LMFDB - Embedded newform 3549.2.a.u.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:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*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			$1.80194$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.801938 q^{2} +1.00000 q^{3} -1.35690 q^{4} +3.04892 q^{5} -0.801938 q^{6} -1.00000 q^{7} +2.69202 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.801938 q^{2} +1.00000 q^{3} -1.35690 q^{4} +3.04892 q^{5} -0.801938 q^{6} -1.00000 q^{7} +2.69202 q^{8} +1.00000 q^{9} -2.44504 q^{10} -2.15883 q^{11} -1.35690 q^{12} +0.801938 q^{14} +3.04892 q^{15} +0.554958 q^{16} +0.801938 q^{17} -0.801938 q^{18} +1.39612 q^{19} -4.13706 q^{20} -1.00000 q^{21} +1.73125 q^{22} +3.02715 q^{23} +2.69202 q^{24} +4.29590 q^{25} +1.00000 q^{27} +1.35690 q^{28} +2.47219 q^{29} -2.44504 q^{30} +6.26875 q^{31} -5.82908 q^{32} -2.15883 q^{33} -0.643104 q^{34} -3.04892 q^{35} -1.35690 q^{36} -10.7506 q^{37} -1.11960 q^{38} +8.20775 q^{40} +5.20775 q^{41} +0.801938 q^{42} -8.63102 q^{43} +2.92931 q^{44} +3.04892 q^{45} -2.42758 q^{46} +9.15883 q^{47} +0.554958 q^{48} +1.00000 q^{49} -3.44504 q^{50} +0.801938 q^{51} +1.21983 q^{53} -0.801938 q^{54} -6.58211 q^{55} -2.69202 q^{56} +1.39612 q^{57} -1.98254 q^{58} +8.63102 q^{59} -4.13706 q^{60} -10.0858 q^{61} -5.02715 q^{62} -1.00000 q^{63} +3.56465 q^{64} +1.73125 q^{66} +12.7899 q^{67} -1.08815 q^{68} +3.02715 q^{69} +2.44504 q^{70} +14.1250 q^{71} +2.69202 q^{72} +10.1250 q^{73} +8.62133 q^{74} +4.29590 q^{75} -1.89440 q^{76} +2.15883 q^{77} +1.33513 q^{79} +1.69202 q^{80} +1.00000 q^{81} -4.17629 q^{82} -8.92692 q^{83} +1.35690 q^{84} +2.44504 q^{85} +6.92154 q^{86} +2.47219 q^{87} -5.81163 q^{88} +2.50604 q^{89} -2.44504 q^{90} -4.10752 q^{92} +6.26875 q^{93} -7.34481 q^{94} +4.25667 q^{95} -5.82908 q^{96} -2.32304 q^{97} -0.801938 q^{98} -2.15883 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} + 2 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 13 q^{19} - 7 q^{20} - 3 q^{21} + 13 q^{22} + 3 q^{23} + 3 q^{24} - q^{25} + 3 q^{27} + q^{29} - 7 q^{30} + 11 q^{31} - 7 q^{32} + 2 q^{33} - 6 q^{34} + 4 q^{37} + 18 q^{38} + 7 q^{40} - 2 q^{41} - 2 q^{42} - 11 q^{43} + 21 q^{44} + 9 q^{46} + 19 q^{47} + 2 q^{48} + 3 q^{49} - 10 q^{50} - 2 q^{51} + 5 q^{53} + 2 q^{54} - 14 q^{55} - 3 q^{56} + 13 q^{57} + 10 q^{58} + 11 q^{59} - 7 q^{60} + 7 q^{61} - 9 q^{62} - 3 q^{63} - 11 q^{64} + 13 q^{66} + 15 q^{67} - 7 q^{68} + 3 q^{69} + 7 q^{70} + 18 q^{71} + 3 q^{72} + 6 q^{73} + 33 q^{74} - q^{75} + 14 q^{76} - 2 q^{77} + 3 q^{79} + 3 q^{81} - 20 q^{82} + 2 q^{83} + 7 q^{85} - 5 q^{86} + q^{87} + 9 q^{88} + 17 q^{89} - 7 q^{90} + 28 q^{92} + 11 q^{93} + q^{94} - 14 q^{95} - 7 q^{96} + 13 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) $ 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 + 2 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 13 * q^19 - 7 * q^20 - 3 * q^21 + 13 * q^22 + 3 * q^23 + 3 * q^24 - q^25 + 3 * q^27 + q^29 - 7 * q^30 + 11 * q^31 - 7 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^37 + 18 * q^38 + 7 * q^40 - 2 * q^41 - 2 * q^42 - 11 * q^43 + 21 * q^44 + 9 * q^46 + 19 * q^47 + 2 * q^48 + 3 * q^49 - 10 * q^50 - 2 * q^51 + 5 * q^53 + 2 * q^54 - 14 * q^55 - 3 * q^56 + 13 * q^57 + 10 * q^58 + 11 * q^59 - 7 * q^60 + 7 * q^61 - 9 * q^62 - 3 * q^63 - 11 * q^64 + 13 * q^66 + 15 * q^67 - 7 * q^68 + 3 * q^69 + 7 * q^70 + 18 * q^71 + 3 * q^72 + 6 * q^73 + 33 * q^74 - q^75 + 14 * q^76 - 2 * q^77 + 3 * q^79 + 3 * q^81 - 20 * q^82 + 2 * q^83 + 7 * q^85 - 5 * q^86 + q^87 + 9 * q^88 + 17 * q^89 - 7 * q^90 + 28 * q^92 + 11 * q^93 + q^94 - 14 * q^95 - 7 * q^96 + 13 * q^97 + 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.801938	−0.567056	−0.283528	−	0.958964i	$-0.591505\pi$
$2$	−0.801938	−0.567056	−0.283528	+	0.958964i	$0.591505\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.35690	−0.678448
$5$	3.04892	1.36352	0.681759	−	0.731577i	$-0.261215\pi$
$5$	3.04892	1.36352	0.681759	+	0.731577i	$0.261215\pi$
$6$	−0.801938	−0.327390
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.69202	0.951773
$9$	1.00000	0.333333
$10$	−2.44504	−0.773190
$11$	−2.15883	−0.650913	−0.325456	−	0.945557i	$-0.605518\pi$
$11$	−2.15883	−0.650913	−0.325456	+	0.945557i	$0.605518\pi$
$12$	−1.35690	−0.391702
$13$	0	0
$13$	0	0
$14$	0.801938	0.214327
$15$	3.04892	0.787227
$16$	0.554958	0.138740
$17$	0.801938	0.194498	0.0972492	−	0.995260i	$-0.468996\pi$
$17$	0.801938	0.194498	0.0972492	+	0.995260i	$0.468996\pi$
$18$	−0.801938	−0.189019
$19$	1.39612	0.320293	0.160146	−	0.987093i	$-0.448803\pi$
$19$	1.39612	0.320293	0.160146	+	0.987093i	$0.448803\pi$
$20$	−4.13706	−0.925075
$21$	−1.00000	−0.218218
$22$	1.73125	0.369104
$23$	3.02715	0.631204	0.315602	−	0.948892i	$-0.397794\pi$
$23$	3.02715	0.631204	0.315602	+	0.948892i	$0.397794\pi$
$24$	2.69202	0.549507
$25$	4.29590	0.859179
$26$	0	0
$27$	1.00000	0.192450
$28$	1.35690	0.256429
$29$	2.47219	0.459074	0.229537	−	0.973300i	$-0.426279\pi$
$29$	2.47219	0.459074	0.229537	+	0.973300i	$0.426279\pi$
$30$	−2.44504	−0.446402
$31$	6.26875	1.12590	0.562950	−	0.826491i	$-0.309666\pi$
$31$	6.26875	1.12590	0.562950	+	0.826491i	$0.309666\pi$
$32$	−5.82908	−1.03045
$33$	−2.15883	−0.375805
$34$	−0.643104	−0.110291
$35$	−3.04892	−0.515361
$36$	−1.35690	−0.226149
$37$	−10.7506	−1.76739	−0.883696	−	0.468061i	$-0.844953\pi$
$37$	−10.7506	−1.76739	−0.883696	+	0.468061i	$0.844953\pi$
$38$	−1.11960	−0.181624
$39$	0	0
$40$	8.20775	1.29776
$41$	5.20775	0.813314	0.406657	−	0.913581i	$-0.366694\pi$
$41$	5.20775	0.813314	0.406657	+	0.913581i	$0.366694\pi$
$42$	0.801938	0.123742
$43$	−8.63102	−1.31622	−0.658109	−	0.752922i	$-0.728644\pi$
$43$	−8.63102	−1.31622	−0.658109	+	0.752922i	$0.728644\pi$
$44$	2.92931	0.441610
$45$	3.04892	0.454506
$46$	−2.42758	−0.357928
