LMFDB - Embedded newform 3174.2.a.bb.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3174,2,Mod(1,3174)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3174, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3174.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3174 = 2 \cdot 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3174.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:	$25.3445176016$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.830830$ of defining polynomial
Character	$\chi$	$=$	3174.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.06731 q^{5} -1.00000 q^{6} -4.42518 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.06731 q^{5} -1.00000 q^{6} -4.42518 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.06731 q^{10} +1.64964 q^{11} -1.00000 q^{12} +5.47112 q^{13} -4.42518 q^{14} -1.06731 q^{15} +1.00000 q^{16} -3.92613 q^{17} +1.00000 q^{18} -6.60149 q^{19} +1.06731 q^{20} +4.42518 q^{21} +1.64964 q^{22} -1.00000 q^{24} -3.86085 q^{25} +5.47112 q^{26} -1.00000 q^{27} -4.42518 q^{28} -6.39946 q^{29} -1.06731 q^{30} -3.01491 q^{31} +1.00000 q^{32} -1.64964 q^{33} -3.92613 q^{34} -4.72304 q^{35} +1.00000 q^{36} +2.21076 q^{37} -6.60149 q^{38} -5.47112 q^{39} +1.06731 q^{40} +4.09177 q^{41} +4.42518 q^{42} +2.91325 q^{43} +1.64964 q^{44} +1.06731 q^{45} -9.62306 q^{47} -1.00000 q^{48} +12.5822 q^{49} -3.86085 q^{50} +3.92613 q^{51} +5.47112 q^{52} +2.23040 q^{53} -1.00000 q^{54} +1.76068 q^{55} -4.42518 q^{56} +6.60149 q^{57} -6.39946 q^{58} +9.75208 q^{59} -1.06731 q^{60} +1.55946 q^{61} -3.01491 q^{62} -4.42518 q^{63} +1.00000 q^{64} +5.83938 q^{65} -1.64964 q^{66} -12.0453 q^{67} -3.92613 q^{68} -4.72304 q^{70} -5.26416 q^{71} +1.00000 q^{72} +7.18556 q^{73} +2.21076 q^{74} +3.86085 q^{75} -6.60149 q^{76} -7.29997 q^{77} -5.47112 q^{78} -2.69381 q^{79} +1.06731 q^{80} +1.00000 q^{81} +4.09177 q^{82} -5.53843 q^{83} +4.42518 q^{84} -4.19039 q^{85} +2.91325 q^{86} +6.39946 q^{87} +1.64964 q^{88} -11.3261 q^{89} +1.06731 q^{90} -24.2107 q^{91} +3.01491 q^{93} -9.62306 q^{94} -7.04583 q^{95} -1.00000 q^{96} -11.9794 q^{97} +12.5822 q^{98} +1.64964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9} + q^{10} - 11 q^{11} - 5 q^{12} + 12 q^{13} - 11 q^{14} - q^{15} + 5 q^{16} + q^{17} + 5 q^{18} - 15 q^{19} + q^{20} + 11 q^{21} - 11 q^{22} - 5 q^{24} + 6 q^{25} + 12 q^{26} - 5 q^{27} - 11 q^{28} + q^{29} - q^{30} - 18 q^{31} + 5 q^{32} + 11 q^{33} + q^{34} - 11 q^{35} + 5 q^{36} - 10 q^{37} - 15 q^{38} - 12 q^{39} + q^{40} - 16 q^{41} + 11 q^{42} - 18 q^{43} - 11 q^{44} + q^{45} - 4 q^{47} - 5 q^{48} + 20 q^{49} + 6 q^{50} - q^{51} + 12 q^{52} + q^{53} - 5 q^{54} - 22 q^{55} - 11 q^{56} + 15 q^{57} + q^{58} + 2 q^{59} - q^{60} + q^{61} - 18 q^{62} - 11 q^{63} + 5 q^{64} - 24 q^{65} + 11 q^{66} - 29 q^{67} + q^{68} - 11 q^{70} - 11 q^{71} + 5 q^{72} - 8 q^{73} - 10 q^{74} - 6 q^{75} - 15 q^{76} + 11 q^{77} - 12 q^{78} - 40 q^{79} + q^{80} + 5 q^{81} - 16 q^{82} - 8 q^{83} + 11 q^{84} - 13 q^{85} - 18 q^{86} - q^{87} - 11 q^{88} - 2 q^{89} + q^{90} - 33 q^{91} + 18 q^{93} - 4 q^{94} - 3 q^{95} - 5 q^{96} - 17 q^{97} + 20 q^{98} - 11 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9 + q^10 - 11 * q^11 - 5 * q^12 + 12 * q^13 - 11 * q^14 - q^15 + 5 * q^16 + q^17 + 5 * q^18 - 15 * q^19 + q^20 + 11 * q^21 - 11 * q^22 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 5 * q^27 - 11 * q^28 + q^29 - q^30 - 18 * q^31 + 5 * q^32 + 11 * q^33 + q^34 - 11 * q^35 + 5 * q^36 - 10 * q^37 - 15 * q^38 - 12 * q^39 + q^40 - 16 * q^41 + 11 * q^42 - 18 * q^43 - 11 * q^44 + q^45 - 4 * q^47 - 5 * q^48 + 20 * q^49 + 6 * q^50 - q^51 + 12 * q^52 + q^53 - 5 * q^54 - 22 * q^55 - 11 * q^56 + 15 * q^57 + q^58 + 2 * q^59 - q^60 + q^61 - 18 * q^62 - 11 * q^63 + 5 * q^64 - 24 * q^65 + 11 * q^66 - 29 * q^67 + q^68 - 11 * q^70 - 11 * q^71 + 5 * q^72 - 8 * q^73 - 10 * q^74 - 6 * q^75 - 15 * q^76 + 11 * q^77 - 12 * q^78 - 40 * q^79 + q^80 + 5 * q^81 - 16 * q^82 - 8 * q^83 + 11 * q^84 - 13 * q^85 - 18 * q^86 - q^87 - 11 * q^88 - 2 * q^89 + q^90 - 33 * q^91 + 18 * q^93 - 4 * q^94 - 3 * q^95 - 5 * q^96 - 17 * q^97 + 20 * q^98 - 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.06731	0.477315	0.238658	−	0.971104i	$-0.423293\pi$
$5$	1.06731	0.477315	0.238658	+	0.971104i	$0.423293\pi$
$6$	−1.00000	−0.408248
$7$	−4.42518	−1.67256	−0.836281	−	0.548302i	$-0.815275\pi$
$7$	−4.42518	−1.67256	−0.836281	+	0.548302i	$0.815275\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.06731	0.337513
$11$	1.64964	0.497386	0.248693	−	0.968582i	$-0.419999\pi$
$11$	1.64964	0.497386	0.248693	+	0.968582i	$0.419999\pi$
$12$	−1.00000	−0.288675
$13$	5.47112	1.51742	0.758708	−	0.651431i	$-0.225831\pi$
$13$	5.47112	1.51742	0.758708	+	0.651431i	$0.225831\pi$
$14$	−4.42518	−1.18268
$15$	−1.06731	−0.275578
$16$	1.00000	0.250000
$17$	−3.92613	−0.952226	−0.476113	−	0.879384i	$-0.657955\pi$
$17$	−3.92613	−0.952226	−0.476113	+	0.879384i	$0.657955\pi$
$18$	1.00000	0.235702
$19$	−6.60149	−1.51449	−0.757243	−	0.653133i	$-0.773454\pi$
$19$	−6.60149	−1.51449	−0.757243	+	0.653133i	$0.773454\pi$
$20$	1.06731	0.238658
$21$	4.42518	0.965654
$22$	1.64964	0.351705
$23$	0	0
$23$	0	0
$24$	−1.00000	−0.204124
$25$	−3.86085	−0.772170
$26$	5.47112	1.07297
$27$	−1.00000	−0.192450
$28$	−4.42518	−0.836281
$29$	−6.39946	−1.18835	−0.594175	−	0.804336i	$-0.702521\pi$
$29$	−6.39946	−1.18835	−0.594175	+	0.804336i	$0.702521\pi$
$30$	−1.06731	−0.194863
$31$	−3.01491	−0.541494	−0.270747	−	0.962650i	$-0.587271\pi$
$31$	−3.01491	−0.541494	−0.270747	+	0.962650i	$0.587271\pi$
$32$	1.00000	0.176777
$33$	−1.64964	−0.287166
$34$	−3.92613	−0.673325
$35$	−4.72304	−0.798339
$36$	1.00000	0.166667
$37$	2.21076	0.363446	0.181723	−	0.983350i	$-0.441833\pi$
