LMFDB - Embedded newform 3549.2.a.s.1.1

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:	$0$
Dimension:	$3$
Coefficient field:	3.3.169.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x - 1 $ x^3 - x^2 - 4*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			1.1
Root			$2.65109$ 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)

$f(q)$	$=$	$q-1.65109 q^{2} -1.00000 q^{3} +0.726109 q^{4} -2.92498 q^{5} +1.65109 q^{6} +1.00000 q^{7} +2.10331 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.65109 q^{2} -1.00000 q^{3} +0.726109 q^{4} -2.92498 q^{5} +1.65109 q^{6} +1.00000 q^{7} +2.10331 q^{8} +1.00000 q^{9} +4.82942 q^{10} +4.37720 q^{11} -0.726109 q^{12} -1.65109 q^{14} +2.92498 q^{15} -4.92498 q^{16} +3.65109 q^{17} -1.65109 q^{18} +5.75441 q^{19} -2.12386 q^{20} -1.00000 q^{21} -7.22717 q^{22} +7.02830 q^{23} -2.10331 q^{24} +3.55553 q^{25} -1.00000 q^{27} +0.726109 q^{28} +1.19887 q^{29} -4.82942 q^{30} +6.47277 q^{31} +3.92498 q^{32} -4.37720 q^{33} -6.02830 q^{34} -2.92498 q^{35} +0.726109 q^{36} +2.92498 q^{37} -9.50106 q^{38} -6.15215 q^{40} +8.60437 q^{41} +1.65109 q^{42} -5.72611 q^{43} +3.17833 q^{44} -2.92498 q^{45} -11.6044 q^{46} +9.58383 q^{47} +4.92498 q^{48} +1.00000 q^{49} -5.87051 q^{50} -3.65109 q^{51} -0.302187 q^{53} +1.65109 q^{54} -12.8032 q^{55} +2.10331 q^{56} -5.75441 q^{57} -1.97945 q^{58} -3.02830 q^{59} +2.12386 q^{60} -0.302187 q^{61} -10.6871 q^{62} +1.00000 q^{63} +3.36945 q^{64} +7.22717 q^{66} +8.70769 q^{67} +2.65109 q^{68} -7.02830 q^{69} +4.82942 q^{70} -13.5371 q^{71} +2.10331 q^{72} -0.932734 q^{73} -4.82942 q^{74} -3.55553 q^{75} +4.17833 q^{76} +4.37720 q^{77} -16.9426 q^{79} +14.4055 q^{80} +1.00000 q^{81} -14.2066 q^{82} +1.26614 q^{83} -0.726109 q^{84} -10.6794 q^{85} +9.45434 q^{86} -1.19887 q^{87} +9.20662 q^{88} +13.3977 q^{89} +4.82942 q^{90} +5.10331 q^{92} -6.47277 q^{93} -15.8238 q^{94} -16.8315 q^{95} -3.92498 q^{96} -11.9250 q^{97} -1.65109 q^{98} +4.37720 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 13 q^{10} + 8 q^{11} - 4 q^{12} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 7 q^{19} + 13 q^{20} - 3 q^{21} + q^{22} + 9 q^{23} - 3 q^{24} + 11 q^{25} - 3 q^{27} + 4 q^{28} - 7 q^{29} - 13 q^{30} + 7 q^{31} + 3 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} - 4 q^{38} + 13 q^{40} - 2 q^{41} - 2 q^{42} - 19 q^{43} + 15 q^{44} - 7 q^{46} + 17 q^{47} + 6 q^{48} + 3 q^{49} + 16 q^{50} - 4 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} - 7 q^{57} - 22 q^{58} + 3 q^{59} - 13 q^{60} + 13 q^{61} - 17 q^{62} + 3 q^{63} + q^{64} - q^{66} - 5 q^{67} + q^{68} - 9 q^{69} + 13 q^{70} - 8 q^{71} + 3 q^{72} + 2 q^{73} - 13 q^{74} - 11 q^{75} + 18 q^{76} + 8 q^{77} - q^{79} + 26 q^{80} + 3 q^{81} - 36 q^{82} - 2 q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} + 7 q^{87} + 21 q^{88} + 19 q^{89} + 13 q^{90} + 12 q^{92} - 7 q^{93} + 7 q^{94} - 3 q^{96} - 27 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 13 * q^10 + 8 * q^11 - 4 * q^12 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 7 * q^19 + 13 * q^20 - 3 * q^21 + q^22 + 9 * q^23 - 3 * q^24 + 11 * q^25 - 3 * q^27 + 4 * q^28 - 7 * q^29 - 13 * q^30 + 7 * q^31 + 3 * q^32 - 8 * q^33 - 6 * q^34 + 4 * q^36 - 4 * q^38 + 13 * q^40 - 2 * q^41 - 2 * q^42 - 19 * q^43 + 15 * q^44 - 7 * q^46 + 17 * q^47 + 6 * q^48 + 3 * q^49 + 16 * q^50 - 4 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 - 7 * q^57 - 22 * q^58 + 3 * q^59 - 13 * q^60 + 13 * q^61 - 17 * q^62 + 3 * q^63 + q^64 - q^66 - 5 * q^67 + q^68 - 9 * q^69 + 13 * q^70 - 8 * q^71 + 3 * q^72 + 2 * q^73 - 13 * q^74 - 11 * q^75 + 18 * q^76 + 8 * q^77 - q^79 + 26 * q^80 + 3 * q^81 - 36 * q^82 - 2 * q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 + 7 * q^87 + 21 * q^88 + 19 * q^89 + 13 * q^90 + 12 * q^92 - 7 * q^93 + 7 * q^94 - 3 * q^96 - 27 * q^97 + 2 * q^98 + 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 $

$2$	−1.65109	−1.16750	−0.583750	−	0.811934i	$-0.698415\pi$
$2$	−1.65109	−1.16750	−0.583750	+	0.811934i	$0.698415\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.726109	0.363055
$5$	−2.92498	−1.30809	−0.654046	−	0.756455i	$-0.726930\pi$
$5$	−2.92498	−1.30809	−0.654046	+	0.756455i	$0.726930\pi$
$6$	1.65109	0.674056
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.10331	0.743633
$9$	1.00000	0.333333
$10$	4.82942	1.52720
$11$	4.37720	1.31978	0.659888	−	0.751364i	$-0.270604\pi$
$11$	4.37720	1.31978	0.659888	+	0.751364i	$0.270604\pi$
$12$	−0.726109	−0.209610
$13$	0	0
$13$	0	0
$14$	−1.65109	−0.441273
$15$	2.92498	0.755228
$16$	−4.92498	−1.23125
$17$	3.65109	0.885520	0.442760	−	0.896640i	$-0.353999\pi$
$17$	3.65109	0.885520	0.442760	+	0.896640i	$0.353999\pi$
$18$	−1.65109	−0.389166
$19$	5.75441	1.32015	0.660076	−	0.751199i	$-0.270524\pi$
$19$	5.75441	1.32015	0.660076	+	0.751199i	$0.270524\pi$
$20$	−2.12386	−0.474909
$21$	−1.00000	−0.218218
$22$	−7.22717	−1.54084
$23$	7.02830	1.46550	0.732751	−	0.680497i	$-0.238236\pi$
$23$	7.02830	1.46550	0.732751	+	0.680497i	$0.238236\pi$
$24$	−2.10331	−0.429337
$25$	3.55553	0.711106
$26$	0	0
$27$	−1.00000	−0.192450
$28$	0.726109	0.137222
$29$	1.19887	0.222625	0.111313	−	0.993785i	$-0.464494\pi$
$29$	1.19887	0.222625	0.111313	+	0.993785i	$0.464494\pi$
$30$	−4.82942	−0.881728
$31$	6.47277	1.16254	0.581271	−	0.813710i	$-0.302555\pi$
$31$	6.47277	1.16254	0.581271	+	0.813710i	$0.302555\pi$
$32$	3.92498	0.693846
$33$	−4.37720	−0.761973
$34$	−6.02830	−1.03384
$35$	−2.92498	−0.494413
$36$	0.726109	0.121018
$37$	2.92498	0.480864	0.240432	−	0.970666i	$-0.422711\pi$
$37$	2.92498	0.480864	0.240432	+	0.970666i	$0.422711\pi$
$38$	−9.50106	−1.54128
$39$	0	0
$40$	−6.15215	−0.972741
$41$	8.60437	1.34378	0.671889	−	0.740652i	$-0.265483\pi$
$41$	8.60437	1.34378	0.671889	+	0.740652i	$0.265483\pi$
$42$	1.65109	0.254769
$43$	−5.72611	−0.873224	−0.436612	−	0.899650i	$-0.643822\pi$