$47$	9.15883	1.33595	0.667977	−	0.744182i	$-0.267161\pi$
$47$	9.15883	1.33595	0.667977	+	0.744182i	$0.267161\pi$
$48$	0.554958	0.0801013
$49$	1.00000	0.142857
$50$	−3.44504	−0.487202
$51$	0.801938	0.112294
$52$	0	0
$53$	1.21983	0.167557	0.0837784	−	0.996484i	$-0.473301\pi$
$53$	1.21983	0.167557	0.0837784	+	0.996484i	$0.473301\pi$
$54$	−0.801938	−0.109130
$55$	−6.58211	−0.887531
$56$	−2.69202	−0.359737
$57$	1.39612	0.184921
$58$	−1.98254	−0.260320
$59$	8.63102	1.12366	0.561832	−	0.827252i	$-0.310097\pi$
$59$	8.63102	1.12366	0.561832	+	0.827252i	$0.310097\pi$
$60$	−4.13706	−0.534093
$61$	−10.0858	−1.29135	−0.645674	−	0.763613i	$-0.723424\pi$
$61$	−10.0858	−1.29135	−0.645674	+	0.763613i	$0.723424\pi$
$62$	−5.02715	−0.638448
$63$	−1.00000	−0.125988
$64$	3.56465	0.445581
$65$	0	0
$66$	1.73125	0.213102
$67$	12.7899	1.56253	0.781265	−	0.624200i	$-0.214575\pi$
$67$	12.7899	1.56253	0.781265	+	0.624200i	$0.214575\pi$
$68$	−1.08815	−0.131957
$69$	3.02715	0.364426
$70$	2.44504	0.292238
$71$	14.1250	1.67633	0.838163	−	0.545419i	$-0.183629\pi$
$71$	14.1250	1.67633	0.838163	+	0.545419i	$0.183629\pi$
$72$	2.69202	0.317258
$73$	10.1250	1.18504	0.592520	−	0.805556i	$-0.298133\pi$
$73$	10.1250	1.18504	0.592520	+	0.805556i	$0.298133\pi$
$74$	8.62133	1.00221
$75$	4.29590	0.496047
$76$	−1.89440	−0.217302
$77$	2.15883	0.246022
$78$	0	0
$79$	1.33513	0.150213	0.0751067	−	0.997176i	$-0.476070\pi$
$79$	1.33513	0.150213	0.0751067	+	0.997176i	$0.476070\pi$
$80$	1.69202	0.189174
$81$	1.00000	0.111111
$82$	−4.17629	−0.461194
$83$	−8.92692	−0.979857	−0.489928	−	0.871763i	$-0.662977\pi$
$83$	−8.92692	−0.979857	−0.489928	+	0.871763i	$0.662977\pi$
$84$	1.35690	0.148049
$85$	2.44504	0.265202
$86$	6.92154	0.746369
$87$	2.47219	0.265046
$88$	−5.81163	−0.619521
$89$	2.50604	0.265640	0.132820	−	0.991140i	$-0.457597\pi$
$89$	2.50604	0.265640	0.132820	+	0.991140i	$0.457597\pi$
$90$	−2.44504	−0.257730
$91$	0	0
$92$	−4.10752	−0.428239
$93$	6.26875	0.650039
$94$	−7.34481	−0.757560
$95$	4.25667	0.436725
$96$	−5.82908	−0.594928
$97$	−2.32304	−0.235869	−0.117935	−	0.993021i	$-0.537627\pi$
$97$	−2.32304	−0.235869	−0.117935	+	0.993021i	$0.537627\pi$
$98$	−0.801938	−0.0810079
$99$	−2.15883	−0.216971
$100$	−5.82908	−0.582908
$101$	14.7724	1.46991	0.734954	−	0.678117i	$-0.237204\pi$
$101$	14.7724	1.46991	0.734954	+	0.678117i	$0.237204\pi$
$102$	−0.643104	−0.0636768
$103$	−10.1642	−1.00151	−0.500755	−	0.865589i	$-0.666944\pi$
$103$	−10.1642	−1.00151	−0.500755	+	0.865589i	$0.666944\pi$
$104$	0	0
$105$	−3.04892	−0.297544
$106$	−0.978230	−0.0950141
$107$	−17.2784	−1.67037	−0.835185	−	0.549969i	$-0.814639\pi$
$107$	−17.2784	−1.67037	−0.835185	+	0.549969i	$0.814639\pi$
$108$	−1.35690	−0.130567
$109$	14.2959	1.36930	0.684649	−	0.728873i	$-0.259955\pi$
$109$	14.2959	1.36930	0.684649	+	0.728873i	$0.259955\pi$
$110$	5.27844	0.503279
$111$	−10.7506	−1.02040
$112$	−0.554958	−0.0524386
$113$	16.2687	1.53044	0.765218	−	0.643772i	$-0.222631\pi$
$113$	16.2687	1.53044	0.765218	+	0.643772i	$0.222631\pi$
$114$	−1.11960	−0.104861
$115$	9.22952	0.860657
$116$	−3.35450	−0.311458
$117$	0	0
$118$	−6.92154	−0.637180
$119$	−0.801938	−0.0735135
$120$	8.20775	0.749262
$121$	−6.33944	−0.576312
$122$	8.08815	0.732266
$123$	5.20775	0.469567
$124$	−8.50604	−0.763865
$125$	−2.14675	−0.192011
$126$	0.801938	0.0714423
$127$	−4.51142	−0.400324	−0.200162	−	0.979763i	$-0.564147\pi$
$127$	−4.51142	−0.400324	−0.200162	+	0.979763i	$0.564147\pi$
$128$	8.79954	0.777777
$129$	−8.63102	−0.759919
$130$	0	0
$131$	1.04892	0.0916443	0.0458222	−	0.998950i	$-0.485409\pi$
$131$	1.04892	0.0916443	0.0458222	+	0.998950i	$0.485409\pi$
$132$	2.92931	0.254964
$133$	−1.39612	−0.121059
$134$	−10.2567	−0.886041
$135$	3.04892	0.262409
$136$	2.15883	0.185118
$137$	−12.3599	−1.05598	−0.527988	−	0.849252i	$-0.677053\pi$
$137$	−12.3599	−1.05598	−0.527988	+	0.849252i	$0.677053\pi$
$138$	−2.42758	−0.206650
$139$	13.6015	1.15366	0.576831	−	0.816863i	$-0.304289\pi$
$139$	13.6015	1.15366	0.576831	+	0.816863i	$0.304289\pi$
$140$	4.13706	0.349646
$141$	9.15883	0.771313
$142$	−11.3274	−0.950571
$143$	0	0
$144$	0.554958	0.0462465
$145$	7.53750	0.625955
$146$	−8.11960	−0.671983
$147$	1.00000	0.0824786
$148$	14.5875	1.19908
$149$	−8.33513	−0.682840	−0.341420	−	0.939911i	$-0.610908\pi$
$149$	−8.33513	−0.682840	−0.341420	+	0.939911i	$0.610908\pi$
$150$	−3.44504	−0.281286
$151$	−11.4819	−0.934382	−0.467191	−	0.884156i	$-0.654734\pi$
$151$	−11.4819	−0.934382	−0.467191	+	0.884156i	$0.654734\pi$
$152$	3.75840	0.304846
$153$	0.801938	0.0648328
$154$	−1.73125	−0.139508
$155$	19.1129	1.53519
$156$	0	0
$157$	−2.99330	−0.238891	−0.119445	−	0.992841i	$-0.538112\pi$
$157$	−2.99330	−0.238891	−0.119445	+	0.992841i	$0.538112\pi$
$158$	−1.07069	−0.0851793
$159$	1.21983	0.0967390
$160$	−17.7724	−1.40503
$161$	−3.02715	−0.238573
$162$	−0.801938	−0.0630062
$163$	15.6353	1.22465	0.612327	−	0.790605i	$-0.290234\pi$
$163$	15.6353	1.22465	0.612327	+	0.790605i	$0.290234\pi$
$164$	−7.06638	−0.551791
$165$	−6.58211	−0.512416
$166$	7.15883	0.555633
$167$	6.70171	0.518594	0.259297	−	0.965798i	$-0.416509\pi$
$167$	6.70171	0.518594	0.259297	+	0.965798i	$0.416509\pi$
$168$	−2.69202	−0.207694
$169$	0	0
$170$	−1.96077	−0.150384
$171$	1.39612	0.106764
$172$	11.7114	0.892986
$173$	−7.05131	−0.536101	−0.268051	−	0.963405i	$-0.586379\pi$
$173$	−7.05131	−0.536101	−0.268051	+	0.963405i	$0.586379\pi$
$174$	−1.98254	−0.150296
$175$	−4.29590	−0.324739
$176$	−1.19806	−0.0903073
$177$	8.63102	0.648747
$178$	−2.00969	−0.150633
$179$	6.46144	0.482950	0.241475	−	0.970407i	$-0.422369\pi$
$179$	6.46144	0.482950	0.241475	+	0.970407i	$0.422369\pi$
$180$	−4.13706	−0.308358
$181$	−0.576728	−0.0428679	−0.0214339	−	0.999770i	$-0.506823\pi$
$181$	−0.576728	−0.0428679	−0.0214339	+	0.999770i	$0.506823\pi$
$182$	0	0
$183$	−10.0858	−0.745560
$184$	8.14914	0.600763
$185$	−32.7778	−2.40987