$37$	2.21076	0.363446	0.181723	+	0.983350i	$0.441833\pi$
$38$	−6.60149	−1.07090
$39$	−5.47112	−0.876080
$40$	1.06731	0.168756
$41$	4.09177	0.639027	0.319514	−	0.947582i	$-0.396480\pi$
$41$	4.09177	0.639027	0.319514	+	0.947582i	$0.396480\pi$
$42$	4.42518	0.682820
$43$	2.91325	0.444266	0.222133	−	0.975016i	$-0.428698\pi$
$43$	2.91325	0.444266	0.222133	+	0.975016i	$0.428698\pi$
$44$	1.64964	0.248693
$45$	1.06731	0.159105
$46$	0	0
$47$	−9.62306	−1.40367	−0.701834	−	0.712341i	$-0.747635\pi$
$47$	−9.62306	−1.40367	−0.701834	+	0.712341i	$0.747635\pi$
$48$	−1.00000	−0.144338
$49$	12.5822	1.79746
$50$	−3.86085	−0.546007
$51$	3.92613	0.549768
$52$	5.47112	0.758708
$53$	2.23040	0.306368	0.153184	−	0.988198i	$-0.451047\pi$
$53$	2.23040	0.306368	0.153184	+	0.988198i	$0.451047\pi$
$54$	−1.00000	−0.136083
$55$	1.76068	0.237410
$56$	−4.42518	−0.591340
$57$	6.60149	0.874389
$58$	−6.39946	−0.840290
$59$	9.75208	1.26961	0.634807	−	0.772671i	$-0.281080\pi$
$59$	9.75208	1.26961	0.634807	+	0.772671i	$0.281080\pi$
$60$	−1.06731	−0.137789
$61$	1.55946	0.199668	0.0998339	−	0.995004i	$-0.468169\pi$
$61$	1.55946	0.199668	0.0998339	+	0.995004i	$0.468169\pi$
$62$	−3.01491	−0.382894
$63$	−4.42518	−0.557520
$64$	1.00000	0.125000
$65$	5.83938	0.724285
$66$	−1.64964	−0.203057
$67$	−12.0453	−1.47157	−0.735784	−	0.677216i	$-0.763186\pi$
$67$	−12.0453	−1.47157	−0.735784	+	0.677216i	$0.763186\pi$
$68$	−3.92613	−0.476113
$69$	0	0
$70$	−4.72304	−0.564511
$71$	−5.26416	−0.624740	−0.312370	−	0.949960i	$-0.601123\pi$
$71$	−5.26416	−0.624740	−0.312370	+	0.949960i	$0.601123\pi$
$72$	1.00000	0.117851
$73$	7.18556	0.841006	0.420503	−	0.907291i	$-0.361854\pi$
$73$	7.18556	0.841006	0.420503	+	0.907291i	$0.361854\pi$
$74$	2.21076	0.256995
$75$	3.86085	0.445813
$76$	−6.60149	−0.757243
$77$	−7.29997	−0.831909
$78$	−5.47112	−0.619482
$79$	−2.69381	−0.303077	−0.151538	−	0.988451i	$-0.548423\pi$
$79$	−2.69381	−0.303077	−0.151538	+	0.988451i	$0.548423\pi$
$80$	1.06731	0.119329
$81$	1.00000	0.111111
$82$	4.09177	0.451861
$83$	−5.53843	−0.607922	−0.303961	−	0.952685i	$-0.598309\pi$
$83$	−5.53843	−0.607922	−0.303961	+	0.952685i	$0.598309\pi$
$84$	4.42518	0.482827
$85$	−4.19039	−0.454512
$86$	2.91325	0.314144
$87$	6.39946	0.686094
$88$	1.64964	0.175853
$89$	−11.3261	−1.20057	−0.600283	−	0.799788i	$-0.704945\pi$
$89$	−11.3261	−1.20057	−0.600283	+	0.799788i	$0.704945\pi$
$90$	1.06731	0.112504
$91$	−24.2107	−2.53797
$92$	0	0
$93$	3.01491	0.312632
$94$	−9.62306	−0.992543
$95$	−7.04583	−0.722887
$96$	−1.00000	−0.102062
$97$	−11.9794	−1.21633	−0.608163	−	0.793812i	$-0.708093\pi$
$97$	−11.9794	−1.21633	−0.608163	+	0.793812i	$0.708093\pi$
$98$	12.5822	1.27100
$99$	1.64964	0.165795
$100$	−3.86085	−0.386085
$101$	−18.4610	−1.83693	−0.918467	−	0.395498i	$-0.870572\pi$
$101$	−18.4610	−1.83693	−0.918467	+	0.395498i	$0.870572\pi$
$102$	3.92613	0.388745
$103$	11.4277	1.12601	0.563003	−	0.826455i	$-0.309646\pi$
$103$	11.4277	1.12601	0.563003	+	0.826455i	$0.309646\pi$
$104$	5.47112	0.536487
$105$	4.72304	0.460921
$106$	2.23040	0.216635
$107$	−14.8641	−1.43697	−0.718485	−	0.695543i	$-0.755164\pi$
$107$	−14.8641	−1.43697	−0.718485	+	0.695543i	$0.755164\pi$
$108$	−1.00000	−0.0962250
$109$	−12.2830	−1.17650	−0.588249	−	0.808680i	$-0.700182\pi$
$109$	−12.2830	−1.17650	−0.588249	+	0.808680i	$0.700182\pi$
$110$	1.76068	0.167874
$111$	−2.21076	−0.209836
$112$	−4.42518	−0.418140
$113$	3.01462	0.283591	0.141796	−	0.989896i	$-0.454712\pi$
$113$	3.01462	0.283591	0.141796	+	0.989896i	$0.454712\pi$
$114$	6.60149	0.618286
$115$	0	0
$116$	−6.39946	−0.594175
$117$	5.47112	0.505805
$118$	9.75208	0.897752
$119$	17.3738	1.59266
$120$	−1.06731	−0.0974315
$121$	−8.27868	−0.752607
$122$	1.55946	0.141186
$123$	−4.09177	−0.368943
$124$	−3.01491	−0.270747
$125$	−9.45727	−0.845884
$126$	−4.42518	−0.394226
$127$	−5.45241	−0.483823	−0.241912	−	0.970298i	$-0.577774\pi$
$127$	−5.45241	−0.483823	−0.241912	+	0.970298i	$0.577774\pi$
$128$	1.00000	0.0883883
$129$	−2.91325	−0.256497
$130$	5.83938	0.512147
$131$	−8.67749	−0.758156	−0.379078	−	0.925365i	$-0.623759\pi$
$131$	−8.67749	−0.758156	−0.379078	+	0.925365i	$0.623759\pi$
$132$	−1.64964	−0.143583
$133$	29.2128	2.53307
$134$	−12.0453	−1.04056
$135$	−1.06731	−0.0918593
$136$	−3.92613	−0.336663
$137$	−8.98175	−0.767363	−0.383682	−	0.923465i	$-0.625344\pi$
$137$	−8.98175	−0.767363	−0.383682	+	0.923465i	$0.625344\pi$
$138$	0	0
$139$	3.06287	0.259789	0.129895	−	0.991528i	$-0.458536\pi$
$139$	3.06287	0.259789	0.129895	+	0.991528i	$0.458536\pi$
$140$	−4.72304	−0.399169
$141$	9.62306	0.810408
$142$	−5.26416	−0.441758
$143$	9.02540	0.754742
$144$	1.00000	0.0833333
$145$	−6.83020	−0.567217
$146$	7.18556	0.594681
$147$	−12.5822	−1.03776
$148$	2.21076	0.181723
$149$	20.4130	1.67230	0.836149	−	0.548502i	$-0.184802\pi$
$149$	20.4130	1.67230	0.836149	+	0.548502i	$0.184802\pi$
$150$	3.86085	0.315237
$151$	−12.7143	−1.03468	−0.517339	−	0.855780i	$-0.673078\pi$
$151$	−12.7143	−1.03468	−0.517339	+	0.855780i	$0.673078\pi$
$152$	−6.60149	−0.535452
$153$	−3.92613	−0.317409
$154$	−7.29997	−0.588249
$155$	−3.21784	−0.258463
$156$	−5.47112	−0.438040
$157$	1.14480	0.0913647	0.0456823	−	0.998956i	$-0.485454\pi$
$157$	1.14480	0.0913647	0.0456823	+	0.998956i	$0.485454\pi$
$158$	−2.69381	−0.214308
$159$	−2.23040	−0.176882
$160$	1.06731	0.0843782
$161$	0	0
$162$	1.00000	0.0785674
$163$	4.80338	0.376230	0.188115	−	0.982147i	$-0.439762\pi$
$163$	4.80338	0.376230	0.188115	+	0.982147i	$0.439762\pi$
$164$	4.09177	0.319514
$165$	−1.76068	−0.137069
$166$	−5.53843	−0.429865
$167$	11.7479	0.909078	0.454539	−	0.890727i	$-0.349804\pi$
$167$	11.7479	0.909078	0.454539	+	0.890727i	$0.349804\pi$
$168$	4.42518	0.341410
$169$	16.9332	1.30255
$170$	−4.19039	−0.321388
$171$	−6.60149	−0.504829