$43$	−5.72611	−0.873224	−0.436612	+	0.899650i	$0.643822\pi$
$44$	3.17833	0.479151
$45$	−2.92498	−0.436031
$46$	−11.6044	−1.71097
$47$	9.58383	1.39794	0.698972	−	0.715149i	$-0.253641\pi$
$47$	9.58383	1.39794	0.698972	+	0.715149i	$0.253641\pi$
$48$	4.92498	0.710860
$49$	1.00000	0.142857
$50$	−5.87051	−0.830216
$51$	−3.65109	−0.511255
$52$	0	0
$53$	−0.302187	−0.0415086	−0.0207543	−	0.999785i	$-0.506607\pi$
$53$	−0.302187	−0.0415086	−0.0207543	+	0.999785i	$0.506607\pi$
$54$	1.65109	0.224685
$55$	−12.8032	−1.72639
$56$	2.10331	0.281067
$57$	−5.75441	−0.762190
$58$	−1.97945	−0.259915
$59$	−3.02830	−0.394251	−0.197125	−	0.980378i	$-0.563161\pi$
$59$	−3.02830	−0.394251	−0.197125	+	0.980378i	$0.563161\pi$
$60$	2.12386	0.274189
$61$	−0.302187	−0.0386911	−0.0193455	−	0.999813i	$-0.506158\pi$
$61$	−0.302187	−0.0386911	−0.0193455	+	0.999813i	$0.506158\pi$
$62$	−10.6871	−1.35727
$63$	1.00000	0.125988
$64$	3.36945	0.421182
$65$	0	0
$66$	7.22717	0.889603
$67$	8.70769	1.06381	0.531907	−	0.846803i	$-0.321476\pi$
$67$	8.70769	1.06381	0.531907	+	0.846803i	$0.321476\pi$
$68$	2.65109	0.321492
$69$	−7.02830	−0.846107
$70$	4.82942	0.577226
$71$	−13.5371	−1.60656	−0.803280	−	0.595602i	$-0.796913\pi$
$71$	−13.5371	−1.60656	−0.803280	+	0.595602i	$0.796913\pi$
$72$	2.10331	0.247878
$73$	−0.932734	−0.109168	−0.0545841	−	0.998509i	$-0.517383\pi$
$73$	−0.932734	−0.109168	−0.0545841	+	0.998509i	$0.517383\pi$
$74$	−4.82942	−0.561409
$75$	−3.55553	−0.410557
$76$	4.17833	0.479287
$77$	4.37720	0.498829
$78$	0	0
$79$	−16.9426	−1.90619	−0.953096	−	0.302668i	$-0.902123\pi$
$79$	−16.9426	−1.90619	−0.953096	+	0.302668i	$0.902123\pi$
$80$	14.4055	1.61058
$81$	1.00000	0.111111
$82$	−14.2066	−1.56886
$83$	1.26614	0.138977	0.0694885	−	0.997583i	$-0.477863\pi$
$83$	1.26614	0.138977	0.0694885	+	0.997583i	$0.477863\pi$
$84$	−0.726109	−0.0792250
$85$	−10.6794	−1.15834
$86$	9.45434	1.01949
$87$	−1.19887	−0.128533
$88$	9.20662	0.981429
$89$	13.3977	1.42016	0.710079	−	0.704122i	$-0.248659\pi$
$89$	13.3977	1.42016	0.710079	+	0.704122i	$0.248659\pi$
$90$	4.82942	0.509066
$91$	0	0
$92$	5.10331	0.532057
$93$	−6.47277	−0.671194
$94$	−15.8238	−1.63210
$95$	−16.8315	−1.72688
$96$	−3.92498	−0.400592
$97$	−11.9250	−1.21080	−0.605399	−	0.795922i	$-0.706987\pi$
$97$	−11.9250	−1.21080	−0.605399	+	0.795922i	$0.706987\pi$
$98$	−1.65109	−0.166786
$99$	4.37720	0.439925
$100$	2.58170	0.258170
$101$	11.0283	1.09736	0.548678	−	0.836034i	$-0.315131\pi$
$101$	11.0283	1.09736	0.548678	+	0.836034i	$0.315131\pi$
$102$	6.02830	0.596890
$103$	−19.4543	−1.91689	−0.958447	−	0.285272i	$-0.907916\pi$
$103$	−19.4543	−1.91689	−0.958447	+	0.285272i	$0.907916\pi$
$104$	0	0
$105$	2.92498	0.285449
$106$	0.498939	0.0484612
$107$	−1.42392	−0.137656	−0.0688279	−	0.997629i	$-0.521926\pi$
$107$	−1.42392	−0.137656	−0.0688279	+	0.997629i	$0.521926\pi$
$108$	−0.726109	−0.0698699
$109$	0.0467198	0.00447494	0.00223747	−	0.999997i	$-0.499288\pi$
$109$	0.0467198	0.00447494	0.00223747	+	0.999997i	$0.499288\pi$
$110$	21.1394	2.01556
$111$	−2.92498	−0.277627
$112$	−4.92498	−0.465367
$113$	−10.3382	−0.972539	−0.486270	−	0.873809i	$-0.661643\pi$
$113$	−10.3382	−0.972539	−0.486270	+	0.873809i	$0.661643\pi$
$114$	9.50106	0.889856
$115$	−20.5577	−1.91701
$116$	0.870514	0.0808252
$117$	0	0
$118$	5.00000	0.460287
$119$	3.65109	0.334695
$120$	6.15215	0.561612
$121$	8.15990	0.741810
$122$	0.498939	0.0451718
$123$	−8.60437	−0.775830
$124$	4.69994	0.422067
$125$	4.22505	0.377900
$126$	−1.65109	−0.147091
$127$	−5.47277	−0.485629	−0.242815	−	0.970073i	$-0.578071\pi$
$127$	−5.47277	−0.485629	−0.242815	+	0.970073i	$0.578071\pi$
$128$	−13.4132	−1.18557
$129$	5.72611	0.504156
$130$	0	0
$131$	16.1706	1.41283	0.706415	−	0.707798i	$-0.250311\pi$
$131$	16.1706	1.41283	0.706415	+	0.707798i	$0.250311\pi$
$132$	−3.17833	−0.276638
$133$	5.75441	0.498970
$134$	−14.3772	−1.24200
$135$	2.92498	0.251743
$136$	7.67939	0.658502
$137$	12.0176	1.02673	0.513367	−	0.858169i	$-0.328398\pi$
$137$	12.0176	1.02673	0.513367	+	0.858169i	$0.328398\pi$
$138$	11.6044	0.987830
$139$	1.34891	0.114413	0.0572064	−	0.998362i	$-0.481781\pi$
$139$	1.34891	0.114413	0.0572064	+	0.998362i	$0.481781\pi$
$140$	−2.12386	−0.179499
$141$	−9.58383	−0.807104
$142$	22.3510	1.87566
$143$	0	0
$144$	−4.92498	−0.410415
$145$	−3.50669	−0.291215
$146$	1.54003	0.127454
$147$	−1.00000	−0.0824786
$148$	2.12386	0.174580
$149$	3.07502	0.251915	0.125958	−	0.992036i	$-0.459800\pi$
$149$	3.07502	0.251915	0.125958	+	0.992036i	$0.459800\pi$
$150$	5.87051	0.479325
$151$	−16.6610	−1.35585	−0.677925	−	0.735131i	$-0.737121\pi$
$151$	−16.6610	−1.35585	−0.677925	+	0.735131i	$0.737121\pi$
$152$	12.1033	0.981708
$153$	3.65109	0.295173
$154$	−7.22717	−0.582382
$155$	−18.9327	−1.52071
$156$	0	0
$157$	12.8294	1.02390	0.511950	−	0.859015i	$-0.328923\pi$
$157$	12.8294	1.02390	0.511950	+	0.859015i	$0.328923\pi$
$158$	27.9738	2.22548
$159$	0.302187	0.0239650
$160$	−11.4805	−0.907614
$161$	7.02830	0.553907
$162$	−1.65109	−0.129722
$163$	21.6044	1.69219	0.846093	−	0.533036i	$-0.178949\pi$
$163$	21.6044	1.69219	0.846093	+	0.533036i	$0.178949\pi$
$164$	6.24772	0.487865
$165$	12.8032	0.996732
$166$	−2.09052	−0.162256
$167$	−21.3198	−1.64978	−0.824888	−	0.565296i	$-0.808762\pi$
$167$	−21.3198	−1.64978	−0.824888	+	0.565296i	$0.808762\pi$
$168$	−2.10331	−0.162274
$169$	0	0
$170$	17.6327	1.35236
$171$	5.75441	0.440050
$172$	−4.15778	−0.317028
$173$	3.12174	0.237341	0.118671	−	0.992934i	$-0.462137\pi$
$173$	3.12174	0.237341	0.118671	+	0.992934i	$0.462137\pi$
$174$	1.97945	0.150062
$175$	3.55553	0.268773
$176$	−21.5577	−1.62497
$177$	3.02830	0.227621
$178$	−22.1209	−1.65803
$179$	18.9709	1.41795	0.708976	−	0.705233i	$-0.249157\pi$
$179$	18.9709	1.41795	0.708976	+	0.705233i	$0.249157\pi$
$180$	−2.12386	−0.158303
$181$	−1.93273	−0.143659	−0.0718295	−	0.997417i	$-0.522884\pi$
$181$	−1.93273	−0.143659	−0.0718295	+	0.997417i	$0.522884\pi$
$182$	0	0
