925
$359$	−2.16263	−0.114139	−0.0570697	−	0.998370i	$-0.518176\pi$
$359$	−2.16263	−0.114139	−0.0570697	+	0.998370i	$0.518176\pi$
$360$	−3.00000	−0.158114
$361$	−17.0308	−0.896358
$362$	−2.27145	−0.119385
$363$	−22.1511	−1.16263
$364$	0	0
$365$	−29.9088	−1.56550
$366$	2.68624	0.140412
$367$	−14.7154	−0.768137	−0.384069	−	0.923305i	$-0.625477\pi$
$367$	−14.7154	−0.768137	−0.384069	+	0.923305i	$0.625477\pi$
$368$	3.60492	0.187919
$369$	−2.80656	−0.146104
$370$	7.63738	0.397048
$371$	10.9187	0.566870
$372$	−8.53180	−0.442353
$373$	−31.8275	−1.64797	−0.823983	−	0.566614i	$-0.808253\pi$
$373$	−31.8275	−1.64797	−0.823983	+	0.566614i	$0.808253\pi$
$374$	4.87802	0.252237
$375$	15.4829	0.799536
$376$	5.33016	0.274882
$377$	0	0
$378$	−0.201640	−0.0103712
$379$	27.6583	1.42071	0.710357	−	0.703842i	$-0.248534\pi$
$379$	27.6583	1.42071	0.710357	+	0.703842i	$0.248534\pi$
$380$	−10.3318	−0.530011
$381$	6.96754	0.356958
$382$	−2.77245	−0.141851
$383$	23.6747	1.20972	0.604861	−	0.796331i	$-0.293229\pi$
$383$	23.6747	1.20972	0.604861	+	0.796331i	$0.293229\pi$
$384$	−6.12852	−0.312745
$385$	−21.6357	−1.10266
$386$	3.20785	0.163275
$387$	0.959341	0.0487661
$388$	−31.8846	−1.61869
$389$	8.79016	0.445679	0.222839	−	0.974855i	$-0.428467\pi$
$389$	8.79016	0.445679	0.222839	+	0.974855i	$0.428467\pi$
$390$	0	0
$391$	4.03081	0.203847
$392$	0.798360	0.0403233
$393$	9.75770	0.492211
$394$	−0.346557	−0.0174593
$395$	−13.3934	−0.673896
$396$	11.2813	0.566907
$397$	17.1269	0.859573	0.429786	−	0.902931i	$-0.358589\pi$
$397$	17.1269	0.859573	0.429786	+	0.902931i	$0.358589\pi$
$398$	−1.60161	−0.0802816
$399$	−1.40328	−0.0702518
$400$	34.2715	1.71357
$401$	−17.8292	−0.890346	−0.445173	−	0.895445i	$-0.646858\pi$
$401$	−17.8292	−0.890346	−0.445173	+	0.895445i	$0.646858\pi$
$402$	−1.53345	−0.0764817
$403$	0	0
$404$	4.25016	0.211454
$405$	−3.75770	−0.186722
$406$	0.564260	0.0280038
$407$	−58.0357	−2.87672
$408$	−3.35442	−0.166069
$409$	17.7479	0.877575	0.438787	−	0.898591i	$-0.355408\pi$
$409$	17.7479	0.877575	0.438787	+	0.898591i	$0.355408\pi$
$410$	−2.12653	−0.105022
$411$	−3.32196	−0.163860
$412$	16.5253	0.814141
$413$	−12.3934	−0.609841
$414$	−0.193441	−0.00950712
$415$	54.7281	2.68650
$416$	0	0
$417$	−0.798360	−0.0390959
$418$	−1.62918	−0.0796858
$419$	7.99835	0.390745	0.195372	−	0.980729i	$-0.437408\pi$
$419$	7.99835	0.390745	0.195372	+	0.980729i	$0.437408\pi$
$420$	7.36262	0.359259
$421$	23.7721	1.15858	0.579291	−	0.815121i	$-0.303330\pi$
$421$	23.7721	1.15858	0.579291	+	0.815121i	$0.303330\pi$
$422$	−5.08132	−0.247355
$423$	6.67638	0.324617
$424$	−8.71704	−0.423337
$425$	38.3203	1.85881
$426$	−0.733440	−0.0355353
$427$	−13.3220	−0.644695
$428$	14.6456	0.707921
$429$	0	0
$430$	0.726895	0.0350540
$431$	−6.03246	−0.290573	−0.145287	−	0.989390i	$-0.546410\pi$
$431$	−6.03246	−0.290573	−0.145287	+	0.989390i	$0.546410\pi$
$432$	−3.75770	−0.180793
$433$	6.29116	0.302334	0.151167	−	0.988508i	$-0.451697\pi$
$433$	6.29116	0.302334	0.151167	+	0.988508i	$0.451697\pi$
$434$	−0.878024	−0.0421465
$435$	10.5154	0.504175
$436$	18.6600	0.893651
$437$	−1.34622	−0.0643986
$438$	1.60492	0.0766860
$439$	29.5039	1.40814	0.704072	−	0.710128i	$-0.251363\pi$
$439$	29.5039	1.40814	0.704072	+	0.710128i	$0.251363\pi$
$440$	17.2731	0.823463
$441$	1.00000	0.0476190
$442$	0	0
$443$	−14.5318	−0.690427	−0.345213	−	0.938524i	$-0.612193\pi$
$443$	−14.5318	−0.690427	−0.345213	+	0.938524i	$0.612193\pi$
$444$	19.7495	0.937270
$445$	−6.78851	−0.321806
$446$	−0.943278	−0.0446655
$447$	−19.5138	−0.922969
$448$	7.04066	0.332640