$186$	−5.02715	−0.368608
$187$	−1.73125	−0.126602
$188$	−12.4276	−0.906375
$189$	−1.00000	−0.0727393
$190$	−3.41358	−0.247647
$191$	−9.12498	−0.660261	−0.330130	−	0.943935i	$-0.607093\pi$
$191$	−9.12498	−0.660261	−0.330130	+	0.943935i	$0.607093\pi$
$192$	3.56465	0.257256
$193$	−7.26636	−0.523044	−0.261522	−	0.965198i	$-0.584224\pi$
$193$	−7.26636	−0.523044	−0.261522	+	0.965198i	$0.584224\pi$
$194$	1.86294	0.133751
$195$	0	0
$196$	−1.35690	−0.0969211
$197$	−5.65519	−0.402915	−0.201458	−	0.979497i	$-0.564568\pi$
$197$	−5.65519	−0.402915	−0.201458	+	0.979497i	$0.564568\pi$
$198$	1.73125	0.123035
$199$	17.2892	1.22560	0.612799	−	0.790239i	$-0.290043\pi$
$199$	17.2892	1.22560	0.612799	+	0.790239i	$0.290043\pi$
$200$	11.5646	0.817744
$201$	12.7899	0.902127
$202$	−11.8465	−0.833520
$203$	−2.47219	−0.173514
$204$	−1.08815	−0.0761855
$205$	15.8780	1.10897
$206$	8.15106	0.567912
$207$	3.02715	0.210401
$208$	0	0
$209$	−3.01400	−0.208483
$210$	2.44504	0.168724
$211$	9.16852	0.631187	0.315594	−	0.948894i	$-0.397796\pi$
$211$	9.16852	0.631187	0.315594	+	0.948894i	$0.397796\pi$
$212$	−1.65519	−0.113679
$213$	14.1250	0.967828
$214$	13.8562	0.947193
$215$	−26.3153	−1.79469
$216$	2.69202	0.183169
$217$	−6.26875	−0.425550
$218$	−11.4644	−0.776468
$219$	10.1250	0.684183
$220$	8.93123	0.602143
$221$	0	0
$222$	8.62133	0.578626
$223$	19.0978	1.27889	0.639443	−	0.768839i	$-0.279165\pi$
$223$	19.0978	1.27889	0.639443	+	0.768839i	$0.279165\pi$
$224$	5.82908	0.389472
$225$	4.29590	0.286393
$226$	−13.0465	−0.867842
$227$	27.9463	1.85486	0.927430	−	0.373996i	$-0.122013\pi$
$227$	27.9463	1.85486	0.927430	+	0.373996i	$0.122013\pi$
$228$	−1.89440	−0.125459
$229$	19.8388	1.31098	0.655492	−	0.755203i	$-0.272461\pi$
$229$	19.8388	1.31098	0.655492	+	0.755203i	$0.272461\pi$
$230$	−7.40150	−0.488041
$231$	2.15883	0.142041
$232$	6.65519	0.436934
$233$	−5.71379	−0.374323	−0.187161	−	0.982329i	$-0.559929\pi$
$233$	−5.71379	−0.374323	−0.187161	+	0.982329i	$0.559929\pi$
$234$	0	0
$235$	27.9245	1.82160
$236$	−11.7114	−0.762347
$237$	1.33513	0.0867257
$238$	0.643104	0.0416862
$239$	−11.3840	−0.736373	−0.368186	−	0.929752i	$-0.620021\pi$
$239$	−11.3840	−0.736373	−0.368186	+	0.929752i	$0.620021\pi$
$240$	1.69202	0.109220
$241$	26.4403	1.70317	0.851583	−	0.524219i	$-0.175643\pi$
$241$	26.4403	1.70317	0.851583	+	0.524219i	$0.175643\pi$
$242$	5.08383	0.326801
$243$	1.00000	0.0641500
$244$	13.6853	0.876113
$245$	3.04892	0.194788
$246$	−4.17629	−0.266271
$247$	0	0
$248$	16.8756	1.07160
$249$	−8.92692	−0.565721
$250$	1.72156	0.108881
$251$	−22.5972	−1.42632	−0.713160	−	0.701001i	$-0.752737\pi$
$251$	−22.5972	−1.42632	−0.713160	+	0.701001i	$0.752737\pi$
$252$	1.35690	0.0854764
$253$	−6.53511	−0.410859
$254$	3.61788	0.227006
$255$	2.44504	0.153114
$256$	−14.1860	−0.886624
$257$	11.0392	0.688608	0.344304	−	0.938858i	$-0.388115\pi$
$257$	11.0392	0.688608	0.344304	+	0.938858i	$0.388115\pi$
$258$	6.92154	0.430916
$259$	10.7506	0.668011
$260$	0	0
$261$	2.47219	0.153025
$262$	−0.841166	−0.0519674
$263$	−14.2470	−0.878506	−0.439253	−	0.898363i	$-0.644757\pi$
$263$	−14.2470	−0.878506	−0.439253	+	0.898363i	$0.644757\pi$
$264$	−5.81163	−0.357681
$265$	3.71917	0.228467
$266$	1.11960	0.0686474
$267$	2.50604	0.153367
$268$	−17.3545	−1.06009
$269$	20.3666	1.24177	0.620886	−	0.783901i	$-0.286773\pi$
$269$	20.3666	1.24177	0.620886	+	0.783901i	$0.286773\pi$
$270$	−2.44504	−0.148801
$271$	16.9976	1.03253	0.516266	−	0.856429i	$-0.327322\pi$
$271$	16.9976	1.03253	0.516266	+	0.856429i	$0.327322\pi$
$272$	0.445042	0.0269846
$273$	0	0
$274$	9.91185	0.598797
$275$	−9.27413	−0.559251
$276$	−4.10752	−0.247244
$277$	−15.2620	−0.917007	−0.458504	−	0.888692i	$-0.651614\pi$
$277$	−15.2620	−0.917007	−0.458504	+	0.888692i	$0.651614\pi$
$278$	−10.9075	−0.654191
$279$	6.26875	0.375300
$280$	−8.20775	−0.490507
$281$	−9.80492	−0.584913	−0.292456	−	0.956279i	$-0.594473\pi$
$281$	−9.80492	−0.584913	−0.292456	+	0.956279i	$0.594473\pi$
$282$	−7.34481	−0.437377
$283$	4.69202	0.278912	0.139456	−	0.990228i	$-0.455465\pi$
$283$	4.69202	0.278912	0.139456	+	0.990228i	$0.455465\pi$
$284$	−19.1661	−1.13730
$285$	4.25667	0.252143
$286$	0	0
$287$	−5.20775	−0.307404
$288$	−5.82908	−0.343482
$289$	−16.3569	−0.962170
$290$	−6.04461	−0.354951
$291$	−2.32304	−0.136179
$292$	−13.7385	−0.803988
$293$	21.0441	1.22941	0.614706	−	0.788757i	$-0.289275\pi$
$293$	21.0441	1.22941	0.614706	+	0.788757i	$0.289275\pi$
$294$	−0.801938	−0.0467700
$295$	26.3153	1.53213
$296$	−28.9409	−1.68216
$297$	−2.15883	−0.125268
$298$	6.68425	0.387208
$299$	0	0
$300$	−5.82908	−0.336542
$301$	8.63102	0.497484
$302$	9.20775	0.529847
$303$	14.7724	0.848652
$304$	0.774791	0.0444373
$305$	−30.7506	−1.76078
$306$	−0.643104	−0.0367638
$307$	12.8140	0.731335	0.365667	−	0.930746i	$-0.380841\pi$
$307$	12.8140	0.731335	0.365667	+	0.930746i	$0.380841\pi$
$308$	−2.92931	−0.166913
$309$	−10.1642	−0.578222
$310$	−15.3274	−0.870535
$311$	9.16315	0.519594	0.259797	−	0.965663i	$-0.416344\pi$
$311$	9.16315	0.519594	0.259797	+	0.965663i	$0.416344\pi$
$312$	0	0
$313$	11.0683	0.625617	0.312809	−	0.949816i	$-0.398730\pi$
$313$	11.0683	0.625617	0.312809	+	0.949816i	$0.398730\pi$
$314$	2.40044	0.135464
$315$	−3.04892	−0.171787
$316$	−1.81163	−0.101912
$317$	15.9420	0.895391	0.447696	−	0.894186i	$-0.352245\pi$
$317$	15.9420	0.895391	0.447696	+	0.894186i	$0.352245\pi$
$318$	−0.978230	−0.0548564
$319$	−5.33704	−0.298817
$320$	10.8683	0.607557
$321$	−17.2784	−0.964388
$322$	2.42758	0.135284
$323$	1.11960	0.0622965
$324$	−1.35690	−0.0753831
$325$	0	0
$326$	−12.5386	−0.694447
$327$	14.2959	0.790565
$328$	14.0194	0.774091
$329$	−9.15883	−0.504943
$330$	5.27844	0.290568
$331$	−5.32736	−0.292818	−0.146409	−	0.989224i	$-0.546772\pi$
$331$	−5.32736	−0.292818	−0.146409	+	0.989224i	$0.546772\pi$
$332$	12.1129	0.664782
$333$	−10.7506	−0.589131