$183$	0.302187	0.0223383
$184$	14.7827	1.08980
$185$	−8.55553	−0.629015
$186$	10.6871	0.783619
$187$	15.9816	1.16869
$188$	6.95891	0.507531
$189$	−1.00000	−0.0727393
$190$	27.7905	2.01613
$191$	−2.27389	−0.164533	−0.0822665	−	0.996610i	$-0.526216\pi$
$191$	−2.27389	−0.164533	−0.0822665	+	0.996610i	$0.526216\pi$
$192$	−3.36945	−0.243169
$193$	4.38708	0.315789	0.157894	−	0.987456i	$-0.449529\pi$
$193$	4.38708	0.315789	0.157894	+	0.987456i	$0.449529\pi$
$194$	19.6893	1.41361
$195$	0	0
$196$	0.726109	0.0518650
$197$	5.25839	0.374645	0.187322	−	0.982298i	$-0.440019\pi$
$197$	5.25839	0.374645	0.187322	+	0.982298i	$0.440019\pi$
$198$	−7.22717	−0.513613
$199$	13.1960	0.935436	0.467718	−	0.883878i	$-0.345076\pi$
$199$	13.1960	0.935436	0.467718	+	0.883878i	$0.345076\pi$
$200$	7.47839	0.528802
$201$	−8.70769	−0.614193
$202$	−18.2087	−1.28116
$203$	1.19887	0.0841445
$204$	−2.65109	−0.185614
$205$	−25.1677	−1.75779
$206$	32.1209	2.23797
$207$	7.02830	0.488500
$208$	0	0
$209$	25.1882	1.74230
$210$	−4.82942	−0.333262
$211$	−17.4415	−1.20073	−0.600363	−	0.799728i	$-0.704977\pi$
$211$	−17.4415	−1.20073	−0.600363	+	0.799728i	$0.704977\pi$
$212$	−0.219421	−0.0150699
$213$	13.5371	0.927547
$214$	2.35103	0.160713
$215$	16.7488	1.14226
$216$	−2.10331	−0.143112
$217$	6.47277	0.439400
$218$	−0.0771387	−0.00522449
$219$	0.932734	0.0630283
$220$	−9.29656	−0.626774
$221$	0	0
$222$	4.82942	0.324130
$223$	−8.00212	−0.535862	−0.267931	−	0.963438i	$-0.586340\pi$
$223$	−8.00212	−0.535862	−0.267931	+	0.963438i	$0.586340\pi$
$224$	3.92498	0.262249
$225$	3.55553	0.237035
$226$	17.0694	1.13544
$227$	8.05952	0.534929	0.267464	−	0.963568i	$-0.413814\pi$
$227$	8.05952	0.534929	0.267464	+	0.963568i	$0.413814\pi$
$228$	−4.17833	−0.276717
$229$	8.48052	0.560408	0.280204	−	0.959940i	$-0.409598\pi$
$229$	8.48052	0.560408	0.280204	+	0.959940i	$0.409598\pi$
$230$	33.9426	2.23811
$231$	−4.37720	−0.287999
$232$	2.52161	0.165552
$233$	−10.2456	−0.671211	−0.335606	−	0.942003i	$-0.608941\pi$
$233$	−10.2456	−0.671211	−0.335606	+	0.942003i	$0.608941\pi$
$234$	0	0
$235$	−28.0325	−1.82864
$236$	−2.19887	−0.143135
$237$	16.9426	1.10054
$238$	−6.02830	−0.390756
$239$	11.3022	0.731078	0.365539	−	0.930796i	$-0.380885\pi$
$239$	11.3022	0.731078	0.365539	+	0.930796i	$0.380885\pi$
$240$	−14.4055	−0.929871
$241$	−1.03605	−0.0667376	−0.0333688	−	0.999443i	$-0.510624\pi$
$241$	−1.03605	−0.0667376	−0.0333688	+	0.999443i	$0.510624\pi$
$242$	−13.4728	−0.866062
$243$	−1.00000	−0.0641500
$244$	−0.219421	−0.0140470
$245$	−2.92498	−0.186870
$246$	14.2066	0.905781
$247$	0	0
$248$	13.6142	0.864506
$249$	−1.26614	−0.0802384
$250$	−6.97595	−0.441198
$251$	13.2838	0.838464	0.419232	−	0.907879i	$-0.362299\pi$
$251$	13.2838	0.838464	0.419232	+	0.907879i	$0.362299\pi$
$252$	0.726109	0.0457406
$253$	30.7643	1.93413
$254$	9.03605	0.566972
$255$	10.6794	0.668769
$256$	15.4076	0.962976
$257$	12.4415	0.776082	0.388041	−	0.921642i	$-0.373152\pi$
$257$	12.4415	0.776082	0.388041	+	0.921642i	$0.373152\pi$
$258$	−9.45434	−0.588602
$259$	2.92498	0.181750
$260$	0	0
$261$	1.19887	0.0742085
$262$	−26.6991	−1.64948
$263$	6.59158	0.406454	0.203227	−	0.979132i	$-0.434857\pi$
$263$	6.59158	0.406454	0.203227	+	0.979132i	$0.434857\pi$
$264$	−9.20662	−0.566629
$265$	0.883892	0.0542970
$266$	−9.50106	−0.582547
$267$	−13.3977	−0.819929
$268$	6.32273	0.386222
$269$	−2.71624	−0.165612	−0.0828059	−	0.996566i	$-0.526388\pi$
$269$	−2.71624	−0.165612	−0.0828059	+	0.996566i	$0.526388\pi$
$270$	−4.82942	−0.293909
$271$	30.7253	1.86643	0.933215	−	0.359319i	$-0.116991\pi$
$271$	30.7253	1.86643	0.933215	+	0.359319i	$0.116991\pi$
$272$	−17.9816	−1.09029
$273$	0	0
$274$	−19.8422	−1.19871
$275$	15.5633	0.938501
$276$	−5.10331	−0.307183
$277$	−21.5654	−1.29574	−0.647870	−	0.761751i	$-0.724340\pi$
$277$	−21.5654	−1.29574	−0.647870	+	0.761751i	$0.724340\pi$
$278$	−2.22717	−0.133577
$279$	6.47277	0.387514
$280$	−6.15215	−0.367662
$281$	−33.2058	−1.98089	−0.990447	−	0.137896i	$-0.955966\pi$
$281$	−33.2058	−1.98089	−0.990447	+	0.137896i	$0.955966\pi$
$282$	15.8238	0.942293
$283$	1.48344	0.0881813	0.0440906	−	0.999028i	$-0.485961\pi$
$283$	1.48344	0.0881813	0.0440906	+	0.999028i	$0.485961\pi$
$284$	−9.82942	−0.583269
$285$	16.8315	0.997015
$286$	0	0
$287$	8.60437	0.507900
$288$	3.92498	0.231282
$289$	−3.66952	−0.215854
$290$	5.78987	0.339993
$291$	11.9250	0.699055
$292$	−0.677267	−0.0396341
$293$	−8.83154	−0.515944	−0.257972	−	0.966152i	$-0.583054\pi$
$293$	−8.83154	−0.515944	−0.257972	+	0.966152i	$0.583054\pi$
$294$	1.65109	0.0962937
$295$	8.85772	0.515716
$296$	6.15215	0.357587
$297$	−4.37720	−0.253991
$298$	−5.07714	−0.294111
$299$	0	0
$300$	−2.58170	−0.149055
$301$	−5.72611	−0.330047
$302$	27.5088	1.58295
$303$	−11.0283	−0.633559
$304$	−28.3404	−1.62543
$305$	0.883892	0.0506115
$306$	−6.02830	−0.344615
$307$	−11.6532	−0.665084	−0.332542	−	0.943088i	$-0.607906\pi$
$307$	−11.6532	−0.665084	−0.332542	+	0.943088i	$0.607906\pi$
$308$	3.17833	0.181102
$309$	19.4543	1.10672
$310$	31.2597	1.77543
$311$	−25.0099	−1.41818	−0.709090	−	0.705118i	$-0.750894\pi$
$311$	−25.0099	−1.41818	−0.709090	+	0.705118i	$0.750894\pi$
$312$	0	0
$313$	−0.186078	−0.0105178	−0.00525889	−	0.999986i	$-0.501674\pi$
$313$	−0.186078	−0.0105178	−0.00525889	+	0.999986i	$0.501674\pi$
$314$	−21.1826	−1.19540
$315$	−2.92498	−0.164804
$316$	−12.3022	−0.692052
$317$	0.540031	0.0303312	0.0151656	−	0.999885i	$-0.495172\pi$
$317$	0.540031	0.0303312	0.0151656	+	0.999885i	$0.495172\pi$
$318$	−0.498939	−0.0279791
$319$	5.24772	0.293816
$320$	−9.85560	−0.550945
$321$	1.42392	0.0794756
$322$	−11.6044	−0.646686
$323$	21.0099	1.16902
$324$	0.726109	0.0403394
$325$	0	0
$326$	−35.6708	−1.97563
$327$	−0.0467198	−0.00258361
$328$	18.0977	0.999277
$329$	9.58383	0.528374
$330$	−21.1394	−1.16368
$331$	−1.54003	−0.0846478	−0.0423239	−	0.999104i	$-0.513476\pi$
$331$	−1.54003	−0.0846478	−0.0423239	+	0.999104i	$0.513476\pi$