$449$	−10.0961	−0.476463	−0.238231	−	0.971208i	$-0.576568\pi$
$449$	−10.0961	−0.476463	−0.238231	+	0.971208i	$0.576568\pi$
$450$	−1.83902	−0.0866922
$451$	16.1593	0.760913
$452$	19.3384	0.909600
$453$	9.11212	0.428125
$454$	3.18359	0.149413
$455$	0	0
$456$	1.12032	0.0524639
$457$	−18.6177	−0.870898	−0.435449	−	0.900213i	$-0.643410\pi$
$457$	−18.6177	−0.870898	−0.435449	+	0.900213i	$0.643410\pi$
$458$	4.51210	0.210836
$459$	−4.20164	−0.196116
$460$	7.06327	0.329327
$461$	−30.7380	−1.43161	−0.715806	−	0.698300i	$-0.753940\pi$
$461$	−30.7380	−1.43161	−0.715806	+	0.698300i	$0.753940\pi$
$462$	1.16098	0.0540137
$463$	30.4747	1.41628	0.708141	−	0.706071i	$-0.249534\pi$
$463$	30.4747	1.41628	0.708141	+	0.706071i	$0.249534\pi$
$464$	10.5154	0.488165
$465$	−16.3626	−0.758798
$466$	−1.54132	−0.0714002
$467$	−10.7006	−0.495167	−0.247583	−	0.968867i	$-0.579636\pi$
$467$	−10.7006	−0.495167	−0.247583	+	0.968867i	$0.579636\pi$
$468$	0	0
$469$	7.60492	0.351163
$470$	5.05871	0.233341
$471$	1.62918	0.0750687
$472$	9.89442	0.455428
$473$	−5.52360	−0.253975
$474$	0.718696	0.0330108
$475$	−12.7984	−0.587229
$476$	8.23245	0.377334
$477$	−10.9187	−0.499932
$478$	3.95148	0.180736
$479$	7.15278	0.326819	0.163409	−	0.986558i	$-0.447751\pi$
$479$	7.15278	0.326819	0.163409	+	0.986558i	$0.447751\pi$
$480$	−8.84722	−0.403818
$481$	0	0
$482$	−3.81112	−0.173592
$483$	0.959341	0.0436515
$484$	−43.4016	−1.97280
$485$	−61.1495	−2.77665
$486$	0.201640	0.00914656
$487$	36.2324	1.64185	0.820924	−	0.571037i	$-0.193459\pi$
$487$	36.2324	1.64185	0.820924	+	0.571037i	$0.193459\pi$
$488$	10.6357	0.481457
$489$	−3.16263	−0.143019
$490$	0.757702	0.0342295
$491$	−7.12032	−0.321336	−0.160668	−	0.987009i	$-0.551365\pi$
$491$	−7.12032	−0.321336	−0.160668	+	0.987009i	$0.551365\pi$
$492$	−5.49901	−0.247914
$493$	11.7577	0.529540
$494$	0	0
$495$	21.6357	0.972454
$496$	−16.3626	−0.734703
$497$	3.63738	0.163159
$498$	−2.93673	−0.131598
$499$	32.2797	1.44504	0.722518	−	0.691352i	$-0.242985\pi$
$499$	32.2797	1.44504	0.722518	+	0.691352i	$0.242985\pi$
$500$	30.3364	1.35668
$501$	10.8374	0.484178
$502$	1.07345	0.0479105
$503$	36.2551	1.61653	0.808267	−	0.588817i	$-0.200406\pi$
$503$	36.2551	1.61653	0.808267	+	0.588817i	$0.200406\pi$
$504$	−0.798360	−0.0355618
$505$	8.15113	0.362721
$506$	1.11378	0.0495134
$507$	0	0
$508$	13.6518	0.605700
$509$	12.5462	0.556101	0.278051	−	0.960566i	$-0.410312\pi$
$509$	12.5462	0.556101	0.278051	+	0.960566i	$0.410312\pi$
$510$	−3.18359	−0.140972
$511$	−7.95934	−0.352101
$512$	−14.8472	−0.656161
$513$	1.40328	0.0619563
$514$	2.37868	0.104919
$515$	31.6928	1.39655
$516$	1.87968	0.0827482
$517$	−38.4406	−1.69062
$518$	2.03246	0.0893012
$519$	−8.87802	−0.389702
$520$	0	0
$521$	−27.0390	−1.18460	−0.592300	−	0.805717i	$-0.701780\pi$
$521$	−27.0390	−1.18460	−0.592300	+	0.805717i	$0.701780\pi$
$522$	−0.564260	−0.0246970
$523$	10.6600	0.466129	0.233064	−	0.972461i	$-0.425125\pi$
$523$	10.6600	0.466129	0.233064	+	0.972461i	$0.425125\pi$
$524$	19.1187	0.835203
$525$	9.12032	0.398044
$526$	−2.85997	−0.124701
$527$	−18.2957	−0.796974
$528$	21.6357	0.941574
$529$	−22.0797	−0.959985
$530$	−8.27311	−0.359361
$531$	12.3934	0.537829
$532$	−2.74950	−0.119206
$533$	0	0
$534$	0.364274	0.0157637
$535$	28.0879	1.21434
$536$	−6.07147	−0.262247
$537$	5.10393	0.220251
$538$	4.23410	0.182545
$539$	−5.75770	−0.248002
$540$	−7.36262	−0.316837
$541$	5.20164	0.223636	0.111818	−	0.993729i	$-0.464333\pi$
$541$	5.20164	0.223636	0.111818	+	0.993729i	$0.464333\pi$
$542$	−2.21969	−0.0953438
$543$	−11.2649	−0.483423
$544$	−9.89243	−0.424135
$545$	35.7869	1.53294
$546$	0	0
