LMFDB - Embedded newform 3549.2.a.q.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 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			1.2
Root			$0.311108$ 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)

$f(q)$	$=$	$q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} -1.52543 q^{5} +0.311108 q^{6} -1.00000 q^{7} -1.21432 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} -1.52543 q^{5} +0.311108 q^{6} -1.00000 q^{7} -1.21432 q^{8} +1.00000 q^{9} -0.474572 q^{10} -1.09679 q^{11} -1.90321 q^{12} -0.311108 q^{14} -1.52543 q^{15} +3.42864 q^{16} +4.42864 q^{17} +0.311108 q^{18} +1.80642 q^{19} +2.90321 q^{20} -1.00000 q^{21} -0.341219 q^{22} +3.80642 q^{23} -1.21432 q^{24} -2.67307 q^{25} +1.00000 q^{27} +1.90321 q^{28} -0.755569 q^{29} -0.474572 q^{30} +4.85728 q^{31} +3.49532 q^{32} -1.09679 q^{33} +1.37778 q^{34} +1.52543 q^{35} -1.90321 q^{36} -5.80642 q^{37} +0.561993 q^{38} +1.85236 q^{40} -11.3319 q^{41} -0.311108 q^{42} +5.24443 q^{43} +2.08742 q^{44} -1.52543 q^{45} +1.18421 q^{46} -2.28100 q^{47} +3.42864 q^{48} +1.00000 q^{49} -0.831613 q^{50} +4.42864 q^{51} -6.00000 q^{53} +0.311108 q^{54} +1.67307 q^{55} +1.21432 q^{56} +1.80642 q^{57} -0.235063 q^{58} -0.474572 q^{59} +2.90321 q^{60} -13.0923 q^{61} +1.51114 q^{62} -1.00000 q^{63} -5.76986 q^{64} -0.341219 q^{66} -9.80642 q^{67} -8.42864 q^{68} +3.80642 q^{69} +0.474572 q^{70} +13.0049 q^{71} -1.21432 q^{72} +3.47949 q^{73} -1.80642 q^{74} -2.67307 q^{75} -3.43801 q^{76} +1.09679 q^{77} -5.37778 q^{79} -5.23014 q^{80} +1.00000 q^{81} -3.52543 q^{82} -13.8938 q^{83} +1.90321 q^{84} -6.75557 q^{85} +1.63158 q^{86} -0.755569 q^{87} +1.33185 q^{88} -13.1383 q^{89} -0.474572 q^{90} -7.24443 q^{92} +4.85728 q^{93} -0.709636 q^{94} -2.75557 q^{95} +3.49532 q^{96} -4.42864 q^{97} +0.311108 q^{98} -1.09679 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + q^4 + 2 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 8 q^{10} - 10 q^{11} + q^{12} - q^{14} + 2 q^{15} - 3 q^{16} + q^{18} - 8 q^{19} + 2 q^{20} - 3 q^{21} - 8 q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} + 3 q^{27} - q^{28} - 2 q^{29} - 8 q^{30} - 12 q^{31} - 3 q^{32} - 10 q^{33} + 4 q^{34} - 2 q^{35} + q^{36} - 4 q^{37} - 12 q^{38} + 12 q^{40} - 14 q^{41} - q^{42} + 16 q^{43} - 14 q^{44} + 2 q^{45} - 10 q^{46} - 3 q^{48} + 3 q^{49} - 29 q^{50} - 18 q^{53} + q^{54} - 8 q^{55} - 3 q^{56} - 8 q^{57} + 26 q^{58} - 8 q^{59} + 2 q^{60} + 14 q^{61} + 4 q^{62} - 3 q^{63} - 11 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 2 q^{69} + 8 q^{70} + 6 q^{71} + 3 q^{72} - 16 q^{73} + 8 q^{74} + 5 q^{75} - 24 q^{76} + 10 q^{77} - 16 q^{79} - 22 q^{80} + 3 q^{81} - 4 q^{82} - 8 q^{83} - q^{84} - 20 q^{85} + 32 q^{86} - 2 q^{87} - 16 q^{88} - 6 q^{89} - 8 q^{90} - 22 q^{92} - 12 q^{93} + 18 q^{94} - 8 q^{95} - 3 q^{96} + q^{98} - 10 q^{99}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + q^4 + 2 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 8 * q^10 - 10 * q^11 + q^12 - q^14 + 2 * q^15 - 3 * q^16 + q^18 - 8 * q^19 + 2 * q^20 - 3 * q^21 - 8 * q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 + 3 * q^27 - q^28 - 2 * q^29 - 8 * q^30 - 12 * q^31 - 3 * q^32 - 10 * q^33 + 4 * q^34 - 2 * q^35 + q^36 - 4 * q^37 - 12 * q^38 + 12 * q^40 - 14 * q^41 - q^42 + 16 * q^43 - 14 * q^44 + 2 * q^45 - 10 * q^46 - 3 * q^48 + 3 * q^49 - 29 * q^50 - 18 * q^53 + q^54 - 8 * q^55 - 3 * q^56 - 8 * q^57 + 26 * q^58 - 8 * q^59 + 2 * q^60 + 14 * q^61 + 4 * q^62 - 3 * q^63 - 11 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 2 * q^69 + 8 * q^70 + 6 * q^71 + 3 * q^72 - 16 * q^73 + 8 * q^74 + 5 * q^75 - 24 * q^76 + 10 * q^77 - 16 * q^79 - 22 * q^80 + 3 * q^81 - 4 * q^82 - 8 * q^83 - q^84 - 20 * q^85 + 32 * q^86 - 2 * q^87 - 16 * q^88 - 6 * q^89 - 8 * q^90 - 22 * q^92 - 12 * q^93 + 18 * q^94 - 8 * q^95 - 3 * q^96 + q^98 - 10 * 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 $

$2$	0.311108	0.219986	0.109993	−	0.993932i	$-0.464917\pi$
$2$	0.311108	0.219986	0.109993	+	0.993932i	$0.464917\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.90321	−0.951606
$5$	−1.52543	−0.682192	−0.341096	−	0.940028i	$-0.610798\pi$
$5$	−1.52543	−0.682192	−0.341096	+	0.940028i	$0.610798\pi$
$6$	0.311108	0.127009
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.21432	−0.429327
$9$	1.00000	0.333333
$10$	−0.474572	−0.150073
$11$	−1.09679	−0.330694	−0.165347	−	0.986235i	$-0.552874\pi$
$11$	−1.09679	−0.330694	−0.165347	+	0.986235i	$0.552874\pi$
$12$	−1.90321	−0.549410
$13$	0	0
$13$	0	0
$14$	−0.311108	−0.0831471
$15$	−1.52543	−0.393864
$16$	3.42864	0.857160
$17$	4.42864	1.07410	0.537051	−	0.843550i	$-0.319538\pi$
$17$	4.42864	1.07410	0.537051	+	0.843550i	$0.319538\pi$
$18$	0.311108	0.0733288
$19$	1.80642	0.414422	0.207211	−	0.978296i	$-0.433561\pi$
$19$	1.80642	0.414422	0.207211	+	0.978296i	$0.433561\pi$
$20$	2.90321	0.649178
$21$	−1.00000	−0.218218
$22$	−0.341219	−0.0727482
$23$	3.80642	0.793694	0.396847	−	0.917885i	$-0.370104\pi$
$23$	3.80642	0.793694	0.396847	+	0.917885i	$0.370104\pi$
$24$	−1.21432	−0.247872
$25$	−2.67307	−0.534614
$26$	0	0
$27$	1.00000	0.192450
$28$	1.90321	0.359673
$29$	−0.755569	−0.140306	−0.0701528	−	0.997536i	$-0.522349\pi$
$29$	−0.755569	−0.140306	−0.0701528	+	0.997536i	$0.522349\pi$
$30$	−0.474572	−0.0866447
$31$	4.85728	0.872393	0.436197	−	0.899851i	$-0.356325\pi$
$31$	4.85728	0.872393	0.436197	+	0.899851i	$0.356325\pi$
$32$	3.49532	0.617890
$33$	−1.09679	−0.190926
$34$	1.37778	0.236288
$35$	1.52543	0.257844
$36$	−1.90321	−0.317202
$37$	−5.80642	−0.954570	−0.477285	−	0.878749i	$-0.658379\pi$
$37$	−5.80642	−0.954570	−0.477285	+	0.878749i	$0.658379\pi$
$38$	0.561993	0.0911672
$39$	0	0
$40$	1.85236	0.292883
$41$	−11.3319	−1.76974	−0.884869	−	0.465840i	$-0.845752\pi$
$41$	−11.3319	−1.76974	−0.884869	+	0.465840i	$0.845752\pi$
$42$	−0.311108	−0.0480050
$43$	5.24443	0.799768	0.399884	−	0.916566i	$-0.369050\pi$
$43$	5.24443	0.799768	0.399884	+	0.916566i	$0.369050\pi$
