LMFDB - Embedded newform 3549.2.a.n.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:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*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			$-1.53209$ 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)

$f(q)$	$=$	$q-1.53209 q^{2} +1.00000 q^{3} +0.347296 q^{4} -0.120615 q^{5} -1.53209 q^{6} +1.00000 q^{7} +2.53209 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.53209 q^{2} +1.00000 q^{3} +0.347296 q^{4} -0.120615 q^{5} -1.53209 q^{6} +1.00000 q^{7} +2.53209 q^{8} +1.00000 q^{9} +0.184793 q^{10} -4.57398 q^{11} +0.347296 q^{12} -1.53209 q^{14} -0.120615 q^{15} -4.57398 q^{16} +4.92127 q^{17} -1.53209 q^{18} +0.758770 q^{19} -0.0418891 q^{20} +1.00000 q^{21} +7.00774 q^{22} -5.47565 q^{23} +2.53209 q^{24} -4.98545 q^{25} +1.00000 q^{27} +0.347296 q^{28} +10.6604 q^{29} +0.184793 q^{30} -8.63816 q^{31} +1.94356 q^{32} -4.57398 q^{33} -7.53983 q^{34} -0.120615 q^{35} +0.347296 q^{36} +4.70233 q^{37} -1.16250 q^{38} -0.305407 q^{40} -10.9067 q^{41} -1.53209 q^{42} +1.26352 q^{43} -1.58853 q^{44} -0.120615 q^{45} +8.38919 q^{46} -5.94356 q^{47} -4.57398 q^{48} +1.00000 q^{49} +7.63816 q^{50} +4.92127 q^{51} +9.49794 q^{53} -1.53209 q^{54} +0.551689 q^{55} +2.53209 q^{56} +0.758770 q^{57} -16.3327 q^{58} +8.99319 q^{59} -0.0418891 q^{60} -9.45336 q^{61} +13.2344 q^{62} +1.00000 q^{63} +6.17024 q^{64} +7.00774 q^{66} -13.0300 q^{67} +1.70914 q^{68} -5.47565 q^{69} +0.184793 q^{70} -2.47565 q^{71} +2.53209 q^{72} -5.89393 q^{73} -7.20439 q^{74} -4.98545 q^{75} +0.263518 q^{76} -4.57398 q^{77} -8.18479 q^{79} +0.551689 q^{80} +1.00000 q^{81} +16.7101 q^{82} -12.2490 q^{83} +0.347296 q^{84} -0.593578 q^{85} -1.93582 q^{86} +10.6604 q^{87} -11.5817 q^{88} +6.75877 q^{89} +0.184793 q^{90} -1.90167 q^{92} -8.63816 q^{93} +9.10607 q^{94} -0.0915189 q^{95} +1.94356 q^{96} +10.0719 q^{97} -1.53209 q^{98} -4.57398 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{15} - 6 q^{16} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} + 9 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} - 6 q^{33} + 6 q^{34} - 6 q^{35} - 12 q^{37} - 6 q^{38} - 3 q^{40} - 6 q^{41} + 9 q^{43} - 15 q^{44} - 6 q^{45} + 21 q^{46} - 3 q^{47} - 6 q^{48} + 3 q^{49} + 6 q^{50} + 6 q^{51} + 3 q^{53} + 3 q^{56} - 9 q^{57} - 30 q^{58} - 15 q^{59} + 3 q^{60} - 15 q^{61} + 9 q^{62} + 3 q^{63} - 3 q^{64} - 3 q^{66} - 9 q^{67} + 21 q^{68} + 3 q^{69} - 3 q^{70} + 12 q^{71} + 3 q^{72} - 30 q^{73} - 21 q^{74} + 3 q^{75} + 6 q^{76} - 6 q^{77} - 21 q^{79} + 3 q^{81} - 24 q^{83} + 3 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} + 9 q^{89} - 3 q^{90} + 6 q^{92} - 9 q^{93} + 15 q^{94} + 30 q^{95} - 9 q^{96} - 3 q^{97} - 6 q^{99}+O(q^{100}) $ 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^15 - 6 * q^16 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 + 9 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 - 6 * q^33 + 6 * q^34 - 6 * q^35 - 12 * q^37 - 6 * q^38 - 3 * q^40 - 6 * q^41 + 9 * q^43 - 15 * q^44 - 6 * q^45 + 21 * q^46 - 3 * q^47 - 6 * q^48 + 3 * q^49 + 6 * q^50 + 6 * q^51 + 3 * q^53 + 3 * q^56 - 9 * q^57 - 30 * q^58 - 15 * q^59 + 3 * q^60 - 15 * q^61 + 9 * q^62 + 3 * q^63 - 3 * q^64 - 3 * q^66 - 9 * q^67 + 21 * q^68 + 3 * q^69 - 3 * q^70 + 12 * q^71 + 3 * q^72 - 30 * q^73 - 21 * q^74 + 3 * q^75 + 6 * q^76 - 6 * q^77 - 21 * q^79 + 3 * q^81 - 24 * q^83 + 3 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 + 9 * q^89 - 3 * q^90 + 6 * q^92 - 9 * q^93 + 15 * q^94 + 30 * q^95 - 9 * q^96 - 3 * q^97 - 6 * 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 $

$2$	−1.53209	−1.08335	−0.541675	−	0.840588i	$-0.682210\pi$
$2$	−1.53209	−1.08335	−0.541675	+	0.840588i	$0.682210\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.347296	0.173648
$5$	−0.120615	−0.0539406	−0.0269703	−	0.999636i	$-0.508586\pi$
$5$	−0.120615	−0.0539406	−0.0269703	+	0.999636i	$0.508586\pi$
$6$	−1.53209	−0.625473
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.53209	0.895229
$9$	1.00000	0.333333
$10$	0.184793	0.0584365
$11$	−4.57398	−1.37911	−0.689553	−	0.724235i	$-0.742193\pi$
$11$	−4.57398	−1.37911	−0.689553	+	0.724235i	$0.742193\pi$
$12$	0.347296	0.100256
$13$	0	0
$13$	0	0
$14$	−1.53209	−0.409468
$15$	−0.120615	−0.0311426
$16$	−4.57398	−1.14349
$17$	4.92127	1.19358	0.596792	−	0.802396i	$-0.296442\pi$
$17$	4.92127	1.19358	0.596792	+	0.802396i	$0.296442\pi$
$18$	−1.53209	−0.361117
$19$	0.758770	0.174074	0.0870369	−	0.996205i	$-0.472260\pi$
$19$	0.758770	0.174074	0.0870369	+	0.996205i	$0.472260\pi$
$20$	−0.0418891	−0.00936668
$21$	1.00000	0.218218
$22$	7.00774	1.49406
$23$	−5.47565	−1.14175	−0.570876	−	0.821036i	$-0.693396\pi$
$23$	−5.47565	−1.14175	−0.570876	+	0.821036i	$0.693396\pi$
$24$	2.53209	0.516860
$25$	−4.98545	−0.997090
$26$	0	0
$27$	1.00000	0.192450
$28$	0.347296	0.0656328
$29$	10.6604	1.97959	0.989797	−	0.142482i	$-0.0455082\pi$
$29$	10.6604	1.97959	0.989797	+	0.142482i	$0.0455082\pi$
$30$	0.184793	0.0337383
$31$	−8.63816	−1.55146	−0.775729	−	0.631066i	$-0.782618\pi$
$31$	−8.63816	−1.55146	−0.775729	+	0.631066i	$0.782618\pi$
$32$	1.94356	0.343577
$33$	−4.57398	−0.796227
$34$	−7.53983	−1.29307
$35$	−0.120615	−0.0203876
$36$	0.347296	0.0578827
$37$	4.70233	0.773059	0.386529	−	0.922277i	$-0.373674\pi$
$37$	4.70233	0.773059	0.386529	+	0.922277i	$0.373674\pi$
$38$	−1.16250	−0.188583
$39$	0	0
$40$	−0.305407	−0.0482891
$41$	−10.9067	−1.70334	−0.851672	−	0.524075i	$-0.824411\pi$
$41$	−10.9067	−1.70334	−0.851672	+	0.524075i	$0.824411\pi$
$42$	−1.53209	−0.236406
$43$	1.26352	0.192685	0.0963424	−	0.995348i	$-0.469286\pi$
$43$	1.26352	0.192685	0.0963424	+	0.995348i	$0.469286\pi$
$44$	−1.58853	−0.239479
$45$	−0.120615	−0.0179802
$46$	8.38919	1.23692
$47$	−5.94356	−0.866958	−0.433479	−	0.901164i	$-0.642714\pi$