$334$	−5.37435	−0.294072
$335$	38.9952	2.13054
$336$	−0.554958	−0.0302754
$337$	−29.5937	−1.61207	−0.806036	−	0.591866i	$-0.798391\pi$
$337$	−29.5937	−1.61207	−0.806036	+	0.591866i	$0.798391\pi$
$338$	0	0
$339$	16.2687	0.883597
$340$	−3.31767	−0.179926
$341$	−13.5332	−0.732863
$342$	−1.11960	−0.0605413
$343$	−1.00000	−0.0539949
$344$	−23.2349	−1.25274
$345$	9.22952	0.496901
$346$	5.65471	0.303999
$347$	20.2717	1.08824	0.544122	−	0.839006i	$-0.316863\pi$
$347$	20.2717	1.08824	0.544122	+	0.839006i	$0.316863\pi$
$348$	−3.35450	−0.179820
$349$	−12.0325	−0.644086	−0.322043	−	0.946725i	$-0.604370\pi$
$349$	−12.0325	−0.644086	−0.322043	+	0.946725i	$0.604370\pi$
$350$	3.44504	0.184145
$351$	0	0
$352$	12.5840	0.670731
$353$	−34.6843	−1.84606	−0.923028	−	0.384732i	$-0.874294\pi$
$353$	−34.6843	−1.84606	−0.923028	+	0.384732i	$0.874294\pi$
$354$	−6.92154	−0.367876
$355$	43.0659	2.28570
$356$	−3.40044	−0.180223
$357$	−0.801938	−0.0424430
$358$	−5.18167	−0.273860
$359$	29.5991	1.56218	0.781090	−	0.624418i	$-0.214664\pi$
$359$	29.5991	1.56218	0.781090	+	0.624418i	$0.214664\pi$
$360$	8.20775	0.432586
$361$	−17.0508	−0.897412
$362$	0.462500	0.0243085
$363$	−6.33944	−0.332734
$364$	0	0
$365$	30.8702	1.61582
$366$	8.08815	0.422774
$367$	33.7362	1.76101	0.880506	−	0.474034i	$-0.157203\pi$
$367$	33.7362	1.76101	0.880506	+	0.474034i	$0.157203\pi$
$368$	1.67994	0.0875729
$369$	5.20775	0.271105
$370$	26.2857	1.36653
$371$	−1.21983	−0.0633305
$372$	−8.50604	−0.441018
$373$	24.5827	1.27284	0.636422	−	0.771341i	$-0.280414\pi$
$373$	24.5827	1.27284	0.636422	+	0.771341i	$0.280414\pi$
$374$	1.38835	0.0717901
$375$	−2.14675	−0.110858
$376$	24.6558	1.27152
$377$	0	0
$378$	0.801938	0.0412472
$379$	1.93230	0.0992554	0.0496277	−	0.998768i	$-0.484197\pi$
$379$	1.93230	0.0992554	0.0496277	+	0.998768i	$0.484197\pi$
$380$	−5.77586	−0.296295
$381$	−4.51142	−0.231127
$382$	7.31767	0.374404
$383$	−18.9638	−0.969003	−0.484501	−	0.874791i	$-0.660999\pi$
$383$	−18.9638	−0.969003	−0.484501	+	0.874791i	$0.660999\pi$
$384$	8.79954	0.449050
$385$	6.58211	0.335455
$386$	5.82717	0.296595
$387$	−8.63102	−0.438740
$388$	3.15213	0.160025
$389$	17.4711	0.885821	0.442911	−	0.896566i	$-0.353946\pi$
$389$	17.4711	0.885821	0.442911	+	0.896566i	$0.353946\pi$
$390$	0	0
$391$	2.42758	0.122768
$392$	2.69202	0.135968
$393$	1.04892	0.0529109
$394$	4.53511	0.228475
$395$	4.07069	0.204819
$396$	2.92931	0.147203
$397$	27.2204	1.36615	0.683077	−	0.730346i	$-0.260641\pi$
$397$	27.2204	1.36615	0.683077	+	0.730346i	$0.260641\pi$
$398$	−13.8649	−0.694982
$399$	−1.39612	−0.0698936
$400$	2.38404	0.119202
$401$	−21.3274	−1.06504	−0.532519	−	0.846418i	$-0.678754\pi$
$401$	−21.3274	−1.06504	−0.532519	+	0.846418i	$0.678754\pi$
$402$	−10.2567	−0.511556
$403$	0	0
$404$	−20.0446	−0.997256
$405$	3.04892	0.151502
$406$	1.98254	0.0983919
$407$	23.2088	1.15042
$408$	2.15883	0.106878
$409$	−27.2597	−1.34790	−0.673952	−	0.738776i	$-0.735404\pi$
$409$	−27.2597	−1.34790	−0.673952	+	0.738776i	$0.735404\pi$
$410$	−12.7332	−0.628846
$411$	−12.3599	−0.609668
$412$	13.7918	0.679472
$413$	−8.63102	−0.424705
$414$	−2.42758	−0.119309
$415$	−27.2174	−1.33605
$416$	0	0
$417$	13.6015	0.666067
$418$	2.41704	0.118221
$419$	27.2989	1.33364	0.666819	−	0.745220i	$-0.267655\pi$
$419$	27.2989	1.33364	0.666819	+	0.745220i	$0.267655\pi$
$420$	4.13706	0.201868
$421$	−0.817003	−0.0398183	−0.0199092	−	0.999802i	$-0.506338\pi$
$421$	−0.817003	−0.0398183	−0.0199092	+	0.999802i	$0.506338\pi$
$422$	−7.35258	−0.357918
$423$	9.15883	0.445318
$424$	3.28382	0.159476
$425$	3.44504	0.167109
$426$	−11.3274	−0.548812
$427$	10.0858	0.488084
$428$	23.4450	1.13326
$429$	0	0
$430$	21.1032	1.01769
$431$	−28.5623	−1.37580	−0.687898	−	0.725808i	$-0.741466\pi$
$431$	−28.5623	−1.37580	−0.687898	+	0.725808i	$0.741466\pi$
$432$	0.554958	0.0267004
$433$	−12.5013	−0.600772	−0.300386	−	0.953818i	$-0.597115\pi$
$433$	−12.5013	−0.600772	−0.300386	+	0.953818i	$0.597115\pi$
$434$	5.02715	0.241311
$435$	7.53750	0.361395
$436$	−19.3980	−0.928998
$437$	4.22627	0.202170
$438$	−8.11960	−0.387970
$439$	4.28514	0.204519	0.102259	−	0.994758i	$-0.467393\pi$
$439$	4.28514	0.204519	0.102259	+	0.994758i	$0.467393\pi$
$440$	−17.7192	−0.844728
$441$	1.00000	0.0476190
$442$	0	0
$443$	−17.5724	−0.834891	−0.417445	−	0.908702i	$-0.637074\pi$
$443$	−17.5724	−0.834891	−0.417445	+	0.908702i	$0.637074\pi$
$444$	14.5875	0.692291
$445$	7.64071	0.362204
$446$	−15.3153	−0.725199
$447$	−8.33513	−0.394238
$448$	−3.56465	−0.168414
$449$	22.5550	1.06443	0.532217	−	0.846608i	$-0.321359\pi$
$449$	22.5550	1.06443	0.532217	+	0.846608i	$0.321359\pi$
$450$	−3.44504	−0.162401
$451$	−11.2427	−0.529397
$452$	−22.0750	−1.03832
$453$	−11.4819	−0.539466
$454$	−22.4112	−1.05181
$455$	0	0
$456$	3.75840	0.176003
$457$	23.7496	1.11096	0.555479	−	0.831531i	$-0.312535\pi$
$457$	23.7496	1.11096	0.555479	+	0.831531i	$0.312535\pi$
$458$	−15.9095	−0.743400
$459$	0.801938	0.0374312
$460$	−12.5235	−0.583911
$461$	−13.4657	−0.627162	−0.313581	−	0.949561i	$-0.601529\pi$
$461$	−13.4657	−0.627162	−0.313581	+	0.949561i	$0.601529\pi$
$462$	−1.73125	−0.0805450
$463$	−25.2556	−1.17373	−0.586864	−	0.809686i	$-0.699638\pi$
$463$	−25.2556	−1.17373	−0.586864	+	0.809686i	$0.699638\pi$
$464$	1.37196	0.0636917
$465$	19.1129	0.886340
$466$	4.58211	0.212262
$467$	−33.9734	−1.57210	−0.786052	−	0.618161i	$-0.787878\pi$
$467$	−33.9734	−1.57210	−0.786052	+	0.618161i	$0.787878\pi$
$468$	0	0
$469$	−12.7899	−0.590581
$470$	−22.3937	−1.03295
$471$	−2.99330	−0.137924
$472$	23.2349	1.06947
$473$	18.6329	0.856744
$474$	−1.07069	−0.0491783
$475$	5.99761	0.275189
$476$	1.08815	0.0498751
$477$	1.21983	0.0558523
$478$	9.12929	0.417564
$479$	0.325437	0.0148696	0.00743480	−	0.999972i	$-0.497633\pi$
$479$	0.325437	0.0148696	0.00743480	+	0.999972i	$0.497633\pi$
$480$	−17.7724	−0.811195
$481$	0	0