$547$	−27.4567	−1.17396	−0.586982	−	0.809600i	$-0.699684\pi$
$547$	−27.4567	−1.17396	−0.586982	+	0.809600i	$0.699684\pi$
$548$	−6.50886	−0.278045
$549$	13.3220	0.568567
$550$	10.5885	0.451496
$551$	−3.92688	−0.167291
$552$	−0.765900	−0.0325989
$553$	−3.56426	−0.151568
$554$	6.08462	0.258511
$555$	37.8764	1.60776
$556$	−1.56426	−0.0663394
$557$	−14.3951	−0.609939	−0.304970	−	0.952362i	$-0.598646\pi$
$557$	−14.3951	−0.609939	−0.304970	+	0.952362i	$0.598646\pi$
$558$	0.878024	0.0371697
$559$	0	0
$560$	14.1203	0.596693
$561$	24.1918	1.02138
$562$	−1.50886	−0.0636473
$563$	10.6213	0.447635	0.223818	−	0.974631i	$-0.428148\pi$
$563$	10.6213	0.447635	0.223818	+	0.974631i	$0.428148\pi$
$564$	13.0813	0.550823
$565$	37.0879	1.56030
$566$	−0.418023	−0.0175708
$567$	−1.00000	−0.0419961
$568$	−2.90394	−0.121847
$569$	−18.4098	−0.771780	−0.385890	−	0.922545i	$-0.626106\pi$
$569$	−18.4098	−0.771780	−0.385890	+	0.922545i	$0.626106\pi$
$570$	1.06327	0.0445354
$571$	−17.0698	−0.714349	−0.357175	−	0.934038i	$-0.616260\pi$
$571$	−17.0698	−0.714349	−0.357175	+	0.934038i	$0.616260\pi$
$572$	0	0
$573$	−13.7495	−0.574394
$574$	−0.565914	−0.0236208
$575$	8.74950	0.364880
$576$	−7.04066	−0.293361
$577$	5.84722	0.243423	0.121711	−	0.992566i	$-0.461162\pi$
$577$	5.84722	0.243423	0.121711	+	0.992566i	$0.461162\pi$
$578$	−0.131827	−0.00548329
$579$	15.9088	0.661148
$580$	20.6033	0.855504
$581$	14.5643	0.604227
$582$	3.28130	0.136014
$583$	62.8665	2.60367
$584$	6.35442	0.262948
$585$	0	0
$586$	3.58396	0.148052
$587$	−32.0489	−1.32280	−0.661399	−	0.750034i	$-0.730037\pi$
$587$	−32.0489	−1.32280	−0.661399	+	0.750034i	$0.730037\pi$
$588$	1.95934	0.0808019
$589$	6.11047	0.251778
$590$	9.39052	0.386602
$591$	−1.71870	−0.0706977
$592$	37.8764	1.55671
$593$	−14.1347	−0.580444	−0.290222	−	0.956959i	$-0.593729\pi$
$593$	−14.1347	−0.580444	−0.290222	+	0.956959i	$0.593729\pi$
$594$	−1.16098	−0.0476356
$595$	15.7885	0.647266
$596$	−38.2341	−1.56613
$597$	−7.94294	−0.325083
$598$	0	0
$599$	−16.5154	−0.674801	−0.337401	−	0.941361i	$-0.609548\pi$
$599$	−16.5154	−0.674801	−0.337401	+	0.941361i	$0.609548\pi$
$600$	−7.28130	−0.297258
$601$	−3.75770	−0.153280	−0.0766399	−	0.997059i	$-0.524419\pi$
$601$	−3.75770	−0.153280	−0.0766399	+	0.997059i	$0.524419\pi$
$602$	0.193441	0.00788408
$603$	−7.60492	−0.309696
$604$	17.8538	0.726459
$605$	−83.2373	−3.38408
$606$	−0.437393	−0.0177679
$607$	10.7026	0.434406	0.217203	−	0.976126i	$-0.430307\pi$
$607$	10.7026	0.434406	0.217203	+	0.976126i	$0.430307\pi$
$608$	3.30391	0.133991
$609$	2.79836	0.113395
$610$	10.0941	0.408697
$611$	0	0
$612$	−8.23245	−0.332777
$613$	8.34001	0.336850	0.168425	−	0.985714i	$-0.446132\pi$
$613$	8.34001	0.336850	0.168425	+	0.985714i	$0.446132\pi$
$614$	−0.775418	−0.0312933
$615$	−10.5462	−0.425264
$616$	4.59672	0.185207
$617$	0.951143	0.0382916	0.0191458	−	0.999817i	$-0.493905\pi$
$617$	0.951143	0.0382916	0.0191458	+	0.999817i	$0.493905\pi$
$618$	−1.70065	−0.0684100
$619$	−13.2098	−0.530948	−0.265474	−	0.964118i	$-0.585528\pi$
$619$	−13.2098	−0.530948	−0.265474	+	0.964118i	$0.585528\pi$
$620$	−32.0600	−1.28756
$621$	−0.959341	−0.0384970
$622$	0.508858	0.0204034
$623$	−1.80656	−0.0723782
$624$	0	0
$625$	12.5787	0.503147
$626$	−5.90262	−0.235916
$627$	−8.07966	−0.322671
$628$	3.19212	0.127380
$629$	42.3511	1.68865
$630$	−0.757702	−0.0301876
$631$	−37.1511	−1.47896	−0.739482	−	0.673177i	$-0.764929\pi$
$631$	−37.1511	−1.47896	−0.739482	+	0.673177i	$0.764929\pi$
$632$	2.84556	0.113190
$633$	−25.2000	−1.00161
$634$	1.97904	0.0785979
$635$	26.1819	1.03900
$636$	−21.3934	−0.848305