$172$	2.91325	0.222133
$173$	−5.11919	−0.389205	−0.194602	−	0.980882i	$-0.562342\pi$
$173$	−5.11919	−0.389205	−0.194602	+	0.980882i	$0.562342\pi$
$174$	6.39946	0.485142
$175$	17.0850	1.29150
$176$	1.64964	0.124347
$177$	−9.75208	−0.733011
$178$	−11.3261	−0.848928
$179$	−18.7474	−1.40124	−0.700622	−	0.713533i	$-0.747094\pi$
$179$	−18.7474	−1.40124	−0.700622	+	0.713533i	$0.747094\pi$
$180$	1.06731	0.0795525
$181$	7.26568	0.540053	0.270027	−	0.962853i	$-0.412967\pi$
$181$	7.26568	0.540053	0.270027	+	0.962853i	$0.412967\pi$
$182$	−24.2107	−1.79462
$183$	−1.55946	−0.115278
$184$	0	0
$185$	2.35956	0.173478
$186$	3.01491	0.221064
$187$	−6.47671	−0.473624
$188$	−9.62306	−0.701834
$189$	4.42518	0.321885
$190$	−7.04583	−0.511158
$191$	−25.1816	−1.82208	−0.911040	−	0.412319i	$-0.864719\pi$
$191$	−25.1816	−1.82208	−0.911040	+	0.412319i	$0.864719\pi$
$192$	−1.00000	−0.0721688
$193$	16.9067	1.21697	0.608486	−	0.793564i	$-0.291777\pi$
$193$	16.9067	1.21697	0.608486	+	0.793564i	$0.291777\pi$
$194$	−11.9794	−0.860072
$195$	−5.83938	−0.418166
$196$	12.5822	0.898731
$197$	−12.8420	−0.914952	−0.457476	−	0.889222i	$-0.651246\pi$
$197$	−12.8420	−0.914952	−0.457476	+	0.889222i	$0.651246\pi$
$198$	1.64964	0.117235
$199$	−13.6046	−0.964402	−0.482201	−	0.876061i	$-0.660162\pi$
$199$	−13.6046	−0.964402	−0.482201	+	0.876061i	$0.660162\pi$
$200$	−3.86085	−0.273003
$201$	12.0453	0.849611
$202$	−18.4610	−1.29891
$203$	28.3188	1.98759
$204$	3.92613	0.274884
$205$	4.36718	0.305017
$206$	11.4277	0.796207
$207$	0	0
$208$	5.47112	0.379354
$209$	−10.8901	−0.753285
$210$	4.72304	0.325920
$211$	−21.1423	−1.45549	−0.727746	−	0.685846i	$-0.759432\pi$
$211$	−21.1423	−1.45549	−0.727746	+	0.685846i	$0.759432\pi$
$212$	2.23040	0.153184
$213$	5.26416	0.360694
$214$	−14.8641	−1.01609
$215$	3.10933	0.212055
$216$	−1.00000	−0.0680414
$217$	13.3415	0.905683
$218$	−12.2830	−0.831909
$219$	−7.18556	−0.485555
$220$	1.76068	0.118705
$221$	−21.4803	−1.44492
$222$	−2.21076	−0.148376
$223$	−2.55189	−0.170887	−0.0854435	−	0.996343i	$-0.527231\pi$
$223$	−2.55189	−0.170887	−0.0854435	+	0.996343i	$0.527231\pi$
$224$	−4.42518	−0.295670
$225$	−3.86085	−0.257390
$226$	3.01462	0.200529
$227$	19.7228	1.30905	0.654524	−	0.756041i	$-0.272869\pi$
$227$	19.7228	1.30905	0.654524	+	0.756041i	$0.272869\pi$
$228$	6.60149	0.437195
$229$	11.2054	0.740473	0.370237	−	0.928937i	$-0.379277\pi$
$229$	11.2054	0.740473	0.370237	+	0.928937i	$0.379277\pi$
$230$	0	0
$231$	7.29997	0.480303
$232$	−6.39946	−0.420145
$233$	18.0191	1.18047	0.590236	−	0.807230i	$-0.299034\pi$
$233$	18.0191	1.18047	0.590236	+	0.807230i	$0.299034\pi$
$234$	5.47112	0.357658
$235$	−10.2708	−0.669992
$236$	9.75208	0.634807
$237$	2.69381	0.174981
$238$	17.3738	1.12618
$239$	27.2479	1.76252	0.881261	−	0.472630i	$-0.156695\pi$
$239$	27.2479	1.76252	0.881261	+	0.472630i	$0.156695\pi$
$240$	−1.06731	−0.0688945
$241$	22.2765	1.43496	0.717478	−	0.696581i	$-0.245296\pi$
$241$	22.2765	1.43496	0.717478	+	0.696581i	$0.245296\pi$
$242$	−8.27868	−0.532173
$243$	−1.00000	−0.0641500
$244$	1.55946	0.0998339
$245$	13.4291	0.857955
$246$	−4.09177	−0.260882
$247$	−36.1176	−2.29811
$248$	−3.01491	−0.191447
$249$	5.53843	0.350984
$250$	−9.45727	−0.598130
$251$	10.1994	0.643779	0.321889	−	0.946777i	$-0.395682\pi$
$251$	10.1994	0.643779	0.321889	+	0.946777i	$0.395682\pi$
$252$	−4.42518	−0.278760
$253$	0	0
$254$	−5.45241	−0.342115
$255$	4.19039	0.262412
$256$	1.00000	0.0625000
$257$	27.8386	1.73652	0.868261	−	0.496108i	$-0.165238\pi$
$257$	27.8386	1.73652	0.868261	+	0.496108i	$0.165238\pi$
$258$	−2.91325	−0.181371
$259$	−9.78300	−0.607886
$260$	5.83938	0.362143
$261$	−6.39946	−0.396117
$262$	−8.67749	−0.536097
$263$	−7.54866	−0.465470	−0.232735	−	0.972540i	$-0.574768\pi$
$263$	−7.54866	−0.465470	−0.232735	+	0.972540i	$0.574768\pi$
$264$	−1.64964	−0.101529
$265$	2.38052	0.146234
$266$	29.2128	1.79115
$267$	11.3261	0.693147
$268$	−12.0453	−0.735784
$269$	5.87690	0.358321	0.179160	−	0.983820i	$-0.442662\pi$
$269$	5.87690	0.358321	0.179160	+	0.983820i	$0.442662\pi$
$270$	−1.06731	−0.0649544
$271$	21.2053	1.28813	0.644065	−	0.764971i	$-0.277247\pi$
$271$	21.2053	1.28813	0.644065	+	0.764971i	$0.277247\pi$
$272$	−3.92613	−0.238056
$273$	24.2107	1.46530
$274$	−8.98175	−0.542608
$275$	−6.36903	−0.384067
$276$	0	0
$277$	3.17305	0.190650	0.0953251	−	0.995446i	$-0.469611\pi$
$277$	3.17305	0.190650	0.0953251	+	0.995446i	$0.469611\pi$
$278$	3.06287	0.183699
$279$	−3.01491	−0.180498
$280$	−4.72304	−0.282255
$281$	18.2707	1.08994	0.544970	−	0.838456i	$-0.316541\pi$
$281$	18.2707	1.08994	0.544970	+	0.838456i	$0.316541\pi$
$282$	9.62306	0.573045
$283$	−22.5002	−1.33750	−0.668750	−	0.743488i	$-0.733170\pi$
$283$	−22.5002	−1.33750	−0.668750	+	0.743488i	$0.733170\pi$
$284$	−5.26416	−0.312370
$285$	7.04583	0.417359
$286$	9.02540	0.533683
$287$	−18.1068	−1.06881
$288$	1.00000	0.0589256
$289$	−1.58552	−0.0932659
$290$	−6.83020	−0.401083
$291$	11.9794	0.702246
$292$	7.18556	0.420503
$293$	10.4017	0.607677	0.303838	−	0.952724i	$-0.401732\pi$
$293$	10.4017	0.607677	0.303838	+	0.952724i	$0.401732\pi$
$294$	−12.5822	−0.733810
$295$	10.4085	0.606005
$296$	2.21076	0.128498
$297$	−1.64964	−0.0957220
$298$	20.4130	1.18249
$299$	0	0
$300$	3.86085	0.222906
$301$	−12.8916	−0.743062
$302$	−12.7143	−0.731628
$303$	18.4610	1.06055
$304$	−6.60149	−0.378622
$305$	1.66442	0.0953044
$306$	−3.92613	−0.224442
$307$	5.13212	0.292905	0.146453	−	0.989218i	$-0.453214\pi$
$307$	5.13212	0.292905	0.146453	+	0.989218i	$0.453214\pi$
$308$	−7.29997	−0.415955
$309$	−11.4277	−0.650100
$310$	−3.21784	−0.182761
$311$	21.3709	1.21183	0.605917	−	0.795528i	$-0.292806\pi$
$311$	21.3709	1.21183	0.605917	+	0.795528i	$0.292806\pi$
$312$	−5.47112	−0.309741
$313$	−15.9653	−0.902411	−0.451205	−	0.892420i	$-0.649006\pi$