$482$	−21.2034	−0.965790
$483$	−3.02715	−0.137740
$484$	8.60196	0.390998
$485$	−7.08277	−0.321612
$486$	−0.801938	−0.0363766
$487$	−10.3696	−0.469890	−0.234945	−	0.972009i	$-0.575491\pi$
$487$	−10.3696	−0.469890	−0.234945	+	0.972009i	$0.575491\pi$
$488$	−27.1511	−1.22907
$489$	15.6353	0.707054
$490$	−2.44504	−0.110456
$491$	−15.6692	−0.707140	−0.353570	−	0.935408i	$-0.615032\pi$
$491$	−15.6692	−0.707140	−0.353570	+	0.935408i	$0.615032\pi$
$492$	−7.06638	−0.318577
$493$	1.98254	0.0892892
$494$	0	0
$495$	−6.58211	−0.295844
$496$	3.47889	0.156207
$497$	−14.1250	−0.633592
$498$	7.15883	0.320795
$499$	−21.5700	−0.965607	−0.482803	−	0.875729i	$-0.660381\pi$
$499$	−21.5700	−0.965607	−0.482803	+	0.875729i	$0.660381\pi$
$500$	2.91292	0.130270
$501$	6.70171	0.299410
$502$	18.1215	0.808803
$503$	−9.46980	−0.422237	−0.211119	−	0.977460i	$-0.567711\pi$
$503$	−9.46980	−0.422237	−0.211119	+	0.977460i	$0.567711\pi$
$504$	−2.69202	−0.119912
$505$	45.0398	2.00425
$506$	5.24075	0.232980
$507$	0	0
$508$	6.12152	0.271599
$509$	5.43834	0.241050	0.120525	−	0.992710i	$-0.461542\pi$
$509$	5.43834	0.241050	0.120525	+	0.992710i	$0.461542\pi$
$510$	−1.96077	−0.0868244
$511$	−10.1250	−0.447903
$512$	−6.22282	−0.275012
$513$	1.39612	0.0616404
$514$	−8.85277	−0.390479
$515$	−30.9898	−1.36558
$516$	11.7114	0.515566
$517$	−19.7724	−0.869589
$518$	−8.62133	−0.378800
$519$	−7.05131	−0.309518
$520$	0	0
$521$	−37.5424	−1.64476	−0.822381	−	0.568937i	$-0.807355\pi$
$521$	−37.5424	−1.64476	−0.822381	+	0.568937i	$0.807355\pi$
$522$	−1.98254	−0.0867735
$523$	31.8485	1.39264	0.696318	−	0.717733i	$-0.254820\pi$
$523$	31.8485	1.39264	0.696318	+	0.717733i	$0.254820\pi$
$524$	−1.42327	−0.0621759
$525$	−4.29590	−0.187488
$526$	11.4252	0.498162
$527$	5.02715	0.218986
$528$	−1.19806	−0.0521390
$529$	−13.8364	−0.601582
$530$	−2.98254	−0.129553
$531$	8.63102	0.374554
$532$	1.89440	0.0821325
$533$	0	0
$534$	−2.00969	−0.0869677
$535$	−52.6805	−2.27758
$536$	34.4306	1.48717
$537$	6.46144	0.278832
$538$	−16.3327	−0.704154
$539$	−2.15883	−0.0929875
$540$	−4.13706	−0.178031
$541$	−22.5652	−0.970155	−0.485078	−	0.874471i	$-0.661209\pi$
$541$	−22.5652	−0.970155	−0.485078	+	0.874471i	$0.661209\pi$
$542$	−13.6310	−0.585503
$543$	−0.576728	−0.0247498
$544$	−4.67456	−0.200420
$545$	43.5870	1.86706
$546$	0	0
$547$	33.1739	1.41841	0.709207	−	0.705001i	$-0.249053\pi$
$547$	33.1739	1.41841	0.709207	+	0.705001i	$0.249053\pi$
$548$	16.7711	0.716425
$549$	−10.0858	−0.430449
$550$	7.43727	0.317126
$551$	3.45148	0.147038
$552$	8.14914	0.346851
$553$	−1.33513	−0.0567753
$554$	12.2392	0.519994
$555$	−32.7778	−1.39134
$556$	−18.4558	−0.782700
$557$	−23.2838	−0.986567	−0.493283	−	0.869869i	$-0.664203\pi$
$557$	−23.2838	−0.986567	−0.493283	+	0.869869i	$0.664203\pi$
$558$	−5.02715	−0.212816
$559$	0	0
$560$	−1.69202	−0.0715010
$561$	−1.73125	−0.0730934
$562$	7.86294	0.331678
$563$	3.26577	0.137636	0.0688178	−	0.997629i	$-0.478077\pi$
$563$	3.26577	0.137636	0.0688178	+	0.997629i	$0.478077\pi$
$564$	−12.4276	−0.523296
$565$	49.6021	2.08677
$566$	−3.76271	−0.158158
$567$	−1.00000	−0.0419961
$568$	38.0248	1.59548
$569$	−22.0780	−0.925557	−0.462779	−	0.886474i	$-0.653148\pi$
$569$	−22.0780	−0.925557	−0.462779	+	0.886474i	$0.653148\pi$
$570$	−3.41358	−0.142979
$571$	−10.8649	−0.454680	−0.227340	−	0.973815i	$-0.573003\pi$
$571$	−10.8649	−0.454680	−0.227340	+	0.973815i	$0.573003\pi$
$572$	0	0
$573$	−9.12498	−0.381202
$574$	4.17629	0.174315
$575$	13.0043	0.542317
$576$	3.56465	0.148527
$577$	−10.5526	−0.439309	−0.219655	−	0.975578i	$-0.570493\pi$
$577$	−10.5526	−0.439309	−0.219655	+	0.975578i	$0.570493\pi$
$578$	13.1172	0.545604
$579$	−7.26636	−0.301979
$580$	−10.2276	−0.424678
$581$	8.92692	0.370351
$582$	1.86294	0.0772212
$583$	−2.63342	−0.109065
$584$	27.2567	1.12789
$585$	0	0
$586$	−16.8761	−0.697145
$587$	1.95971	0.0808857	0.0404429	−	0.999182i	$-0.487123\pi$
$587$	1.95971	0.0808857	0.0404429	+	0.999182i	$0.487123\pi$
$588$	−1.35690	−0.0559574
$589$	8.75196	0.360618
$590$	−21.1032	−0.868805
$591$	−5.65519	−0.232623
$592$	−5.96615	−0.245207
$593$	−40.9178	−1.68029	−0.840147	−	0.542359i	$-0.817531\pi$
$593$	−40.9178	−1.68029	−0.840147	+	0.542359i	$0.817531\pi$
$594$	1.73125	0.0710341
$595$	−2.44504	−0.100237
$596$	11.3099	0.463271
$597$	17.2892	0.707600
$598$	0	0
$599$	15.7875	0.645058	0.322529	−	0.946560i	$-0.395467\pi$
$599$	15.7875	0.645058	0.322529	+	0.946560i	$0.395467\pi$
$600$	11.5646	0.472125
$601$	−14.1782	−0.578341	−0.289171	−	0.957278i	$-0.593380\pi$
$601$	−14.1782	−0.578341	−0.289171	+	0.957278i	$0.593380\pi$
$602$	−6.92154	−0.282101
$603$	12.7899	0.520843
$604$	15.5797	0.633930
$605$	−19.3284	−0.785812
$606$	−11.8465	−0.481233
$607$	−33.6222	−1.36468	−0.682341	−	0.731034i	$-0.739038\pi$
$607$	−33.6222	−1.36468	−0.682341	+	0.731034i	$0.739038\pi$
$608$	−8.13813	−0.330045
$609$	−2.47219	−0.100178
$610$	24.6601	0.998458
$611$	0	0
$612$	−1.08815	−0.0439857
$613$	−38.7157	−1.56371	−0.781856	−	0.623459i	$-0.785727\pi$
$613$	−38.7157	−1.56371	−0.781856	+	0.623459i	$0.785727\pi$
$614$	−10.2760	−0.414707
$615$	15.8780	0.640263
$616$	5.81163	0.234157
$617$	−28.1696	−1.13406	−0.567032	−	0.823695i	$-0.691909\pi$
$617$	−28.1696	−1.13406	−0.567032	+	0.823695i	$0.691909\pi$
$618$	8.15106	0.327884
$619$	13.0556	0.524750	0.262375	−	0.964966i	$-0.415494\pi$
$619$	13.0556	0.524750	0.262375	+	0.964966i	$0.415494\pi$
$620$	−25.9342	−1.04154
$621$	3.02715	0.121475
$622$	−7.34827	−0.294639
$623$	−2.50604	−0.100402
$624$	0	0
$625$	−28.0248	−1.12099
$626$	−8.87608	−0.354760
$627$	−3.01400	−0.120368
$628$	4.06159	0.162075
$629$	−8.62133	−0.343755
$630$	2.44504	0.0974128
$631$	26.9869	1.07433	0.537165	−	0.843477i	$-0.319495\pi$
$631$	26.9869	1.07433	0.537165	+	0.843477i	$0.319495\pi$
$632$	3.59419	0.142969
$633$	9.16852	0.364416
$634$	−12.7845	−0.507737
$635$	−13.7549	−0.545848