$637$	0	0
$638$	3.24884	0.128623
$639$	−3.63738	−0.143892
$640$	−23.0292	−0.910307
$641$	−16.9593	−0.669854	−0.334927	−	0.942244i	$-0.608712\pi$
$641$	−16.9593	−0.669854	−0.334927	+	0.942244i	$0.608712\pi$
$642$	−1.50721	−0.0594846
$643$	−22.6131	−0.891774	−0.445887	−	0.895089i	$-0.647112\pi$
$643$	−22.6131	−0.891774	−0.445887	+	0.895089i	$0.647112\pi$
$644$	1.87968	0.0740697
$645$	3.60492	0.141944
$646$	1.18888	0.0467760
$647$	1.28296	0.0504382	0.0252191	−	0.999682i	$-0.491972\pi$
$647$	1.28296	0.0504382	0.0252191	+	0.999682i	$0.491972\pi$
$648$	0.798360	0.0313626
$649$	−71.3577	−2.80103
$650$	0	0
$651$	−4.35442	−0.170663
$652$	−6.19668	−0.242681
$653$	−48.9803	−1.91675	−0.958374	−	0.285517i	$-0.907835\pi$
$653$	−48.9803	−1.91675	−0.958374	+	0.285517i	$0.907835\pi$
$654$	−1.92034	−0.0750911
$655$	36.6665	1.43268
$656$	−10.5462	−0.411760
$657$	7.95934	0.310523
$658$	1.34622	0.0524813
$659$	10.2115	0.397783	0.198892	−	0.980021i	$-0.436266\pi$
$659$	10.2115	0.397783	0.198892	+	0.980021i	$0.436266\pi$
$660$	42.3918	1.65010
$661$	−25.7072	−0.999894	−0.499947	−	0.866056i	$-0.666647\pi$
$661$	−25.7072	−0.999894	−0.499947	+	0.866056i	$0.666647\pi$
$662$	7.00033	0.272076
$663$	0	0
$664$	−11.6275	−0.451236
$665$	−5.27311	−0.204482
$666$	−2.03246	−0.0787562
$667$	2.68458	0.103947
$668$	21.2341	0.821572
$669$	−4.67804	−0.180863
$670$	−5.76226	−0.222616
$671$	−76.7039	−2.96112
$672$	−2.35442	−0.0908238
$673$	8.58886	0.331076	0.165538	−	0.986203i	$-0.447064\pi$
$673$	8.58886	0.331076	0.165538	+	0.986203i	$0.447064\pi$
$674$	−1.10227	−0.0424580
$675$	−9.12032	−0.351041
$676$	0	0
$677$	8.70065	0.334393	0.167197	−	0.985924i	$-0.446529\pi$
$677$	8.70065	0.334393	0.167197	+	0.985924i	$0.446529\pi$
$678$	−1.99015	−0.0764312
$679$	−16.2731	−0.624504
$680$	−12.6049	−0.483377
$681$	15.7885	0.605017
$682$	−5.05540	−0.193581
$683$	−22.4747	−0.859972	−0.429986	−	0.902836i	$-0.641482\pi$
$683$	−22.4747	−0.859972	−0.429986	+	0.902836i	$0.641482\pi$
$684$	2.74950	0.105130
$685$	−12.4829	−0.476949
$686$	0.201640	0.00769864
$687$	22.3770	0.853737
$688$	3.60492	0.137436
$689$	0	0
$690$	−0.726895	−0.0276724
$691$	23.8275	0.906441	0.453221	−	0.891398i	$-0.350275\pi$
$691$	23.8275	0.906441	0.453221	+	0.891398i	$0.350275\pi$
$692$	−17.3951	−0.661262
$693$	5.75770	0.218717
$694$	−4.45015	−0.168925
$695$	−3.00000	−0.113796
$696$	−2.23410	−0.0846833
$697$	−11.7921	−0.446659
$698$	−2.69079	−0.101848
$699$	−7.64392	−0.289120
$700$	17.8698	0.675416
$701$	−51.9885	−1.96358	−0.981789	−	0.189974i	$-0.939160\pi$
$701$	−51.9885	−1.96358	−0.981789	+	0.189974i	$0.939160\pi$
$702$	0	0
$703$	−14.1446	−0.533473
$704$	40.5380	1.52783
$705$	25.0879	0.944864
$706$	−5.50886	−0.207329
$707$	2.16918	0.0815804
$708$	24.2830	0.912609
$709$	7.63407	0.286704	0.143352	−	0.989672i	$-0.454212\pi$
$709$	7.63407	0.286704	0.143352	+	0.989672i	$0.454212\pi$
$710$	−2.75605	−0.103433
$711$	3.56426	0.133670
$712$	1.44228	0.0540519
$713$	−4.17738	−0.156444
$714$	−0.847217	−0.0317063
$715$	0	0
$716$	10.0003	0.373730
$717$	19.5967	0.731853
$718$	0.436073	0.0162741
$719$	−29.1043	−1.08541	−0.542703	−	0.839925i	$-0.682599\pi$
$719$	−29.1043	−1.08541	−0.542703	+	0.839925i	$0.682599\pi$
$720$	−14.1203	−0.526233
$721$	8.43409	0.314102
$722$	3.43409	0.127803
$723$	−18.9006	−0.702922
$724$	−22.0718	−0.820292
$725$	25.5219	0.947861
$726$	4.46655	0.165769
$727$	−4.23245	−0.156973	−0.0784864	−	0.996915i	$-0.525009\pi$
$727$	−4.23245	−0.156973	−0.0784864	+	0.996915i	$0.525009\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	6.03081	0.223210
$731$	4.03081	0.149085