$332$	0.919357	0.0504562
$333$	2.92498	0.160288
$334$	35.2010	1.92611
$335$	−25.4698	−1.39157
$336$	4.92498	0.268680
$337$	2.82942	0.154128	0.0770642	−	0.997026i	$-0.475445\pi$
$337$	2.82942	0.154128	0.0770642	+	0.997026i	$0.475445\pi$
$338$	0	0
$339$	10.3382	0.561496
$340$	−7.75441	−0.420542
$341$	28.3326	1.53430
$342$	−9.50106	−0.513759
$343$	1.00000	0.0539949
$344$	−12.0438	−0.649358
$345$	20.5577	1.10679
$346$	−5.15428	−0.277096
$347$	−25.3900	−1.36301	−0.681503	−	0.731815i	$-0.738673\pi$
$347$	−25.3900	−1.36301	−0.681503	+	0.731815i	$0.738673\pi$
$348$	−0.870514	−0.0466645
$349$	1.08569	0.0581156	0.0290578	−	0.999578i	$-0.490749\pi$
$349$	1.08569	0.0581156	0.0290578	+	0.999578i	$0.490749\pi$
$350$	−5.87051	−0.313792
$351$	0	0
$352$	17.1805	0.915721
$353$	−10.5294	−0.560421	−0.280211	−	0.959939i	$-0.590404\pi$
$353$	−10.5294	−0.560421	−0.280211	+	0.959939i	$0.590404\pi$
$354$	−5.00000	−0.265747
$355$	39.5958	2.10153
$356$	9.72823	0.515595
$357$	−3.65109	−0.193236
$358$	−31.3227	−1.65546
$359$	−27.2087	−1.43602	−0.718011	−	0.696031i	$-0.754947\pi$
$359$	−27.2087	−1.43602	−0.718011	+	0.696031i	$0.754947\pi$
$360$	−6.15215	−0.324247
$361$	14.1132	0.742799
$362$	3.19112	0.167722
$363$	−8.15990	−0.428284
$364$	0	0
$365$	2.72823	0.142802
$366$	−0.498939	−0.0260799
$367$	−6.25839	−0.326685	−0.163343	−	0.986569i	$-0.552228\pi$
$367$	−6.25839	−0.326685	−0.163343	+	0.986569i	$0.552228\pi$
$368$	−34.6142	−1.80439
$369$	8.60437	0.447926
$370$	14.1260	0.734375
$371$	−0.302187	−0.0156888
$372$	−4.69994	−0.243680
$373$	−1.17833	−0.0610115	−0.0305058	−	0.999535i	$-0.509712\pi$
$373$	−1.17833	−0.0610115	−0.0305058	+	0.999535i	$0.509712\pi$
$374$	−26.3871	−1.36444
$375$	−4.22505	−0.218181
$376$	20.1578	1.03956
$377$	0	0
$378$	1.65109	0.0849231
$379$	24.2066	1.24341	0.621705	−	0.783251i	$-0.286440\pi$
$379$	24.2066	1.24341	0.621705	+	0.783251i	$0.286440\pi$
$380$	−12.2215	−0.626952
$381$	5.47277	0.280378
$382$	3.75441	0.192092
$383$	2.49119	0.127294	0.0636469	−	0.997972i	$-0.479727\pi$
$383$	2.49119	0.127294	0.0636469	+	0.997972i	$0.479727\pi$
$384$	13.4132	0.684492
$385$	−12.8032	−0.652514
$386$	−7.24347	−0.368683
$387$	−5.72611	−0.291075
$388$	−8.65884	−0.439586
$389$	23.6065	1.19690	0.598448	−	0.801161i	$-0.295784\pi$
$389$	23.6065	1.19690	0.598448	+	0.801161i	$0.295784\pi$
$390$	0	0
$391$	25.6610	1.29773
$392$	2.10331	0.106233
$393$	−16.1706	−0.815698
$394$	−8.68209	−0.437398
$395$	49.5569	2.49348
$396$	3.17833	0.159717
$397$	8.84704	0.444020	0.222010	−	0.975044i	$-0.428738\pi$
$397$	8.84704	0.444020	0.222010	+	0.975044i	$0.428738\pi$
$398$	−21.7877	−1.09212
$399$	−5.75441	−0.288081
$400$	−17.5109	−0.875547
$401$	18.9143	0.944536	0.472268	−	0.881455i	$-0.343436\pi$
$401$	18.9143	0.944536	0.472268	+	0.881455i	$0.343436\pi$
$402$	14.3772	0.717070
$403$	0	0
$404$	8.00775	0.398400
$405$	−2.92498	−0.145344
$406$	−1.97945	−0.0982386
$407$	12.8032	0.634633
$408$	−7.67939	−0.380186
$409$	−3.49894	−0.173011	−0.0865057	−	0.996251i	$-0.527570\pi$
$409$	−3.49894	−0.173011	−0.0865057	+	0.996251i	$0.527570\pi$
$410$	41.5541	2.05221
$411$	−12.0176	−0.592786
$412$	−14.1260	−0.695937
$413$	−3.02830	−0.149013
$414$	−11.6044	−0.570324
$415$	−3.70344	−0.181795
$416$	0	0
$417$	−1.34891	−0.0660562
$418$	−41.5881	−2.03414
$419$	28.8315	1.40851	0.704257	−	0.709946i	$-0.251280\pi$
$419$	28.8315	1.40851	0.704257	+	0.709946i	$0.251280\pi$
$420$	2.12386	0.103634
$421$	−34.3227	−1.67279	−0.836394	−	0.548129i	$-0.815340\pi$
$421$	−34.3227	−1.67279	−0.836394	+	0.548129i	$0.815340\pi$
$422$	28.7976	1.40185
$423$	9.58383	0.465982
$424$	−0.635593	−0.0308671
$425$	12.9816	0.629699
$426$	−22.3510	−1.08291
$427$	−0.302187	−0.0146238
$428$	−1.03392	−0.0499766
$429$	0	0
$430$	−27.6538	−1.33358
$431$	−29.3559	−1.41402	−0.707011	−	0.707203i	$-0.749957\pi$
$431$	−29.3559	−1.41402	−0.707011	+	0.707203i	$0.749957\pi$
$432$	4.92498	0.236953
$433$	28.6065	1.37474	0.687370	−	0.726307i	$-0.258765\pi$
$433$	28.6065	1.37474	0.687370	+	0.726307i	$0.258765\pi$
$434$	−10.6871	−0.512999
$435$	3.50669	0.168133
$436$	0.0339237	0.00162465
$437$	40.4437	1.93468
$438$	−1.54003	−0.0735855
$439$	34.4797	1.64563	0.822813	−	0.568311i	$-0.192403\pi$
$439$	34.4797	1.64563	0.822813	+	0.568311i	$0.192403\pi$
$440$	−26.9292	−1.28380
$441$	1.00000	0.0476190
$442$	0	0
$443$	−12.9066	−0.613209	−0.306605	−	0.951837i	$-0.599193\pi$
$443$	−12.9066	−0.613209	−0.306605	+	0.951837i	$0.599193\pi$
$444$	−2.12386	−0.100794
$445$	−39.1882	−1.85770
$446$	13.2123	0.625618
$447$	−3.07502	−0.145443
$448$	3.36945	0.159192
$449$	5.63830	0.266088	0.133044	−	0.991110i	$-0.457525\pi$
$449$	5.63830	0.266088	0.133044	+	0.991110i	$0.457525\pi$
$450$	−5.87051	−0.276739
$451$	37.6631	1.77349
$452$	−7.50669	−0.353085
$453$	16.6610	0.782800
$454$	−13.3070	−0.624529
$455$	0	0
$456$	−12.1033	−0.566790
$457$	−37.9893	−1.77707	−0.888533	−	0.458813i	$-0.848275\pi$
$457$	−37.9893	−1.77707	−0.888533	+	0.458813i	$0.848275\pi$
$458$	−14.0021	−0.654276
$459$	−3.65109	−0.170418
$460$	−14.9271	−0.695980
$461$	6.60730	0.307733	0.153866	−	0.988092i	$-0.450828\pi$
$461$	6.60730	0.307733	0.153866	+	0.988092i	$0.450828\pi$
$462$	7.22717	0.336238
$463$	−9.98933	−0.464243	−0.232122	−	0.972687i	$-0.574567\pi$
$463$	−9.98933	−0.464243	−0.232122	+	0.972687i	$0.574567\pi$
$464$	−5.90444	−0.274107
$465$	18.9327	0.877985
$466$	16.9164	0.783639
$467$	3.42100	0.158305	0.0791525	−	0.996863i	$-0.474779\pi$
$467$	3.42100	0.158305	0.0791525	+	0.996863i	$0.474779\pi$
$468$	0	0
$469$	8.70769	0.402084
$470$	46.2843	2.13494
$471$	−12.8294	−0.591149
$472$	−6.36945	−0.293178
$473$	−25.0643	−1.15246
$474$	−27.9738	−1.28488
$475$	20.4600	0.938768
$476$	2.65109	0.121513
$477$	−0.302187	−0.0138362
$478$	−18.6610	−0.853533
$479$	−19.8414	−0.906577	−0.453289	−	0.891364i	$-0.649749\pi$
$479$	−19.8414	−0.906577	−0.453289	+	0.891364i	$0.649749\pi$
$480$	11.4805	0.524011