$47$	−5.94356	−0.866958	−0.433479	+	0.901164i	$0.642714\pi$
$48$	−4.57398	−0.660197
$49$	1.00000	0.142857
$50$	7.63816	1.08020
$51$	4.92127	0.689116
$52$	0	0
$53$	9.49794	1.30464	0.652321	−	0.757943i	$-0.273795\pi$
$53$	9.49794	1.30464	0.652321	+	0.757943i	$0.273795\pi$
$54$	−1.53209	−0.208491
$55$	0.551689	0.0743898
$56$	2.53209	0.338365
$57$	0.758770	0.100502
$58$	−16.3327	−2.14459
$59$	8.99319	1.17081	0.585407	−	0.810740i	$-0.300935\pi$
$59$	8.99319	1.17081	0.585407	+	0.810740i	$0.300935\pi$
$60$	−0.0418891	−0.00540786
$61$	−9.45336	−1.21038	−0.605190	−	0.796081i	$-0.706903\pi$
$61$	−9.45336	−1.21038	−0.605190	+	0.796081i	$0.706903\pi$
$62$	13.2344	1.68077
$63$	1.00000	0.125988
$64$	6.17024	0.771281
$65$	0	0
$66$	7.00774	0.862593
$67$	−13.0300	−1.59187	−0.795936	−	0.605381i	$-0.793021\pi$
$67$	−13.0300	−1.59187	−0.795936	+	0.605381i	$0.793021\pi$
$68$	1.70914	0.207264
$69$	−5.47565	−0.659191
$70$	0.184793	0.0220869
$71$	−2.47565	−0.293806	−0.146903	−	0.989151i	$-0.546930\pi$
$71$	−2.47565	−0.293806	−0.146903	+	0.989151i	$0.546930\pi$
$72$	2.53209	0.298410
$73$	−5.89393	−0.689833	−0.344916	−	0.938633i	$-0.612093\pi$
$73$	−5.89393	−0.689833	−0.344916	+	0.938633i	$0.612093\pi$
$74$	−7.20439	−0.837494
$75$	−4.98545	−0.575670
$76$	0.263518	0.0302276
$77$	−4.57398	−0.521253
$78$	0	0
$79$	−8.18479	−0.920861	−0.460431	−	0.887696i	$-0.652305\pi$
$79$	−8.18479	−0.920861	−0.460431	+	0.887696i	$0.652305\pi$
$80$	0.551689	0.0616807
$81$	1.00000	0.111111
$82$	16.7101	1.84532
$83$	−12.2490	−1.34450	−0.672250	−	0.740325i	$-0.734672\pi$
$83$	−12.2490	−1.34450	−0.672250	+	0.740325i	$0.734672\pi$
$84$	0.347296	0.0378931
$85$	−0.593578	−0.0643826
$86$	−1.93582	−0.208745
$87$	10.6604	1.14292
$88$	−11.5817	−1.23462
$89$	6.75877	0.716428	0.358214	−	0.933639i	$-0.383386\pi$
$89$	6.75877	0.716428	0.358214	+	0.933639i	$0.383386\pi$
$90$	0.184793	0.0194788
$91$	0	0
$92$	−1.90167	−0.198263
$93$	−8.63816	−0.895735
$94$	9.10607	0.939219
$95$	−0.0915189	−0.00938964
$96$	1.94356	0.198364
$97$	10.0719	1.02265	0.511324	−	0.859388i	$-0.329155\pi$
$97$	10.0719	1.02265	0.511324	+	0.859388i	$0.329155\pi$
$98$	−1.53209	−0.154764
$99$	−4.57398	−0.459702
$100$	−1.73143	−0.173143
$101$	−5.95811	−0.592854	−0.296427	−	0.955055i	$-0.595795\pi$
$101$	−5.95811	−0.592854	−0.296427	+	0.955055i	$0.595795\pi$
$102$	−7.53983	−0.746554
$103$	−2.75877	−0.271830	−0.135915	−	0.990721i	$-0.543397\pi$
$103$	−2.75877	−0.271830	−0.135915	+	0.990721i	$0.543397\pi$
$104$	0	0
$105$	−0.120615	−0.0117708
$106$	−14.5517	−1.41339
$107$	−3.86484	−0.373628	−0.186814	−	0.982395i	$-0.559816\pi$
$107$	−3.86484	−0.373628	−0.186814	+	0.982395i	$0.559816\pi$
$108$	0.347296	0.0334186
$109$	12.0496	1.15415	0.577073	−	0.816693i	$-0.304195\pi$
$109$	12.0496	1.15415	0.577073	+	0.816693i	$0.304195\pi$
$110$	−0.845237	−0.0805902
$111$	4.70233	0.446326
$112$	−4.57398	−0.432200
$113$	7.57398	0.712500	0.356250	−	0.934391i	$-0.384055\pi$
$113$	7.57398	0.712500	0.356250	+	0.934391i	$0.384055\pi$
$114$	−1.16250	−0.108878
$115$	0.660444	0.0615868
$116$	3.70233	0.343753
$117$	0	0
$118$	−13.7784	−1.26840
$119$	4.92127	0.451132
$120$	−0.305407	−0.0278797
$121$	9.92127	0.901934
$122$	14.4834	1.31126
$123$	−10.9067	−0.983426
$124$	−3.00000	−0.269408
$125$	1.20439	0.107724
$126$	−1.53209	−0.136489
$127$	−9.87939	−0.876654	−0.438327	−	0.898816i	$-0.644429\pi$
$127$	−9.87939	−0.876654	−0.438327	+	0.898816i	$0.644429\pi$
$128$	−13.3405	−1.17914
$129$	1.26352	0.111247
$130$	0	0
$131$	15.5253	1.35645	0.678225	−	0.734854i	$-0.262749\pi$
$131$	15.5253	1.35645	0.678225	+	0.734854i	$0.262749\pi$
$132$	−1.58853	−0.138263
$133$	0.758770	0.0657937
$134$	19.9632	1.72455
$135$	−0.120615	−0.0103809
$136$	12.4611	1.06853
$137$	1.56624	0.133813	0.0669063	−	0.997759i	$-0.478687\pi$
$137$	1.56624	0.133813	0.0669063	+	0.997759i	$0.478687\pi$
$138$	8.38919	0.714135
$139$	10.5030	0.890852	0.445426	−	0.895319i	$-0.353052\pi$
$139$	10.5030	0.890852	0.445426	+	0.895319i	$0.353052\pi$
$140$	−0.0418891	−0.00354027
$141$	−5.94356	−0.500538
$142$	3.79292	0.318295
$143$	0	0
$144$	−4.57398	−0.381165
$145$	−1.28581	−0.106780
$146$	9.03003	0.747331
$147$	1.00000	0.0824786
$148$	1.63310	0.134240
$149$	−0.248970	−0.0203964	−0.0101982	−	0.999948i	$-0.503246\pi$
$149$	−0.248970	−0.0203964	−0.0101982	+	0.999948i	$0.503246\pi$
$150$	7.63816	0.623653
$151$	−18.9513	−1.54224	−0.771118	−	0.636693i	$-0.780302\pi$
$151$	−18.9513	−1.54224	−0.771118	+	0.636693i	$0.780302\pi$
$152$	1.92127	0.155836
$153$	4.92127	0.397861
$154$	7.00774	0.564700
$155$	1.04189	0.0836865
$156$	0	0
$157$	−18.6827	−1.49104	−0.745522	−	0.666481i	$-0.767800\pi$
$157$	−18.6827	−1.49104	−0.745522	+	0.666481i	$0.767800\pi$
$158$	12.5398	0.997615
$159$	9.49794	0.753236
$160$	−0.234422	−0.0185327
$161$	−5.47565	−0.431542
$162$	−1.53209	−0.120372
$163$	−20.0351	−1.56927	−0.784634	−	0.619959i	$-0.787149\pi$
$163$	−20.0351	−1.56927	−0.784634	+	0.619959i	$0.787149\pi$
$164$	−3.78787	−0.295783
$165$	0.551689	0.0429489
$166$	18.7665	1.45656
$167$	2.01960	0.156281	0.0781407	−	0.996942i	$-0.475102\pi$
$167$	2.01960	0.156281	0.0781407	+	0.996942i	$0.475102\pi$
$168$	2.53209	0.195355
$169$	0	0
$170$	0.909415	0.0697489
$171$	0.758770	0.0580246
$172$	0.438815	0.0334594
$173$	2.19934	0.167213	0.0836064	−	0.996499i	$-0.473356\pi$
$173$	2.19934	0.167213	0.0836064	+	0.996499i	$0.473356\pi$
$174$	−16.3327	−1.23818
$175$	−4.98545	−0.376865
$176$	20.9213	1.57700
$177$	8.99319	0.675970
$178$	−10.3550	−0.776143
$179$	−8.57667	−0.641050	−0.320525	−	0.947240i	$-0.603859\pi$
$179$	−8.57667	−0.641050	−0.320525	+	0.947240i	$0.603859\pi$
$180$	−0.0418891	−0.00312223
$181$	11.8844	0.883363	0.441682	−	0.897172i	$-0.354382\pi$
$181$	11.8844	0.883363	0.441682	+	0.897172i	$0.354382\pi$
$182$	0	0
$183$	−9.45336	−0.698813
$184$	−13.8648	−1.02213
$185$	−0.567171	−0.0416992