$44$	2.08742	0.314690
$45$	−1.52543	−0.227397
$46$	1.18421	0.174602
$47$	−2.28100	−0.332718	−0.166359	−	0.986065i	$-0.553201\pi$
$47$	−2.28100	−0.332718	−0.166359	+	0.986065i	$0.553201\pi$
$48$	3.42864	0.494881
$49$	1.00000	0.142857
$50$	−0.831613	−0.117608
$51$	4.42864	0.620134
$52$	0	0
$53$	−6.00000	−0.824163	−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000	−0.824163	−0.412082	+	0.911147i	$0.635198\pi$
$54$	0.311108	0.0423364
$55$	1.67307	0.225597
$56$	1.21432	0.162270
$57$	1.80642	0.239267
$58$	−0.235063	−0.0308653
$59$	−0.474572	−0.0617841	−0.0308920	−	0.999523i	$-0.509835\pi$
$59$	−0.474572	−0.0617841	−0.0308920	+	0.999523i	$0.509835\pi$
$60$	2.90321	0.374803
$61$	−13.0923	−1.67630	−0.838151	−	0.545438i	$-0.816363\pi$
$61$	−13.0923	−1.67630	−0.838151	+	0.545438i	$0.816363\pi$
$62$	1.51114	0.191915
$63$	−1.00000	−0.125988
$64$	−5.76986	−0.721232
$65$	0	0
$66$	−0.341219	−0.0420012
$67$	−9.80642	−1.19805	−0.599023	−	0.800732i	$-0.704444\pi$
$67$	−9.80642	−1.19805	−0.599023	+	0.800732i	$0.704444\pi$
$68$	−8.42864	−1.02212
$69$	3.80642	0.458240
$70$	0.474572	0.0567223
$71$	13.0049	1.54340	0.771700	−	0.635987i	$-0.219407\pi$
$71$	13.0049	1.54340	0.771700	+	0.635987i	$0.219407\pi$
$72$	−1.21432	−0.143109
$73$	3.47949	0.407244	0.203622	−	0.979050i	$-0.434729\pi$
$73$	3.47949	0.407244	0.203622	+	0.979050i	$0.434729\pi$
$74$	−1.80642	−0.209993
$75$	−2.67307	−0.308660
$76$	−3.43801	−0.394366
$77$	1.09679	0.124991
$78$	0	0
$79$	−5.37778	−0.605048	−0.302524	−	0.953142i	$-0.597829\pi$
$79$	−5.37778	−0.605048	−0.302524	+	0.953142i	$0.597829\pi$
$80$	−5.23014	−0.584748
$81$	1.00000	0.111111
$82$	−3.52543	−0.389318
$83$	−13.8938	−1.52505	−0.762524	−	0.646960i	$-0.776040\pi$
$83$	−13.8938	−1.52505	−0.762524	+	0.646960i	$0.776040\pi$
$84$	1.90321	0.207657
$85$	−6.75557	−0.732744
$86$	1.63158	0.175938
$87$	−0.755569	−0.0810055
$88$	1.33185	0.141976
$89$	−13.1383	−1.39265	−0.696327	−	0.717724i	$-0.745184\pi$
$89$	−13.1383	−1.39265	−0.696327	+	0.717724i	$0.745184\pi$
$90$	−0.474572	−0.0500243
$91$	0	0
$92$	−7.24443	−0.755284
$93$	4.85728	0.503676
$94$	−0.709636	−0.0731933
$95$	−2.75557	−0.282715
$96$	3.49532	0.356739
$97$	−4.42864	−0.449660	−0.224830	−	0.974398i	$-0.572183\pi$
$97$	−4.42864	−0.449660	−0.224830	+	0.974398i	$0.572183\pi$
$98$	0.311108	0.0314266
$99$	−1.09679	−0.110231
$100$	5.08742	0.508742
$101$	−9.28592	−0.923983	−0.461992	−	0.886884i	$-0.652865\pi$
$101$	−9.28592	−0.923983	−0.461992	+	0.886884i	$0.652865\pi$
$102$	1.37778	0.136421
$103$	−0.815792	−0.0803824	−0.0401912	−	0.999192i	$-0.512797\pi$
$103$	−0.815792	−0.0803824	−0.0401912	+	0.999192i	$0.512797\pi$
$104$	0	0
$105$	1.52543	0.148866
$106$	−1.86665	−0.181305
$107$	6.56199	0.634372	0.317186	−	0.948363i	$-0.397262\pi$
$107$	6.56199	0.634372	0.317186	+	0.948363i	$0.397262\pi$
$108$	−1.90321	−0.183137
$109$	−12.2953	−1.17767	−0.588837	−	0.808252i	$-0.700414\pi$
$109$	−12.2953	−1.17767	−0.588837	+	0.808252i	$0.700414\pi$
$110$	0.520505	0.0496282
$111$	−5.80642	−0.551121
$112$	−3.42864	−0.323976
$113$	3.24443	0.305210	0.152605	−	0.988287i	$-0.451234\pi$
$113$	3.24443	0.305210	0.152605	+	0.988287i	$0.451234\pi$
$114$	0.561993	0.0526354
$115$	−5.80642	−0.541452
$116$	1.43801	0.133516
$117$	0	0
$118$	−0.147643	−0.0135917
$119$	−4.42864	−0.405973
$120$	1.85236	0.169096
$121$	−9.79706	−0.890641
$122$	−4.07313	−0.368764
$123$	−11.3319	−1.02176
$124$	−9.24443	−0.830174
$125$	11.7047	1.04690
$126$	−0.311108	−0.0277157
$127$	−2.62222	−0.232684	−0.116342	−	0.993209i	$-0.537117\pi$
$127$	−2.62222	−0.232684	−0.116342	+	0.993209i	$0.537117\pi$
$128$	−8.78568	−0.776552
$129$	5.24443	0.461746
$130$	0	0
$131$	18.3684	1.60486	0.802428	−	0.596749i	$-0.203541\pi$
$131$	18.3684	1.60486	0.802428	+	0.596749i	$0.203541\pi$
$132$	2.08742	0.181687
$133$	−1.80642	−0.156637
$134$	−3.05086	−0.263554
$135$	−1.52543	−0.131288
$136$	−5.37778	−0.461141
$137$	−16.3827	−1.39967	−0.699835	−	0.714305i	$-0.746743\pi$
$137$	−16.3827	−1.39967	−0.699835	+	0.714305i	$0.746743\pi$
$138$	1.18421	0.100806
$139$	3.18421	0.270081	0.135041	−	0.990840i	$-0.456884\pi$
$139$	3.18421	0.270081	0.135041	+	0.990840i	$0.456884\pi$
$140$	−2.90321	−0.245366
$141$	−2.28100	−0.192095
$142$	4.04593	0.339527
$143$	0	0
$144$	3.42864	0.285720
$145$	1.15257	0.0957153
$146$	1.08250	0.0895882
$147$	1.00000	0.0824786
$148$	11.0509	0.908375
$149$	16.0874	1.31793	0.658966	−	0.752172i	$-0.270994\pi$
$149$	16.0874	1.31793	0.658966	+	0.752172i	$0.270994\pi$
$150$	−0.831613	−0.0679009
$151$	1.51114	0.122975	0.0614873	−	0.998108i	$-0.480416\pi$
$151$	1.51114	0.122975	0.0614873	+	0.998108i	$0.480416\pi$
$152$	−2.19358	−0.177923
$153$	4.42864	0.358034
$154$	0.341219	0.0274962
$155$	−7.40943	−0.595140
$156$	0	0
$157$	2.85728	0.228036	0.114018	−	0.993479i	$-0.463628\pi$
$157$	2.85728	0.228036	0.114018	+	0.993479i	$0.463628\pi$
$158$	−1.67307	−0.133102
$159$	−6.00000	−0.475831
$160$	−5.33185	−0.421520
$161$	−3.80642	−0.299988
$162$	0.311108	0.0244429
$163$	−13.8064	−1.08140	−0.540701	−	0.841215i	$-0.681841\pi$
$163$	−13.8064	−1.08140	−0.540701	+	0.841215i	$0.681841\pi$
$164$	21.5669	1.68409
$165$	1.67307	0.130248
$166$	−4.32248	−0.335490
$167$	−0.769859	−0.0595735	−0.0297867	−	0.999556i	$-0.509483\pi$
$167$	−0.769859	−0.0595735	−0.0297867	+	0.999556i	$0.509483\pi$
$168$	1.21432	0.0936868
$169$	0	0
$170$	−2.10171	−0.161194
$171$	1.80642	0.138141
$172$	−9.98126	−0.761064
$173$	−5.67307	−0.431316	−0.215658	−	0.976469i	$-0.569190\pi$
$173$	−5.67307	−0.431316	−0.215658	+	0.976469i	$0.569190\pi$
$174$	−0.235063	−0.0178201
$175$	2.67307	0.202065
$176$	−3.76049	−0.283458
$177$	−0.474572	−0.0356710
$178$	−4.08742	−0.306365
$179$	−21.9081	−1.63749	−0.818745	−	0.574157i	$-0.805330\pi$
$179$	−21.9081	−1.63749	−0.818745	+	0.574157i	$0.805330\pi$
$180$	2.90321	0.216393
$181$	−0.488863	−0.0363369	−0.0181684	−	0.999835i	$-0.505784\pi$
$181$	−0.488863	−0.0363369	−0.0181684	+	0.999835i	$0.505784\pi$