$636$	−1.65519	−0.0656324
$637$	0	0
$638$	4.27998	0.169446
$639$	14.1250	0.558776
$640$	26.8291	1.06051
$641$	40.1323	1.58513	0.792565	−	0.609788i	$-0.208745\pi$
$641$	40.1323	1.58513	0.792565	+	0.609788i	$0.208745\pi$
$642$	13.8562	0.546862
$643$	34.7560	1.37064	0.685322	−	0.728241i	$-0.259662\pi$
$643$	34.7560	1.37064	0.685322	+	0.728241i	$0.259662\pi$
$644$	4.10752	0.161859
$645$	−26.3153	−1.03616
$646$	−0.897853	−0.0353256
$647$	−4.08947	−0.160774	−0.0803869	−	0.996764i	$-0.525616\pi$
$647$	−4.08947	−0.160774	−0.0803869	+	0.996764i	$0.525616\pi$
$648$	2.69202	0.105753
$649$	−18.6329	−0.731407
$650$	0	0
$651$	−6.26875	−0.245692
$652$	−21.2155	−0.830864
$653$	−14.2319	−0.556938	−0.278469	−	0.960445i	$-0.589827\pi$
$653$	−14.2319	−0.556938	−0.278469	+	0.960445i	$0.589827\pi$
$654$	−11.4644	−0.448294
$655$	3.19806	0.124959
$656$	2.89008	0.112839
$657$	10.1250	0.395013
$658$	7.34481	0.286331
$659$	23.0696	0.898665	0.449332	−	0.893365i	$-0.351662\pi$
$659$	23.0696	0.898665	0.449332	+	0.893365i	$0.351662\pi$
$660$	8.93123	0.347648
$661$	11.3545	0.441639	0.220819	−	0.975315i	$-0.429127\pi$
$661$	11.3545	0.441639	0.220819	+	0.975315i	$0.429127\pi$
$662$	4.27221	0.166044
$663$	0	0
$664$	−24.0315	−0.932601
$665$	−4.25667	−0.165067
$666$	8.62133	0.334070
$667$	7.48368	0.289769
$668$	−9.09352	−0.351839
$669$	19.0978	0.738365
$670$	−31.2717	−1.20813
$671$	21.7735	0.840555
$672$	5.82908	0.224862
$673$	47.0960	1.81542	0.907709	−	0.419600i	$-0.137829\pi$
$673$	47.0960	1.81542	0.907709	+	0.419600i	$0.137829\pi$
$674$	23.7323	0.914135
$675$	4.29590	0.165349
$676$	0	0
$677$	−20.0653	−0.771173	−0.385586	−	0.922672i	$-0.626001\pi$
$677$	−20.0653	−0.771173	−0.385586	+	0.922672i	$0.626001\pi$
$678$	−13.0465	−0.501049
$679$	2.32304	0.0891502
$680$	6.58211	0.252412
$681$	27.9463	1.07090
$682$	10.8528	0.415574
$683$	33.9715	1.29988	0.649942	−	0.759984i	$-0.274793\pi$
$683$	33.9715	1.29988	0.649942	+	0.759984i	$0.274793\pi$
$684$	−1.89440	−0.0724340
$685$	−37.6843	−1.43984
$686$	0.801938	0.0306181
$687$	19.8388	0.756896
$688$	−4.78986	−0.182612
$689$	0	0
$690$	−7.40150	−0.281770
$691$	33.7845	1.28522	0.642611	−	0.766193i	$-0.277851\pi$
$691$	33.7845	1.28522	0.642611	+	0.766193i	$0.277851\pi$
$692$	9.56789	0.363717
$693$	2.15883	0.0820073
$694$	−16.2567	−0.617095
$695$	41.4698	1.57304
$696$	6.65519	0.252264
$697$	4.17629	0.158188
$698$	9.64933	0.365233
$699$	−5.71379	−0.216115
$700$	5.82908	0.220319
$701$	−2.13036	−0.0804625	−0.0402313	−	0.999190i	$-0.512809\pi$
$701$	−2.13036	−0.0804625	−0.0402313	+	0.999190i	$0.512809\pi$
$702$	0	0
$703$	−15.0092	−0.566083
$704$	−7.69548	−0.290034
$705$	27.9245	1.05170
$706$	27.8146	1.04682
$707$	−14.7724	−0.555573
$708$	−11.7114	−0.440141
$709$	−30.2180	−1.13486	−0.567431	−	0.823421i	$-0.692063\pi$
$709$	−30.2180	−1.13486	−0.567431	+	0.823421i	$0.692063\pi$
$710$	−34.5362	−1.29612
$711$	1.33513	0.0500711
$712$	6.74632	0.252829
$713$	18.9764	0.710673
$714$	0.643104	0.0240676
$715$	0	0
$716$	−8.76749	−0.327657
$717$	−11.3840	−0.425145
$718$	−23.7366	−0.885843
$719$	9.88577	0.368677	0.184339	−	0.982863i	$-0.440986\pi$
$719$	9.88577	0.368677	0.184339	+	0.982863i	$0.440986\pi$
$720$	1.69202	0.0630579
$721$	10.1642	0.378535
$722$	13.6737	0.508883
$723$	26.4403	0.983324
$724$	0.782560	0.0290836
$725$	10.6203	0.394427
$726$	5.08383	0.188679
$727$	−23.5579	−0.873716	−0.436858	−	0.899531i	$-0.643909\pi$
$727$	−23.5579	−0.873716	−0.436858	+	0.899531i	$0.643909\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−24.7560	−0.916261
$731$	−6.92154	−0.256003
$732$	13.6853	0.505824
$733$	−0.958852	−0.0354160	−0.0177080	−	0.999843i	$-0.505637\pi$
$733$	−0.958852	−0.0354160	−0.0177080	+	0.999843i	$0.505637\pi$
$734$	−27.0543	−0.998592
$735$	3.04892	0.112461
$736$	−17.6455	−0.650422
$737$	−27.6112	−1.01707
$738$	−4.17629	−0.153731
$739$	2.06339	0.0759031	0.0379515	−	0.999280i	$-0.487917\pi$
$739$	2.06339	0.0759031	0.0379515	+	0.999280i	$0.487917\pi$
$740$	44.4760	1.63497
$741$	0	0
$742$	0.978230	0.0359119
$743$	−43.4494	−1.59400	−0.797001	−	0.603978i	$-0.793582\pi$
$743$	−43.4494	−1.59400	−0.797001	+	0.603978i	$0.793582\pi$
$744$	16.8756	0.618690
$745$	−25.4131	−0.931064
$746$	−19.7138	−0.721773
$747$	−8.92692	−0.326619
$748$	2.34913	0.0858926
$749$	17.2784	0.631340
$750$	1.72156	0.0628625
$751$	−33.7778	−1.23257	−0.616284	−	0.787524i	$-0.711363\pi$
$751$	−33.7778	−1.23257	−0.616284	+	0.787524i	$0.711363\pi$
$752$	5.08277	0.185350
$753$	−22.5972	−0.823487
$754$	0	0
$755$	−35.0073	−1.27405
$756$	1.35690	0.0493498
$757$	−45.0525	−1.63746	−0.818730	−	0.574178i	$-0.805322\pi$
$757$	−45.0525	−1.63746	−0.818730	+	0.574178i	$0.805322\pi$
$758$	−1.54958	−0.0562833
$759$	−6.53511	−0.237209
$760$	11.4590	0.415663
$761$	−18.8605	−0.683694	−0.341847	−	0.939756i	$-0.611052\pi$
$761$	−18.8605	−0.683694	−0.341847	+	0.939756i	$0.611052\pi$
$762$	3.61788	0.131062
$763$	−14.2959	−0.517546
$764$	12.3817	0.447952
$765$	2.44504	0.0884007
$766$	15.2078	0.549478
$767$	0	0
$768$	−14.1860	−0.511892
$769$	6.20642	0.223809	0.111905	−	0.993719i	$-0.464305\pi$
$769$	6.20642	0.223809	0.111905	+	0.993719i	$0.464305\pi$
$770$	−5.27844	−0.190222
$771$	11.0392	0.397568
$772$	9.85969	0.354858
$773$	−14.9299	−0.536991	−0.268496	−	0.963281i	$-0.586526\pi$
$773$	−14.9299	−0.536991	−0.268496	+	0.963281i	$0.586526\pi$
$774$	6.92154	0.248790
$775$	26.9299	0.967351
$776$	−6.25368	−0.224494
$777$	10.7506	0.385677
$778$	−14.0108	−0.502310
$779$	7.27067	0.260499
$780$	0	0
$781$	−30.4935	−1.09114
$782$	−1.94677	−0.0696164
$783$	2.47219	0.0883488
$784$	0.554958	0.0198199
$785$	−9.12631	−0.325732
$786$	−0.841166	−0.0300034
$787$	48.2174	1.71877	0.859383	−	0.511332i	$-0.170848\pi$
$787$	48.2174	1.71877	0.859383	+	0.511332i	$0.170848\pi$
$788$	7.67350	0.273357
$789$	−14.2470	−0.507206
$790$	−3.26444	−0.116143
$791$	−16.2687	−0.578450