$186$	13.2344	0.970395
$187$	−22.5098	−1.64608
$188$	−2.06418	−0.150546
$189$	1.00000	0.0727393
$190$	0.140215	0.0101723
$191$	−13.8007	−0.998581	−0.499290	−	0.866435i	$-0.666406\pi$
$191$	−13.8007	−0.998581	−0.499290	+	0.866435i	$0.666406\pi$
$192$	6.17024	0.445299
$193$	−18.2148	−1.31113	−0.655566	−	0.755138i	$-0.727570\pi$
$193$	−18.2148	−1.31113	−0.655566	+	0.755138i	$0.727570\pi$
$194$	−15.4311	−1.10789
$195$	0	0
$196$	0.347296	0.0248069
$197$	−3.56893	−0.254275	−0.127138	−	0.991885i	$-0.540579\pi$
$197$	−3.56893	−0.254275	−0.127138	+	0.991885i	$0.540579\pi$
$198$	7.00774	0.498018
$199$	−9.73648	−0.690201	−0.345100	−	0.938566i	$-0.612155\pi$
$199$	−9.73648	−0.690201	−0.345100	+	0.938566i	$0.612155\pi$
$200$	−12.6236	−0.892624
$201$	−13.0300	−0.919067
$202$	9.12836	0.642269
$203$	10.6604	0.748217
$204$	1.70914	0.119664
$205$	1.31551	0.0918794
$206$	4.22668	0.294487
$207$	−5.47565	−0.380584
$208$	0	0
$209$	−3.47060	−0.240066
$210$	0.184793	0.0127519
$211$	−22.0574	−1.51849	−0.759246	−	0.650804i	$-0.774432\pi$
$211$	−22.0574	−1.51849	−0.759246	+	0.650804i	$0.774432\pi$
$212$	3.29860	0.226549
$213$	−2.47565	−0.169629
$214$	5.92127	0.404770
$215$	−0.152399	−0.0103935
$216$	2.53209	0.172287
$217$	−8.63816	−0.586396
$218$	−18.4611	−1.25034
$219$	−5.89393	−0.398275
$220$	0.191600	0.0129176
$221$	0	0
$222$	−7.20439	−0.483527
$223$	3.45336	0.231254	0.115627	−	0.993293i	$-0.463112\pi$
$223$	3.45336	0.231254	0.115627	+	0.993293i	$0.463112\pi$
$224$	1.94356	0.129860
$225$	−4.98545	−0.332363
$226$	−11.6040	−0.771887
$227$	5.12061	0.339867	0.169934	−	0.985456i	$-0.445645\pi$
$227$	5.12061	0.339867	0.169934	+	0.985456i	$0.445645\pi$
$228$	0.263518	0.0174519
$229$	15.3628	1.01520	0.507600	−	0.861593i	$-0.330533\pi$
$229$	15.3628	1.01520	0.507600	+	0.861593i	$0.330533\pi$
$230$	−1.01186	−0.0667200
$231$	−4.57398	−0.300946
$232$	26.9932	1.77219
$233$	6.23173	0.408254	0.204127	−	0.978944i	$-0.434564\pi$
$233$	6.23173	0.408254	0.204127	+	0.978944i	$0.434564\pi$
$234$	0	0
$235$	0.716881	0.0467642
$236$	3.12330	0.203310
$237$	−8.18479	−0.531659
$238$	−7.53983	−0.488735
$239$	4.45336	0.288064	0.144032	−	0.989573i	$-0.453993\pi$
$239$	4.45336	0.288064	0.144032	+	0.989573i	$0.453993\pi$
$240$	0.551689	0.0356114
$241$	9.04694	0.582765	0.291382	−	0.956607i	$-0.405885\pi$
$241$	9.04694	0.582765	0.291382	+	0.956607i	$0.405885\pi$
$242$	−15.2003	−0.977111
$243$	1.00000	0.0641500
$244$	−3.28312	−0.210180
$245$	−0.120615	−0.00770579
$246$	16.7101	1.06540
$247$	0	0
$248$	−21.8726	−1.38891
$249$	−12.2490	−0.776247
$250$	−1.84524	−0.116703
$251$	−1.94356	−0.122677	−0.0613383	−	0.998117i	$-0.519537\pi$
$251$	−1.94356	−0.122677	−0.0613383	+	0.998117i	$0.519537\pi$
$252$	0.347296	0.0218776
$253$	25.0455	1.57460
$254$	15.1361	0.949723
$255$	−0.593578	−0.0371713
$256$	8.09833	0.506145
$257$	−20.5594	−1.28246	−0.641231	−	0.767348i	$-0.721576\pi$
$257$	−20.5594	−1.28246	−0.641231	+	0.767348i	$0.721576\pi$
$258$	−1.93582	−0.120519
$259$	4.70233	0.292189
$260$	0	0
$261$	10.6604	0.659865
$262$	−23.7861	−1.46951
$263$	16.1061	0.993143	0.496571	−	0.867996i	$-0.334592\pi$
$263$	16.1061	0.993143	0.496571	+	0.867996i	$0.334592\pi$
$264$	−11.5817	−0.712806
$265$	−1.14559	−0.0703731
$266$	−1.16250	−0.0712777
$267$	6.75877	0.413630
$268$	−4.52528	−0.276426
$269$	−4.29767	−0.262033	−0.131017	−	0.991380i	$-0.541824\pi$
$269$	−4.29767	−0.262033	−0.131017	+	0.991380i	$0.541824\pi$
$270$	0.184793	0.0112461
$271$	−11.9017	−0.722975	−0.361488	−	0.932377i	$-0.617731\pi$
$271$	−11.9017	−0.722975	−0.361488	+	0.932377i	$0.617731\pi$
$272$	−22.5098	−1.36486
$273$	0	0
$274$	−2.39961	−0.144966
$275$	22.8033	1.37509
$276$	−1.90167	−0.114467
$277$	10.8229	0.650288	0.325144	−	0.945665i	$-0.394587\pi$
$277$	10.8229	0.650288	0.325144	+	0.945665i	$0.394587\pi$
$278$	−16.0915	−0.965105
$279$	−8.63816	−0.517153
$280$	−0.305407	−0.0182516
$281$	−6.83481	−0.407730	−0.203865	−	0.978999i	$-0.565350\pi$
$281$	−6.83481	−0.407730	−0.203865	+	0.978999i	$0.565350\pi$
$282$	9.10607	0.542258
$283$	−22.7442	−1.35200	−0.676002	−	0.736900i	$-0.736289\pi$
$283$	−22.7442	−1.35200	−0.676002	+	0.736900i	$0.736289\pi$
$284$	−0.859785	−0.0510188
$285$	−0.0915189	−0.00542111
$286$	0	0
$287$	−10.9067	−0.643804
$288$	1.94356	0.114526
$289$	7.21894	0.424644
$290$	1.96997	0.115681
$291$	10.0719	0.590426
$292$	−2.04694	−0.119788
$293$	−20.9982	−1.22673	−0.613365	−	0.789799i	$-0.710185\pi$
$293$	−20.9982	−1.22673	−0.613365	+	0.789799i	$0.710185\pi$
$294$	−1.53209	−0.0893532
$295$	−1.08471	−0.0631544
$296$	11.9067	0.692064
$297$	−4.57398	−0.265409
$298$	0.381445	0.0220965
$299$	0	0
$300$	−1.73143	−0.0999641
$301$	1.26352	0.0728280
$302$	29.0351	1.67078
$303$	−5.95811	−0.342285
$304$	−3.47060	−0.199053
$305$	1.14022	0.0652885
$306$	−7.53983	−0.431023
$307$	15.8821	0.906438	0.453219	−	0.891399i	$-0.350276\pi$
$307$	15.8821	0.906438	0.453219	+	0.891399i	$0.350276\pi$
$308$	−1.58853	−0.0905147
$309$	−2.75877	−0.156941
$310$	−1.59627	−0.0906619
$311$	−10.1976	−0.578252	−0.289126	−	0.957291i	$-0.593365\pi$
$311$	−10.1976	−0.578252	−0.289126	+	0.957291i	$0.593365\pi$
$312$	0	0
$313$	−18.6578	−1.05460	−0.527299	−	0.849680i	$-0.676795\pi$
$313$	−18.6578	−1.05460	−0.527299	+	0.849680i	$0.676795\pi$
$314$	28.6236	1.61532
$315$	−0.120615	−0.00679587
$316$	−2.84255	−0.159906
$317$	15.3746	0.863526	0.431763	−	0.901987i	$-0.357892\pi$
$317$	15.3746	0.863526	0.431763	+	0.901987i	$0.357892\pi$
$318$	−14.5517	−0.816018
$319$	−48.7606	−2.73007
$320$	−0.744223	−0.0416033
$321$	−3.86484	−0.215714
$322$	8.38919	0.467511
$323$	3.73412	0.207772
$324$	0.347296	0.0192942
$325$	0	0
$326$	30.6955	1.70007
$327$	12.0496	0.666346
$328$	−27.6168	−1.52488
$329$	−5.94356	−0.327679
$330$	−0.845237	−0.0465288
$331$	6.95636	0.382356	0.191178	−	0.981555i	$-0.438769\pi$