$182$	0	0
$183$	−13.0923	−0.967814
$184$	−4.62222	−0.340754
$185$	8.85728	0.651200
$186$	1.51114	0.110802
$187$	−4.85728	−0.355199
$188$	4.34122	0.316616
$189$	−1.00000	−0.0727393
$190$	−0.857279	−0.0621936
$191$	25.1338	1.81862	0.909310	−	0.416119i	$-0.136610\pi$
$191$	25.1338	1.81862	0.909310	+	0.416119i	$0.136610\pi$
$192$	−5.76986	−0.416404
$193$	6.66370	0.479664	0.239832	−	0.970814i	$-0.422908\pi$
$193$	6.66370	0.479664	0.239832	+	0.970814i	$0.422908\pi$
$194$	−1.37778	−0.0989192
$195$	0	0
$196$	−1.90321	−0.135944
$197$	−18.1891	−1.29592	−0.647961	−	0.761674i	$-0.724378\pi$
$197$	−18.1891	−1.29592	−0.647961	+	0.761674i	$0.724378\pi$
$198$	−0.341219	−0.0242494
$199$	14.1017	0.999644	0.499822	−	0.866128i	$-0.333399\pi$
$199$	14.1017	0.999644	0.499822	+	0.866128i	$0.333399\pi$
$200$	3.24596	0.229524
$201$	−9.80642	−0.691692
$202$	−2.88892	−0.203264
$203$	0.755569	0.0530305
$204$	−8.42864	−0.590123
$205$	17.2859	1.20730
$206$	−0.253799	−0.0176830
$207$	3.80642	0.264565
$208$	0	0
$209$	−1.98126	−0.137047
$210$	0.474572	0.0327486
$211$	8.13335	0.559923	0.279962	−	0.960011i	$-0.409678\pi$
$211$	8.13335	0.559923	0.279962	+	0.960011i	$0.409678\pi$
$212$	11.4193	0.784279
$213$	13.0049	0.891083
$214$	2.04149	0.139553
$215$	−8.00000	−0.545595
$216$	−1.21432	−0.0826240
$217$	−4.85728	−0.329734
$218$	−3.82516	−0.259073
$219$	3.47949	0.235122
$220$	−3.18421	−0.214679
$221$	0	0
$222$	−1.80642	−0.121239
$223$	−9.53972	−0.638827	−0.319413	−	0.947615i	$-0.603486\pi$
$223$	−9.53972	−0.638827	−0.319413	+	0.947615i	$0.603486\pi$
$224$	−3.49532	−0.233541
$225$	−2.67307	−0.178205
$226$	1.00937	0.0671422
$227$	1.81087	0.120192	0.0600958	−	0.998193i	$-0.480859\pi$
$227$	1.81087	0.120192	0.0600958	+	0.998193i	$0.480859\pi$
$228$	−3.43801	−0.227688
$229$	13.9684	0.923055	0.461528	−	0.887126i	$-0.347302\pi$
$229$	13.9684	0.923055	0.461528	+	0.887126i	$0.347302\pi$
$230$	−1.80642	−0.119112
$231$	1.09679	0.0721634
$232$	0.917502	0.0602370
$233$	7.51114	0.492071	0.246035	−	0.969261i	$-0.420872\pi$
$233$	7.51114	0.492071	0.246035	+	0.969261i	$0.420872\pi$
$234$	0	0
$235$	3.47949	0.226977
$236$	0.903212	0.0587941
$237$	−5.37778	−0.349325
$238$	−1.37778	−0.0893085
$239$	−21.9541	−1.42009	−0.710045	−	0.704156i	$-0.751326\pi$
$239$	−21.9541	−1.42009	−0.710045	+	0.704156i	$0.751326\pi$
$240$	−5.23014	−0.337604
$241$	−25.8479	−1.66501	−0.832505	−	0.554017i	$-0.813094\pi$
$241$	−25.8479	−1.66501	−0.832505	+	0.554017i	$0.813094\pi$
$242$	−3.04794	−0.195929
$243$	1.00000	0.0641500
$244$	24.9175	1.59518
$245$	−1.52543	−0.0974560
$246$	−3.52543	−0.224773
$247$	0	0
$248$	−5.89829	−0.374542
$249$	−13.8938	−0.880487
$250$	3.64143	0.230304
$251$	−23.2257	−1.46599	−0.732996	−	0.680232i	$-0.761879\pi$
$251$	−23.2257	−1.46599	−0.732996	+	0.680232i	$0.761879\pi$
$252$	1.90321	0.119891
$253$	−4.17484	−0.262470
$254$	−0.815792	−0.0511873
$255$	−6.75557	−0.423050
$256$	8.80642	0.550401
$257$	27.7748	1.73254	0.866272	−	0.499573i	$-0.166510\pi$
$257$	27.7748	1.73254	0.866272	+	0.499573i	$0.166510\pi$
$258$	1.63158	0.101578
$259$	5.80642	0.360794
$260$	0	0
$261$	−0.755569	−0.0467685
$262$	5.71456	0.353047
$263$	−6.68244	−0.412057	−0.206028	−	0.978546i	$-0.566054\pi$
$263$	−6.68244	−0.412057	−0.206028	+	0.978546i	$0.566054\pi$
$264$	1.33185	0.0819698
$265$	9.15257	0.562238
$266$	−0.561993	−0.0344580
$267$	−13.1383	−0.804049
$268$	18.6637	1.14007
$269$	−22.1432	−1.35009	−0.675047	−	0.737774i	$-0.735877\pi$
$269$	−22.1432	−1.35009	−0.675047	+	0.737774i	$0.735877\pi$
$270$	−0.474572	−0.0288816
$271$	2.19358	0.133250	0.0666251	−	0.997778i	$-0.478777\pi$
$271$	2.19358	0.133250	0.0666251	+	0.997778i	$0.478777\pi$
$272$	15.1842	0.920678
$273$	0	0
$274$	−5.09679	−0.307908
$275$	2.93179	0.176794
$276$	−7.24443	−0.436064
$277$	27.3274	1.64194	0.820972	−	0.570968i	$-0.193432\pi$
$277$	27.3274	1.64194	0.820972	+	0.570968i	$0.193432\pi$
$278$	0.990632	0.0594142
$279$	4.85728	0.290798
$280$	−1.85236	−0.110699
$281$	22.8430	1.36270	0.681349	−	0.731958i	$-0.261394\pi$
$281$	22.8430	1.36270	0.681349	+	0.731958i	$0.261394\pi$
$282$	−0.709636	−0.0422582
$283$	−21.1240	−1.25569	−0.627845	−	0.778338i	$-0.716063\pi$
$283$	−21.1240	−1.25569	−0.627845	+	0.778338i	$0.716063\pi$
$284$	−24.7511	−1.46871
$285$	−2.75557	−0.163226
$286$	0	0
$287$	11.3319	0.668898
$288$	3.49532	0.205963
$289$	2.61285	0.153697
$290$	0.358572	0.0210561
$291$	−4.42864	−0.259611
$292$	−6.62222	−0.387536
$293$	11.6271	0.679265	0.339632	−	0.940558i	$-0.389697\pi$
$293$	11.6271	0.679265	0.339632	+	0.940558i	$0.389697\pi$
$294$	0.311108	0.0181442
$295$	0.723926	0.0421486
$296$	7.05086	0.409823
$297$	−1.09679	−0.0636421
$298$	5.00492	0.289927
$299$	0	0
$300$	5.08742	0.293722
$301$	−5.24443	−0.302284
$302$	0.470127	0.0270528
$303$	−9.28592	−0.533462
$304$	6.19358	0.355226
$305$	19.9714	1.14356
$306$	1.37778	0.0787627
$307$	−32.8573	−1.87526	−0.937632	−	0.347629i	$-0.886987\pi$
$307$	−32.8573	−1.87526	−0.937632	+	0.347629i	$0.886987\pi$
$308$	−2.08742	−0.118942
$309$	−0.815792	−0.0464088
$310$	−2.30513	−0.130923
$311$	−18.3684	−1.04158	−0.520789	−	0.853686i	$-0.674362\pi$
$311$	−18.3684	−1.04158	−0.520789	+	0.853686i	$0.674362\pi$
$312$	0	0
$313$	7.11108	0.401942	0.200971	−	0.979597i	$-0.435590\pi$
$313$	7.11108	0.401942	0.200971	+	0.979597i	$0.435590\pi$
$314$	0.888922	0.0501648
$315$	1.52543	0.0859481
$316$	10.2351	0.575767
$317$	−8.47457	−0.475979	−0.237990	−	0.971268i	$-0.576488\pi$
$317$	−8.47457	−0.475979	−0.237990	+	0.971268i	$0.576488\pi$
$318$	−1.86665	−0.104676
$319$	0.828699	0.0463982
$320$	8.80150	0.492019
$321$	6.56199	0.366255
$322$	−1.18421	−0.0659933
$323$	8.00000	0.445132
$324$	−1.90321	−0.105734
$325$	0	0
$326$	−4.29529	−0.237894
$327$	−12.2953	−0.679931
$328$	13.7605	0.759796
$329$	2.28100	0.125755
$330$	0.520505	0.0286529
$331$	−28.2034	−1.55020	−0.775100	−	0.631838i	$-0.782301\pi$
$331$	−28.2034	−1.55020	−0.775100	+	0.631838i	$0.782301\pi$
$332$	26.4429	1.45124
$333$	−5.80642	−0.318190