$792$	−5.81163	−0.206507
$793$	0	0
$794$	−21.8291	−0.774685
$795$	3.71917	0.131905
$796$	−23.4596	−0.831505
$797$	23.5284	0.833419	0.416709	−	0.909040i	$-0.363183\pi$
$797$	23.5284	0.833419	0.416709	+	0.909040i	$0.363183\pi$
$798$	1.11960	0.0396336
$799$	7.34481	0.259841
$800$	−25.0411	−0.885338
$801$	2.50604	0.0885466
$802$	17.1032	0.603935
$803$	−21.8582	−0.771357
$804$	−17.3545	−0.612046
$805$	−9.22952	−0.325298
$806$	0	0
$807$	20.3666	0.716938
$808$	39.7676	1.39902
$809$	−47.3997	−1.66648	−0.833242	−	0.552908i	$-0.813518\pi$
$809$	−47.3997	−1.66648	−0.833242	+	0.552908i	$0.813518\pi$
$810$	−2.44504	−0.0859100
$811$	−14.4125	−0.506092	−0.253046	−	0.967454i	$-0.581432\pi$
$811$	−14.4125	−0.506092	−0.253046	+	0.967454i	$0.581432\pi$
$812$	3.35450	0.117720
$813$	16.9976	0.596132
$814$	−18.6120	−0.652351
$815$	47.6708	1.66984
$816$	0.445042	0.0155796
$817$	−12.0500	−0.421576
$818$	21.8605	0.764336
$819$	0	0
$820$	−21.5448	−0.752377
$821$	−19.9409	−0.695943	−0.347971	−	0.937505i	$-0.613129\pi$
$821$	−19.9409	−0.695943	−0.347971	+	0.937505i	$0.613129\pi$
$822$	9.91185	0.345716
$823$	31.3961	1.09440	0.547200	−	0.837002i	$-0.315694\pi$
$823$	31.3961	1.09440	0.547200	+	0.837002i	$0.315694\pi$
$824$	−27.3623	−0.953210
$825$	−9.27413	−0.322884
$826$	6.92154	0.240831
$827$	15.5109	0.539368	0.269684	−	0.962949i	$-0.413081\pi$
$827$	15.5109	0.539368	0.269684	+	0.962949i	$0.413081\pi$
$828$	−4.10752	−0.142746
$829$	−37.5362	−1.30369	−0.651843	−	0.758354i	$-0.726004\pi$
$829$	−37.5362	−1.30369	−0.651843	+	0.758354i	$0.726004\pi$
$830$	21.8267	0.757616
$831$	−15.2620	−0.529434
$832$	0	0
$833$	0.801938	0.0277855
$834$	−10.9075	−0.377697
$835$	20.4330	0.707112
$836$	4.08968	0.141445
$837$	6.26875	0.216680
$838$	−21.8920	−0.756247
$839$	−27.6122	−0.953280	−0.476640	−	0.879099i	$-0.658146\pi$
$839$	−27.6122	−0.953280	−0.476640	+	0.879099i	$0.658146\pi$
$840$	−8.20775	−0.283194
$841$	−22.8883	−0.789251
$842$	0.655186	0.0225792
$843$	−9.80492	−0.337699
$844$	−12.4407	−0.428228
$845$	0	0
$846$	−7.34481	−0.252520
$847$	6.33944	0.217826
$848$	0.676956	0.0232468
$849$	4.69202	0.161030
$850$	−2.76271	−0.0947601
$851$	−32.5437	−1.11558
$852$	−19.1661	−0.656621
$853$	30.2314	1.03510	0.517552	−	0.855652i	$-0.326843\pi$
$853$	30.2314	1.03510	0.517552	+	0.855652i	$0.326843\pi$
$854$	−8.08815	−0.276771
$855$	4.25667	0.145575
$856$	−46.5139	−1.58981
$857$	−14.4179	−0.492506	−0.246253	−	0.969206i	$-0.579199\pi$
$857$	−14.4179	−0.492506	−0.246253	+	0.969206i	$0.579199\pi$
$858$	0	0
$859$	−16.8062	−0.573422	−0.286711	−	0.958017i	$-0.592562\pi$
$859$	−16.8062	−0.573422	−0.286711	+	0.958017i	$0.592562\pi$
$860$	35.7071	1.21760
$861$	−5.20775	−0.177480
$862$	22.9051	0.780152
$863$	−17.9608	−0.611392	−0.305696	−	0.952129i	$-0.598889\pi$
$863$	−17.9608	−0.611392	−0.305696	+	0.952129i	$0.598889\pi$
$864$	−5.82908	−0.198309
$865$	−21.4989	−0.730983
$866$	10.0252	0.340671
$867$	−16.3569	−0.555509
$868$	8.50604	0.288714
$869$	−2.88231	−0.0977758
$870$	−6.04461	−0.204931
$871$	0	0
$872$	38.4849	1.30326
$873$	−2.32304	−0.0786231
$874$	−3.38921	−0.114642
$875$	2.14675	0.0725735
$876$	−13.7385	−0.464182
$877$	−20.3744	−0.687993	−0.343997	−	0.938971i	$-0.611781\pi$
$877$	−20.3744	−0.687993	−0.343997	+	0.938971i	$0.611781\pi$
$878$	−3.43642	−0.115973
$879$	21.0441	0.709801
$880$	−3.65279	−0.123136
$881$	11.0425	0.372030	0.186015	−	0.982547i	$-0.440443\pi$
$881$	11.0425	0.372030	0.186015	+	0.982547i	$0.440443\pi$
$882$	−0.801938	−0.0270026
$883$	−53.5260	−1.80129	−0.900647	−	0.434552i	$-0.856907\pi$
$883$	−53.5260	−1.80129	−0.900647	+	0.434552i	$0.856907\pi$
$884$	0	0
$885$	26.3153	0.884578
$886$	14.0920	0.473429
$887$	39.7706	1.33537	0.667683	−	0.744446i	$-0.267286\pi$
$887$	39.7706	1.33537	0.667683	+	0.744446i	$0.267286\pi$
$888$	−28.9409	−0.971194
$889$	4.51142	0.151308
$890$	−6.12737	−0.205390
$891$	−2.15883	−0.0723236
$892$	−25.9138	−0.867657
$893$	12.7869	0.427896
$894$	6.68425	0.223555
$895$	19.7004	0.658511
$896$	−8.79954	−0.293972
$897$	0	0
$898$	−18.0877	−0.603593
$899$	15.4975	0.516872
$900$	−5.82908	−0.194303
$901$	0.978230	0.0325896
$902$	9.01592	0.300197
$903$	8.63102	0.287222
$904$	43.7958	1.45663
$905$	−1.75840	−0.0584511
$906$	9.20775	0.305907
$907$	−13.5381	−0.449525	−0.224762	−	0.974414i	$-0.572161\pi$
$907$	−13.5381	−0.449525	−0.224762	+	0.974414i	$0.572161\pi$
$908$	−37.9202	−1.25843
$909$	14.7724	0.489970
$910$	0	0
$911$	−4.19434	−0.138965	−0.0694824	−	0.997583i	$-0.522135\pi$
$911$	−4.19434	−0.138965	−0.0694824	+	0.997583i	$0.522135\pi$
$912$	0.774791	0.0256559
$913$	19.2717	0.637801
$914$	−19.0457	−0.629975
$915$	−30.7506	−1.01658
$916$	−26.9191	−0.889434
$917$	−1.04892	−0.0346383
$918$	−0.643104	−0.0212256
$919$	1.94630	0.0642024	0.0321012	−	0.999485i	$-0.489780\pi$
$919$	1.94630	0.0642024	0.0321012	+	0.999485i	$0.489780\pi$
$920$	24.8461	0.819151
$921$	12.8140	0.422236
$922$	10.7987	0.355636
$923$	0	0
$924$	−2.92931	−0.0963673
$925$	−46.1836	−1.51851
$926$	20.2534	0.665569
$927$	−10.1642	−0.333836
$928$	−14.4106	−0.473051
$929$	24.5948	0.806928	0.403464	−	0.914995i	$-0.367806\pi$
$929$	24.5948	0.806928	0.403464	+	0.914995i	$0.367806\pi$
$930$	−15.3274	−0.502604
$931$	1.39612	0.0457561
$932$	7.75302	0.253959
$933$	9.16315	0.299988
$934$	27.2446	0.891470
$935$	−5.27844	−0.172623
$936$	0	0
$937$	−9.88663	−0.322982	−0.161491	−	0.986874i	$-0.551630\pi$
$937$	−9.88663	−0.322982	−0.161491	+	0.986874i	$0.551630\pi$
$938$	10.2567	0.334892
$939$	11.0683	0.361200
$940$	−37.8907	−1.23586
$941$	−23.1468	−0.754563	−0.377281	−	0.926099i	$-0.623141\pi$
$941$	−23.1468	−0.754563	−0.377281	+	0.926099i	$0.623141\pi$
$942$	2.40044	0.0782104
$943$	15.7646	0.513367
$944$	4.78986	0.155897
$945$	−3.04892	−0.0991813
$946$	−14.9425	−0.485821
$947$	−14.2903	−0.464371	−0.232185	−	0.972672i	$-0.574588\pi$
$947$	−14.2903	−0.464371	−0.232185	+	0.972672i	$0.574588\pi$