$331$	6.95636	0.382356	0.191178	+	0.981555i	$0.438769\pi$
$332$	−4.25402	−0.233470
$333$	4.70233	0.257686
$334$	−3.09421	−0.169307
$335$	1.57161	0.0858664
$336$	−4.57398	−0.249531
$337$	−12.1111	−0.659735	−0.329867	−	0.944027i	$-0.607004\pi$
$337$	−12.1111	−0.659735	−0.329867	+	0.944027i	$0.607004\pi$
$338$	0	0
$339$	7.57398	0.411362
$340$	−0.206148	−0.0111799
$341$	39.5107	2.13963
$342$	−1.16250	−0.0628610
$343$	1.00000	0.0539949
$344$	3.19934	0.172497
$345$	0.660444	0.0355571
$346$	−3.36959	−0.181150
$347$	−24.9172	−1.33762	−0.668811	−	0.743432i	$-0.733197\pi$
$347$	−24.9172	−1.33762	−0.668811	+	0.743432i	$0.733197\pi$
$348$	3.70233	0.198466
$349$	4.09421	0.219158	0.109579	−	0.993978i	$-0.465050\pi$
$349$	4.09421	0.219158	0.109579	+	0.993978i	$0.465050\pi$
$350$	7.63816	0.408277
$351$	0	0
$352$	−8.88981	−0.473829
$353$	6.79561	0.361694	0.180847	−	0.983511i	$-0.442116\pi$
$353$	6.79561	0.361694	0.180847	+	0.983511i	$0.442116\pi$
$354$	−13.7784	−0.732312
$355$	0.298600	0.0158481
$356$	2.34730	0.124406
$357$	4.92127	0.260461
$358$	13.1402	0.694482
$359$	9.77425	0.515865	0.257933	−	0.966163i	$-0.416959\pi$
$359$	9.77425	0.515865	0.257933	+	0.966163i	$0.416959\pi$
$360$	−0.305407	−0.0160964
$361$	−18.4243	−0.969698
$362$	−18.2080	−0.956992
$363$	9.92127	0.520732
$364$	0	0
$365$	0.710895	0.0372100
$366$	14.4834	0.757059
$367$	−5.40198	−0.281981	−0.140990	−	0.990011i	$-0.545029\pi$
$367$	−5.40198	−0.281981	−0.140990	+	0.990011i	$0.545029\pi$
$368$	25.0455	1.30559
$369$	−10.9067	−0.567781
$370$	0.868956	0.0451749
$371$	9.49794	0.493109
$372$	−3.00000	−0.155543
$373$	−35.5594	−1.84120	−0.920599	−	0.390510i	$-0.872299\pi$
$373$	−35.5594	−1.84120	−0.920599	+	0.390510i	$0.872299\pi$
$374$	34.4870	1.78328
$375$	1.20439	0.0621946
$376$	−15.0496	−0.776125
$377$	0	0
$378$	−1.53209	−0.0788021
$379$	−12.3250	−0.633093	−0.316547	−	0.948577i	$-0.602523\pi$
$379$	−12.3250	−0.633093	−0.316547	+	0.948577i	$0.602523\pi$
$380$	−0.0317842	−0.00163049
$381$	−9.87939	−0.506136
$382$	21.1438	1.08181
$383$	6.38507	0.326262	0.163131	−	0.986604i	$-0.447841\pi$
$383$	6.38507	0.326262	0.163131	+	0.986604i	$0.447841\pi$
$384$	−13.3405	−0.680779
$385$	0.551689	0.0281167
$386$	27.9067	1.42041
$387$	1.26352	0.0642282
$388$	3.49794	0.177581
$389$	−23.4492	−1.18892	−0.594462	−	0.804124i	$-0.702635\pi$
$389$	−23.4492	−1.18892	−0.594462	+	0.804124i	$0.702635\pi$
$390$	0	0
$391$	−26.9472	−1.36278
$392$	2.53209	0.127890
$393$	15.5253	0.783147
$394$	5.46791	0.275469
$395$	0.987207	0.0496718
$396$	−1.58853	−0.0798264
$397$	−17.4260	−0.874587	−0.437293	−	0.899319i	$-0.644063\pi$
$397$	−17.4260	−0.874587	−0.437293	+	0.899319i	$0.644063\pi$
$398$	14.9172	0.747729
$399$	0.758770	0.0379860
$400$	22.8033	1.14017
$401$	9.28136	0.463489	0.231745	−	0.972777i	$-0.425557\pi$
$401$	9.28136	0.463489	0.231745	+	0.972777i	$0.425557\pi$
$402$	19.9632	0.995672
$403$	0	0
$404$	−2.06923	−0.102948
$405$	−0.120615	−0.00599340
$406$	−16.3327	−0.810581
$407$	−21.5084	−1.06613
$408$	12.4611	0.616917
$409$	−14.4875	−0.716361	−0.358181	−	0.933652i	$-0.616603\pi$
$409$	−14.4875	−0.716361	−0.358181	+	0.933652i	$0.616603\pi$
$410$	−2.01548	−0.0995375
$411$	1.56624	0.0772568
$412$	−0.958111	−0.0472027
$413$	8.99319	0.442526
$414$	8.38919	0.412306
$415$	1.47741	0.0725230
$416$	0	0
$417$	10.5030	0.514334
$418$	5.31727	0.260076
$419$	5.53890	0.270593	0.135296	−	0.990805i	$-0.456801\pi$
$419$	5.53890	0.270593	0.135296	+	0.990805i	$0.456801\pi$
$420$	−0.0418891	−0.00204398
$421$	−24.8949	−1.21330	−0.606651	−	0.794968i	$-0.707487\pi$
$421$	−24.8949	−1.21330	−0.606651	+	0.794968i	$0.707487\pi$
$422$	33.7939	1.64506
$423$	−5.94356	−0.288986
$424$	24.0496	1.16795
$425$	−24.5348	−1.19011
$426$	3.79292	0.183768
$427$	−9.45336	−0.457480
$428$	−1.34224	−0.0648798
$429$	0	0
$430$	0.233489	0.0112598
$431$	−17.1070	−0.824015	−0.412008	−	0.911180i	$-0.635172\pi$
$431$	−17.1070	−0.824015	−0.412008	+	0.911180i	$0.635172\pi$
$432$	−4.57398	−0.220066
$433$	−11.8966	−0.571715	−0.285858	−	0.958272i	$-0.592278\pi$
$433$	−11.8966	−0.571715	−0.285858	+	0.958272i	$0.592278\pi$
$434$	13.2344	0.635273
$435$	−1.28581	−0.0616497
$436$	4.18479	0.200415
$437$	−4.15476	−0.198749
$438$	9.03003	0.431471
$439$	−12.4347	−0.593476	−0.296738	−	0.954959i	$-0.595899\pi$
$439$	−12.4347	−0.593476	−0.296738	+	0.954959i	$0.595899\pi$
$440$	1.39693	0.0665958
$441$	1.00000	0.0476190
$442$	0	0
$443$	2.27631	0.108151	0.0540754	−	0.998537i	$-0.482779\pi$
$443$	2.27631	0.108151	0.0540754	+	0.998537i	$0.482779\pi$
$444$	1.63310	0.0775037
$445$	−0.815207	−0.0386445
$446$	−5.29086	−0.250529
$447$	−0.248970	−0.0117759
$448$	6.17024	0.291517
$449$	−0.175297	−0.00827278	−0.00413639	−	0.999991i	$-0.501317\pi$
$449$	−0.175297	−0.00827278	−0.00413639	+	0.999991i	$0.501317\pi$
$450$	7.63816	0.360066
$451$	49.8871	2.34909
$452$	2.63041	0.123724
$453$	−18.9513	−0.890410
$454$	−7.84524	−0.368195
$455$	0	0
$456$	1.92127	0.0899719
$457$	11.5047	0.538169	0.269085	−	0.963117i	$-0.413279\pi$
$457$	11.5047	0.538169	0.269085	+	0.963117i	$0.413279\pi$
$458$	−23.5371	−1.09982
$459$	4.92127	0.229705
$460$	0.229370	0.0106944
$461$	−8.48070	−0.394986	−0.197493	−	0.980304i	$-0.563280\pi$
$461$	−8.48070	−0.394986	−0.197493	+	0.980304i	$0.563280\pi$
$462$	7.00774	0.326030
$463$	11.2790	0.524180	0.262090	−	0.965043i	$-0.415588\pi$
$463$	11.2790	0.524180	0.262090	+	0.965043i	$0.415588\pi$
$464$	−48.7606	−2.26366
$465$	1.04189	0.0483164
$466$	−9.54757	−0.442283
$467$	20.3063	0.939665	0.469833	−	0.882755i	$-0.344314\pi$
$467$	20.3063	0.939665	0.469833	+	0.882755i	$0.344314\pi$
$468$	0	0
$469$	−13.0300	−0.601671
$470$	−1.09833	−0.0506620
$471$	−18.6827	−0.860855
$472$	22.7716	1.04815
$473$	−5.77930	−0.265733
$474$	12.5398	0.575973
$475$	−3.78281	−0.173567
$476$	1.70914	0.0783383
$477$	9.49794	0.434881
$478$	−6.82295	−0.312074