$732$	26.1023	0.964768
$733$	28.6993	1.06003	0.530017	−	0.847987i	$-0.322186\pi$
$733$	28.6993	1.06003	0.530017	+	0.847987i	$0.322186\pi$
$734$	2.96721	0.109522
$735$	3.75770	0.138605
$736$	−2.25869	−0.0832566
$737$	43.7869	1.61291
$738$	0.565914	0.0208316
$739$	−2.52327	−0.0928199	−0.0464100	−	0.998922i	$-0.514778\pi$
$739$	−2.52327	−0.0928199	−0.0464100	+	0.998922i	$0.514778\pi$
$740$	74.2127	2.72811
$741$	0	0
$742$	−2.20164	−0.0808247
$743$	26.7170	0.980153	0.490077	−	0.871679i	$-0.336969\pi$
$743$	26.7170	0.980153	0.490077	+	0.871679i	$0.336969\pi$
$744$	3.47640	0.127451
$745$	−73.3269	−2.68649
$746$	6.41769	0.234968
$747$	−14.5643	−0.532878
$748$	47.4000	1.73311
$749$	7.47474	0.273121
$750$	−3.12198	−0.113998
$751$	−37.6829	−1.37507	−0.687535	−	0.726151i	$-0.741307\pi$
$751$	−37.6829	−1.37507	−0.687535	+	0.726151i	$0.741307\pi$
$752$	25.0879	0.914860
$753$	5.32362	0.194003
$754$	0	0
$755$	34.2406	1.24614
$756$	−1.95934	−0.0712606
$757$	−6.40982	−0.232969	−0.116485	−	0.993193i	$-0.537163\pi$
$757$	−6.40982	−0.232969	−0.116485	+	0.993193i	$0.537163\pi$
$758$	−5.57702	−0.202566
$759$	5.52360	0.200494
$760$	4.20984	0.152707
$761$	4.21149	0.152666	0.0763332	−	0.997082i	$-0.475679\pi$
$761$	4.21149	0.152666	0.0763332	+	0.997082i	$0.475679\pi$
$762$	−1.40493	−0.0508953
$763$	9.52360	0.344778
$764$	−26.9400	−0.974654
$765$	−15.7885	−0.570835
$766$	−4.77377	−0.172483
$767$	0	0
$768$	−12.8456	−0.463524
$769$	−27.3856	−0.987549	−0.493774	−	0.869590i	$-0.664383\pi$
$769$	−27.3856	−0.987549	−0.493774	+	0.869590i	$0.664383\pi$
$770$	4.36262	0.157218
$771$	11.7967	0.424848
$772$	31.1708	1.12186
$773$	8.78395	0.315937	0.157968	−	0.987444i	$-0.449506\pi$
$773$	8.78395	0.315937	0.157968	+	0.987444i	$0.449506\pi$
$774$	−0.193441	−0.00695310
$775$	−39.7137	−1.42656
$776$	12.9918	0.466378
$777$	10.0797	0.361606
$778$	−1.77245	−0.0635452
$779$	3.93839	0.141107
$780$	0	0
$781$	20.9429	0.749397
$782$	−0.812771	−0.0290646
$783$	−2.79836	−0.100005
$784$	3.75770	0.134204
$785$	6.12198	0.218503
$786$	−1.96754	−0.0701798
$787$	−31.5039	−1.12299	−0.561496	−	0.827479i	$-0.689774\pi$
$787$	−31.5039	−1.12299	−0.561496	+	0.827479i	$0.689774\pi$
$788$	−3.36751	−0.119963
$789$	−14.1836	−0.504949
$790$	2.70065	0.0960847
$791$	9.86983	0.350931
$792$	−4.59672	−0.163337
$793$	0	0
$794$	−3.45346	−0.122559
$795$	−41.0292	−1.45515
$796$	−15.5629	−0.551614
$797$	28.4570	1.00800	0.504000	−	0.863704i	$-0.331861\pi$
$797$	28.4570	1.00800	0.504000	+	0.863704i	$0.331861\pi$
$798$	0.282957	0.0100166
$799$	28.0518	0.992400
$800$	−21.4731	−0.759188
$801$	1.80656	0.0638316
$802$	3.59507	0.126946
$803$	−45.8275	−1.61722
$804$	−14.9006	−0.525505
$805$	3.60492	0.127057
$806$	0	0
$807$	20.9983	0.739177
$808$	−1.73179	−0.0609240
$809$	−22.2994	−0.784004	−0.392002	−	0.919964i	$-0.628217\pi$
$809$	−22.2994	−0.784004	−0.392002	+	0.919964i	$0.628217\pi$
$810$	0.757702	0.0266229
$811$	−40.2616	−1.41378	−0.706888	−	0.707325i	$-0.749902\pi$
$811$	−40.2616	−1.41378	−0.706888	+	0.707325i	$0.749902\pi$
$812$	5.48294	0.192414
$813$	−11.0082	−0.386074
$814$	11.7023	0.410165
$815$	−11.8842	−0.416287
$816$	−15.7885	−0.552708
$817$	−1.34622	−0.0470984
$818$	−3.57867	−0.125125
$819$	0	0
$820$	−20.6636	−0.721605
$821$	16.0649	0.560670	0.280335	−	0.959902i	$-0.409555\pi$
$821$	16.0649	0.560670	0.280335	+	0.959902i	$0.409555\pi$
$822$	0.669839	0.0233633
$823$	−7.40328	−0.258062	−0.129031	−	0.991641i	$-0.541187\pi$
$823$	−7.40328	−0.258062	−0.129031	+	0.991641i	$0.541187\pi$
$824$	−6.73344	−0.234570
$825$	52.5121	1.82824
$826$	2.49901	0.0869516