$313$	−15.9653	−0.902411	−0.451205	+	0.892420i	$0.649006\pi$
$314$	1.14480	0.0646046
$315$	−4.72304	−0.266113
$316$	−2.69381	−0.151538
$317$	10.8838	0.611297	0.305649	−	0.952144i	$-0.401127\pi$
$317$	10.8838	0.611297	0.305649	+	0.952144i	$0.401127\pi$
$318$	−2.23040	−0.125074
$319$	−10.5568	−0.591069
$320$	1.06731	0.0596644
$321$	14.8641	0.829634
$322$	0	0
$323$	25.9183	1.44213
$324$	1.00000	0.0555556
$325$	−21.1232	−1.17170
$326$	4.80338	0.266035
$327$	12.2830	0.679251
$328$	4.09177	0.225930
$329$	42.5838	2.34772
$330$	−1.76068	−0.0969222
$331$	−13.5079	−0.742459	−0.371230	−	0.928541i	$-0.621064\pi$
$331$	−13.5079	−0.742459	−0.371230	+	0.928541i	$0.621064\pi$
$332$	−5.53843	−0.303961
$333$	2.21076	0.121149
$334$	11.7479	0.642815
$335$	−12.8561	−0.702402
$336$	4.42518	0.241413
$337$	1.90607	0.103830	0.0519152	−	0.998651i	$-0.483467\pi$
$337$	1.90607	0.103830	0.0519152	+	0.998651i	$0.483467\pi$
$338$	16.9332	0.921042
$339$	−3.01462	−0.163732
$340$	−4.19039	−0.227256
$341$	−4.97353	−0.269332
$342$	−6.60149	−0.356968
$343$	−24.7024	−1.33380
$344$	2.91325	0.157072
$345$	0	0
$346$	−5.11919	−0.275209
$347$	9.62944	0.516936	0.258468	−	0.966020i	$-0.416782\pi$
$347$	9.62944	0.516936	0.258468	+	0.966020i	$0.416782\pi$
$348$	6.39946	0.343047
$349$	−31.7107	−1.69744	−0.848719	−	0.528845i	$-0.822625\pi$
$349$	−31.7107	−1.69744	−0.848719	+	0.528845i	$0.822625\pi$
$350$	17.0850	0.913230
$351$	−5.47112	−0.292027
$352$	1.64964	0.0879263
$353$	7.73095	0.411477	0.205738	−	0.978607i	$-0.434040\pi$
$353$	7.73095	0.411477	0.205738	+	0.978607i	$0.434040\pi$
$354$	−9.75208	−0.518317
$355$	−5.61848	−0.298198
$356$	−11.3261	−0.600283
$357$	−17.3738	−0.919520
$358$	−18.7474	−0.990829
$359$	37.0366	1.95472	0.977359	−	0.211586i	$-0.0678628\pi$
$359$	37.0366	1.95472	0.977359	+	0.211586i	$0.0678628\pi$
$360$	1.06731	0.0562521
$361$	24.5797	1.29367
$362$	7.26568	0.381875
$363$	8.27868	0.434518
$364$	−24.2107	−1.26899
$365$	7.66921	0.401425
$366$	−1.55946	−0.0815140
$367$	12.1890	0.636260	0.318130	−	0.948047i	$-0.396945\pi$
$367$	12.1890	0.636260	0.318130	+	0.948047i	$0.396945\pi$
$368$	0	0
$369$	4.09177	0.213009
$370$	2.35956	0.122668
$371$	−9.86991	−0.512420
$372$	3.01491	0.156316
$373$	−5.54618	−0.287170	−0.143585	−	0.989638i	$-0.545863\pi$
$373$	−5.54618	−0.287170	−0.143585	+	0.989638i	$0.545863\pi$
$374$	−6.47671	−0.334903
$375$	9.45727	0.488371
$376$	−9.62306	−0.496271
$377$	−35.0122	−1.80322
$378$	4.42518	0.227607
$379$	10.2328	0.525626	0.262813	−	0.964847i	$-0.415350\pi$
$379$	10.2328	0.525626	0.262813	+	0.964847i	$0.415350\pi$
$380$	−7.04583	−0.361444
$381$	5.45241	0.279336
$382$	−25.1816	−1.28840
$383$	4.49082	0.229470	0.114735	−	0.993396i	$-0.463398\pi$
$383$	4.49082	0.229470	0.114735	+	0.993396i	$0.463398\pi$
$384$	−1.00000	−0.0510310
$385$	−7.79133	−0.397083
$386$	16.9067	0.860530
$387$	2.91325	0.148089
$388$	−11.9794	−0.608163
$389$	−3.41829	−0.173314	−0.0866571	−	0.996238i	$-0.527618\pi$
$389$	−3.41829	−0.173314	−0.0866571	+	0.996238i	$0.527618\pi$
$390$	−5.83938	−0.295688
$391$	0	0
$392$	12.5822	0.635499
$393$	8.67749	0.437721
$394$	−12.8420	−0.646969
$395$	−2.87512	−0.144663
$396$	1.64964	0.0828977
$397$	−25.0502	−1.25723	−0.628617	−	0.777715i	$-0.716379\pi$
$397$	−25.0502	−1.25723	−0.628617	+	0.777715i	$0.716379\pi$
$398$	−13.6046	−0.681935
$399$	−29.2128	−1.46247
$400$	−3.86085	−0.193043
$401$	8.95685	0.447284	0.223642	−	0.974671i	$-0.428205\pi$
$401$	8.95685	0.447284	0.223642	+	0.974671i	$0.428205\pi$
$402$	12.0453	0.600765
$403$	−16.4950	−0.821672
$404$	−18.4610	−0.918467
$405$	1.06731	0.0530350
$406$	28.3188	1.40544
$407$	3.64696	0.180773
$408$	3.92613	0.194372
$409$	−23.2815	−1.15120	−0.575599	−	0.817732i	$-0.695231\pi$
$409$	−23.2815	−1.15120	−0.575599	+	0.817732i	$0.695231\pi$
$410$	4.36718	0.215680
$411$	8.98175	0.443037
$412$	11.4277	0.563003
$413$	−43.1547	−2.12351
$414$	0	0
$415$	−5.91121	−0.290170
$416$	5.47112	0.268244
$417$	−3.06287	−0.149989
$418$	−10.8901	−0.532653
$419$	2.24964	0.109902	0.0549510	−	0.998489i	$-0.482500\pi$
$419$	2.24964	0.109902	0.0549510	+	0.998489i	$0.482500\pi$
$420$	4.72304	0.230461
$421$	18.6618	0.909521	0.454761	−	0.890614i	$-0.349725\pi$
$421$	18.6618	0.909521	0.454761	+	0.890614i	$0.349725\pi$
$422$	−21.1423	−1.02919
$423$	−9.62306	−0.467889
$424$	2.23040	0.108318
$425$	15.1582	0.735281
$426$	5.26416	0.255049
$427$	−6.90087	−0.333957
$428$	−14.8641	−0.718485
$429$	−9.02540	−0.435750
$430$	3.10933	0.149945
$431$	−4.81723	−0.232038	−0.116019	−	0.993247i	$-0.537013\pi$
$431$	−4.81723	−0.232038	−0.116019	+	0.993247i	$0.537013\pi$
$432$	−1.00000	−0.0481125
$433$	6.25528	0.300609	0.150305	−	0.988640i	$-0.451975\pi$
$433$	6.25528	0.300609	0.150305	+	0.988640i	$0.451975\pi$
$434$	13.3415	0.640414
$435$	6.83020	0.327483
$436$	−12.2830	−0.588249
$437$	0	0
$438$	−7.18556	−0.343339
$439$	−13.5454	−0.646486	−0.323243	−	0.946316i	$-0.604773\pi$
$439$	−13.5454	−0.646486	−0.323243	+	0.946316i	$0.604773\pi$
$440$	1.76068	0.0839371
$441$	12.5822	0.599154
$442$	−21.4803	−1.02171
$443$	5.53987	0.263207	0.131603	−	0.991302i	$-0.457987\pi$
$443$	5.53987	0.263207	0.131603	+	0.991302i	$0.457987\pi$
$444$	−2.21076	−0.104918
$445$	−12.0885	−0.573048
$446$	−2.55189	−0.120835
$447$	−20.4130	−0.965502
$448$	−4.42518	−0.209070
$449$	−13.5471	−0.639327	−0.319664	−	0.947531i	$-0.603570\pi$
$449$	−13.5471	−0.639327	−0.319664	+	0.947531i	$0.603570\pi$
$450$	−3.86085	−0.182002
$451$	6.74996	0.317843
$452$	3.01462	0.141796
$453$	12.7143	0.597372
$454$	19.7228	0.925637
$455$	−25.8403	−1.21141
$456$	6.60149	0.309143
$457$	11.1137	0.519877	0.259939	−	0.965625i	$-0.416298\pi$
$457$	11.1137	0.519877	0.259939	+	0.965625i	$0.416298\pi$
$458$	11.2054	0.523594
$459$	3.92613	0.183256
$460$	0	0