$481$	0	0
$482$	1.71061	0.0779161
$483$	−7.02830	−0.319799
$484$	5.92498	0.269317
$485$	34.8804	1.58384
$486$	1.65109	0.0748951
$487$	6.10331	0.276567	0.138284	−	0.990393i	$-0.455841\pi$
$487$	6.10331	0.276567	0.138284	+	0.990393i	$0.455841\pi$
$488$	−0.635593	−0.0287720
$489$	−21.6044	−0.976984
$490$	4.82942	0.218171
$491$	−2.36653	−0.106800	−0.0534000	−	0.998573i	$-0.517006\pi$
$491$	−2.36653	−0.106800	−0.0534000	+	0.998573i	$0.517006\pi$
$492$	−6.24772	−0.281669
$493$	4.37720	0.197139
$494$	0	0
$495$	−12.8032	−0.575463
$496$	−31.8783	−1.43138
$497$	−13.5371	−0.607222
$498$	2.09052	0.0936783
$499$	4.29231	0.192150	0.0960752	−	0.995374i	$-0.469371\pi$
$499$	4.29231	0.192150	0.0960752	+	0.995374i	$0.469371\pi$
$500$	3.06785	0.137198
$501$	21.3198	0.952499
$502$	−21.9327	−0.978906
$503$	−2.11106	−0.0941276	−0.0470638	−	0.998892i	$-0.514986\pi$
$503$	−2.11106	−0.0941276	−0.0470638	+	0.998892i	$0.514986\pi$
$504$	2.10331	0.0936890
$505$	−32.2576	−1.43544
$506$	−50.7947	−2.25810
$507$	0	0
$508$	−3.97383	−0.176310
$509$	24.3764	1.08047	0.540233	−	0.841516i	$-0.318336\pi$
$509$	24.3764	1.08047	0.540233	+	0.841516i	$0.318336\pi$
$510$	−17.6327	−0.780788
$511$	−0.932734	−0.0412617
$512$	1.38708	0.0613007
$513$	−5.75441	−0.254063
$514$	−20.5422	−0.906076
$515$	56.9036	2.50747
$516$	4.15778	0.183036
$517$	41.9504	1.84497
$518$	−4.82942	−0.212193
$519$	−3.12174	−0.137029
$520$	0	0
$521$	−17.8401	−0.781589	−0.390794	−	0.920478i	$-0.627800\pi$
$521$	−17.8401	−0.781589	−0.390794	+	0.920478i	$0.627800\pi$
$522$	−1.97945	−0.0866383
$523$	−31.0558	−1.35797	−0.678987	−	0.734150i	$-0.737581\pi$
$523$	−31.0558	−1.35797	−0.678987	+	0.734150i	$0.737581\pi$
$524$	11.7416	0.512935
$525$	−3.55553	−0.155176
$526$	−10.8833	−0.474535
$527$	23.6327	1.02946
$528$	21.5577	0.938176
$529$	26.3969	1.14769
$530$	−1.45939	−0.0633917
$531$	−3.02830	−0.131417
$532$	4.17833	0.181154
$533$	0	0
$534$	22.1209	0.957266
$535$	4.16495	0.180067
$536$	18.3150	0.791087
$537$	−18.9709	−0.818655
$538$	4.48476	0.193352
$539$	4.37720	0.188539
$540$	2.12386	0.0913963
$541$	33.3900	1.43555	0.717774	−	0.696276i	$-0.245161\pi$
$541$	33.3900	1.43555	0.717774	+	0.696276i	$0.245161\pi$
$542$	−50.7304	−2.17906
$543$	1.93273	0.0829416
$544$	14.3305	0.614414
$545$	−0.136655	−0.00585364
$546$	0	0
$547$	9.12306	0.390074	0.195037	−	0.980796i	$-0.437517\pi$
$547$	9.12306	0.390074	0.195037	+	0.980796i	$0.437517\pi$
$548$	8.72611	0.372761
$549$	−0.302187	−0.0128970
$550$	−25.6964	−1.09570
$551$	6.89881	0.293899
$552$	−14.7827	−0.629194
$553$	−16.9426	−0.720473
$554$	35.6065	1.51278
$555$	8.55553	0.363162
$556$	0.979454	0.0415381
$557$	38.0296	1.61137	0.805683	−	0.592347i	$-0.201798\pi$
$557$	38.0296	1.61137	0.805683	+	0.592347i	$0.201798\pi$
$558$	−10.6871	−0.452423
$559$	0	0
$560$	14.4055	0.608743
$561$	−15.9816	−0.674743
$562$	54.8259	2.31269
$563$	−3.36653	−0.141882	−0.0709411	−	0.997481i	$-0.522600\pi$
$563$	−3.36653	−0.141882	−0.0709411	+	0.997481i	$0.522600\pi$
$564$	−6.95891	−0.293023
$565$	30.2392	1.27217
$566$	−2.44930	−0.102952
$567$	1.00000	0.0419961
$568$	−28.4728	−1.19469
$569$	−17.9327	−0.751779	−0.375890	−	0.926664i	$-0.622663\pi$
$569$	−17.9327	−0.751779	−0.375890	+	0.926664i	$0.622663\pi$
$570$	−27.7905	−1.16401
$571$	39.4274	1.64998	0.824992	−	0.565144i	$-0.191180\pi$
$571$	39.4274	1.64998	0.824992	+	0.565144i	$0.191180\pi$
$572$	0	0
$573$	2.27389	0.0949931
$574$	−14.2066	−0.592973
$575$	24.9893	1.04213
$576$	3.36945	0.140394
$577$	−16.4239	−0.683737	−0.341868	−	0.939748i	$-0.611060\pi$
$577$	−16.4239	−0.683737	−0.341868	+	0.939748i	$0.611060\pi$
$578$	6.05872	0.252009
$579$	−4.38708	−0.182321
$580$	−2.54624	−0.105727
$581$	1.26614	0.0525284
$582$	−19.6893	−0.816146
$583$	−1.32273	−0.0547820
$584$	−1.96183	−0.0811811
$585$	0	0
$586$	14.5817	0.602365
$587$	14.9271	0.616108	0.308054	−	0.951369i	$-0.400322\pi$
$587$	14.9271	0.616108	0.308054	+	0.951369i	$0.400322\pi$
$588$	−0.726109	−0.0299442
$589$	37.2469	1.53473
$590$	−14.6249	−0.602098
$591$	−5.25839	−0.216301
$592$	−14.4055	−0.592062
$593$	−29.9164	−1.22852	−0.614260	−	0.789103i	$-0.710546\pi$
$593$	−29.9164	−1.22852	−0.614260	+	0.789103i	$0.710546\pi$
$594$	7.22717	0.296534
$595$	−10.6794	−0.437812
$596$	2.23280	0.0914590
$597$	−13.1960	−0.540074
$598$	0	0
$599$	35.1911	1.43787	0.718935	−	0.695077i	$-0.244630\pi$
$599$	35.1911	1.43787	0.718935	+	0.695077i	$0.244630\pi$
$600$	−7.47839	−0.305304
$601$	17.1316	0.698813	0.349406	−	0.936971i	$-0.386383\pi$
$601$	17.1316	0.698813	0.349406	+	0.936971i	$0.386383\pi$
$602$	9.45434	0.385330
$603$	8.70769	0.354604
$604$	−12.0977	−0.492248
$605$	−23.8676	−0.970356
$606$	18.2087	0.739680
$607$	22.4466	0.911079	0.455540	−	0.890216i	$-0.349446\pi$
$607$	22.4466	0.911079	0.455540	+	0.890216i	$0.349446\pi$
$608$	22.5860	0.915981
$609$	−1.19887	−0.0485808
$610$	−1.45939	−0.0590889
$611$	0	0
$612$	2.65109	0.107164
$613$	20.2058	0.816106	0.408053	−	0.912958i	$-0.366208\pi$
$613$	20.2058	0.816106	0.408053	+	0.912958i	$0.366208\pi$
$614$	19.2405	0.776485
$615$	25.1677	1.01486
$616$	9.20662	0.370945
$617$	−38.6815	−1.55726	−0.778630	−	0.627484i	$-0.784085\pi$
$617$	−38.6815	−1.55726	−0.778630	+	0.627484i	$0.784085\pi$
$618$	−32.1209	−1.29209
$619$	−32.5109	−1.30672	−0.653362	−	0.757045i	$-0.726642\pi$
$619$	−32.5109	−1.30672	−0.653362	+	0.757045i	$0.726642\pi$
$620$	−13.7472	−0.552102
$621$	−7.02830	−0.282036
$622$	41.2936	1.65572
$623$	13.3977	0.536769
$624$	0	0
$625$	−30.1359	−1.20543
$626$	0.307233	0.0122795
$627$	−25.1882	−1.00592
$628$	9.31556	0.371731
$629$	10.6794	0.425815
$630$	4.82942	0.192409
$631$	37.8620	1.50726	0.753630	−	0.657298i	$-0.228301\pi$
$631$	37.8620	1.50726	0.753630	+	0.657298i	$0.228301\pi$
$632$	−35.6356	−1.41751
$633$	17.4415	0.693239
$634$	−0.891642	−0.0354116
$635$	16.0078	0.635248
$636$	0.219421	0.00870060
$637$	0	0
$638$	−8.66447	−0.343030
$639$	−13.5371	−0.535520