$334$	−0.239509	−0.0131054
$335$	14.9590	0.817297
$336$	−3.42864	−0.187048
$337$	−24.5303	−1.33625	−0.668127	−	0.744048i	$-0.732904\pi$
$337$	−24.5303	−1.33625	−0.668127	+	0.744048i	$0.732904\pi$
$338$	0	0
$339$	3.24443	0.176213
$340$	12.8573	0.697284
$341$	−5.32741	−0.288495
$342$	0.561993	0.0303891
$343$	−1.00000	−0.0539949
$344$	−6.36842	−0.343362
$345$	−5.80642	−0.312607
$346$	−1.76494	−0.0948836
$347$	−9.52098	−0.511113	−0.255557	−	0.966794i	$-0.582259\pi$
$347$	−9.52098	−0.511113	−0.255557	+	0.966794i	$0.582259\pi$
$348$	1.43801	0.0770853
$349$	−9.37778	−0.501981	−0.250991	−	0.967990i	$-0.580756\pi$
$349$	−9.37778	−0.501981	−0.250991	+	0.967990i	$0.580756\pi$
$350$	0.831613	0.0444516
$351$	0	0
$352$	−3.83362	−0.204333
$353$	11.5067	0.612439	0.306220	−	0.951961i	$-0.400936\pi$
$353$	11.5067	0.612439	0.306220	+	0.951961i	$0.400936\pi$
$354$	−0.147643	−0.00784715
$355$	−19.8381	−1.05290
$356$	25.0049	1.32526
$357$	−4.42864	−0.234388
$358$	−6.81579	−0.360226
$359$	15.3733	0.811374	0.405687	−	0.914012i	$-0.367032\pi$
$359$	15.3733	0.811374	0.405687	+	0.914012i	$0.367032\pi$
$360$	1.85236	0.0976278
$361$	−15.7368	−0.828254
$362$	−0.152089	−0.00799362
$363$	−9.79706	−0.514212
$364$	0	0
$365$	−5.30772	−0.277819
$366$	−4.07313	−0.212906
$367$	−24.8988	−1.29971	−0.649853	−	0.760060i	$-0.725169\pi$
$367$	−24.8988	−1.29971	−0.649853	+	0.760060i	$0.725169\pi$
$368$	13.0509	0.680323
$369$	−11.3319	−0.589913
$370$	2.75557	0.143255
$371$	6.00000	0.311504
$372$	−9.24443	−0.479301
$373$	17.1842	0.889765	0.444882	−	0.895589i	$-0.353246\pi$
$373$	17.1842	0.889765	0.444882	+	0.895589i	$0.353246\pi$
$374$	−1.51114	−0.0781391
$375$	11.7047	0.604429
$376$	2.76986	0.142845
$377$	0	0
$378$	−0.311108	−0.0160017
$379$	−13.1240	−0.674134	−0.337067	−	0.941481i	$-0.609435\pi$
$379$	−13.1240	−0.674134	−0.337067	+	0.941481i	$0.609435\pi$
$380$	5.24443	0.269034
$381$	−2.62222	−0.134340
$382$	7.81933	0.400072
$383$	30.7511	1.57131	0.785654	−	0.618666i	$-0.212326\pi$
$383$	30.7511	1.57131	0.785654	+	0.618666i	$0.212326\pi$
$384$	−8.78568	−0.448342
$385$	−1.67307	−0.0852676
$386$	2.07313	0.105520
$387$	5.24443	0.266589
$388$	8.42864	0.427899
$389$	14.8573	0.753294	0.376647	−	0.926357i	$-0.377077\pi$
$389$	14.8573	0.753294	0.376647	+	0.926357i	$0.377077\pi$
$390$	0	0
$391$	16.8573	0.852509
$392$	−1.21432	−0.0613324
$393$	18.3684	0.926564
$394$	−5.65878	−0.285085
$395$	8.20342	0.412759
$396$	2.08742	0.104897
$397$	5.93978	0.298109	0.149054	−	0.988829i	$-0.452377\pi$
$397$	5.93978	0.298109	0.149054	+	0.988829i	$0.452377\pi$
$398$	4.38715	0.219908
$399$	−1.80642	−0.0904343
$400$	−9.16500	−0.458250
$401$	6.87157	0.343150	0.171575	−	0.985171i	$-0.445114\pi$
$401$	6.87157	0.343150	0.171575	+	0.985171i	$0.445114\pi$
$402$	−3.05086	−0.152163
$403$	0	0
$404$	17.6731	0.879268
$405$	−1.52543	−0.0757991
$406$	0.235063	0.0116660
$407$	6.36842	0.315671
$408$	−5.37778	−0.266240
$409$	31.0005	1.53287	0.766437	−	0.642319i	$-0.222028\pi$
$409$	31.0005	1.53287	0.766437	+	0.642319i	$0.222028\pi$
$410$	5.37778	0.265590
$411$	−16.3827	−0.808099
$412$	1.55262	0.0764923
$413$	0.474572	0.0233522
$414$	1.18421	0.0582007
$415$	21.1941	1.04038
$416$	0	0
$417$	3.18421	0.155931
$418$	−0.616387	−0.0301485
$419$	5.32741	0.260261	0.130130	−	0.991497i	$-0.458460\pi$
$419$	5.32741	0.260261	0.130130	+	0.991497i	$0.458460\pi$
$420$	−2.90321	−0.141662
$421$	−11.2257	−0.547107	−0.273553	−	0.961857i	$-0.588199\pi$
$421$	−11.2257	−0.547107	−0.273553	+	0.961857i	$0.588199\pi$
$422$	2.53035	0.123175
$423$	−2.28100	−0.110906
$424$	7.28592	0.353835
$425$	−11.8381	−0.574231
$426$	4.04593	0.196026
$427$	13.0923	0.633583
$428$	−12.4889	−0.603672
$429$	0	0
$430$	−2.48886	−0.120024
$431$	15.1985	0.732086	0.366043	−	0.930598i	$-0.380712\pi$
$431$	15.1985	0.732086	0.366043	+	0.930598i	$0.380712\pi$
$432$	3.42864	0.164960
$433$	8.82564	0.424133	0.212067	−	0.977255i	$-0.431981\pi$
$433$	8.82564	0.424133	0.212067	+	0.977255i	$0.431981\pi$
$434$	−1.51114	−0.0725369
$435$	1.15257	0.0552613
$436$	23.4005	1.12068
$437$	6.87601	0.328924
$438$	1.08250	0.0517238
$439$	23.1842	1.10652	0.553261	−	0.833008i	$-0.313383\pi$
$439$	23.1842	1.10652	0.553261	+	0.833008i	$0.313383\pi$
$440$	−2.03164	−0.0968548
$441$	1.00000	0.0476190
$442$	0	0
$443$	10.2953	0.489144	0.244572	−	0.969631i	$-0.421353\pi$
$443$	10.2953	0.489144	0.244572	+	0.969631i	$0.421353\pi$
$444$	11.0509	0.524450
$445$	20.0415	0.950058
$446$	−2.96788	−0.140533
$447$	16.0874	0.760909
$448$	5.76986	0.272600
$449$	35.6084	1.68046	0.840232	−	0.542227i	$-0.182419\pi$
$449$	35.6084	1.68046	0.840232	+	0.542227i	$0.182419\pi$
$450$	−0.831613	−0.0392026
$451$	12.4286	0.585242
$452$	−6.17484	−0.290440
$453$	1.51114	0.0709994
$454$	0.563376	0.0264405
$455$	0	0
$456$	−2.19358	−0.102724
$457$	−27.2543	−1.27490	−0.637451	−	0.770491i	$-0.720011\pi$
$457$	−27.2543	−1.27490	−0.637451	+	0.770491i	$0.720011\pi$
$458$	4.34567	0.203060
$459$	4.42864	0.206711
$460$	11.0509	0.515249
$461$	28.7797	1.34040	0.670202	−	0.742179i	$-0.266207\pi$
$461$	28.7797	1.34040	0.670202	+	0.742179i	$0.266207\pi$
$462$	0.341219	0.0158750
$463$	−29.4193	−1.36723	−0.683615	−	0.729843i	$-0.739593\pi$
$463$	−29.4193	−1.36723	−0.683615	+	0.729843i	$0.739593\pi$
$464$	−2.59057	−0.120264
$465$	−7.40943	−0.343604
$466$	2.33677	0.108249
$467$	7.14272	0.330526	0.165263	−	0.986250i	$-0.447153\pi$
$467$	7.14272	0.330526	0.165263	+	0.986250i	$0.447153\pi$
$468$	0	0
$469$	9.80642	0.452819
$470$	1.08250	0.0499319
$471$	2.85728	0.131656
$472$	0.576283	0.0265256
$473$	−5.75203	−0.264479
$474$	−1.67307	−0.0768467
$475$	−4.82870	−0.221556
$476$	8.42864	0.386326
$477$	−6.00000	−0.274721
$478$	−6.83008	−0.312401
$479$	−16.5575	−0.756534	−0.378267	−	0.925697i	$-0.623480\pi$
$479$	−16.5575	−0.756534	−0.378267	+	0.925697i	$0.623480\pi$
$480$	−5.33185	−0.243365
$481$	0	0
$482$	−8.04149	−0.366280
$483$	−3.80642	−0.173198
$484$	18.6459	0.847540
$485$	6.75557	0.306755
$486$	0.311108	0.0141121