$461$	−33.3324	−1.55245	−0.776223	−	0.630459i	$-0.782867\pi$
$461$	−33.3324	−1.55245	−0.776223	+	0.630459i	$0.782867\pi$
$462$	7.29997	0.339625
$463$	−19.4351	−0.903228	−0.451614	−	0.892213i	$-0.649152\pi$
$463$	−19.4351	−0.903228	−0.451614	+	0.892213i	$0.649152\pi$
$464$	−6.39946	−0.297087
$465$	3.21784	0.149224
$466$	18.0191	0.834720
$467$	33.5250	1.55135	0.775676	−	0.631131i	$-0.217409\pi$
$467$	33.5250	1.55135	0.775676	+	0.631131i	$0.217409\pi$
$468$	5.47112	0.252903
$469$	53.3027	2.46129
$470$	−10.2708	−0.473756
$471$	−1.14480	−0.0527494
$472$	9.75208	0.448876
$473$	4.80582	0.220972
$474$	2.69381	0.123731
$475$	25.4874	1.16944
$476$	17.3738	0.796328
$477$	2.23040	0.102123
$478$	27.2479	1.24629
$479$	1.65573	0.0756521	0.0378260	−	0.999284i	$-0.487957\pi$
$479$	1.65573	0.0756521	0.0378260	+	0.999284i	$0.487957\pi$
$480$	−1.06731	−0.0487158
$481$	12.0953	0.551499
$482$	22.2765	1.01467
$483$	0	0
$484$	−8.27868	−0.376303
$485$	−12.7857	−0.580571
$486$	−1.00000	−0.0453609
$487$	−20.9954	−0.951394	−0.475697	−	0.879609i	$-0.657804\pi$
$487$	−20.9954	−0.951394	−0.475697	+	0.879609i	$0.657804\pi$
$488$	1.55946	0.0705932
$489$	−4.80338	−0.217216
$490$	13.4291	0.606666
$491$	25.8128	1.16492	0.582458	−	0.812861i	$-0.302091\pi$
$491$	25.8128	1.16492	0.582458	+	0.812861i	$0.302091\pi$
$492$	−4.09177	−0.184471
$493$	25.1251	1.13158
$494$	−36.1176	−1.62501
$495$	1.76068	0.0791367
$496$	−3.01491	−0.135374
$497$	23.2948	1.04492
$498$	5.53843	0.248183
$499$	−6.43766	−0.288189	−0.144095	−	0.989564i	$-0.546027\pi$
$499$	−6.43766	−0.288189	−0.144095	+	0.989564i	$0.546027\pi$
$500$	−9.45727	−0.422942
$501$	−11.7479	−0.524856
$502$	10.1994	0.455220
$503$	−10.1631	−0.453151	−0.226576	−	0.973994i	$-0.572753\pi$
$503$	−10.1631	−0.453151	−0.226576	+	0.973994i	$0.572753\pi$
$504$	−4.42518	−0.197113
$505$	−19.7035	−0.876796
$506$	0	0
$507$	−16.9332	−0.752028
$508$	−5.45241	−0.241912
$509$	−26.2279	−1.16253	−0.581266	−	0.813714i	$-0.697442\pi$
$509$	−26.2279	−1.16253	−0.581266	+	0.813714i	$0.697442\pi$
$510$	4.19039	0.185554
$511$	−31.7974	−1.40663
$512$	1.00000	0.0441942
$513$	6.60149	0.291463
$514$	27.8386	1.22791
$515$	12.1969	0.537460
$516$	−2.91325	−0.128249
$517$	−15.8746	−0.698165
$518$	−9.78300	−0.429840
$519$	5.11919	0.224708
$520$	5.83938	0.256074
$521$	−15.4025	−0.674798	−0.337399	−	0.941362i	$-0.609547\pi$
$521$	−15.4025	−0.674798	−0.337399	+	0.941362i	$0.609547\pi$
$522$	−6.39946	−0.280097
$523$	26.2241	1.14670	0.573349	−	0.819311i	$-0.305644\pi$
$523$	26.2241	1.14670	0.573349	+	0.819311i	$0.305644\pi$
$524$	−8.67749	−0.379078
$525$	−17.0850	−0.745649
$526$	−7.54866	−0.329137
$527$	11.8369	0.515625
$528$	−1.64964	−0.0717915
$529$	0	0
$530$	2.38052	0.103403
$531$	9.75208	0.423204
$532$	29.2128	1.26654
$533$	22.3866	0.969670
$534$	11.3261	0.490129
$535$	−15.8646	−0.685887
$536$	−12.0453	−0.520278
$537$	18.7474	0.809008
$538$	5.87690	0.253371
$539$	20.7562	0.894033
$540$	−1.06731	−0.0459297
$541$	0.996978	0.0428634	0.0214317	−	0.999770i	$-0.493178\pi$
$541$	0.996978	0.0428634	0.0214317	+	0.999770i	$0.493178\pi$
$542$	21.2053	0.910845
$543$	−7.26568	−0.311800
$544$	−3.92613	−0.168331
$545$	−13.1098	−0.561560
$546$	24.2107	1.03612
$547$	5.83245	0.249377	0.124689	−	0.992196i	$-0.460207\pi$
$547$	5.83245	0.249377	0.124689	+	0.992196i	$0.460207\pi$
$548$	−8.98175	−0.383682
$549$	1.55946	0.0665559
$550$	−6.36903	−0.271576
$551$	42.2460	1.79974
$552$	0	0
$553$	11.9206	0.506914
$554$	3.17305	0.134810
$555$	−2.35956	−0.100158
$556$	3.06287	0.129895
$557$	32.8498	1.39189	0.695946	−	0.718094i	$-0.254985\pi$
$557$	32.8498	1.39189	0.695946	+	0.718094i	$0.254985\pi$
$558$	−3.01491	−0.127631
$559$	15.9387	0.674136
$560$	−4.72304	−0.199585
$561$	6.47671	0.273447
$562$	18.2707	0.770704
$563$	12.0434	0.507568	0.253784	−	0.967261i	$-0.418325\pi$
$563$	12.0434	0.507568	0.253784	+	0.967261i	$0.418325\pi$
$564$	9.62306	0.405204
$565$	3.21753	0.135362
$566$	−22.5002	−0.945755
$567$	−4.42518	−0.185840
$568$	−5.26416	−0.220879
$569$	12.9218	0.541708	0.270854	−	0.962620i	$-0.412694\pi$
$569$	12.9218	0.541708	0.270854	+	0.962620i	$0.412694\pi$
$570$	7.04583	0.295117
$571$	−33.8981	−1.41859	−0.709296	−	0.704911i	$-0.750987\pi$
$571$	−33.8981	−1.41859	−0.709296	+	0.704911i	$0.750987\pi$
$572$	9.02540	0.377371
$573$	25.1816	1.05198
$574$	−18.1068	−0.755764
$575$	0	0
$576$	1.00000	0.0416667
$577$	−22.4539	−0.934768	−0.467384	−	0.884054i	$-0.654803\pi$
$577$	−22.4539	−0.934768	−0.467384	+	0.884054i	$0.654803\pi$
$578$	−1.58552	−0.0659490
$579$	−16.9067	−0.702619
$580$	−6.83020	−0.283609
$581$	24.5086	1.01679
$582$	11.9794	0.496563
$583$	3.67936	0.152383
$584$	7.18556	0.297341
$585$	5.83938	0.241428
$586$	10.4017	0.429692
$587$	−1.15068	−0.0474935	−0.0237467	−	0.999718i	$-0.507560\pi$
$587$	−1.15068	−0.0474935	−0.0237467	+	0.999718i	$0.507560\pi$
$588$	−12.5822	−0.518882
$589$	19.9029	0.820086
$590$	10.4085	0.428511
$591$	12.8420	0.528248
$592$	2.21076	0.0908616
$593$	−3.28119	−0.134742	−0.0673712	−	0.997728i	$-0.521461\pi$
$593$	−3.28119	−0.134742	−0.0673712	+	0.997728i	$0.521461\pi$
$594$	−1.64964	−0.0676857
$595$	18.5432	0.760199
$596$	20.4130	0.836149
$597$	13.6046	0.556798
$598$	0	0
$599$	3.76746	0.153934	0.0769671	−	0.997034i	$-0.475476\pi$
$599$	3.76746	0.153934	0.0769671	+	0.997034i	$0.475476\pi$
$600$	3.86085	0.157619
$601$	19.6834	0.802904	0.401452	−	0.915880i	$-0.368506\pi$
$601$	19.6834	0.802904	0.401452	+	0.915880i	$0.368506\pi$
$602$	−12.8916	−0.525424
$603$	−12.0453	−0.490523
$604$	−12.7143	−0.517339
$605$	−8.83590	−0.359231
$606$	18.4610	0.749925
$607$	42.9460	1.74313	0.871563	−	0.490284i	$-0.163107\pi$
$607$	42.9460	1.74313	0.871563	+	0.490284i	$0.163107\pi$
$608$	−6.60149	−0.267726
$609$	−28.3188	−1.14753
$610$	1.66442	0.0673904