$640$	39.2335	1.55084
$641$	22.8628	0.903025	0.451512	−	0.892265i	$-0.350885\pi$
$641$	22.8628	0.903025	0.451512	+	0.892265i	$0.350885\pi$
$642$	−2.35103	−0.0927877
$643$	−43.5830	−1.71875	−0.859373	−	0.511349i	$-0.829146\pi$
$643$	−43.5830	−1.71875	−0.859373	+	0.511349i	$0.829146\pi$
$644$	5.10331	0.201099
$645$	−16.7488	−0.659483
$646$	−34.6893	−1.36483
$647$	−3.00775	−0.118247	−0.0591234	−	0.998251i	$-0.518831\pi$
$647$	−3.00775	−0.118247	−0.0591234	+	0.998251i	$0.518831\pi$
$648$	2.10331	0.0826259
$649$	−13.2555	−0.520323
$650$	0	0
$651$	−6.47277	−0.253688
$652$	15.6871	0.614356
$653$	−33.9242	−1.32756	−0.663778	−	0.747930i	$-0.731048\pi$
$653$	−33.9242	−1.32756	−0.663778	+	0.747930i	$0.731048\pi$
$654$	0.0771387	0.00301636
$655$	−47.2987	−1.84811
$656$	−42.3764	−1.65452
$657$	−0.932734	−0.0363894
$658$	−15.8238	−0.616876
$659$	−43.4594	−1.69294	−0.846469	−	0.532438i	$-0.821276\pi$
$659$	−43.4594	−1.69294	−0.846469	+	0.532438i	$0.821276\pi$
$660$	9.29656	0.361868
$661$	−38.2859	−1.48915	−0.744574	−	0.667540i	$-0.767347\pi$
$661$	−38.2859	−1.48915	−0.744574	+	0.667540i	$0.767347\pi$
$662$	2.54274	0.0988262
$663$	0	0
$664$	2.66309	0.103348
$665$	−16.8315	−0.652699
$666$	−4.82942	−0.187136
$667$	8.42605	0.326258
$668$	−15.4805	−0.598959
$669$	8.00212	0.309380
$670$	42.0531	1.62465
$671$	−1.32273	−0.0510635
$672$	−3.92498	−0.151410
$673$	28.1805	1.08628	0.543138	−	0.839643i	$-0.317236\pi$
$673$	28.1805	1.08628	0.543138	+	0.839643i	$0.317236\pi$
$674$	−4.67164	−0.179945
$675$	−3.55553	−0.136852
$676$	0	0
$677$	−31.7253	−1.21930	−0.609651	−	0.792670i	$-0.708691\pi$
$677$	−31.7253	−1.21930	−0.609651	+	0.792670i	$0.708691\pi$
$678$	−17.0694	−0.655546
$679$	−11.9250	−0.457639
$680$	−22.4621	−0.861382
$681$	−8.05952	−0.308841
$682$	−46.7798	−1.79129
$683$	−8.57395	−0.328073	−0.164037	−	0.986454i	$-0.552452\pi$
$683$	−8.57395	−0.328073	−0.164037	+	0.986454i	$0.552452\pi$
$684$	4.17833	0.159762
$685$	−35.1514	−1.34306
$686$	−1.65109	−0.0630390
$687$	−8.48052	−0.323552
$688$	28.2010	1.07515
$689$	0	0
$690$	−33.9426	−1.29217
$691$	6.95036	0.264404	0.132202	−	0.991223i	$-0.457795\pi$
$691$	6.95036	0.264404	0.132202	+	0.991223i	$0.457795\pi$
$692$	2.26672	0.0861678
$693$	4.37720	0.166276
$694$	41.9213	1.59131
$695$	−3.94553	−0.149662
$696$	−2.52161	−0.0955813
$697$	31.4154	1.18994
$698$	−1.79257	−0.0678500
$699$	10.2456	0.387524
$700$	2.58170	0.0975793
$701$	−21.8443	−0.825049	−0.412525	−	0.910946i	$-0.635353\pi$
$701$	−21.8443	−0.825049	−0.412525	+	0.910946i	$0.635353\pi$
$702$	0	0
$703$	16.8315	0.634814
$704$	14.7488	0.555865
$705$	28.0325	1.05577
$706$	17.3850	0.654291
$707$	11.0283	0.414762
$708$	2.19887	0.0826388
$709$	−9.74373	−0.365934	−0.182967	−	0.983119i	$-0.558570\pi$
$709$	−9.74373	−0.365934	−0.182967	+	0.983119i	$0.558570\pi$
$710$	−65.3764	−2.45353
$711$	−16.9426	−0.635397
$712$	28.1797	1.05608
$713$	45.4925	1.70371
$714$	6.02830	0.225603
$715$	0	0
$716$	13.7750	0.514794
$717$	−11.3022	−0.422088
$718$	44.9242	1.67656
$719$	−5.04592	−0.188181	−0.0940905	−	0.995564i	$-0.529994\pi$
$719$	−5.04592	−0.188181	−0.0940905	+	0.995564i	$0.529994\pi$
$720$	14.4055	0.536861
$721$	−19.4543	−0.724518
$722$	−23.3022	−0.867218
$723$	1.03605	0.0385310
$724$	−1.40338	−0.0521561
$725$	4.26264	0.158310
$726$	13.4728	0.500021
$727$	6.66659	0.247250	0.123625	−	0.992329i	$-0.460548\pi$
$727$	6.66659	0.247250	0.123625	+	0.992329i	$0.460548\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.50457	−0.166721
$731$	−20.9066	−0.773257
$732$	0.219421	0.00811002
$733$	−47.4076	−1.75104	−0.875520	−	0.483181i	$-0.839481\pi$
$733$	−47.4076	−1.75104	−0.875520	+	0.483181i	$0.839481\pi$
$734$	10.3332	0.381405
$735$	2.92498	0.107890
$736$	27.5860	1.01683
$737$	38.1153	1.40400
$738$	−14.2066	−0.522953
$739$	−6.18045	−0.227352	−0.113676	−	0.993518i	$-0.536263\pi$
$739$	−6.18045	−0.227352	−0.113676	+	0.993518i	$0.536263\pi$
$740$	−6.21225	−0.228367
$741$	0	0
$742$	0.498939	0.0183166
$743$	23.3334	0.856020	0.428010	−	0.903774i	$-0.359215\pi$
$743$	23.3334	0.856020	0.428010	+	0.903774i	$0.359215\pi$
$744$	−13.6142	−0.499122
$745$	−8.99437	−0.329528
$746$	1.94553	0.0712309
$747$	1.26614	0.0463257
$748$	11.6044	0.424298
$749$	−1.42392	−0.0520290
$750$	6.97595	0.254726
$751$	−0.976750	−0.0356421	−0.0178211	−	0.999841i	$-0.505673\pi$
$751$	−0.976750	−0.0356421	−0.0178211	+	0.999841i	$0.505673\pi$
$752$	−47.2002	−1.72121
$753$	−13.2838	−0.484087
$754$	0	0
$755$	48.7331	1.77358
$756$	−0.726109	−0.0264083
$757$	−8.76508	−0.318572	−0.159286	−	0.987232i	$-0.550919\pi$
$757$	−8.76508	−0.318572	−0.159286	+	0.987232i	$0.550919\pi$
$758$	−39.9674	−1.45168
$759$	−30.7643	−1.11667
$760$	−35.4020	−1.28417
$761$	21.4551	0.777748	0.388874	−	0.921291i	$-0.372864\pi$
$761$	21.4551	0.777748	0.388874	+	0.921291i	$0.372864\pi$
$762$	−9.03605	−0.327341
$763$	0.0467198	0.00169137
$764$	−1.65109	−0.0597345
$765$	−10.6794	−0.386114
$766$	−4.11319	−0.148615
$767$	0	0
$768$	−15.4076	−0.555975
$769$	−22.1500	−0.798751	−0.399375	−	0.916788i	$-0.630773\pi$
$769$	−22.1500	−0.798751	−0.399375	+	0.916788i	$0.630773\pi$
$770$	21.1394	0.761810
$771$	−12.4415	−0.448071
$772$	3.18550	0.114649
$773$	19.1599	0.689134	0.344567	−	0.938762i	$-0.388026\pi$
$773$	19.1599	0.689134	0.344567	+	0.938762i	$0.388026\pi$
$774$	9.45434	0.339829
$775$	23.0141	0.826692
$776$	−25.0820	−0.900390
$777$	−2.92498	−0.104933
$778$	−38.9765	−1.39738
$779$	49.5131	1.77399
$780$	0	0
$781$	−59.2547	−2.12030
$782$	−42.3687	−1.51510
$783$	−1.19887	−0.0428443
$784$	−4.92498	−0.175892
$785$	−37.5259	−1.33936
$786$	26.6991	0.952327
$787$	−44.1797	−1.57483	−0.787417	−	0.616420i	$-0.788582\pi$
$787$	−44.1797	−1.57483	−0.787417	+	0.616420i	$0.788582\pi$
$788$	3.81817	0.136017
$789$	−6.59158	−0.234666
$790$	−81.8230	−2.91113
$791$	−10.3382	−0.367585
$792$	9.20662	0.327143
$793$	0	0
$794$	−14.6073	−0.518394
$795$	−0.883892	−0.0313484