$487$	−21.7146	−0.983981	−0.491990	−	0.870601i	$-0.663730\pi$
$487$	−21.7146	−0.983981	−0.491990	+	0.870601i	$0.663730\pi$
$488$	15.8983	0.719682
$489$	−13.8064	−0.624348
$490$	−0.474572	−0.0214390
$491$	−26.1748	−1.18125	−0.590627	−	0.806945i	$-0.701120\pi$
$491$	−26.1748	−1.18125	−0.590627	+	0.806945i	$0.701120\pi$
$492$	21.5669	0.972312
$493$	−3.34614	−0.150703
$494$	0	0
$495$	1.67307	0.0751989
$496$	16.6539	0.747780
$497$	−13.0049	−0.583350
$498$	−4.32248	−0.193695
$499$	24.9403	1.11648	0.558240	−	0.829680i	$-0.311477\pi$
$499$	24.9403	1.11648	0.558240	+	0.829680i	$0.311477\pi$
$500$	−22.2766	−0.996238
$501$	−0.769859	−0.0343948
$502$	−7.22570	−0.322499
$503$	−14.6351	−0.652548	−0.326274	−	0.945275i	$-0.605793\pi$
$503$	−14.6351	−0.652548	−0.326274	+	0.945275i	$0.605793\pi$
$504$	1.21432	0.0540901
$505$	14.1650	0.630334
$506$	−1.29883	−0.0577398
$507$	0	0
$508$	4.99063	0.221423
$509$	7.59856	0.336800	0.168400	−	0.985719i	$-0.446140\pi$
$509$	7.59856	0.336800	0.168400	+	0.985719i	$0.446140\pi$
$510$	−2.10171	−0.0930653
$511$	−3.47949	−0.153924
$512$	20.3111	0.897633
$513$	1.80642	0.0797556
$514$	8.64095	0.381136
$515$	1.24443	0.0548362
$516$	−9.98126	−0.439401
$517$	2.50177	0.110028
$518$	1.80642	0.0793697
$519$	−5.67307	−0.249020
$520$	0	0
$521$	−25.7560	−1.12839	−0.564196	−	0.825641i	$-0.690814\pi$
$521$	−25.7560	−1.12839	−0.564196	+	0.825641i	$0.690814\pi$
$522$	−0.235063	−0.0102884
$523$	−19.5081	−0.853029	−0.426514	−	0.904481i	$-0.640259\pi$
$523$	−19.5081	−0.853029	−0.426514	+	0.904481i	$0.640259\pi$
$524$	−34.9590	−1.52719
$525$	2.67307	0.116662
$526$	−2.07896	−0.0906469
$527$	21.5111	0.937040
$528$	−3.76049	−0.163654
$529$	−8.51114	−0.370049
$530$	2.84743	0.123685
$531$	−0.474572	−0.0205947
$532$	3.43801	0.149057
$533$	0	0
$534$	−4.08742	−0.176880
$535$	−10.0098	−0.432763
$536$	11.9081	0.514353
$537$	−21.9081	−0.945406
$538$	−6.88892	−0.297003
$539$	−1.09679	−0.0472420
$540$	2.90321	0.124934
$541$	−43.8163	−1.88381	−0.941904	−	0.335881i	$-0.890966\pi$
$541$	−43.8163	−1.88381	−0.941904	+	0.335881i	$0.890966\pi$
$542$	0.682439	0.0293133
$543$	−0.488863	−0.0209791
$544$	15.4795	0.663678
$545$	18.7556	0.803400
$546$	0	0
$547$	−43.2257	−1.84820	−0.924099	−	0.382154i	$-0.875182\pi$
$547$	−43.2257	−1.84820	−0.924099	+	0.382154i	$0.875182\pi$
$548$	31.1798	1.33193
$549$	−13.0923	−0.558768
$550$	0.912103	0.0388922
$551$	−1.36488	−0.0581457
$552$	−4.62222	−0.196735
$553$	5.37778	0.228687
$554$	8.50177	0.361206
$555$	8.85728	0.375971
$556$	−6.06022	−0.257011
$557$	−11.5254	−0.488348	−0.244174	−	0.969731i	$-0.578517\pi$
$557$	−11.5254	−0.488348	−0.244174	+	0.969731i	$0.578517\pi$
$558$	1.51114	0.0639715
$559$	0	0
$560$	5.23014	0.221014
$561$	−4.85728	−0.205074
$562$	7.10663	0.299775
$563$	44.2034	1.86295	0.931476	−	0.363803i	$-0.118522\pi$
$563$	44.2034	1.86295	0.931476	+	0.363803i	$0.118522\pi$
$564$	4.34122	0.182798
$565$	−4.94914	−0.208212
$566$	−6.57184	−0.276235
$567$	−1.00000	−0.0419961
$568$	−15.7921	−0.662623
$569$	33.4924	1.40407	0.702037	−	0.712140i	$-0.252274\pi$
$569$	33.4924	1.40407	0.702037	+	0.712140i	$0.252274\pi$
$570$	−0.857279	−0.0359075
$571$	−2.23506	−0.0935345	−0.0467672	−	0.998906i	$-0.514892\pi$
$571$	−2.23506	−0.0935345	−0.0467672	+	0.998906i	$0.514892\pi$
$572$	0	0
$573$	25.1338	1.04998
$574$	3.52543	0.147149
$575$	−10.1748	−0.424320
$576$	−5.76986	−0.240411
$577$	−20.0415	−0.834338	−0.417169	−	0.908829i	$-0.636978\pi$
$577$	−20.0415	−0.834338	−0.417169	+	0.908829i	$0.636978\pi$
$578$	0.812877	0.0338112
$579$	6.66370	0.276934
$580$	−2.19358	−0.0910833
$581$	13.8938	0.576414
$582$	−1.37778	−0.0571110
$583$	6.58073	0.272546
$584$	−4.22522	−0.174841
$585$	0	0
$586$	3.61729	0.149429
$587$	14.1891	0.585648	0.292824	−	0.956166i	$-0.405405\pi$
$587$	14.1891	0.585648	0.292824	+	0.956166i	$0.405405\pi$
$588$	−1.90321	−0.0784871
$589$	8.77430	0.361539
$590$	0.225219	0.00927212
$591$	−18.1891	−0.748201
$592$	−19.9081	−0.818219
$593$	20.6593	0.848374	0.424187	−	0.905575i	$-0.360560\pi$
$593$	20.6593	0.848374	0.424187	+	0.905575i	$0.360560\pi$
$594$	−0.341219	−0.0140004
$595$	6.75557	0.276951
$596$	−30.6178	−1.25415
$597$	14.1017	0.577145
$598$	0	0
$599$	−36.1561	−1.47730	−0.738649	−	0.674090i	$-0.764536\pi$
$599$	−36.1561	−1.47730	−0.738649	+	0.674090i	$0.764536\pi$
$600$	3.24596	0.132516
$601$	−45.6829	−1.86344	−0.931722	−	0.363171i	$-0.881694\pi$
$601$	−45.6829	−1.86344	−0.931722	+	0.363171i	$0.881694\pi$
$602$	−1.63158	−0.0664984
$603$	−9.80642	−0.399348
$604$	−2.87601	−0.117023
$605$	14.9447	0.607588
$606$	−2.88892	−0.117354
$607$	−11.8381	−0.480492	−0.240246	−	0.970712i	$-0.577228\pi$
$607$	−11.8381	−0.480492	−0.240246	+	0.970712i	$0.577228\pi$
$608$	6.31402	0.256067
$609$	0.755569	0.0306172
$610$	6.21326	0.251568
$611$	0	0
$612$	−8.42864	−0.340708
$613$	14.9590	0.604188	0.302094	−	0.953278i	$-0.402314\pi$
$613$	14.9590	0.604188	0.302094	+	0.953278i	$0.402314\pi$
$614$	−10.2222	−0.412533
$615$	17.2859	0.697036
$616$	−1.33185	−0.0536618
$617$	2.49331	0.100377	0.0501884	−	0.998740i	$-0.484018\pi$
$617$	2.49331	0.100377	0.0501884	+	0.998740i	$0.484018\pi$
$618$	−0.253799	−0.0102093
$619$	−25.1526	−1.01097	−0.505483	−	0.862836i	$-0.668686\pi$
$619$	−25.1526	−1.01097	−0.505483	+	0.862836i	$0.668686\pi$
$620$	14.1017	0.566338
$621$	3.80642	0.152747
$622$	−5.71456	−0.229133
$623$	13.1383	0.526374
$624$	0	0
$625$	−4.48934	−0.179574
$626$	2.21231	0.0884218
$627$	−1.98126	−0.0791241
$628$	−5.43801	−0.217000
$629$	−25.7146	−1.02531
$630$	0.474572	0.0189074
$631$	40.1116	1.59682	0.798408	−	0.602117i	$-0.205676\pi$
$631$	40.1116	1.59682	0.798408	+	0.602117i	$0.205676\pi$
$632$	6.53035	0.259763
$633$	8.13335	0.323272
$634$	−2.63651	−0.104709
$635$	4.00000	0.158735
$636$	11.4193	0.452804
$637$	0	0
$638$	0.257815	0.0102070
$639$	13.0049	0.514467
$640$	13.4019	0.529757
$641$	−35.5308	−1.40338	−0.701692	−	0.712481i	$-0.747572\pi$
$641$	−35.5308	−1.40338	−0.701692	+	0.712481i	$0.747572\pi$