$827$	52.4226	1.82291	0.911456	−	0.411398i	$-0.134959\pi$
$827$	52.4226	1.82291	0.911456	+	0.411398i	$0.134959\pi$
$828$	−1.87968	−0.0653233
$829$	9.41769	0.327090	0.163545	−	0.986536i	$-0.447707\pi$
$829$	9.41769	0.327090	0.163545	+	0.986536i	$0.447707\pi$
$830$	−11.0354	−0.383043
$831$	30.1757	1.04678
$832$	0	0
$833$	4.20164	0.145578
$834$	0.160981	0.00557432
$835$	40.7236	1.40930
$836$	−15.8308	−0.547520
$837$	4.35442	0.150511
$838$	−1.61278	−0.0557127
$839$	44.7301	1.54426	0.772128	−	0.635467i	$-0.219192\pi$
$839$	44.7301	1.54426	0.772128	+	0.635467i	$0.219192\pi$
$840$	−3.00000	−0.103510
$841$	−21.1692	−0.729972
$842$	−4.79340	−0.165192
$843$	−7.48294	−0.257726
$844$	−49.3754	−1.69957
$845$	0	0
$846$	−1.34622	−0.0462841
$847$	−22.1511	−0.761122
$848$	−41.0292	−1.40895
$849$	−2.07312	−0.0711493
$850$	−7.72689	−0.265030
$851$	9.66984	0.331478
$852$	−7.12687	−0.244162
$853$	41.4550	1.41939	0.709697	−	0.704507i	$-0.248832\pi$
$853$	41.4550	1.41939	0.709697	+	0.704507i	$0.248832\pi$
$854$	2.68624	0.0919211
$855$	5.27311	0.180336
$856$	−5.96754	−0.203966
$857$	19.9885	0.682794	0.341397	−	0.939919i	$-0.389100\pi$
$857$	19.9885	0.682794	0.341397	+	0.939919i	$0.389100\pi$
$858$	0	0
$859$	29.9642	1.02237	0.511183	−	0.859472i	$-0.329207\pi$
$859$	29.9642	1.02237	0.511183	+	0.859472i	$0.329207\pi$
$860$	7.06327	0.240855
$861$	−2.80656	−0.0956473
$862$	1.21638	0.0414302
$863$	−25.1351	−0.855608	−0.427804	−	0.903872i	$-0.640713\pi$
$863$	−25.1351	−0.855608	−0.427804	+	0.903872i	$0.640713\pi$
$864$	2.35442	0.0800991
$865$	−33.3610	−1.13431
$866$	−1.26855	−0.0431070
$867$	−0.653776	−0.0222034
$868$	−8.53180	−0.289588
$869$	−20.5219	−0.696159
$870$	−2.12032	−0.0718857
$871$	0	0
$872$	−7.60327	−0.257479
$873$	16.2731	0.550761
$874$	0.271452	0.00918201
$875$	15.4829	0.523419
$876$	15.5951	0.526909
$877$	−25.7445	−0.869331	−0.434666	−	0.900592i	$-0.643133\pi$
$877$	−25.7445	−0.869331	−0.434666	+	0.900592i	$0.643133\pi$
$878$	−5.94916	−0.200774
$879$	17.7741	0.599505
$880$	81.3006	2.74064
$881$	51.1006	1.72162	0.860812	−	0.508923i	$-0.169956\pi$
$881$	51.1006	1.72162	0.860812	+	0.508923i	$0.169956\pi$
$882$	−0.201640	−0.00678956
$883$	−26.6115	−0.895547	−0.447774	−	0.894147i	$-0.647783\pi$
$883$	−26.6115	−0.895547	−0.447774	+	0.894147i	$0.647783\pi$
$884$	0	0
$885$	46.5708	1.56546
$886$	2.93019	0.0984416
$887$	−25.0308	−0.840452	−0.420226	−	0.907419i	$-0.638049\pi$
$887$	−25.0308	−0.840452	−0.420226	+	0.907419i	$0.638049\pi$
$888$	−8.04720	−0.270046
$889$	6.96754	0.233684
$890$	1.36883	0.0458834
$891$	−5.75770	−0.192890
$892$	−9.16587	−0.306896
$893$	−9.36883	−0.313516
$894$	3.93475	0.131598
$895$	19.1790	0.641084
$896$	−6.12852	−0.204740
$897$	0	0
$898$	2.03577	0.0679344
$899$	−12.1852	−0.406401
$900$	−17.8698	−0.595661
$901$	−45.8764	−1.52836
$902$	−3.25836	−0.108492
$903$	0.959341	0.0319249
$904$	−7.87968	−0.262074
$905$	−42.3302	−1.40710
$906$	−1.83737	−0.0610424
$907$	16.7072	0.554753	0.277377	−	0.960761i	$-0.410535\pi$
$907$	16.7072	0.554753	0.277377	+	0.960761i	$0.410535\pi$
$908$	30.9351	1.02662
$909$	−2.16918	−0.0719471
$910$	0	0
$911$	57.5593	1.90702	0.953512	−	0.301354i	$-0.0974386\pi$
$911$	57.5593	1.90702	0.953512	+	0.301354i	$0.0974386\pi$
$912$	5.27311	0.174610
$913$	83.8567	2.77525
$914$	3.75406	0.124173
$915$	50.0600	1.65493
$916$	43.8442	1.44865
$917$	9.75770	0.322228
$918$	0.847217	0.0279623
$919$	−14.2731	−0.470826	−0.235413	−	0.971895i	$-0.575644\pi$
$919$	−14.2731	−0.470826	−0.235413	+	0.971895i	$0.575644\pi$
$920$	−2.87802	−0.0948857
$921$	−3.84556	−0.126716
$922$	6.19800	0.204120