$796$	9.58170	0.339615
$797$	13.6561	0.483725	0.241863	−	0.970310i	$-0.422242\pi$
$797$	13.6561	0.483725	0.241863	+	0.970310i	$0.422242\pi$
$798$	9.50106	0.336334
$799$	34.9914	1.23791
$800$	13.9554	0.493398
$801$	13.3977	0.473386
$802$	−31.2293	−1.10274
$803$	−4.08277	−0.144078
$804$	−6.32273	−0.222986
$805$	−20.5577	−0.724562
$806$	0	0
$807$	2.71624	0.0956161
$808$	23.1960	0.816031
$809$	34.0078	1.19565	0.597824	−	0.801627i	$-0.296032\pi$
$809$	34.0078	1.19565	0.597824	+	0.801627i	$0.296032\pi$
$810$	4.82942	0.169689
$811$	21.4084	0.751751	0.375876	−	0.926670i	$-0.377342\pi$
$811$	21.4084	0.751751	0.375876	+	0.926670i	$0.377342\pi$
$812$	0.870514	0.0305491
$813$	−30.7253	−1.07758
$814$	−21.1394	−0.740934
$815$	−63.1924	−2.21353
$816$	17.9816	0.629481
$817$	−32.9504	−1.15279
$818$	5.77707	0.201991
$819$	0	0
$820$	−18.2745	−0.638172
$821$	−27.1367	−0.947076	−0.473538	−	0.880773i	$-0.657023\pi$
$821$	−27.1367	−0.947076	−0.473538	+	0.880773i	$0.657023\pi$
$822$	19.8422	0.692077
$823$	−46.6417	−1.62583	−0.812914	−	0.582383i	$-0.802120\pi$
$823$	−46.6417	−1.62583	−0.812914	+	0.582383i	$0.802120\pi$
$824$	−40.9186	−1.42547
$825$	−15.5633	−0.541844
$826$	5.00000	0.173972
$827$	27.2789	0.948582	0.474291	−	0.880368i	$-0.342705\pi$
$827$	27.2789	0.948582	0.474291	+	0.880368i	$0.342705\pi$
$828$	5.10331	0.177352
$829$	−25.3219	−0.879467	−0.439734	−	0.898128i	$-0.644927\pi$
$829$	−25.3219	−0.879467	−0.439734	+	0.898128i	$0.644927\pi$
$830$	6.11473	0.212245
$831$	21.5654	0.748096
$832$	0	0
$833$	3.65109	0.126503
$834$	2.22717	0.0771206
$835$	62.3601	2.15806
$836$	18.2894	0.632552
$837$	−6.47277	−0.223731
$838$	−47.6036	−1.64444
$839$	−0.366529	−0.0126540	−0.00632700	−	0.999980i	$-0.502014\pi$
$839$	−0.366529	−0.0126540	−0.00632700	+	0.999980i	$0.502014\pi$
$840$	6.15215	0.212270
$841$	−27.5627	−0.950438
$842$	56.6700	1.95298
$843$	33.2058	1.14367
$844$	−12.6645	−0.435929
$845$	0	0
$846$	−15.8238	−0.544033
$847$	8.15990	0.280378
$848$	1.48827	0.0511072
$849$	−1.48344	−0.0509115
$850$	−21.4338	−0.735173
$851$	20.5577	0.704707
$852$	9.82942	0.336750
$853$	49.3134	1.68846	0.844229	−	0.535983i	$-0.180059\pi$
$853$	49.3134	1.68846	0.844229	+	0.535983i	$0.180059\pi$
$854$	0.498939	0.0170733
$855$	−16.8315	−0.575627
$856$	−2.99495	−0.102365
$857$	26.0878	0.891143	0.445571	−	0.895246i	$-0.353001\pi$
$857$	26.0878	0.891143	0.445571	+	0.895246i	$0.353001\pi$
$858$	0	0
$859$	29.6815	1.01272	0.506360	−	0.862322i	$-0.330991\pi$
$859$	29.6815	1.01272	0.506360	+	0.862322i	$0.330991\pi$
$860$	12.1614	0.414702
$861$	−8.60437	−0.293236
$862$	48.4693	1.65087
$863$	−17.8804	−0.608655	−0.304328	−	0.952567i	$-0.598432\pi$
$863$	−17.8804	−0.608655	−0.304328	+	0.952567i	$0.598432\pi$
$864$	−3.92498	−0.133531
$865$	−9.13103	−0.310464
$866$	−47.2320	−1.60501
$867$	3.66952	0.124623
$868$	4.69994	0.159526
$869$	−74.1612	−2.51575
$870$	−5.78987	−0.196295
$871$	0	0
$872$	0.0982663	0.00332772
$873$	−11.9250	−0.403600
$874$	−66.7763	−2.25874
$875$	4.22505	0.142833
$876$	0.677267	0.0228827
$877$	−25.6121	−0.864860	−0.432430	−	0.901668i	$-0.642344\pi$
$877$	−25.6121	−0.864860	−0.432430	+	0.901668i	$0.642344\pi$
$878$	−56.9292	−1.92127
$879$	8.83154	0.297881
$880$	63.0558	2.12561
$881$	−42.1642	−1.42055	−0.710273	−	0.703926i	$-0.751429\pi$
$881$	−42.1642	−1.42055	−0.710273	+	0.703926i	$0.751429\pi$
$882$	−1.65109	−0.0555952
$883$	−32.9992	−1.11051	−0.555256	−	0.831680i	$-0.687380\pi$
$883$	−32.9992	−1.11051	−0.555256	+	0.831680i	$0.687380\pi$
$884$	0	0
$885$	−8.85772	−0.297749
$886$	21.3099	0.715921
$887$	9.28669	0.311816	0.155908	−	0.987772i	$-0.450170\pi$
$887$	9.28669	0.311816	0.155908	+	0.987772i	$0.450170\pi$
$888$	−6.15215	−0.206453
$889$	−5.47277	−0.183551
$890$	64.7034	2.16886
$891$	4.37720	0.146642
$892$	−5.81042	−0.194547
$893$	55.1492	1.84550
$894$	5.07714	0.169805
$895$	−55.4896	−1.85481
$896$	−13.4132	−0.448105
$897$	0	0
$898$	−9.30936	−0.310657
$899$	7.76003	0.258812
$900$	2.58170	0.0860568
$901$	−1.10331	−0.0367567
$902$	−62.1853	−2.07054
$903$	5.72611	0.190553
$904$	−21.7445	−0.723212
$905$	5.65322	0.187919
$906$	−27.5088	−0.913919
$907$	21.2448	0.705422	0.352711	−	0.935732i	$-0.385260\pi$
$907$	21.2448	0.705422	0.352711	+	0.935732i	$0.385260\pi$
$908$	5.85209	0.194208
$909$	11.0283	0.365785
$910$	0	0
$911$	−54.0785	−1.79170	−0.895850	−	0.444357i	$-0.853432\pi$
$911$	−54.0785	−1.79170	−0.895850	+	0.444357i	$0.853432\pi$
$912$	28.3404	0.938443
$913$	5.54215	0.183419
$914$	62.7239	2.07472
$915$	−0.883892	−0.0292206
$916$	6.15778	0.203459
$917$	16.1706	0.534000
$918$	6.02830	0.198963
$919$	−18.9426	−0.624859	−0.312429	−	0.949941i	$-0.601143\pi$
$919$	−18.9426	−0.624859	−0.312429	+	0.949941i	$0.601143\pi$
$920$	−43.2392	−1.42555
$921$	11.6532	0.383987
$922$	−10.9093	−0.359277
$923$	0	0
$924$	−3.17833	−0.104559
$925$	10.3999	0.341946
$926$	16.4933	0.542004
$927$	−19.4543	−0.638964
$928$	4.70556	0.154468
$929$	45.3347	1.48738	0.743692	−	0.668522i	$-0.233073\pi$
$929$	45.3347	1.48738	0.743692	+	0.668522i	$0.233073\pi$
$930$	−31.2597	−1.02505
$931$	5.75441	0.188593
$932$	−7.43942	−0.243686
$933$	25.0099	0.818786
$934$	−5.64839	−0.184821
$935$	−46.7459	−1.52875
$936$	0	0
$937$	3.71544	0.121378	0.0606890	−	0.998157i	$-0.480670\pi$
$937$	3.71544	0.121378	0.0606890	+	0.998157i	$0.480670\pi$
$938$	−14.3772	−0.469432
$939$	0.186078	0.00607244
$940$	−20.3547	−0.663897
$941$	4.28376	0.139647	0.0698233	−	0.997559i	$-0.477756\pi$
$941$	4.28376	0.139647	0.0698233	+	0.997559i	$0.477756\pi$
$942$	21.1826	0.690166
$943$	60.4741	1.96931
$944$	14.9143	0.485419
$945$	2.92498	0.0951497
$946$	41.3836	1.34550
$947$	25.0205	0.813059	0.406529	−	0.913638i	$-0.366739\pi$
$947$	25.0205	0.813059	0.406529	+	0.913638i	$0.366739\pi$
$948$	12.3022	0.399556
$949$	0	0
$950$	−33.7813	−1.09601
$951$	−0.540031	−0.0175117
$952$	7.67939	0.248890
$953$	−2.84434	−0.0921372	−0.0460686	−	0.998938i	$-0.514669\pi$