$479$	23.0027	1.05102	0.525510	−	0.850788i	$-0.323875\pi$
$479$	23.0027	1.05102	0.525510	+	0.850788i	$0.323875\pi$
$480$	−0.234422	−0.0106999
$481$	0	0
$482$	−13.8607	−0.631338
$483$	−5.47565	−0.249151
$484$	3.44562	0.156619
$485$	−1.21482	−0.0551622
$486$	−1.53209	−0.0694970
$487$	−17.1976	−0.779297	−0.389648	−	0.920964i	$-0.627403\pi$
$487$	−17.1976	−0.779297	−0.389648	+	0.920964i	$0.627403\pi$
$488$	−23.9368	−1.08357
$489$	−20.0351	−0.906018
$490$	0.184793	0.00834808
$491$	40.5577	1.83034	0.915171	−	0.403066i	$-0.132055\pi$
$491$	40.5577	1.83034	0.915171	+	0.403066i	$0.132055\pi$
$492$	−3.78787	−0.170770
$493$	52.4630	2.36281
$494$	0	0
$495$	0.551689	0.0247966
$496$	39.5107	1.77408
$497$	−2.47565	−0.111048
$498$	18.7665	0.840947
$499$	5.54757	0.248343	0.124172	−	0.992261i	$-0.460373\pi$
$499$	5.54757	0.248343	0.124172	+	0.992261i	$0.460373\pi$
$500$	0.418281	0.0187061
$501$	2.01960	0.0902291
$502$	2.97771	0.132902
$503$	−22.7588	−1.01476	−0.507382	−	0.861721i	$-0.669387\pi$
$503$	−22.7588	−1.01476	−0.507382	+	0.861721i	$0.669387\pi$
$504$	2.53209	0.112788
$505$	0.718636	0.0319789
$506$	−38.3719	−1.70584
$507$	0	0
$508$	−3.43107	−0.152229
$509$	25.0196	1.10897	0.554487	−	0.832192i	$-0.312914\pi$
$509$	25.0196	1.10897	0.554487	+	0.832192i	$0.312914\pi$
$510$	0.909415	0.0402696
$511$	−5.89393	−0.260732
$512$	14.2736	0.630811
$513$	0.758770	0.0335005
$514$	31.4989	1.38936
$515$	0.332748	0.0146626
$516$	0.438815	0.0193178
$517$	27.1857	1.19563
$518$	−7.20439	−0.316543
$519$	2.19934	0.0965403
$520$	0	0
$521$	10.0051	0.438329	0.219165	−	0.975688i	$-0.429667\pi$
$521$	10.0051	0.438329	0.219165	+	0.975688i	$0.429667\pi$
$522$	−16.3327	−0.714865
$523$	−43.6049	−1.90671	−0.953355	−	0.301850i	$-0.902396\pi$
$523$	−43.6049	−1.90671	−0.953355	+	0.301850i	$0.902396\pi$
$524$	5.39187	0.235545
$525$	−4.98545	−0.217583
$526$	−24.6759	−1.07592
$527$	−42.5107	−1.85180
$528$	20.9213	0.910482
$529$	6.98276	0.303598
$530$	1.75515	0.0762388
$531$	8.99319	0.390271
$532$	0.263518	0.0114250
$533$	0	0
$534$	−10.3550	−0.448106
$535$	0.466156	0.0201537
$536$	−32.9932	−1.42509
$537$	−8.57667	−0.370110
$538$	6.58441	0.283874
$539$	−4.57398	−0.197015
$540$	−0.0418891	−0.00180262
$541$	−31.1002	−1.33710	−0.668551	−	0.743666i	$-0.733085\pi$
$541$	−31.1002	−1.33710	−0.668551	+	0.743666i	$0.733085\pi$
$542$	18.2344	0.783236
$543$	11.8844	0.510010
$544$	9.56481	0.410088
$545$	−1.45336	−0.0622552
$546$	0	0
$547$	38.5827	1.64968	0.824838	−	0.565370i	$-0.191267\pi$
$547$	38.5827	1.64968	0.824838	+	0.565370i	$0.191267\pi$
$548$	0.543948	0.0232363
$549$	−9.45336	−0.403460
$550$	−34.9368	−1.48971
$551$	8.08883	0.344596
$552$	−13.8648	−0.590127
$553$	−8.18479	−0.348053
$554$	−16.5817	−0.704490
$555$	−0.567171	−0.0240751
$556$	3.64765	0.154695
$557$	−41.1840	−1.74502	−0.872510	−	0.488595i	$-0.837509\pi$
$557$	−41.1840	−1.74502	−0.872510	+	0.488595i	$0.837509\pi$
$558$	13.2344	0.560258
$559$	0	0
$560$	0.551689	0.0233131
$561$	−22.5098	−0.950365
$562$	10.4715	0.441715
$563$	−22.7638	−0.959381	−0.479690	−	0.877438i	$-0.659251\pi$
$563$	−22.7638	−0.959381	−0.479690	+	0.877438i	$0.659251\pi$
$564$	−2.06418	−0.0869176
$565$	−0.913534	−0.0384326
$566$	34.8462	1.46469
$567$	1.00000	0.0419961
$568$	−6.26857	−0.263023
$569$	−26.2986	−1.10249	−0.551247	−	0.834342i	$-0.685848\pi$
$569$	−26.2986	−1.10249	−0.551247	+	0.834342i	$0.685848\pi$
$570$	0.140215	0.00587297
$571$	13.8435	0.579332	0.289666	−	0.957128i	$-0.406456\pi$
$571$	13.8435	0.579332	0.289666	+	0.957128i	$0.406456\pi$
$572$	0	0
$573$	−13.8007	−0.576531
$574$	16.7101	0.697465
$575$	27.2986	1.13843
$576$	6.17024	0.257094
$577$	−13.9290	−0.579872	−0.289936	−	0.957046i	$-0.593634\pi$
$577$	−13.9290	−0.579872	−0.289936	+	0.957046i	$0.593634\pi$
$578$	−11.0601	−0.460038
$579$	−18.2148	−0.756982
$580$	−0.446556	−0.0185422
$581$	−12.2490	−0.508173
$582$	−15.4311	−0.639639
$583$	−43.4434	−1.79924
$584$	−14.9240	−0.617558
$585$	0	0
$586$	32.1712	1.32898
$587$	43.3928	1.79101	0.895506	−	0.445049i	$-0.146814\pi$
$587$	43.3928	1.79101	0.895506	+	0.445049i	$0.146814\pi$
$588$	0.347296	0.0143223
$589$	−6.55438	−0.270068
$590$	1.66187	0.0684183
$591$	−3.56893	−0.146806
$592$	−21.5084	−0.883989
$593$	2.20708	0.0906340	0.0453170	−	0.998973i	$-0.485570\pi$
$593$	2.20708	0.0906340	0.0453170	+	0.998973i	$0.485570\pi$
$594$	7.00774	0.287531
$595$	−0.593578	−0.0243343
$596$	−0.0864665	−0.00354180
$597$	−9.73648	−0.398488
$598$	0	0
$599$	33.1729	1.35541	0.677705	−	0.735334i	$-0.262975\pi$
$599$	33.1729	1.35541	0.677705	+	0.735334i	$0.262975\pi$
$600$	−12.6236	−0.515357
$601$	18.7124	0.763296	0.381648	−	0.924308i	$-0.375357\pi$
$601$	18.7124	0.763296	0.381648	+	0.924308i	$0.375357\pi$
$602$	−1.93582	−0.0788982
$603$	−13.0300	−0.530624
$604$	−6.58172	−0.267806
$605$	−1.19665	−0.0486508
$606$	9.12836	0.370814
$607$	−1.14889	−0.0466320	−0.0233160	−	0.999728i	$-0.507422\pi$
$607$	−1.14889	−0.0466320	−0.0233160	+	0.999728i	$0.507422\pi$
$608$	1.47472	0.0598077
$609$	10.6604	0.431983
$610$	−1.74691	−0.0707304
$611$	0	0
$612$	1.70914	0.0690879
$613$	12.7760	0.516018	0.258009	−	0.966143i	$-0.416934\pi$
$613$	12.7760	0.516018	0.258009	+	0.966143i	$0.416934\pi$
$614$	−24.3327	−0.981990
$615$	1.31551	0.0530466
$616$	−11.5817	−0.466641
$617$	−7.25847	−0.292215	−0.146107	−	0.989269i	$-0.546675\pi$
$617$	−7.25847	−0.292215	−0.146107	+	0.989269i	$0.546675\pi$
$618$	4.22668	0.170022
$619$	−10.8966	−0.437972	−0.218986	−	0.975728i	$-0.570275\pi$
$619$	−10.8966	−0.437972	−0.218986	+	0.975728i	$0.570275\pi$
$620$	0.361844	0.0145320
$621$	−5.47565	−0.219730
$622$	15.6236	0.626450
$623$	6.75877	0.270784
$624$	0	0
$625$	24.7820	0.991280
$626$	28.5853	1.14250
$627$	−3.47060	−0.138602
$628$	−6.48845	−0.258917
$629$	23.1415	0.922711
$630$	0.184793	0.00736231
$631$	26.3705	1.04979	0.524897	−	0.851166i	$-0.324104\pi$