$611$	−52.6489	−2.12995
$612$	−3.92613	−0.158704
$613$	−23.3854	−0.944526	−0.472263	−	0.881458i	$-0.656563\pi$
$613$	−23.3854	−0.944526	−0.472263	+	0.881458i	$0.656563\pi$
$614$	5.13212	0.207115
$615$	−4.36718	−0.176102
$616$	−7.29997	−0.294124
$617$	−7.46322	−0.300458	−0.150229	−	0.988651i	$-0.548001\pi$
$617$	−7.46322	−0.300458	−0.150229	+	0.988651i	$0.548001\pi$
$618$	−11.4277	−0.459690
$619$	−32.5795	−1.30948	−0.654741	−	0.755853i	$-0.727222\pi$
$619$	−32.5795	−1.30948	−0.654741	+	0.755853i	$0.727222\pi$
$620$	−3.21784	−0.129232
$621$	0	0
$622$	21.3709	0.856896
$623$	50.1201	2.00802
$624$	−5.47112	−0.219020
$625$	9.21043	0.368417
$626$	−15.9653	−0.638101
$627$	10.8901	0.434909
$628$	1.14480	0.0456823
$629$	−8.67972	−0.346083
$630$	−4.72304	−0.188170
$631$	17.2415	0.686374	0.343187	−	0.939267i	$-0.388494\pi$
$631$	17.2415	0.686374	0.343187	+	0.939267i	$0.388494\pi$
$632$	−2.69381	−0.107154
$633$	21.1423	0.840329
$634$	10.8838	0.432252
$635$	−5.81941	−0.230936
$636$	−2.23040	−0.0884410
$637$	68.8389	2.72750
$638$	−10.5568	−0.417949
$639$	−5.26416	−0.208247
$640$	1.06731	0.0421891
$641$	−40.6615	−1.60603	−0.803017	−	0.595957i	$-0.796773\pi$
$641$	−40.6615	−1.60603	−0.803017	+	0.595957i	$0.796773\pi$
$642$	14.8641	0.586640
$643$	11.4111	0.450008	0.225004	−	0.974358i	$-0.427760\pi$
$643$	11.4111	0.450008	0.225004	+	0.974358i	$0.427760\pi$
$644$	0	0
$645$	−3.10933	−0.122430
$646$	25.9183	1.01974
$647$	34.5625	1.35879	0.679396	−	0.733772i	$-0.262242\pi$
$647$	34.5625	1.35879	0.679396	+	0.733772i	$0.262242\pi$
$648$	1.00000	0.0392837
$649$	16.0875	0.631488
$650$	−21.1232	−0.828519
$651$	−13.3415	−0.522896
$652$	4.80338	0.188115
$653$	8.57392	0.335524	0.167762	−	0.985828i	$-0.446346\pi$
$653$	8.57392	0.335524	0.167762	+	0.985828i	$0.446346\pi$
$654$	12.2830	0.480303
$655$	−9.26156	−0.361879
$656$	4.09177	0.159757
$657$	7.18556	0.280335
$658$	42.5838	1.66009
$659$	4.22348	0.164523	0.0822616	−	0.996611i	$-0.473786\pi$
$659$	4.22348	0.164523	0.0822616	+	0.996611i	$0.473786\pi$
$660$	−1.76068	−0.0685344
$661$	23.1140	0.899029	0.449514	−	0.893273i	$-0.351597\pi$
$661$	23.1140	0.899029	0.449514	+	0.893273i	$0.351597\pi$
$662$	−13.5079	−0.524998
$663$	21.4803	0.834226
$664$	−5.53843	−0.214933
$665$	31.1791	1.20907
$666$	2.21076	0.0856651
$667$	0	0
$668$	11.7479	0.454539
$669$	2.55189	0.0986617
$670$	−12.8561	−0.496673
$671$	2.57255	0.0993120
$672$	4.42518	0.170705
$673$	−45.0158	−1.73523	−0.867616	−	0.497235i	$-0.834349\pi$
$673$	−45.0158	−1.73523	−0.867616	+	0.497235i	$0.834349\pi$
$674$	1.90607	0.0734192
$675$	3.86085	0.148604
$676$	16.9332	0.651275
$677$	31.0382	1.19290	0.596448	−	0.802652i	$-0.296578\pi$
$677$	31.0382	1.19290	0.596448	+	0.802652i	$0.296578\pi$
$678$	−3.01462	−0.115776
$679$	53.0111	2.03438
$680$	−4.19039	−0.160694
$681$	−19.7228	−0.755779
$682$	−4.97353	−0.190446
$683$	−25.9817	−0.994164	−0.497082	−	0.867704i	$-0.665595\pi$
$683$	−25.9817	−0.994164	−0.497082	+	0.867704i	$0.665595\pi$
$684$	−6.60149	−0.252414
$685$	−9.58631	−0.366274
$686$	−24.7024	−0.943141
$687$	−11.2054	−0.427512
$688$	2.91325	0.111067
$689$	12.2028	0.464888
$690$	0	0
$691$	33.5110	1.27482	0.637410	−	0.770525i	$-0.280006\pi$
$691$	33.5110	1.27482	0.637410	+	0.770525i	$0.280006\pi$
$692$	−5.11919	−0.194602
$693$	−7.29997	−0.277303
$694$	9.62944	0.365529
$695$	3.26903	0.124001
$696$	6.39946	0.242571
$697$	−16.0648	−0.608498
$698$	−31.7107	−1.20027
$699$	−18.0191	−0.681546
$700$	17.0850	0.645751
$701$	5.85943	0.221308	0.110654	−	0.993859i	$-0.464706\pi$
$701$	5.85943	0.221308	0.110654	+	0.993859i	$0.464706\pi$
$702$	−5.47112	−0.206494
$703$	−14.5943	−0.550434
$704$	1.64964	0.0621733
$705$	10.2708	0.386820
$706$	7.73095	0.290958
$707$	81.6931	3.07238
$708$	−9.75208	−0.366506
$709$	−45.0960	−1.69362	−0.846808	−	0.531899i	$-0.821479\pi$
$709$	−45.0960	−1.69362	−0.846808	+	0.531899i	$0.821479\pi$
$710$	−5.61848	−0.210858
$711$	−2.69381	−0.101026
$712$	−11.3261	−0.424464
$713$	0	0
$714$	−17.3738	−0.650199
$715$	9.63289	0.360250
$716$	−18.7474	−0.700622
$717$	−27.2479	−1.01759
$718$	37.0366	1.38219
$719$	−32.9210	−1.22775	−0.613874	−	0.789404i	$-0.710390\pi$
$719$	−32.9210	−1.22775	−0.613874	+	0.789404i	$0.710390\pi$
$720$	1.06731	0.0397763
$721$	−50.5697	−1.88331
$722$	24.5797	0.914762
$723$	−22.2765	−0.828472
$724$	7.26568	0.270027
$725$	24.7074	0.917609
$726$	8.27868	0.307250
$727$	2.50599	0.0929421	0.0464710	−	0.998920i	$-0.485202\pi$
$727$	2.50599	0.0929421	0.0464710	+	0.998920i	$0.485202\pi$
$728$	−24.2107	−0.897308
$729$	1.00000	0.0370370
$730$	7.66921	0.283850
$731$	−11.4378	−0.423042
$732$	−1.55946	−0.0576391
$733$	11.0964	0.409856	0.204928	−	0.978777i	$-0.434304\pi$
$733$	11.0964	0.409856	0.204928	+	0.978777i	$0.434304\pi$
$734$	12.1890	0.449903
$735$	−13.4291	−0.495341
$736$	0	0
$737$	−19.8705	−0.731938
$738$	4.09177	0.150620
$739$	−36.1487	−1.32975	−0.664876	−	0.746954i	$-0.731515\pi$
$739$	−36.1487	−1.32975	−0.664876	+	0.746954i	$0.731515\pi$
$740$	2.35956	0.0867392
$741$	36.1176	1.32681
$742$	−9.86991	−0.362336
$743$	−26.5639	−0.974534	−0.487267	−	0.873253i	$-0.662006\pi$
$743$	−26.5639	−0.974534	−0.487267	+	0.873253i	$0.662006\pi$
$744$	3.01491	0.110532
$745$	21.7870	0.798213
$746$	−5.54618	−0.203060
$747$	−5.53843	−0.202641
$748$	−6.47671	−0.236812
$749$	65.7764	2.40342
$750$	9.45727	0.345331
$751$	−13.7898	−0.503198	−0.251599	−	0.967832i	$-0.580956\pi$
$751$	−13.7898	−0.503198	−0.251599	+	0.967832i	$0.580956\pi$
$752$	−9.62306	−0.350917
$753$	−10.1994	−0.371686
$754$	−35.0122	−1.27507
$755$	−13.5701	−0.493868
$756$	4.42518	0.160942
$757$	38.1039	1.38491	0.692455	−	0.721461i	$-0.256529\pi$
$757$	38.1039	1.38491	0.692455	+	0.721461i	$0.256529\pi$
$758$	10.2328	0.371674
$759$	0	0
$760$	−7.04583	−0.255579