$642$	2.04149	0.0805711
$643$	−13.2444	−0.522309	−0.261155	−	0.965297i	$-0.584103\pi$
$643$	−13.2444	−0.522309	−0.261155	+	0.965297i	$0.584103\pi$
$644$	7.24443	0.285471
$645$	−8.00000	−0.315000
$646$	2.48886	0.0979230
$647$	−0.120446	−0.00473523	−0.00236761	−	0.999997i	$-0.500754\pi$
$647$	−0.120446	−0.00473523	−0.00236761	+	0.999997i	$0.500754\pi$
$648$	−1.21432	−0.0477030
$649$	0.520505	0.0204316
$650$	0	0
$651$	−4.85728	−0.190372
$652$	26.2766	1.02907
$653$	−15.7146	−0.614958	−0.307479	−	0.951555i	$-0.599485\pi$
$653$	−15.7146	−0.614958	−0.307479	+	0.951555i	$0.599485\pi$
$654$	−3.82516	−0.149576
$655$	−28.0197	−1.09482
$656$	−38.8528	−1.51695
$657$	3.47949	0.135748
$658$	0.709636	0.0276645
$659$	14.1748	0.552173	0.276087	−	0.961133i	$-0.410962\pi$
$659$	14.1748	0.552173	0.276087	+	0.961133i	$0.410962\pi$
$660$	−3.18421	−0.123945
$661$	7.21279	0.280545	0.140272	−	0.990113i	$-0.455202\pi$
$661$	7.21279	0.280545	0.140272	+	0.990113i	$0.455202\pi$
$662$	−8.77430	−0.341023
$663$	0	0
$664$	16.8716	0.654744
$665$	2.75557	0.106856
$666$	−1.80642	−0.0699975
$667$	−2.87601	−0.111360
$668$	1.46520	0.0566905
$669$	−9.53972	−0.368827
$670$	4.65386	0.179794
$671$	14.3595	0.554343
$672$	−3.49532	−0.134835
$673$	−39.3274	−1.51596	−0.757980	−	0.652278i	$-0.773814\pi$
$673$	−39.3274	−1.51596	−0.757980	+	0.652278i	$0.773814\pi$
$674$	−7.63158	−0.293958
$675$	−2.67307	−0.102887
$676$	0	0
$677$	27.2672	1.04796	0.523981	−	0.851730i	$-0.324446\pi$
$677$	27.2672	1.04796	0.523981	+	0.851730i	$0.324446\pi$
$678$	1.00937	0.0387645
$679$	4.42864	0.169956
$680$	8.20342	0.314587
$681$	1.81087	0.0693927
$682$	−1.65740	−0.0634650
$683$	16.6811	0.638283	0.319141	−	0.947707i	$-0.396606\pi$
$683$	16.6811	0.638283	0.319141	+	0.947707i	$0.396606\pi$
$684$	−3.43801	−0.131455
$685$	24.9906	0.954843
$686$	−0.311108	−0.0118782
$687$	13.9684	0.532926
$688$	17.9813	0.685529
$689$	0	0
$690$	−1.80642	−0.0687694
$691$	15.2543	0.580300	0.290150	−	0.956981i	$-0.406295\pi$
$691$	15.2543	0.580300	0.290150	+	0.956981i	$0.406295\pi$
$692$	10.7971	0.410442
$693$	1.09679	0.0416635
$694$	−2.96205	−0.112438
$695$	−4.85728	−0.184247
$696$	0.917502	0.0347778
$697$	−50.1847	−1.90088
$698$	−2.91750	−0.110429
$699$	7.51114	0.284097
$700$	−5.08742	−0.192286
$701$	−34.5906	−1.30647	−0.653234	−	0.757156i	$-0.726588\pi$
$701$	−34.5906	−1.30647	−0.653234	+	0.757156i	$0.726588\pi$
$702$	0	0
$703$	−10.4889	−0.395595
$704$	6.32831	0.238507
$705$	3.47949	0.131045
$706$	3.57982	0.134728
$707$	9.28592	0.349233
$708$	0.903212	0.0339448
$709$	−14.5433	−0.546183	−0.273092	−	0.961988i	$-0.588046\pi$
$709$	−14.5433	−0.546183	−0.273092	+	0.961988i	$0.588046\pi$
$710$	−6.17178	−0.231623
$711$	−5.37778	−0.201683
$712$	15.9541	0.597904
$713$	18.4889	0.692413
$714$	−1.37778	−0.0515623
$715$	0	0
$716$	41.6958	1.55825
$717$	−21.9541	−0.819890
$718$	4.78277	0.178491
$719$	3.34614	0.124790	0.0623950	−	0.998052i	$-0.480126\pi$
$719$	3.34614	0.124790	0.0623950	+	0.998052i	$0.480126\pi$
$720$	−5.23014	−0.194916
$721$	0.815792	0.0303817
$722$	−4.89585	−0.182205
$723$	−25.8479	−0.961294
$724$	0.930409	0.0345784
$725$	2.01969	0.0750094
$726$	−3.04794	−0.113120
$727$	23.2257	0.861393	0.430697	−	0.902497i	$-0.358268\pi$
$727$	23.2257	0.861393	0.430697	+	0.902497i	$0.358268\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.65127	−0.0611163
$731$	23.2257	0.859033
$732$	24.9175	0.920977
$733$	−10.8889	−0.402192	−0.201096	−	0.979572i	$-0.564450\pi$
$733$	−10.8889	−0.402192	−0.201096	+	0.979572i	$0.564450\pi$
$734$	−7.74620	−0.285917
$735$	−1.52543	−0.0562662
$736$	13.3047	0.490416
$737$	10.7556	0.396186
$738$	−3.52543	−0.129773
$739$	33.8064	1.24359	0.621795	−	0.783180i	$-0.286404\pi$
$739$	33.8064	1.24359	0.621795	+	0.783180i	$0.286404\pi$
$740$	−16.8573	−0.619686
$741$	0	0
$742$	1.86665	0.0685268
$743$	46.5990	1.70955	0.854776	−	0.518996i	$-0.173694\pi$
$743$	46.5990	1.70955	0.854776	+	0.518996i	$0.173694\pi$
$744$	−5.89829	−0.216242
$745$	−24.5402	−0.899083
$746$	5.34614	0.195736
$747$	−13.8938	−0.508349
$748$	9.24443	0.338010
$749$	−6.56199	−0.239770
$750$	3.64143	0.132966
$751$	17.2444	0.629258	0.314629	−	0.949215i	$-0.398120\pi$
$751$	17.2444	0.629258	0.314629	+	0.949215i	$0.398120\pi$
$752$	−7.82071	−0.285192
$753$	−23.2257	−0.846391
$754$	0	0
$755$	−2.30513	−0.0838923
$756$	1.90321	0.0692191
$757$	19.8193	0.720346	0.360173	−	0.932886i	$-0.382718\pi$
$757$	19.8193	0.720346	0.360173	+	0.932886i	$0.382718\pi$
$758$	−4.08297	−0.148300
$759$	−4.17484	−0.151537
$760$	3.34614	0.121377
$761$	24.2810	0.880185	0.440093	−	0.897952i	$-0.354946\pi$
$761$	24.2810	0.880185	0.440093	+	0.897952i	$0.354946\pi$
$762$	−0.815792	−0.0295530
$763$	12.2953	0.445119
$764$	−47.8350	−1.73061
$765$	−6.75557	−0.244248
$766$	9.56691	0.345667
$767$	0	0
$768$	8.80642	0.317774
$769$	−8.78721	−0.316875	−0.158437	−	0.987369i	$-0.550646\pi$
$769$	−8.78721	−0.316875	−0.158437	+	0.987369i	$0.550646\pi$
$770$	−0.520505	−0.0187577
$771$	27.7748	1.00028
$772$	−12.6824	−0.456451
$773$	43.6271	1.56916	0.784580	−	0.620028i	$-0.212879\pi$
$773$	43.6271	1.56916	0.784580	+	0.620028i	$0.212879\pi$
$774$	1.63158	0.0586461
$775$	−12.9839	−0.466394
$776$	5.37778	0.193051
$777$	5.80642	0.208304
$778$	4.62222	0.165714
$779$	−20.4701	−0.733418
$780$	0	0
$781$	−14.2636	−0.510393
$782$	5.24443	0.187540
$783$	−0.755569	−0.0270018
$784$	3.42864	0.122451
$785$	−4.35857	−0.155564
$786$	5.71456	0.203832
$787$	17.6860	0.630437	0.315219	−	0.949019i	$-0.397922\pi$
$787$	17.6860	0.630437	0.315219	+	0.949019i	$0.397922\pi$
$788$	34.6178	1.23321
$789$	−6.68244	−0.237901
$790$	2.55215	0.0908014
$791$	−3.24443	−0.115359
$792$	1.33185	0.0473253
$793$	0	0
$794$	1.84791	0.0655799
$795$	9.15257	0.324608
$796$	−26.8385	−0.951267
$797$	−38.0228	−1.34683	−0.673417	−	0.739262i	$-0.735174\pi$
$797$	−38.0228	−1.34683	−0.673417	+	0.739262i	$0.735174\pi$
$798$	−0.561993	−0.0198943
$799$	−10.1017	−0.357373
$800$	−9.34323	−0.330333