$953$	−2.84434	−0.0921372	−0.0460686	+	0.998938i	$0.514669\pi$
$954$	0.498939	0.0161537
$955$	6.65109	0.215224
$956$	8.20662	0.265421
$957$	−5.24772	−0.169635
$958$	32.7600	1.05843
$959$	12.0176	0.388069
$960$	9.85560	0.318088
$961$	10.8967	0.351506
$962$	0	0
$963$	−1.42392	−0.0458853
$964$	−0.752283	−0.0242294
$965$	−12.8321	−0.413081
$966$	11.6044	0.373365
$967$	6.68444	0.214957	0.107478	−	0.994207i	$-0.465722\pi$
$967$	6.68444	0.214957	0.107478	+	0.994207i	$0.465722\pi$
$968$	17.1628	0.551634
$969$	−21.0099	−0.674934
$970$	−57.5908	−1.84913
$971$	−26.6278	−0.854528	−0.427264	−	0.904127i	$-0.640523\pi$
$971$	−26.6278	−0.854528	−0.427264	+	0.904127i	$0.640523\pi$
$972$	−0.726109	−0.0232900
$973$	1.34891	0.0432440
$974$	−10.0771	−0.322892
$975$	0	0
$976$	1.48827	0.0476382
$977$	27.8179	0.889975	0.444987	−	0.895537i	$-0.353208\pi$
$977$	27.8179	0.889975	0.444987	+	0.895537i	$0.353208\pi$
$978$	35.6708	1.14063
$979$	58.6447	1.87429
$980$	−2.12386	−0.0678442
$981$	0.0467198	0.00149165
$982$	3.90736	0.124689
$983$	−51.3454	−1.63766	−0.818832	−	0.574033i	$-0.805378\pi$
$983$	−51.3454	−1.63766	−0.818832	+	0.574033i	$0.805378\pi$
$984$	−18.0977	−0.576933
$985$	−15.3807	−0.490070
$986$	−7.22717	−0.230160
$987$	−9.58383	−0.305057
$988$	0	0
$989$	−40.2448	−1.27971
$990$	21.1394	0.671853
$991$	−23.3745	−0.742515	−0.371258	−	0.928530i	$-0.621073\pi$
$991$	−23.3745	−0.742515	−0.371258	+	0.928530i	$0.621073\pi$
$992$	25.4055	0.806625
$993$	1.54003	0.0488714
$994$	22.3510	0.708932
$995$	−38.5979	−1.22364
$996$	−0.919357	−0.0291309
$997$	−28.7955	−0.911963	−0.455981	−	0.889989i	$-0.650712\pi$
$997$	−28.7955	−0.911963	−0.455981	+	0.889989i	$0.650712\pi$
$998$	−7.08701	−0.224335
$999$	−2.92498	−0.0925424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.s.1.1		3
13.4	even	6		273.2.k.d.211.1	yes	6
13.10	even	6		273.2.k.d.22.1	✓	6
13.12	even	2		3549.2.a.h.1.3		3
39.17	odd	6		819.2.o.d.757.3		6
39.23	odd	6		819.2.o.d.568.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.d.22.1	✓	6	13.10	even	6
273.2.k.d.211.1	yes	6	13.4	even	6
819.2.o.d.568.3		6	39.23	odd	6
819.2.o.d.757.3		6	39.17	odd	6
3549.2.a.h.1.3		3	13.12	even	2
3549.2.a.s.1.1		3	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-1.65109 q^{2} -1.00000 q^{3} +0.726109 q^{4} -2.92498 q^{5} +1.65109 q^{6} +1.00000 q^{7} +2.10331 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.65109 q^{2} -1.00000 q^{3} +0.726109 q^{4} -2.92498 q^{5} +1.65109 q^{6} +1.00000 q^{7} +2.10331 q^{8} +1.00000 q^{9} +4.82942 q^{10} +4.37720 q^{11} -0.726109 q^{12} -1.65109 q^{14} +2.92498 q^{15} -4.92498 q^{16} +3.65109 q^{17} -1.65109 q^{18} +5.75441 q^{19} -2.12386 q^{20} -1.00000 q^{21} -7.22717 q^{22} +7.02830 q^{23} -2.10331 q^{24} +3.55553 q^{25} -1.00000 q^{27} +0.726109 q^{28} +1.19887 q^{29} -4.82942 q^{30} +6.47277 q^{31} +3.92498 q^{32} -4.37720 q^{33} -6.02830 q^{34} -2.92498 q^{35} +0.726109 q^{36} +2.92498 q^{37} -9.50106 q^{38} -6.15215 q^{40} +8.60437 q^{41} +1.65109 q^{42} -5.72611 q^{43} +3.17833 q^{44} -2.92498 q^{45} -11.6044 q^{46} +9.58383 q^{47} +4.92498 q^{48} +1.00000 q^{49} -5.87051 q^{50} -3.65109 q^{51} -0.302187 q^{53} +1.65109 q^{54} -12.8032 q^{55} +2.10331 q^{56} -5.75441 q^{57} -1.97945 q^{58} -3.02830 q^{59} +2.12386 q^{60} -0.302187 q^{61} -10.6871 q^{62} +1.00000 q^{63} +3.36945 q^{64} +7.22717 q^{66} +8.70769 q^{67} +2.65109 q^{68} -7.02830 q^{69} +4.82942 q^{70} -13.5371 q^{71} +2.10331 q^{72} -0.932734 q^{73} -4.82942 q^{74} -3.55553 q^{75} +4.17833 q^{76} +4.37720 q^{77} -16.9426 q^{79} +14.4055 q^{80} +1.00000 q^{81} -14.2066 q^{82} +1.26614 q^{83} -0.726109 q^{84} -10.6794 q^{85} +9.45434 q^{86} -1.19887 q^{87} +9.20662 q^{88} +13.3977 q^{89} +4.82942 q^{90} +5.10331 q^{92} -6.47277 q^{93} -15.8238 q^{94} -16.8315 q^{95} -3.92498 q^{96} -11.9250 q^{97} -1.65109 q^{98} +4.37720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} - 3 q^{3} + 4 q^{4} - 2 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} + 13 q^{10} + 8 q^{11} - 4 q^{12} + 2 q^{14} - 6 q^{16} + 4 q^{17} + 2 q^{18} + 7 q^{19} + 13 q^{20} - 3 q^{21} + q^{22} + 9 q^{23} - 3 q^{24} + 11 q^{25} - 3 q^{27} + 4 q^{28} - 7 q^{29} - 13 q^{30} + 7 q^{31} + 3 q^{32} - 8 q^{33} - 6 q^{34} + 4 q^{36} - 4 q^{38} + 13 q^{40} - 2 q^{41} - 2 q^{42} - 19 q^{43} + 15 q^{44} - 7 q^{46} + 17 q^{47} + 6 q^{48} + 3 q^{49} + 16 q^{50} - 4 q^{51} + 13 q^{53} - 2 q^{54} + 3 q^{56} - 7 q^{57} - 22 q^{58} + 3 q^{59} - 13 q^{60} + 13 q^{61} - 17 q^{62} + 3 q^{63} + q^{64} - q^{66} - 5 q^{67} + q^{68} - 9 q^{69} + 13 q^{70} - 8 q^{71} + 3 q^{72} + 2 q^{73} - 13 q^{74} - 11 q^{75} + 18 q^{76} + 8 q^{77} - q^{79} + 26 q^{80} + 3 q^{81} - 36 q^{82} - 2 q^{83} - 4 q^{84} - 13 q^{85} - 17 q^{86} + 7 q^{87} + 21 q^{88} + 19 q^{89} + 13 q^{90} + 12 q^{92} - 7 q^{93} + 7 q^{94} - 3 q^{96} - 27 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 - 3 * q^3 + 4 * q^4 - 2 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 + 13 * q^10 + 8 * q^11 - 4 * q^12 + 2 * q^14 - 6 * q^16 + 4 * q^17 + 2 * q^18 + 7 * q^19 + 13 * q^20 - 3 * q^21 + q^22 + 9 * q^23 - 3 * q^24 + 11 * q^25 - 3 * q^27 + 4 * q^28 - 7 * q^29 - 13 * q^30 + 7 * q^31 + 3 * q^32 - 8 * q^33 - 6 * q^34 + 4 * q^36 - 4 * q^38 + 13 * q^40 - 2 * q^41 - 2 * q^42 - 19 * q^43 + 15 * q^44 - 7 * q^46 + 17 * q^47 + 6 * q^48 + 3 * q^49 + 16 * q^50 - 4 * q^51 + 13 * q^53 - 2 * q^54 + 3 * q^56 - 7 * q^57 - 22 * q^58 + 3 * q^59 - 13 * q^60 + 13 * q^61 - 17 * q^62 + 3 * q^63 + q^64 - q^66 - 5 * q^67 + q^68 - 9 * q^69 + 13 * q^70 - 8 * q^71 + 3 * q^72 + 2 * q^73 - 13 * q^74 - 11 * q^75 + 18 * q^76 + 8 * q^77 - q^79 + 26 * q^80 + 3 * q^81 - 36 * q^82 - 2 * q^83 - 4 * q^84 - 13 * q^85 - 17 * q^86 + 7 * q^87 + 21 * q^88 + 19 * q^89 + 13 * q^90 + 12 * q^92 - 7 * q^93 + 7 * q^94 - 3 * q^96 - 27 * q^97 + 2 * q^98 + 8 * q^99

Introduction

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