$761$	43.2965	1.56950	0.784748	−	0.619815i	$-0.212792\pi$
$761$	43.2965	1.56950	0.784748	+	0.619815i	$0.212792\pi$
$762$	5.45241	0.197520
$763$	54.3545	1.96776
$764$	−25.1816	−0.911040
$765$	−4.19039	−0.151504
$766$	4.49082	0.162260
$767$	53.3548	1.92653
$768$	−1.00000	−0.0360844
$769$	35.0733	1.26477	0.632387	−	0.774652i	$-0.282075\pi$
$769$	35.0733	1.26477	0.632387	+	0.774652i	$0.282075\pi$
$770$	−7.79133	−0.280780
$771$	−27.8386	−1.00258
$772$	16.9067	0.608486
$773$	14.8799	0.535192	0.267596	−	0.963531i	$-0.413771\pi$
$773$	14.8799	0.535192	0.267596	+	0.963531i	$0.413771\pi$
$774$	2.91325	0.104715
$775$	11.6401	0.418126
$776$	−11.9794	−0.430036
$777$	9.78300	0.350963
$778$	−3.41829	−0.122552
$779$	−27.0118	−0.967798
$780$	−5.83938	−0.209083
$781$	−8.68398	−0.310737
$782$	0	0
$783$	6.39946	0.228698
$784$	12.5822	0.449365
$785$	1.22185	0.0436097
$786$	8.67749	0.309516
$787$	−36.5315	−1.30221	−0.651103	−	0.758989i	$-0.725694\pi$
$787$	−36.5315	−1.30221	−0.651103	+	0.758989i	$0.725694\pi$
$788$	−12.8420	−0.457476
$789$	7.54866	0.268740
$790$	−2.87512	−0.102292
$791$	−13.3402	−0.474324
$792$	1.64964	0.0586175
$793$	8.53197	0.302979
$794$	−25.0502	−0.888998
$795$	−2.38052	−0.0844284
$796$	−13.6046	−0.482201
$797$	45.5877	1.61480	0.807399	−	0.590006i	$-0.200875\pi$
$797$	45.5877	1.61480	0.807399	+	0.590006i	$0.200875\pi$
$798$	−29.2128	−1.03412
$799$	37.7814	1.33661
$800$	−3.86085	−0.136502
$801$	−11.3261	−0.400188
$802$	8.95685	0.316277
$803$	11.8536	0.418305
$804$	12.0453	0.424805
$805$	0	0
$806$	−16.4950	−0.581010
$807$	−5.87690	−0.206877
$808$	−18.4610	−0.649454
$809$	−21.8252	−0.767332	−0.383666	−	0.923472i	$-0.625339\pi$
$809$	−21.8252	−0.767332	−0.383666	+	0.923472i	$0.625339\pi$
$810$	1.06731	0.0375014
$811$	30.3605	1.06610	0.533050	−	0.846084i	$-0.321046\pi$
$811$	30.3605	1.06610	0.533050	+	0.846084i	$0.321046\pi$
$812$	28.3188	0.993794
$813$	−21.2053	−0.743702
$814$	3.64696	0.127826
$815$	5.12669	0.179580
$816$	3.92613	0.137442
$817$	−19.2318	−0.672835
$818$	−23.2815	−0.814020
$819$	−24.2107	−0.845990
$820$	4.36718	0.152509
$821$	−34.0023	−1.18669	−0.593344	−	0.804949i	$-0.702192\pi$
$821$	−34.0023	−1.18669	−0.593344	+	0.804949i	$0.702192\pi$
$822$	8.98175	0.313275
$823$	52.3590	1.82512	0.912561	−	0.408941i	$-0.134102\pi$
$823$	52.3590	1.82512	0.912561	+	0.408941i	$0.134102\pi$
$824$	11.4277	0.398103
$825$	6.36903	0.221741
$826$	−43.1547	−1.50155
$827$	20.0689	0.697864	0.348932	−	0.937148i	$-0.386544\pi$
$827$	20.0689	0.697864	0.348932	+	0.937148i	$0.386544\pi$
$828$	0	0
$829$	−30.6227	−1.06357	−0.531785	−	0.846879i	$-0.678479\pi$
$829$	−30.6227	−1.06357	−0.531785	+	0.846879i	$0.678479\pi$
$830$	−5.91121	−0.205181
$831$	−3.17305	−0.110072
$832$	5.47112	0.189677
$833$	−49.3994	−1.71159
$834$	−3.06287	−0.106058
$835$	12.5386	0.433916
$836$	−10.8901	−0.376642
$837$	3.01491	0.104211
$838$	2.24964	0.0777125
$839$	−39.9432	−1.37899	−0.689497	−	0.724289i	$-0.742168\pi$
$839$	−39.9432	−1.37899	−0.689497	+	0.724289i	$0.742168\pi$
$840$	4.72304	0.162960
$841$	11.9531	0.412175
$842$	18.6618	0.643129
$843$	−18.2707	−0.629277
$844$	−21.1423	−0.727746
$845$	18.0729	0.621727
$846$	−9.62306	−0.330848
$847$	36.6346	1.25878
$848$	2.23040	0.0765921
$849$	22.5002	0.772206
$850$	15.1582	0.519922
$851$	0	0
$852$	5.26416	0.180347
$853$	−3.87282	−0.132603	−0.0663014	−	0.997800i	$-0.521120\pi$
$853$	−3.87282	−0.132603	−0.0663014	+	0.997800i	$0.521120\pi$
$854$	−6.90087	−0.236143
$855$	−7.04583	−0.240962
$856$	−14.8641	−0.508045
$857$	7.20505	0.246120	0.123060	−	0.992399i	$-0.460729\pi$
$857$	7.20505	0.246120	0.123060	+	0.992399i	$0.460729\pi$
$858$	−9.02540	−0.308122
$859$	10.2462	0.349595	0.174797	−	0.984604i	$-0.444073\pi$
$859$	10.2462	0.349595	0.174797	+	0.984604i	$0.444073\pi$
$860$	3.10933	0.106027
$861$	18.1068	0.617079
$862$	−4.81723	−0.164076
$863$	37.1420	1.26433	0.632164	−	0.774835i	$-0.282167\pi$
$863$	37.1420	1.26433	0.632164	+	0.774835i	$0.282167\pi$
$864$	−1.00000	−0.0340207
$865$	−5.46376	−0.185773
$866$	6.25528	0.212563
$867$	1.58552	0.0538471
$868$	13.3415	0.452841
$869$	−4.44382	−0.150746
$870$	6.83020	0.231565
$871$	−65.9013	−2.23298
$872$	−12.2830	−0.415955
$873$	−11.9794	−0.405442
$874$	0	0
$875$	41.8501	1.41479
$876$	−7.18556	−0.242778
$877$	−1.43016	−0.0482930	−0.0241465	−	0.999708i	$-0.507687\pi$
$877$	−1.43016	−0.0482930	−0.0241465	+	0.999708i	$0.507687\pi$
$878$	−13.5454	−0.457134
$879$	−10.4017	−0.350842
$880$	1.76068	0.0593525
$881$	19.8790	0.669740	0.334870	−	0.942264i	$-0.391308\pi$
$881$	19.8790	0.669740	0.334870	+	0.942264i	$0.391308\pi$
$882$	12.5822	0.423666
$883$	16.2884	0.548147	0.274073	−	0.961709i	$-0.411629\pi$
$883$	16.2884	0.548147	0.274073	+	0.961709i	$0.411629\pi$
$884$	−21.4803	−0.722461
$885$	−10.4085	−0.349877
$886$	5.53987	0.186115
$887$	−21.9710	−0.737713	−0.368857	−	0.929486i	$-0.620251\pi$
$887$	−21.9710	−0.737713	−0.368857	+	0.929486i	$0.620251\pi$
$888$	−2.21076	−0.0741882
$889$	24.1279	0.809224
$890$	−12.0885	−0.405206
$891$	1.64964	0.0552651
$892$	−2.55189	−0.0854435
$893$	63.5266	2.12583
$894$	−20.4130	−0.682713
$895$	−20.0092	−0.668835
$896$	−4.42518	−0.147835
$897$	0	0
$898$	−13.5471	−0.452073
$899$	19.2938	0.643485
$900$	−3.86085	−0.128695
$901$	−8.75682	−0.291732
$902$	6.74996	0.224749
$903$	12.8916	0.429007
$904$	3.01462	0.100265
$905$	7.75472	0.257776
$906$	12.7143	0.422406
$907$	−47.0082	−1.56088	−0.780441	−	0.625229i	$-0.785005\pi$
$907$	−47.0082	−1.56088	−0.780441	+	0.625229i	$0.785005\pi$
$908$	19.7228	0.654524
$909$	−18.4610	−0.612311
$910$	−25.8403	−0.856597
$911$	11.5694	0.383310	0.191655	−	0.981462i	$-0.438615\pi$
$911$	11.5694	0.383310	0.191655	+	0.981462i	$0.438615\pi$
$912$	6.60149	0.218597
$913$	−9.13643	−0.302372
$914$	11.1137	0.367609