$631$	26.3705	1.04979	0.524897	+	0.851166i	$0.324104\pi$
$632$	−20.7246	−0.824381
$633$	−22.0574	−0.876702
$634$	−23.5553	−0.935501
$635$	1.19160	0.0472872
$636$	3.29860	0.130798
$637$	0	0
$638$	74.7056	2.95762
$639$	−2.47565	−0.0979353
$640$	1.60906	0.0636037
$641$	9.56481	0.377787	0.188894	−	0.981998i	$-0.439510\pi$
$641$	9.56481	0.377787	0.188894	+	0.981998i	$0.439510\pi$
$642$	5.92127	0.233694
$643$	48.7606	1.92293	0.961466	−	0.274924i	$-0.0886527\pi$
$643$	48.7606	1.92293	0.961466	+	0.274924i	$0.0886527\pi$
$644$	−1.90167	−0.0749365
$645$	−0.152399	−0.00600070
$646$	−5.72100	−0.225090
$647$	−18.3455	−0.721238	−0.360619	−	0.932713i	$-0.617434\pi$
$647$	−18.3455	−0.721238	−0.360619	+	0.932713i	$0.617434\pi$
$648$	2.53209	0.0994698
$649$	−41.1347	−1.61468
$650$	0	0
$651$	−8.63816	−0.338556
$652$	−6.95811	−0.272501
$653$	3.53714	0.138419	0.0692095	−	0.997602i	$-0.477952\pi$
$653$	3.53714	0.138419	0.0692095	+	0.997602i	$0.477952\pi$
$654$	−18.4611	−0.721886
$655$	−1.87258	−0.0731677
$656$	49.8871	1.94777
$657$	−5.89393	−0.229944
$658$	9.10607	0.354991
$659$	20.7510	0.808345	0.404173	−	0.914683i	$-0.367559\pi$
$659$	20.7510	0.808345	0.404173	+	0.914683i	$0.367559\pi$
$660$	0.191600	0.00745801
$661$	22.4516	0.873266	0.436633	−	0.899640i	$-0.356171\pi$
$661$	22.4516	0.873266	0.436633	+	0.899640i	$0.356171\pi$
$662$	−10.6578	−0.414225
$663$	0	0
$664$	−31.0155	−1.20363
$665$	−0.0915189	−0.00354895
$666$	−7.20439	−0.279165
$667$	−58.3729	−2.26021
$668$	0.701400	0.0271380
$669$	3.45336	0.133515
$670$	−2.40785	−0.0930234
$671$	43.2395	1.66924
$672$	1.94356	0.0749746
$673$	24.0438	0.926819	0.463409	−	0.886144i	$-0.346626\pi$
$673$	24.0438	0.926819	0.463409	+	0.886144i	$0.346626\pi$
$674$	18.5553	0.714724
$675$	−4.98545	−0.191890
$676$	0	0
$677$	−38.5321	−1.48091	−0.740454	−	0.672107i	$-0.765390\pi$
$677$	−38.5321	−1.48091	−0.740454	+	0.672107i	$0.765390\pi$
$678$	−11.6040	−0.445649
$679$	10.0719	0.386525
$680$	−1.50299	−0.0576372
$681$	5.12061	0.196222
$682$	−60.5340	−2.31796
$683$	25.6195	0.980303	0.490151	−	0.871637i	$-0.336942\pi$
$683$	25.6195	0.980303	0.490151	+	0.871637i	$0.336942\pi$
$684$	0.263518	0.0100759
$685$	−0.188911	−0.00721793
$686$	−1.53209	−0.0584954
$687$	15.3628	0.586127
$688$	−5.77930	−0.220334
$689$	0	0
$690$	−1.01186	−0.0385208
$691$	−34.3087	−1.30516	−0.652582	−	0.757718i	$-0.726314\pi$
$691$	−34.3087	−1.30516	−0.652582	+	0.757718i	$0.726314\pi$
$692$	0.763823	0.0290362
$693$	−4.57398	−0.173751
$694$	38.1753	1.44911
$695$	−1.26682	−0.0480531
$696$	26.9932	1.02317
$697$	−53.6750	−2.03309
$698$	−6.27269	−0.237425
$699$	6.23173	0.235706
$700$	−1.73143	−0.0654419
$701$	−2.03415	−0.0768287	−0.0384144	−	0.999262i	$-0.512231\pi$
$701$	−2.03415	−0.0768287	−0.0384144	+	0.999262i	$0.512231\pi$
$702$	0	0
$703$	3.56799	0.134569
$704$	−28.2226	−1.06368
$705$	0.716881	0.0269993
$706$	−10.4115	−0.391841
$707$	−5.95811	−0.224078
$708$	3.12330	0.117381
$709$	14.3027	0.537150	0.268575	−	0.963259i	$-0.413447\pi$
$709$	14.3027	0.537150	0.268575	+	0.963259i	$0.413447\pi$
$710$	−0.457482	−0.0171690
$711$	−8.18479	−0.306954
$712$	17.1138	0.641367
$713$	47.2995	1.77138
$714$	−7.53983	−0.282171
$715$	0	0
$716$	−2.97864	−0.111317
$717$	4.45336	0.166314
$718$	−14.9750	−0.558863
$719$	0.205327	0.00765739	0.00382869	−	0.999993i	$-0.498781\pi$
$719$	0.205327	0.00765739	0.00382869	+	0.999993i	$0.498781\pi$
$720$	0.551689	0.0205602
$721$	−2.75877	−0.102742
$722$	28.2276	1.05052
$723$	9.04694	0.336459
$724$	4.12742	0.153394
$725$	−53.1471	−1.97384
$726$	−15.2003	−0.564135
$727$	18.0395	0.669049	0.334524	−	0.942387i	$-0.391424\pi$
$727$	18.0395	0.669049	0.334524	+	0.942387i	$0.391424\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.08915	−0.0403114
$731$	6.21812	0.229985
$732$	−3.28312	−0.121348
$733$	20.9760	0.774765	0.387382	−	0.921919i	$-0.373379\pi$
$733$	20.9760	0.774765	0.387382	+	0.921919i	$0.373379\pi$
$734$	8.27631	0.305484
$735$	−0.120615	−0.00444894
$736$	−10.6423	−0.392279
$737$	59.5991	2.19536
$738$	16.7101	0.615106
$739$	−22.1019	−0.813033	−0.406517	−	0.913643i	$-0.633257\pi$
$739$	−22.1019	−0.813033	−0.406517	+	0.913643i	$0.633257\pi$
$740$	−0.196976	−0.00724099
$741$	0	0
$742$	−14.5517	−0.534209
$743$	−6.12330	−0.224642	−0.112321	−	0.993672i	$-0.535829\pi$
$743$	−6.12330	−0.224642	−0.112321	+	0.993672i	$0.535829\pi$
$744$	−21.8726	−0.801888
$745$	0.0300295	0.00110020
$746$	54.4802	1.99466
$747$	−12.2490	−0.448166
$748$	−7.81757	−0.285839
$749$	−3.86484	−0.141218
$750$	−1.84524	−0.0673785
$751$	14.2517	0.520050	0.260025	−	0.965602i	$-0.416269\pi$
$751$	14.2517	0.520050	0.260025	+	0.965602i	$0.416269\pi$
$752$	27.1857	0.991361
$753$	−1.94356	−0.0708274
$754$	0	0
$755$	2.28581	0.0831890
$756$	0.347296	0.0126310
$757$	−10.9094	−0.396509	−0.198255	−	0.980151i	$-0.563527\pi$
$757$	−10.9094	−0.396509	−0.198255	+	0.980151i	$0.563527\pi$
$758$	18.8830	0.685862
$759$	25.0455	0.909094
$760$	−0.231734	−0.00840588
$761$	−51.3346	−1.86088	−0.930439	−	0.366446i	$-0.880574\pi$
$761$	−51.3346	−1.86088	−0.930439	+	0.366446i	$0.880574\pi$
$762$	15.1361	0.548323
$763$	12.0496	0.436226
$764$	−4.79292	−0.173402
$765$	−0.593578	−0.0214609
$766$	−9.78249	−0.353456
$767$	0	0
$768$	8.09833	0.292223
$769$	−8.92221	−0.321743	−0.160872	−	0.986975i	$-0.551430\pi$
$769$	−8.92221	−0.321743	−0.160872	+	0.986975i	$0.551430\pi$
$770$	−0.845237	−0.0304602
$771$	−20.5594	−0.740430
$772$	−6.32594	−0.227676
$773$	51.9172	1.86733	0.933665	−	0.358147i	$-0.116591\pi$
$773$	51.9172	1.86733	0.933665	+	0.358147i	$0.116591\pi$
$774$	−1.93582	−0.0695817
$775$	43.0651	1.54694
$776$	25.5030	0.915504
$777$	4.70233	0.168695
$778$	35.9263	1.28802
$779$	−8.27570	−0.296508
$780$	0	0
$781$	11.3236	0.405189
$782$	41.2855	1.47637
$783$	10.6604	0.380973
$784$	−4.57398	−0.163356
$785$	2.25341	0.0804278