$801$	−13.1383	−0.464218
$802$	2.13780	0.0754883
$803$	−3.81627	−0.134673
$804$	18.6637	0.658218
$805$	5.80642	0.204650
$806$	0	0
$807$	−22.1432	−0.779477
$808$	11.2761	0.396691
$809$	−8.63512	−0.303595	−0.151797	−	0.988412i	$-0.548506\pi$
$809$	−8.63512	−0.303595	−0.151797	+	0.988412i	$0.548506\pi$
$810$	−0.474572	−0.0166748
$811$	26.6923	0.937293	0.468646	−	0.883386i	$-0.344742\pi$
$811$	26.6923	0.937293	0.468646	+	0.883386i	$0.344742\pi$
$812$	−1.43801	−0.0504642
$813$	2.19358	0.0769321
$814$	1.98126	0.0694433
$815$	21.0607	0.737724
$816$	15.1842	0.531554
$817$	9.47367	0.331442
$818$	9.64449	0.337212
$819$	0	0
$820$	−32.8988	−1.14887
$821$	10.5763	0.369115	0.184557	−	0.982822i	$-0.440915\pi$
$821$	10.5763	0.369115	0.184557	+	0.982822i	$0.440915\pi$
$822$	−5.09679	−0.177771
$823$	7.22570	0.251872	0.125936	−	0.992038i	$-0.459807\pi$
$823$	7.22570	0.251872	0.125936	+	0.992038i	$0.459807\pi$
$824$	0.990632	0.0345103
$825$	2.93179	0.102072
$826$	0.147643	0.00513716
$827$	−35.4652	−1.23325	−0.616623	−	0.787259i	$-0.711500\pi$
$827$	−35.4652	−1.23325	−0.616623	+	0.787259i	$0.711500\pi$
$828$	−7.24443	−0.251761
$829$	−44.0513	−1.52997	−0.764983	−	0.644050i	$-0.777253\pi$
$829$	−44.0513	−1.52997	−0.764983	+	0.644050i	$0.777253\pi$
$830$	6.59364	0.228868
$831$	27.3274	0.947977
$832$	0	0
$833$	4.42864	0.153443
$834$	0.990632	0.0343028
$835$	1.17436	0.0406405
$836$	3.77077	0.130415
$837$	4.85728	0.167892
$838$	1.65740	0.0572538
$839$	27.2587	0.941076	0.470538	−	0.882380i	$-0.344060\pi$
$839$	27.2587	0.941076	0.470538	+	0.882380i	$0.344060\pi$
$840$	−1.85236	−0.0639124
$841$	−28.4291	−0.980314
$842$	−3.49240	−0.120356
$843$	22.8430	0.786754
$844$	−15.4795	−0.532826
$845$	0	0
$846$	−0.709636	−0.0243978
$847$	9.79706	0.336631
$848$	−20.5718	−0.706440
$849$	−21.1240	−0.724973
$850$	−3.68292	−0.126323
$851$	−22.1017	−0.757637
$852$	−24.7511	−0.847960
$853$	36.8988	1.26339	0.631695	−	0.775217i	$-0.282360\pi$
$853$	36.8988	1.26339	0.631695	+	0.775217i	$0.282360\pi$
$854$	4.07313	0.139380
$855$	−2.75557	−0.0942385
$856$	−7.96836	−0.272353
$857$	−26.3269	−0.899311	−0.449655	−	0.893202i	$-0.648453\pi$
$857$	−26.3269	−0.899311	−0.449655	+	0.893202i	$0.648453\pi$
$858$	0	0
$859$	25.3274	0.864160	0.432080	−	0.901835i	$-0.357780\pi$
$859$	25.3274	0.864160	0.432080	+	0.901835i	$0.357780\pi$
$860$	15.2257	0.519192
$861$	11.3319	0.386188
$862$	4.72837	0.161049
$863$	−36.1102	−1.22920	−0.614602	−	0.788837i	$-0.710683\pi$
$863$	−36.1102	−1.22920	−0.614602	+	0.788837i	$0.710683\pi$
$864$	3.49532	0.118913
$865$	8.65386	0.294240
$866$	2.74572	0.0933035
$867$	2.61285	0.0887370
$868$	9.24443	0.313776
$869$	5.89829	0.200086
$870$	0.358572	0.0121567
$871$	0	0
$872$	14.9304	0.505607
$873$	−4.42864	−0.149887
$874$	2.13918	0.0723589
$875$	−11.7047	−0.395692
$876$	−6.62222	−0.223744
$877$	−9.44785	−0.319031	−0.159516	−	0.987195i	$-0.550993\pi$
$877$	−9.44785	−0.319031	−0.159516	+	0.987195i	$0.550993\pi$
$878$	7.21279	0.243420
$879$	11.6271	0.392174
$880$	5.73636	0.193373
$881$	−7.77478	−0.261939	−0.130970	−	0.991386i	$-0.541809\pi$
$881$	−7.77478	−0.261939	−0.130970	+	0.991386i	$0.541809\pi$
$882$	0.311108	0.0104755
$883$	−48.8069	−1.64248	−0.821241	−	0.570581i	$-0.806718\pi$
$883$	−48.8069	−1.64248	−0.821241	+	0.570581i	$0.806718\pi$
$884$	0	0
$885$	0.723926	0.0243345
$886$	3.20294	0.107605
$887$	23.9367	0.803716	0.401858	−	0.915702i	$-0.368365\pi$
$887$	23.9367	0.803716	0.401858	+	0.915702i	$0.368365\pi$
$888$	7.05086	0.236611
$889$	2.62222	0.0879463
$890$	6.23506	0.209000
$891$	−1.09679	−0.0367438
$892$	18.1561	0.607911
$893$	−4.12045	−0.137885
$894$	5.00492	0.167390
$895$	33.4193	1.11708
$896$	8.78568	0.293509
$897$	0	0
$898$	11.0781	0.369679
$899$	−3.67001	−0.122402
$900$	5.08742	0.169581
$901$	−26.5718	−0.885236
$902$	3.86665	0.128745
$903$	−5.24443	−0.174524
$904$	−3.93978	−0.131035
$905$	0.745724	0.0247887
$906$	0.470127	0.0156189
$907$	10.1146	0.335850	0.167925	−	0.985800i	$-0.446293\pi$
$907$	10.1146	0.335850	0.167925	+	0.985800i	$0.446293\pi$
$908$	−3.44647	−0.114375
$909$	−9.28592	−0.307994
$910$	0	0
$911$	−33.2543	−1.10176	−0.550882	−	0.834583i	$-0.685708\pi$
$911$	−33.2543	−1.10176	−0.550882	+	0.834583i	$0.685708\pi$
$912$	6.19358	0.205090
$913$	15.2386	0.504324
$914$	−8.47902	−0.280461
$915$	19.9714	0.660235
$916$	−26.5847	−0.878385
$917$	−18.3684	−0.606579
$918$	1.37778	0.0454737
$919$	−32.6865	−1.07823	−0.539113	−	0.842233i	$-0.681241\pi$
$919$	−32.6865	−1.07823	−0.539113	+	0.842233i	$0.681241\pi$
$920$	7.05086	0.232460
$921$	−32.8573	−1.08268
$922$	8.95359	0.294871
$923$	0	0
$924$	−2.08742	−0.0686711
$925$	15.5210	0.510327
$926$	−9.15257	−0.300772
$927$	−0.815792	−0.0267941
$928$	−2.64095	−0.0866935
$929$	21.9126	0.718928	0.359464	−	0.933159i	$-0.382959\pi$
$929$	21.9126	0.718928	0.359464	+	0.933159i	$0.382959\pi$
$930$	−2.30513	−0.0755882
$931$	1.80642	0.0592032
$932$	−14.2953	−0.468258
$933$	−18.3684	−0.601355
$934$	2.22216	0.0727112
$935$	7.40943	0.242314
$936$	0	0
$937$	51.7275	1.68986	0.844931	−	0.534875i	$-0.179641\pi$
$937$	51.7275	1.68986	0.844931	+	0.534875i	$0.179641\pi$
$938$	3.05086	0.0996140
$939$	7.11108	0.232061
$940$	−6.62222	−0.215993
$941$	7.15701	0.233312	0.116656	−	0.993172i	$-0.462783\pi$
$941$	7.15701	0.233312	0.116656	+	0.993172i	$0.462783\pi$
$942$	0.888922	0.0289626
$943$	−43.1338	−1.40463
$944$	−1.62714	−0.0529588
$945$	1.52543	0.0496222
$946$	−1.78950	−0.0581817
$947$	47.6686	1.54902	0.774511	−	0.632560i	$-0.217996\pi$
$947$	47.6686	1.54902	0.774511	+	0.632560i	$0.217996\pi$
$948$	10.2351	0.332419
$949$	0	0
$950$	−1.50225	−0.0487393
$951$	−8.47457	−0.274807
$952$	5.37778	0.174295
$953$	48.9215	1.58472	0.792362	−	0.610052i	$-0.208851\pi$
$953$	48.9215	1.58472	0.792362	+	0.610052i	$0.208851\pi$
$954$	−1.86665	−0.0604349
$955$	−38.3398	−1.24065
$956$	41.7832	1.35137
$957$	0.828699	0.0267880
$958$	−5.15118	−0.166427
$959$	16.3827	0.529025
$960$	8.80150	0.284067
$961$	−7.40684	−0.238930
$962$	0	0