$923$	0	0
$924$	11.2813	0.371128
$925$	91.9298	3.02263
$926$	−6.14492	−0.201935
$927$	−8.43409	−0.277012
$928$	−6.58852	−0.216279
$929$	−53.8131	−1.76555	−0.882775	−	0.469795i	$-0.844328\pi$
$929$	−53.8131	−1.76555	−0.882775	+	0.469795i	$0.844328\pi$
$930$	3.29935	0.108190
$931$	−1.40328	−0.0459906
$932$	−14.9771	−0.490590
$933$	2.52360	0.0826190
$934$	2.15767	0.0706013
$935$	90.9055	2.97293
$936$	0	0
$937$	59.2715	1.93631	0.968157	−	0.250344i	$-0.0805437\pi$
$937$	59.2715	1.93631	0.968157	+	0.250344i	$0.0805437\pi$
$938$	−1.53345	−0.0500690
$939$	−29.2731	−0.955292
$940$	49.1557	1.60328
$941$	16.3367	0.532561	0.266281	−	0.963896i	$-0.414205\pi$
$941$	16.3367	0.532561	0.266281	+	0.963896i	$0.414205\pi$
$942$	−0.328507	−0.0107034
$943$	−2.69245	−0.0876782
$944$	46.5708	1.51575
$945$	−3.75770	−0.122238
$946$	1.11378	0.0362120
$947$	−57.4180	−1.86584	−0.932918	−	0.360090i	$-0.882746\pi$
$947$	−57.4180	−1.86584	−0.932918	+	0.360090i	$0.882746\pi$
$948$	6.98360	0.226817
$949$	0	0
$950$	2.58066	0.0837276
$951$	9.81476	0.318265
$952$	−3.35442	−0.108717
$953$	24.6829	0.799559	0.399779	−	0.916611i	$-0.369087\pi$
$953$	24.6829	0.799559	0.399779	+	0.916611i	$0.369087\pi$
$954$	2.20164	0.0712807
$955$	−51.6665	−1.67189
$956$	38.3967	1.24184
$957$	16.1121	0.520831
$958$	−1.44228	−0.0465981
$959$	−3.32196	−0.107272
$960$	−26.4567	−0.853886
$961$	−12.0390	−0.388355
$962$	0	0
$963$	−7.47474	−0.240870
$964$	−37.0328	−1.19275
$965$	59.7806	1.92441
$966$	−0.193441	−0.00622387
$967$	−18.2098	−0.585589	−0.292794	−	0.956175i	$-0.594585\pi$
$967$	−18.2098	−0.585589	−0.292794	+	0.956175i	$0.594585\pi$
$968$	17.6846	0.568404
$969$	5.89607	0.189409
$970$	12.3302	0.395898
$971$	9.24395	0.296653	0.148326	−	0.988938i	$-0.452611\pi$
$971$	9.24395	0.296653	0.148326	+	0.988938i	$0.452611\pi$
$972$	1.95934	0.0628459
$973$	−0.798360	−0.0255943
$974$	−7.30590	−0.234096
$975$	0	0
$976$	50.0600	1.60238
$977$	−11.7495	−0.375900	−0.187950	−	0.982179i	$-0.560184\pi$
$977$	−11.7495	−0.375900	−0.187950	+	0.982179i	$0.560184\pi$
$978$	0.637713	0.0203918
$979$	−10.4016	−0.332437
$980$	7.36262	0.235190
$981$	−9.52360	−0.304065
$982$	1.43574	0.0458163
$983$	−24.1121	−0.769057	−0.384529	−	0.923113i	$-0.625636\pi$
$983$	−24.1121	−0.769057	−0.384529	+	0.923113i	$0.625636\pi$
$984$	2.24065	0.0714292
$985$	−6.45835	−0.205780
$986$	−2.37082	−0.0755023
$987$	6.67638	0.212512
$988$	0	0
$989$	0.920336	0.0292650
$990$	−4.36262	−0.138653
$991$	−25.0226	−0.794869	−0.397435	−	0.917630i	$-0.630099\pi$
$991$	−25.0226	−0.794869	−0.397435	+	0.917630i	$0.630099\pi$
$992$	10.2521	0.325506
$993$	34.7170	1.10171
$994$	−0.733440	−0.0232633
$995$	−29.8472	−0.946220
$996$	−28.5364	−0.904209
$997$	45.8990	1.45364	0.726818	−	0.686830i	$-0.240999\pi$
$997$	45.8990	1.45364	0.726818	+	0.686830i	$0.240999\pi$
$998$	−6.50886	−0.206034
$999$	−10.0797	−0.318906

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.l.1.2		3
13.4	even	6		273.2.k.b.211.2	yes	6
13.10	even	6		273.2.k.b.22.2	✓	6
13.12	even	2		3549.2.a.m.1.2		3
39.17	odd	6		819.2.o.f.757.2		6
39.23	odd	6		819.2.o.f.568.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.b.22.2	✓	6	13.10	even	6
273.2.k.b.211.2	yes	6	13.4	even	6
819.2.o.f.568.2		6	39.23	odd	6
819.2.o.f.757.2		6	39.17	odd	6
3549.2.a.l.1.2		3	1.1	even	1	trivial