$786$	−23.7861	−0.848423
$787$	−1.28136	−0.0456757	−0.0228378	−	0.999739i	$-0.507270\pi$
$787$	−1.28136	−0.0456757	−0.0228378	+	0.999739i	$0.507270\pi$
$788$	−1.23947	−0.0441545
$789$	16.1061	0.573391
$790$	−1.51249	−0.0538119
$791$	7.57398	0.269300
$792$	−11.5817	−0.411538
$793$	0	0
$794$	26.6982	0.947484
$795$	−1.14559	−0.0406300
$796$	−3.38144	−0.119852
$797$	−48.4466	−1.71607	−0.858033	−	0.513595i	$-0.828313\pi$
$797$	−48.4466	−1.71607	−0.858033	+	0.513595i	$0.828313\pi$
$798$	−1.16250	−0.0411522
$799$	−29.2499	−1.03479
$800$	−9.68954	−0.342577
$801$	6.75877	0.238809
$802$	−14.2199	−0.502121
$803$	26.9587	0.951353
$804$	−4.52528	−0.159594
$805$	0.660444	0.0232776
$806$	0	0
$807$	−4.29767	−0.151285
$808$	−15.0865	−0.530740
$809$	10.2849	0.361597	0.180798	−	0.983520i	$-0.442132\pi$
$809$	10.2849	0.361597	0.180798	+	0.983520i	$0.442132\pi$
$810$	0.184793	0.00649295
$811$	3.60813	0.126698	0.0633492	−	0.997991i	$-0.479822\pi$
$811$	3.60813	0.126698	0.0633492	+	0.997991i	$0.479822\pi$
$812$	3.70233	0.129926
$813$	−11.9017	−0.417410
$814$	32.9527	1.15499
$815$	2.41653	0.0846472
$816$	−22.5098	−0.788001
$817$	0.958720	0.0335414
$818$	22.1962	0.776070
$819$	0	0
$820$	0.456873	0.0159547
$821$	51.7398	1.80573	0.902865	−	0.429923i	$-0.141459\pi$
$821$	51.7398	1.80573	0.902865	+	0.429923i	$0.141459\pi$
$822$	−2.39961	−0.0836962
$823$	37.6519	1.31246	0.656231	−	0.754560i	$-0.272150\pi$
$823$	37.6519	1.31246	0.656231	+	0.754560i	$0.272150\pi$
$824$	−6.98545	−0.243350
$825$	22.8033	0.793911
$826$	−13.7784	−0.479411
$827$	−31.3509	−1.09018	−0.545089	−	0.838378i	$-0.683504\pi$
$827$	−31.3509	−1.09018	−0.545089	+	0.838378i	$0.683504\pi$
$828$	−1.90167	−0.0660877
$829$	38.4635	1.33589	0.667946	−	0.744210i	$-0.267174\pi$
$829$	38.4635	1.33589	0.667946	+	0.744210i	$0.267174\pi$
$830$	−2.26352	−0.0785679
$831$	10.8229	0.375444
$832$	0	0
$833$	4.92127	0.170512
$834$	−16.0915	−0.557204
$835$	−0.243594	−0.00842990
$836$	−1.20533	−0.0416871
$837$	−8.63816	−0.298578
$838$	−8.48608	−0.293147
$839$	−17.6099	−0.607961	−0.303980	−	0.952678i	$-0.598316\pi$
$839$	−17.6099	−0.607961	−0.303980	+	0.952678i	$0.598316\pi$
$840$	−0.305407	−0.0105376
$841$	84.6451	2.91880
$842$	38.1411	1.31443
$843$	−6.83481	−0.235403
$844$	−7.66044	−0.263683
$845$	0	0
$846$	9.10607	0.313073
$847$	9.92127	0.340899
$848$	−43.4434	−1.49185
$849$	−22.7442	−0.780580
$850$	37.5895	1.28931
$851$	−25.7483	−0.882642
$852$	−0.859785	−0.0294557
$853$	47.8120	1.63705	0.818526	−	0.574469i	$-0.194791\pi$
$853$	47.8120	1.63705	0.818526	+	0.574469i	$0.194791\pi$
$854$	14.4834	0.495611
$855$	−0.0915189	−0.00312988
$856$	−9.78611	−0.334482
$857$	−17.7537	−0.606455	−0.303228	−	0.952918i	$-0.598064\pi$
$857$	−17.7537	−0.606455	−0.303228	+	0.952918i	$0.598064\pi$
$858$	0	0
$859$	28.9103	0.986408	0.493204	−	0.869914i	$-0.335826\pi$
$859$	28.9103	0.986408	0.493204	+	0.869914i	$0.335826\pi$
$860$	−0.0529276	−0.00180482
$861$	−10.9067	−0.371700
$862$	26.2094	0.892697
$863$	12.2594	0.417315	0.208657	−	0.977989i	$-0.433091\pi$
$863$	12.2594	0.417315	0.208657	+	0.977989i	$0.433091\pi$
$864$	1.94356	0.0661214
$865$	−0.265273	−0.00901955
$866$	18.2267	0.619368
$867$	7.21894	0.245168
$868$	−3.00000	−0.101827
$869$	37.4371	1.26997
$870$	1.96997	0.0667883
$871$	0	0
$872$	30.5107	1.03322
$873$	10.0719	0.340883
$874$	6.36547	0.215315
$875$	1.20439	0.0407159
$876$	−2.04694	−0.0691597
$877$	5.71925	0.193125	0.0965626	−	0.995327i	$-0.469215\pi$
$877$	5.71925	0.193125	0.0965626	+	0.995327i	$0.469215\pi$
$878$	19.0511	0.642942
$879$	−20.9982	−0.708253
$880$	−2.52341	−0.0850643
$881$	−8.74422	−0.294600	−0.147300	−	0.989092i	$-0.547058\pi$
$881$	−8.74422	−0.294600	−0.147300	+	0.989092i	$0.547058\pi$
$882$	−1.53209	−0.0515881
$883$	20.9923	0.706446	0.353223	−	0.935539i	$-0.385086\pi$
$883$	20.9923	0.706446	0.353223	+	0.935539i	$0.385086\pi$
$884$	0	0
$885$	−1.08471	−0.0364622
$886$	−3.48751	−0.117165
$887$	13.7743	0.462494	0.231247	−	0.972895i	$-0.425719\pi$
$887$	13.7743	0.462494	0.231247	+	0.972895i	$0.425719\pi$
$888$	11.9067	0.399564
$889$	−9.87939	−0.331344
$890$	1.24897	0.0418656
$891$	−4.57398	−0.153234
$892$	1.19934	0.0401569
$893$	−4.50980	−0.150915
$894$	0.381445	0.0127574
$895$	1.03447	0.0345786
$896$	−13.3405	−0.445674
$897$	0	0
$898$	0.268571	0.00896232
$899$	−92.0866	−3.07126
$900$	−1.73143	−0.0577143
$901$	46.7420	1.55720
$902$	−76.4315	−2.54489
$903$	1.26352	0.0420473
$904$	19.1780	0.637850
$905$	−1.43344	−0.0476491
$906$	29.0351	0.964626
$907$	25.4908	0.846408	0.423204	−	0.906034i	$-0.360905\pi$
$907$	25.4908	0.846408	0.423204	+	0.906034i	$0.360905\pi$
$908$	1.77837	0.0590173
$909$	−5.95811	−0.197618
$910$	0	0
$911$	−15.8485	−0.525085	−0.262543	−	0.964920i	$-0.584561\pi$
$911$	−15.8485	−0.525085	−0.262543	+	0.964920i	$0.584561\pi$
$912$	−3.47060	−0.114923
$913$	56.0265	1.85421
$914$	−17.6263	−0.583026
$915$	1.14022	0.0376943
$916$	5.33544	0.176288
$917$	15.5253	0.512690
$918$	−7.53983	−0.248851
$919$	44.7921	1.47755	0.738777	−	0.673949i	$-0.235403\pi$
$919$	44.7921	1.47755	0.738777	+	0.673949i	$0.235403\pi$
$920$	1.67230	0.0551342
$921$	15.8821	0.523332
$922$	12.9932	0.427908
$923$	0	0
$924$	−1.58853	−0.0522587
$925$	−23.4433	−0.770810
$926$	−17.2804	−0.567870
$927$	−2.75877	−0.0906099
$928$	20.7192	0.680143
$929$	−18.6587	−0.612172	−0.306086	−	0.952004i	$-0.599019\pi$
$929$	−18.6587	−0.612172	−0.306086	+	0.952004i	$0.599019\pi$
$930$	−1.59627	−0.0523436
$931$	0.758770	0.0248677
$932$	2.16426	0.0708926
$933$	−10.1976	−0.333854
$934$	−31.1111	−1.01799
$935$	2.71501	0.0887905
$936$	0	0
$937$	57.1653	1.86751	0.933755	−	0.357914i	$-0.116512\pi$
$937$	57.1653	1.86751	0.933755	+	0.357914i	$0.116512\pi$
$938$	19.9632	0.651820
$939$	−18.6578	−0.608873
$940$	0.248970	0.00812052
$941$	−11.7665	−0.383577	−0.191789	−	0.981436i	$-0.561429\pi$