$948$	−1.81163	−0.0588389
$949$	0	0
$950$	−4.80971	−0.156048
$951$	15.9420	0.516954
$952$	−2.15883	−0.0699682
$953$	−51.5411	−1.66958	−0.834790	−	0.550569i	$-0.814411\pi$
$953$	−51.5411	−1.66958	−0.834790	+	0.550569i	$0.814411\pi$
$954$	−0.978230	−0.0316714
$955$	−27.8213	−0.900277
$956$	15.4470	0.499590
$957$	−5.33704	−0.172522
$958$	−0.260980	−0.00843189
$959$	12.3599	0.399121
$960$	10.8683	0.350773
$961$	8.29722	0.267652
$962$	0	0
$963$	−17.2784	−0.556790
$964$	−35.8767	−1.15551
$965$	−22.1545	−0.713179
$966$	2.42758	0.0781062
$967$	20.0944	0.646192	0.323096	−	0.946366i	$-0.395276\pi$
$967$	20.0944	0.646192	0.323096	+	0.946366i	$0.395276\pi$
$968$	−17.0659	−0.548519
$969$	1.11960	0.0359669
$970$	5.67994	0.182372
$971$	−37.9181	−1.21685	−0.608425	−	0.793612i	$-0.708198\pi$
$971$	−37.9181	−1.21685	−0.608425	+	0.793612i	$0.708198\pi$
$972$	−1.35690	−0.0435225
$973$	−13.6015	−0.436044
$974$	8.31575	0.266454
$975$	0	0
$976$	−5.59717	−0.179161
$977$	2.92931	0.0937170	0.0468585	−	0.998902i	$-0.485079\pi$
$977$	2.92931	0.0937170	0.0468585	+	0.998902i	$0.485079\pi$
$978$	−12.5386	−0.400939
$979$	−5.41013	−0.172908
$980$	−4.13706	−0.132154
$981$	14.2959	0.456433
$982$	12.5657	0.400988
$983$	−59.9879	−1.91332	−0.956659	−	0.291211i	$-0.905942\pi$
$983$	−59.9879	−1.91332	−0.956659	+	0.291211i	$0.905942\pi$
$984$	14.0194	0.446921
$985$	−17.2422	−0.549382
$986$	−1.58987	−0.0506319
$987$	−9.15883	−0.291529
$988$	0	0
$989$	−26.1274	−0.830802
$990$	5.27844	0.167760
$991$	8.83818	0.280754	0.140377	−	0.990098i	$-0.455169\pi$
$991$	8.83818	0.280754	0.140377	+	0.990098i	$0.455169\pi$
$992$	−36.5411	−1.16018
$993$	−5.32736	−0.169059
$994$	11.3274	0.359282
$995$	52.7133	1.67112
$996$	12.1129	0.383812
$997$	−31.7077	−1.00419	−0.502096	−	0.864812i	$-0.667438\pi$
$997$	−31.7077	−1.00419	−0.502096	+	0.864812i	$0.667438\pi$
$998$	17.2978	0.547553
$999$	−10.7506	−0.340135

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.k.c.22.1	✓	6	13.10	even	6
273.2.k.c.211.1	yes	6	13.4	even	6
819.2.o.e.568.3		6	39.23	odd	6
819.2.o.e.757.3		6	39.17	odd	6
3549.2.a.i.1.3		3	13.12	even	2
3549.2.a.u.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)

\(f(q)\)	\(=\)	\(q-0.801938 q^{2} +1.00000 q^{3} -1.35690 q^{4} +3.04892 q^{5} -0.801938 q^{6} -1.00000 q^{7} +2.69202 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.801938 q^{2} +1.00000 q^{3} -1.35690 q^{4} +3.04892 q^{5} -0.801938 q^{6} -1.00000 q^{7} +2.69202 q^{8} +1.00000 q^{9} -2.44504 q^{10} -2.15883 q^{11} -1.35690 q^{12} +0.801938 q^{14} +3.04892 q^{15} +0.554958 q^{16} +0.801938 q^{17} -0.801938 q^{18} +1.39612 q^{19} -4.13706 q^{20} -1.00000 q^{21} +1.73125 q^{22} +3.02715 q^{23} +2.69202 q^{24} +4.29590 q^{25} +1.00000 q^{27} +1.35690 q^{28} +2.47219 q^{29} -2.44504 q^{30} +6.26875 q^{31} -5.82908 q^{32} -2.15883 q^{33} -0.643104 q^{34} -3.04892 q^{35} -1.35690 q^{36} -10.7506 q^{37} -1.11960 q^{38} +8.20775 q^{40} +5.20775 q^{41} +0.801938 q^{42} -8.63102 q^{43} +2.92931 q^{44} +3.04892 q^{45} -2.42758 q^{46} +9.15883 q^{47} +0.554958 q^{48} +1.00000 q^{49} -3.44504 q^{50} +0.801938 q^{51} +1.21983 q^{53} -0.801938 q^{54} -6.58211 q^{55} -2.69202 q^{56} +1.39612 q^{57} -1.98254 q^{58} +8.63102 q^{59} -4.13706 q^{60} -10.0858 q^{61} -5.02715 q^{62} -1.00000 q^{63} +3.56465 q^{64} +1.73125 q^{66} +12.7899 q^{67} -1.08815 q^{68} +3.02715 q^{69} +2.44504 q^{70} +14.1250 q^{71} +2.69202 q^{72} +10.1250 q^{73} +8.62133 q^{74} +4.29590 q^{75} -1.89440 q^{76} +2.15883 q^{77} +1.33513 q^{79} +1.69202 q^{80} +1.00000 q^{81} -4.17629 q^{82} -8.92692 q^{83} +1.35690 q^{84} +2.44504 q^{85} +6.92154 q^{86} +2.47219 q^{87} -5.81163 q^{88} +2.50604 q^{89} -2.44504 q^{90} -4.10752 q^{92} +6.26875 q^{93} -7.34481 q^{94} +4.25667 q^{95} -5.82908 q^{96} -2.32304 q^{97} -0.801938 q^{98} -2.15883 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 2 q^{2} + 3 q^{3} + 2 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} + 2 q^{11} - 2 q^{14} + 2 q^{16} - 2 q^{17} + 2 q^{18} + 13 q^{19} - 7 q^{20} - 3 q^{21} + 13 q^{22} + 3 q^{23} + 3 q^{24} - q^{25} + 3 q^{27} + q^{29} - 7 q^{30} + 11 q^{31} - 7 q^{32} + 2 q^{33} - 6 q^{34} + 4 q^{37} + 18 q^{38} + 7 q^{40} - 2 q^{41} - 2 q^{42} - 11 q^{43} + 21 q^{44} + 9 q^{46} + 19 q^{47} + 2 q^{48} + 3 q^{49} - 10 q^{50} - 2 q^{51} + 5 q^{53} + 2 q^{54} - 14 q^{55} - 3 q^{56} + 13 q^{57} + 10 q^{58} + 11 q^{59} - 7 q^{60} + 7 q^{61} - 9 q^{62} - 3 q^{63} - 11 q^{64} + 13 q^{66} + 15 q^{67} - 7 q^{68} + 3 q^{69} + 7 q^{70} + 18 q^{71} + 3 q^{72} + 6 q^{73} + 33 q^{74} - q^{75} + 14 q^{76} - 2 q^{77} + 3 q^{79} + 3 q^{81} - 20 q^{82} + 2 q^{83} + 7 q^{85} - 5 q^{86} + q^{87} + 9 q^{88} + 17 q^{89} - 7 q^{90} + 28 q^{92} + 11 q^{93} + q^{94} - 14 q^{95} - 7 q^{96} + 13 q^{97} + 2 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 2 * q^2 + 3 * q^3 + 2 * q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 + 2 * q^11 - 2 * q^14 + 2 * q^16 - 2 * q^17 + 2 * q^18 + 13 * q^19 - 7 * q^20 - 3 * q^21 + 13 * q^22 + 3 * q^23 + 3 * q^24 - q^25 + 3 * q^27 + q^29 - 7 * q^30 + 11 * q^31 - 7 * q^32 + 2 * q^33 - 6 * q^34 + 4 * q^37 + 18 * q^38 + 7 * q^40 - 2 * q^41 - 2 * q^42 - 11 * q^43 + 21 * q^44 + 9 * q^46 + 19 * q^47 + 2 * q^48 + 3 * q^49 - 10 * q^50 - 2 * q^51 + 5 * q^53 + 2 * q^54 - 14 * q^55 - 3 * q^56 + 13 * q^57 + 10 * q^58 + 11 * q^59 - 7 * q^60 + 7 * q^61 - 9 * q^62 - 3 * q^63 - 11 * q^64 + 13 * q^66 + 15 * q^67 - 7 * q^68 + 3 * q^69 + 7 * q^70 + 18 * q^71 + 3 * q^72 + 6 * q^73 + 33 * q^74 - q^75 + 14 * q^76 - 2 * q^77 + 3 * q^79 + 3 * q^81 - 20 * q^82 + 2 * q^83 + 7 * q^85 - 5 * q^86 + q^87 + 9 * q^88 + 17 * q^89 - 7 * q^90 + 28 * q^92 + 11 * q^93 + q^94 - 14 * q^95 - 7 * q^96 + 13 * q^97 + 2 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

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