$963$	6.56199	0.211457
$964$	49.1941	1.58443
$965$	−10.1650	−0.327223
$966$	−1.18421	−0.0381013
$967$	51.1338	1.64435	0.822177	−	0.569233i	$-0.192760\pi$
$967$	51.1338	1.64435	0.822177	+	0.569233i	$0.192760\pi$
$968$	11.8968	0.382376
$969$	8.00000	0.256997
$970$	2.10171	0.0674818
$971$	0.920565	0.0295423	0.0147712	−	0.999891i	$-0.495298\pi$
$971$	0.920565	0.0295423	0.0147712	+	0.999891i	$0.495298\pi$
$972$	−1.90321	−0.0610456
$973$	−3.18421	−0.102081
$974$	−6.75557	−0.216462
$975$	0	0
$976$	−44.8889	−1.43686
$977$	0.769859	0.0246300	0.0123150	−	0.999924i	$-0.496080\pi$
$977$	0.769859	0.0246300	0.0123150	+	0.999924i	$0.496080\pi$
$978$	−4.29529	−0.137348
$979$	14.4099	0.460543
$980$	2.90321	0.0927397
$981$	−12.2953	−0.392558
$982$	−8.14320	−0.259860
$983$	−42.1891	−1.34562	−0.672812	−	0.739813i	$-0.734914\pi$
$983$	−42.1891	−1.34562	−0.672812	+	0.739813i	$0.734914\pi$
$984$	13.7605	0.438668
$985$	27.7462	0.884067
$986$	−1.04101	−0.0331525
$987$	2.28100	0.0726049
$988$	0	0
$989$	19.9625	0.634771
$990$	0.520505	0.0165427
$991$	19.7333	0.626849	0.313424	−	0.949613i	$-0.398524\pi$
$991$	19.7333	0.626849	0.313424	+	0.949613i	$0.398524\pi$
$992$	16.9777	0.539043
$993$	−28.2034	−0.895008
$994$	−4.04593	−0.128329
$995$	−21.5111	−0.681949
$996$	26.4429	0.837876
$997$	−5.34614	−0.169314	−0.0846570	−	0.996410i	$-0.526979\pi$
$997$	−5.34614	−0.169314	−0.0846570	+	0.996410i	$0.526979\pi$
$998$	7.75911	0.245610
$999$	−5.80642	−0.183707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.q.1.2		3
13.5	odd	4		273.2.c.b.64.3	✓	6
13.8	odd	4		273.2.c.b.64.4	yes	6
13.12	even	2		3549.2.a.k.1.2		3
39.5	even	4		819.2.c.c.64.4		6
39.8	even	4		819.2.c.c.64.3		6
52.31	even	4		4368.2.h.o.337.5		6
52.47	even	4		4368.2.h.o.337.2		6
91.34	even	4		1911.2.c.h.883.4		6
91.83	even	4		1911.2.c.h.883.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.c.b.64.3	✓	6	13.5	odd	4
273.2.c.b.64.4	yes	6	13.8	odd	4
819.2.c.c.64.3		6	39.8	even	4
819.2.c.c.64.4		6	39.5	even	4
1911.2.c.h.883.3		6	91.83	even	4
1911.2.c.h.883.4		6	91.34	even	4
3549.2.a.k.1.2		3	13.12	even	2
3549.2.a.q.1.2		3	1.1	even	1	trivial
4368.2.h.o.337.2		6	52.47	even	4
4368.2.h.o.337.5		6	52.31	even	4

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)

\(f(q)\)	\(=\)	\(q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} -1.52543 q^{5} +0.311108 q^{6} -1.00000 q^{7} -1.21432 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.311108 q^{2} +1.00000 q^{3} -1.90321 q^{4} -1.52543 q^{5} +0.311108 q^{6} -1.00000 q^{7} -1.21432 q^{8} +1.00000 q^{9} -0.474572 q^{10} -1.09679 q^{11} -1.90321 q^{12} -0.311108 q^{14} -1.52543 q^{15} +3.42864 q^{16} +4.42864 q^{17} +0.311108 q^{18} +1.80642 q^{19} +2.90321 q^{20} -1.00000 q^{21} -0.341219 q^{22} +3.80642 q^{23} -1.21432 q^{24} -2.67307 q^{25} +1.00000 q^{27} +1.90321 q^{28} -0.755569 q^{29} -0.474572 q^{30} +4.85728 q^{31} +3.49532 q^{32} -1.09679 q^{33} +1.37778 q^{34} +1.52543 q^{35} -1.90321 q^{36} -5.80642 q^{37} +0.561993 q^{38} +1.85236 q^{40} -11.3319 q^{41} -0.311108 q^{42} +5.24443 q^{43} +2.08742 q^{44} -1.52543 q^{45} +1.18421 q^{46} -2.28100 q^{47} +3.42864 q^{48} +1.00000 q^{49} -0.831613 q^{50} +4.42864 q^{51} -6.00000 q^{53} +0.311108 q^{54} +1.67307 q^{55} +1.21432 q^{56} +1.80642 q^{57} -0.235063 q^{58} -0.474572 q^{59} +2.90321 q^{60} -13.0923 q^{61} +1.51114 q^{62} -1.00000 q^{63} -5.76986 q^{64} -0.341219 q^{66} -9.80642 q^{67} -8.42864 q^{68} +3.80642 q^{69} +0.474572 q^{70} +13.0049 q^{71} -1.21432 q^{72} +3.47949 q^{73} -1.80642 q^{74} -2.67307 q^{75} -3.43801 q^{76} +1.09679 q^{77} -5.37778 q^{79} -5.23014 q^{80} +1.00000 q^{81} -3.52543 q^{82} -13.8938 q^{83} +1.90321 q^{84} -6.75557 q^{85} +1.63158 q^{86} -0.755569 q^{87} +1.33185 q^{88} -13.1383 q^{89} -0.474572 q^{90} -7.24443 q^{92} +4.85728 q^{93} -0.709636 q^{94} -2.75557 q^{95} +3.49532 q^{96} -4.42864 q^{97} +0.311108 q^{98} -1.09679 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + q^4 + 2 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} - 8 q^{10} - 10 q^{11} + q^{12} - q^{14} + 2 q^{15} - 3 q^{16} + q^{18} - 8 q^{19} + 2 q^{20} - 3 q^{21} - 8 q^{22} - 2 q^{23} + 3 q^{24} + 5 q^{25} + 3 q^{27} - q^{28} - 2 q^{29} - 8 q^{30} - 12 q^{31} - 3 q^{32} - 10 q^{33} + 4 q^{34} - 2 q^{35} + q^{36} - 4 q^{37} - 12 q^{38} + 12 q^{40} - 14 q^{41} - q^{42} + 16 q^{43} - 14 q^{44} + 2 q^{45} - 10 q^{46} - 3 q^{48} + 3 q^{49} - 29 q^{50} - 18 q^{53} + q^{54} - 8 q^{55} - 3 q^{56} - 8 q^{57} + 26 q^{58} - 8 q^{59} + 2 q^{60} + 14 q^{61} + 4 q^{62} - 3 q^{63} - 11 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 2 q^{69} + 8 q^{70} + 6 q^{71} + 3 q^{72} - 16 q^{73} + 8 q^{74} + 5 q^{75} - 24 q^{76} + 10 q^{77} - 16 q^{79} - 22 q^{80} + 3 q^{81} - 4 q^{82} - 8 q^{83} - q^{84} - 20 q^{85} + 32 q^{86} - 2 q^{87} - 16 q^{88} - 6 q^{89} - 8 q^{90} - 22 q^{92} - 12 q^{93} + 18 q^{94} - 8 q^{95} - 3 q^{96} + q^{98} - 10 q^{99}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + q^4 + 2 * q^5 + q^6 - 3 * q^7 + 3 * q^8 + 3 * q^9 - 8 * q^10 - 10 * q^11 + q^12 - q^14 + 2 * q^15 - 3 * q^16 + q^18 - 8 * q^19 + 2 * q^20 - 3 * q^21 - 8 * q^22 - 2 * q^23 + 3 * q^24 + 5 * q^25 + 3 * q^27 - q^28 - 2 * q^29 - 8 * q^30 - 12 * q^31 - 3 * q^32 - 10 * q^33 + 4 * q^34 - 2 * q^35 + q^36 - 4 * q^37 - 12 * q^38 + 12 * q^40 - 14 * q^41 - q^42 + 16 * q^43 - 14 * q^44 + 2 * q^45 - 10 * q^46 - 3 * q^48 + 3 * q^49 - 29 * q^50 - 18 * q^53 + q^54 - 8 * q^55 - 3 * q^56 - 8 * q^57 + 26 * q^58 - 8 * q^59 + 2 * q^60 + 14 * q^61 + 4 * q^62 - 3 * q^63 - 11 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 2 * q^69 + 8 * q^70 + 6 * q^71 + 3 * q^72 - 16 * q^73 + 8 * q^74 + 5 * q^75 - 24 * q^76 + 10 * q^77 - 16 * q^79 - 22 * q^80 + 3 * q^81 - 4 * q^82 - 8 * q^83 - q^84 - 20 * q^85 + 32 * q^86 - 2 * q^87 - 16 * q^88 - 6 * q^89 - 8 * q^90 - 22 * q^92 - 12 * q^93 + 18 * q^94 - 8 * q^95 - 3 * q^96 + q^98 - 10 * q^99

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