$941$	−11.7665	−0.383577	−0.191789	+	0.981436i	$0.561429\pi$
$942$	28.6236	0.932608
$943$	59.7214	1.94480
$944$	−41.1347	−1.33882
$945$	−0.120615	−0.00392360
$946$	8.85441	0.287882
$947$	−6.79561	−0.220828	−0.110414	−	0.993886i	$-0.535218\pi$
$947$	−6.79561	−0.220828	−0.110414	+	0.993886i	$0.535218\pi$
$948$	−2.84255	−0.0923217
$949$	0	0
$950$	5.79561	0.188034
$951$	15.3746	0.498557
$952$	12.4611	0.403867
$953$	22.7847	0.738068	0.369034	−	0.929416i	$-0.379689\pi$
$953$	22.7847	0.738068	0.369034	+	0.929416i	$0.379689\pi$
$954$	−14.5517	−0.471128
$955$	1.66456	0.0538640
$956$	1.54664	0.0500218
$957$	−48.7606	−1.57621
$958$	−35.2422	−1.13862
$959$	1.56624	0.0505764
$960$	−0.744223	−0.0240197
$961$	43.6177	1.40702
$962$	0	0
$963$	−3.86484	−0.124543
$964$	3.14197	0.101196
$965$	2.19698	0.0707232
$966$	8.38919	0.269918
$967$	38.8033	1.24783	0.623916	−	0.781492i	$-0.285541\pi$
$967$	38.8033	1.24783	0.623916	+	0.781492i	$0.285541\pi$
$968$	25.1215	0.807437
$969$	3.73412	0.119957
$970$	1.86122	0.0597600
$971$	−21.7885	−0.699225	−0.349613	−	0.936894i	$-0.613687\pi$
$971$	−21.7885	−0.699225	−0.349613	+	0.936894i	$0.613687\pi$
$972$	0.347296	0.0111395
$973$	10.5030	0.336710
$974$	26.3482	0.844252
$975$	0	0
$976$	43.2395	1.38406
$977$	35.8007	1.14536	0.572682	−	0.819777i	$-0.305903\pi$
$977$	35.8007	1.14536	0.572682	+	0.819777i	$0.305903\pi$
$978$	30.6955	0.981535
$979$	−30.9145	−0.988031
$980$	−0.0418891	−0.00133810
$981$	12.0496	0.384715
$982$	−62.1380	−1.98290
$983$	−16.7060	−0.532837	−0.266419	−	0.963857i	$-0.585840\pi$
$983$	−16.7060	−0.532837	−0.266419	+	0.963857i	$0.585840\pi$
$984$	−27.6168	−0.880391
$985$	0.430465	0.0137158
$986$	−80.3779	−2.55975
$987$	−5.94356	−0.189186
$988$	0	0
$989$	−6.91859	−0.219998
$990$	−0.845237	−0.0268634
$991$	14.1834	0.450549	0.225275	−	0.974295i	$-0.427672\pi$
$991$	14.1834	0.450549	0.225275	+	0.974295i	$0.427672\pi$
$992$	−16.7888	−0.533045
$993$	6.95636	0.220753
$994$	3.79292	0.120304
$995$	1.17436	0.0372298
$996$	−4.25402	−0.134794
$997$	−5.55674	−0.175984	−0.0879919	−	0.996121i	$-0.528045\pi$
$997$	−5.55674	−0.175984	−0.0879919	+	0.996121i	$0.528045\pi$
$998$	−8.49937	−0.269043
$999$	4.70233	0.148775

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.53209 q^{2} +1.00000 q^{3} +0.347296 q^{4} -0.120615 q^{5} -1.53209 q^{6} +1.00000 q^{7} +2.53209 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.53209 q^{2} +1.00000 q^{3} +0.347296 q^{4} -0.120615 q^{5} -1.53209 q^{6} +1.00000 q^{7} +2.53209 q^{8} +1.00000 q^{9} +0.184793 q^{10} -4.57398 q^{11} +0.347296 q^{12} -1.53209 q^{14} -0.120615 q^{15} -4.57398 q^{16} +4.92127 q^{17} -1.53209 q^{18} +0.758770 q^{19} -0.0418891 q^{20} +1.00000 q^{21} +7.00774 q^{22} -5.47565 q^{23} +2.53209 q^{24} -4.98545 q^{25} +1.00000 q^{27} +0.347296 q^{28} +10.6604 q^{29} +0.184793 q^{30} -8.63816 q^{31} +1.94356 q^{32} -4.57398 q^{33} -7.53983 q^{34} -0.120615 q^{35} +0.347296 q^{36} +4.70233 q^{37} -1.16250 q^{38} -0.305407 q^{40} -10.9067 q^{41} -1.53209 q^{42} +1.26352 q^{43} -1.58853 q^{44} -0.120615 q^{45} +8.38919 q^{46} -5.94356 q^{47} -4.57398 q^{48} +1.00000 q^{49} +7.63816 q^{50} +4.92127 q^{51} +9.49794 q^{53} -1.53209 q^{54} +0.551689 q^{55} +2.53209 q^{56} +0.758770 q^{57} -16.3327 q^{58} +8.99319 q^{59} -0.0418891 q^{60} -9.45336 q^{61} +13.2344 q^{62} +1.00000 q^{63} +6.17024 q^{64} +7.00774 q^{66} -13.0300 q^{67} +1.70914 q^{68} -5.47565 q^{69} +0.184793 q^{70} -2.47565 q^{71} +2.53209 q^{72} -5.89393 q^{73} -7.20439 q^{74} -4.98545 q^{75} +0.263518 q^{76} -4.57398 q^{77} -8.18479 q^{79} +0.551689 q^{80} +1.00000 q^{81} +16.7101 q^{82} -12.2490 q^{83} +0.347296 q^{84} -0.593578 q^{85} -1.93582 q^{86} +10.6604 q^{87} -11.5817 q^{88} +6.75877 q^{89} +0.184793 q^{90} -1.90167 q^{92} -8.63816 q^{93} +9.10607 q^{94} -0.0915189 q^{95} +1.94356 q^{96} +10.0719 q^{97} -1.53209 q^{98} -4.57398 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{3} - 6 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 6 q^{11} - 6 q^{15} - 6 q^{16} + 6 q^{17} - 9 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{22} + 3 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{27} + 9 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} - 6 q^{33} + 6 q^{34} - 6 q^{35} - 12 q^{37} - 6 q^{38} - 3 q^{40} - 6 q^{41} + 9 q^{43} - 15 q^{44} - 6 q^{45} + 21 q^{46} - 3 q^{47} - 6 q^{48} + 3 q^{49} + 6 q^{50} + 6 q^{51} + 3 q^{53} + 3 q^{56} - 9 q^{57} - 30 q^{58} - 15 q^{59} + 3 q^{60} - 15 q^{61} + 9 q^{62} + 3 q^{63} - 3 q^{64} - 3 q^{66} - 9 q^{67} + 21 q^{68} + 3 q^{69} - 3 q^{70} + 12 q^{71} + 3 q^{72} - 30 q^{73} - 21 q^{74} + 3 q^{75} + 6 q^{76} - 6 q^{77} - 21 q^{79} + 3 q^{81} - 24 q^{83} + 3 q^{85} - 15 q^{86} + 9 q^{87} - 3 q^{88} + 9 q^{89} - 3 q^{90} + 6 q^{92} - 9 q^{93} + 15 q^{94} + 30 q^{95} - 9 q^{96} - 3 q^{97} - 6 q^{99}+O(q^{100}) \) 3 * q + 3 * q^3 - 6 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 6 * q^11 - 6 * q^15 - 6 * q^16 + 6 * q^17 - 9 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^22 + 3 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 + 9 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 - 6 * q^33 + 6 * q^34 - 6 * q^35 - 12 * q^37 - 6 * q^38 - 3 * q^40 - 6 * q^41 + 9 * q^43 - 15 * q^44 - 6 * q^45 + 21 * q^46 - 3 * q^47 - 6 * q^48 + 3 * q^49 + 6 * q^50 + 6 * q^51 + 3 * q^53 + 3 * q^56 - 9 * q^57 - 30 * q^58 - 15 * q^59 + 3 * q^60 - 15 * q^61 + 9 * q^62 + 3 * q^63 - 3 * q^64 - 3 * q^66 - 9 * q^67 + 21 * q^68 + 3 * q^69 - 3 * q^70 + 12 * q^71 + 3 * q^72 - 30 * q^73 - 21 * q^74 + 3 * q^75 + 6 * q^76 - 6 * q^77 - 21 * q^79 + 3 * q^81 - 24 * q^83 + 3 * q^85 - 15 * q^86 + 9 * q^87 - 3 * q^88 + 9 * q^89 - 3 * q^90 + 6 * q^92 - 9 * q^93 + 15 * q^94 + 30 * q^95 - 9 * q^96 - 3 * q^97 - 6 * q^99

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