3549.2.a.m.1.2		3	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-0.201640 q^{2} -1.00000 q^{3} -1.95934 q^{4} -3.75770 q^{5} +0.201640 q^{6} -1.00000 q^{7} +0.798360 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.201640 q^{2} -1.00000 q^{3} -1.95934 q^{4} -3.75770 q^{5} +0.201640 q^{6} -1.00000 q^{7} +0.798360 q^{8} +1.00000 q^{9} +0.757702 q^{10} -5.75770 q^{11} +1.95934 q^{12} +0.201640 q^{14} +3.75770 q^{15} +3.75770 q^{16} +4.20164 q^{17} -0.201640 q^{18} -1.40328 q^{19} +7.36262 q^{20} +1.00000 q^{21} +1.16098 q^{22} +0.959341 q^{23} -0.798360 q^{24} +9.12032 q^{25} -1.00000 q^{27} +1.95934 q^{28} +2.79836 q^{29} -0.757702 q^{30} -4.35442 q^{31} -2.35442 q^{32} +5.75770 q^{33} -0.847217 q^{34} +3.75770 q^{35} -1.95934 q^{36} +10.0797 q^{37} +0.282957 q^{38} -3.00000 q^{40} -2.80656 q^{41} -0.201640 q^{42} +0.959341 q^{43} +11.2813 q^{44} -3.75770 q^{45} -0.193441 q^{46} +6.67638 q^{47} -3.75770 q^{48} +1.00000 q^{49} -1.83902 q^{50} -4.20164 q^{51} -10.9187 q^{53} +0.201640 q^{54} +21.6357 q^{55} -0.798360 q^{56} +1.40328 q^{57} -0.564260 q^{58} +12.3934 q^{59} -7.36262 q^{60} +13.3220 q^{61} +0.878024 q^{62} -1.00000 q^{63} -7.04066 q^{64} -1.16098 q^{66} -7.60492 q^{67} -8.23245 q^{68} -0.959341 q^{69} -0.757702 q^{70} -3.63738 q^{71} +0.798360 q^{72} +7.95934 q^{73} -2.03246 q^{74} -9.12032 q^{75} +2.74950 q^{76} +5.75770 q^{77} +3.56426 q^{79} -14.1203 q^{80} +1.00000 q^{81} +0.565914 q^{82} -14.5643 q^{83} -1.95934 q^{84} -15.7885 q^{85} -0.193441 q^{86} -2.79836 q^{87} -4.59672 q^{88} +1.80656 q^{89} +0.757702 q^{90} -1.87968 q^{92} +4.35442 q^{93} -1.34622 q^{94} +5.27311 q^{95} +2.35442 q^{96} +16.2731 q^{97} -0.201640 q^{98} -5.75770 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 4 q^{4} - 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 4 * q^4 - 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 4 q^{4} - 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} - 8 q^{11} - 4 q^{12} + 2 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{19} + 11 q^{20} + 3 q^{21} - 7 q^{22} - 7 q^{23} - 3 q^{24} + 7 q^{25} - 3 q^{27} - 4 q^{28} + 9 q^{29} + 7 q^{30} - 5 q^{31} + q^{32} + 8 q^{33} - 10 q^{34} + 2 q^{35} + 4 q^{36} + 20 q^{38} - 9 q^{40} - 6 q^{41} - 7 q^{43} + 3 q^{44} - 2 q^{45} - 3 q^{46} - 9 q^{47} - 2 q^{48} + 3 q^{49} - 16 q^{50} - 12 q^{51} - 13 q^{53} + 26 q^{55} - 3 q^{56} + 3 q^{57} + 10 q^{58} - 11 q^{59} - 11 q^{60} + 19 q^{61} - 27 q^{62} - 3 q^{63} - 31 q^{64} + 7 q^{66} - 21 q^{67} + 13 q^{68} + 7 q^{69} + 7 q^{70} - 22 q^{71} + 3 q^{72} + 14 q^{73} - 19 q^{74} - 7 q^{75} + 2 q^{76} + 8 q^{77} - q^{79} - 22 q^{80} + 3 q^{81} + 40 q^{82} - 32 q^{83} + 4 q^{84} - q^{85} - 3 q^{86} - 9 q^{87} - 15 q^{88} + 3 q^{89} - 7 q^{90} - 26 q^{92} + 5 q^{93} + q^{94} - 12 q^{95} - q^{96} + 21 q^{97} - 8 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 4 * q^4 - 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 - 8 * q^11 - 4 * q^12 + 2 * q^15 + 2 * q^16 + 12 * q^17 - 3 * q^19 + 11 * q^20 + 3 * q^21 - 7 * q^22 - 7 * q^23 - 3 * q^24 + 7 * q^25 - 3 * q^27 - 4 * q^28 + 9 * q^29 + 7 * q^30 - 5 * q^31 + q^32 + 8 * q^33 - 10 * q^34 + 2 * q^35 + 4 * q^36 + 20 * q^38 - 9 * q^40 - 6 * q^41 - 7 * q^43 + 3 * q^44 - 2 * q^45 - 3 * q^46 - 9 * q^47 - 2 * q^48 + 3 * q^49 - 16 * q^50 - 12 * q^51 - 13 * q^53 + 26 * q^55 - 3 * q^56 + 3 * q^57 + 10 * q^58 - 11 * q^59 - 11 * q^60 + 19 * q^61 - 27 * q^62 - 3 * q^63 - 31 * q^64 + 7 * q^66 - 21 * q^67 + 13 * q^68 + 7 * q^69 + 7 * q^70 - 22 * q^71 + 3 * q^72 + 14 * q^73 - 19 * q^74 - 7 * q^75 + 2 * q^76 + 8 * q^77 - q^79 - 22 * q^80 + 3 * q^81 + 40 * q^82 - 32 * q^83 + 4 * q^84 - q^85 - 3 * q^86 - 9 * q^87 - 15 * q^88 + 3 * q^89 - 7 * q^90 - 26 * q^92 + 5 * q^93 + q^94 - 12 * q^95 - q^96 + 21 * q^97 - 8 * q^99

Introduction

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