$915$	−1.66442	−0.0550240
$916$	11.2054	0.370237
$917$	38.3994	1.26806
$918$	3.92613	0.129582
$919$	−35.1441	−1.15930	−0.579648	−	0.814867i	$-0.696810\pi$
$919$	−35.1441	−1.15930	−0.579648	+	0.814867i	$0.696810\pi$
$920$	0	0
$921$	−5.13212	−0.169109
$922$	−33.3324	−1.09774
$923$	−28.8008	−0.947991
$924$	7.29997	0.240151
$925$	−8.53541	−0.280642
$926$	−19.4351	−0.638679
$927$	11.4277	0.375335
$928$	−6.39946	−0.210073
$929$	−35.7727	−1.17366	−0.586832	−	0.809709i	$-0.699625\pi$
$929$	−35.7727	−1.17366	−0.586832	+	0.809709i	$0.699625\pi$
$930$	3.21784	0.105517
$931$	−83.0615	−2.72223
$932$	18.0191	0.590236
$933$	−21.3709	−0.699653
$934$	33.5250	1.09697
$935$	−6.91265	−0.226068
$936$	5.47112	0.178829
$937$	−17.6705	−0.577270	−0.288635	−	0.957439i	$-0.593201\pi$
$937$	−17.6705	−0.577270	−0.288635	+	0.957439i	$0.593201\pi$
$938$	53.3027	1.74039
$939$	15.9653	0.521007
$940$	−10.2708	−0.334996
$941$	15.9220	0.519041	0.259521	−	0.965738i	$-0.416435\pi$
$941$	15.9220	0.519041	0.259521	+	0.965738i	$0.416435\pi$
$942$	−1.14480	−0.0372995
$943$	0	0
$944$	9.75208	0.317403
$945$	4.72304	0.153640
$946$	4.80582	0.156251
$947$	−19.3751	−0.629606	−0.314803	−	0.949157i	$-0.601938\pi$
$947$	−19.3751	−0.629606	−0.314803	+	0.949157i	$0.601938\pi$
$948$	2.69381	0.0874907
$949$	39.3131	1.27616
$950$	25.4874	0.826920
$951$	−10.8838	−0.352933
$952$	17.3738	0.563089
$953$	29.5147	0.956073	0.478037	−	0.878340i	$-0.341349\pi$
$953$	29.5147	0.956073	0.478037	+	0.878340i	$0.341349\pi$
$954$	2.23040	0.0722117
$955$	−26.8766	−0.869706
$956$	27.2479	0.881261
$957$	10.5568	0.341254
$958$	1.65573	0.0534941
$959$	39.7459	1.28346
$960$	−1.06731	−0.0344472
$961$	−21.9103	−0.706784
$962$	12.0953	0.389969
$963$	−14.8641	−0.478990
$964$	22.2765	0.717478
$965$	18.0447	0.580879
$966$	0	0
$967$	5.25882	0.169112	0.0845562	−	0.996419i	$-0.473053\pi$
$967$	5.25882	0.169112	0.0845562	+	0.996419i	$0.473053\pi$
$968$	−8.27868	−0.266087
$969$	−25.9183	−0.832616
$970$	−12.7857	−0.410525
$971$	−20.5102	−0.658204	−0.329102	−	0.944294i	$-0.606746\pi$
$971$	−20.5102	−0.658204	−0.329102	+	0.944294i	$0.606746\pi$
$972$	−1.00000	−0.0320750
$973$	−13.5538	−0.434513
$974$	−20.9954	−0.672737
$975$	21.1232	0.676483
$976$	1.55946	0.0499169
$977$	−1.74232	−0.0557418	−0.0278709	−	0.999612i	$-0.508873\pi$
$977$	−1.74232	−0.0557418	−0.0278709	+	0.999612i	$0.508873\pi$
$978$	−4.80338	−0.153595
$979$	−18.6840	−0.597145
$980$	13.4291	0.428978
$981$	−12.2830	−0.392166
$982$	25.8128	0.823720
$983$	−0.0235072	−0.000749763 0	−0.000374881	−	1.00000i	$-0.500119\pi$
$983$	−0.0235072	−0.000749763 0	−0.000374881		1.00000i	$0.500119\pi$
$984$	−4.09177	−0.130441
$985$	−13.7063	−0.436720
$986$	25.1251	0.800146
$987$	−42.5838	−1.35546
$988$	−36.1176	−1.14905
$989$	0	0
$990$	1.76068	0.0559581
$991$	−15.8169	−0.502441	−0.251220	−	0.967930i	$-0.580832\pi$
$991$	−15.8169	−0.502441	−0.251220	+	0.967930i	$0.580832\pi$
$992$	−3.01491	−0.0957236
$993$	13.5079	0.428659
$994$	23.2948	0.738868
$995$	−14.5203	−0.460324
$996$	5.53843	0.175492
$997$	−9.79242	−0.310129	−0.155065	−	0.987904i	$-0.549559\pi$
$997$	−9.79242	−0.310129	−0.155065	+	0.987904i	$0.549559\pi$
$998$	−6.43766	−0.203780
$999$	−2.21076	−0.0699453

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3174.2.a.bb.1.4		5
3.2	odd	2		9522.2.a.br.1.2		5
23.7	odd	22		138.2.e.b.49.1	yes	10
23.10	odd	22		138.2.e.b.31.1	✓	10
23.22	odd	2		3174.2.a.ba.1.2		5
69.53	even	22		414.2.i.e.325.1		10
69.56	even	22		414.2.i.e.307.1		10
69.68	even	2		9522.2.a.bs.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.b.31.1	✓	10	23.10	odd	22
138.2.e.b.49.1	yes	10	23.7	odd	22
414.2.i.e.307.1		10	69.56	even	22
414.2.i.e.325.1		10	69.53	even	22
3174.2.a.ba.1.2		5	23.22	odd	2
3174.2.a.bb.1.4		5	1.1	even	1	trivial
9522.2.a.br.1.2		5	3.2	odd	2
9522.2.a.bs.1.4		5	69.68	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3174 = 2 \cdot 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3174.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.06731 q^{5} -1.00000 q^{6} -4.42518 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.06731 q^{5} -1.00000 q^{6} -4.42518 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.06731 q^{10} +1.64964 q^{11} -1.00000 q^{12} +5.47112 q^{13} -4.42518 q^{14} -1.06731 q^{15} +1.00000 q^{16} -3.92613 q^{17} +1.00000 q^{18} -6.60149 q^{19} +1.06731 q^{20} +4.42518 q^{21} +1.64964 q^{22} -1.00000 q^{24} -3.86085 q^{25} +5.47112 q^{26} -1.00000 q^{27} -4.42518 q^{28} -6.39946 q^{29} -1.06731 q^{30} -3.01491 q^{31} +1.00000 q^{32} -1.64964 q^{33} -3.92613 q^{34} -4.72304 q^{35} +1.00000 q^{36} +2.21076 q^{37} -6.60149 q^{38} -5.47112 q^{39} +1.06731 q^{40} +4.09177 q^{41} +4.42518 q^{42} +2.91325 q^{43} +1.64964 q^{44} +1.06731 q^{45} -9.62306 q^{47} -1.00000 q^{48} +12.5822 q^{49} -3.86085 q^{50} +3.92613 q^{51} +5.47112 q^{52} +2.23040 q^{53} -1.00000 q^{54} +1.76068 q^{55} -4.42518 q^{56} +6.60149 q^{57} -6.39946 q^{58} +9.75208 q^{59} -1.06731 q^{60} +1.55946 q^{61} -3.01491 q^{62} -4.42518 q^{63} +1.00000 q^{64} +5.83938 q^{65} -1.64964 q^{66} -12.0453 q^{67} -3.92613 q^{68} -4.72304 q^{70} -5.26416 q^{71} +1.00000 q^{72} +7.18556 q^{73} +2.21076 q^{74} +3.86085 q^{75} -6.60149 q^{76} -7.29997 q^{77} -5.47112 q^{78} -2.69381 q^{79} +1.06731 q^{80} +1.00000 q^{81} +4.09177 q^{82} -5.53843 q^{83} +4.42518 q^{84} -4.19039 q^{85} +2.91325 q^{86} +6.39946 q^{87} +1.64964 q^{88} -11.3261 q^{89} +1.06731 q^{90} -24.2107 q^{91} +3.01491 q^{93} -9.62306 q^{94} -7.04583 q^{95} -1.00000 q^{96} -11.9794 q^{97} +12.5822 q^{98} +1.64964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + q^{5} - 5 q^{6} - 11 q^{7} + 5 q^{8} + 5 q^{9} + q^{10} - 11 q^{11} - 5 q^{12} + 12 q^{13} - 11 q^{14} - q^{15} + 5 q^{16} + q^{17} + 5 q^{18} - 15 q^{19} + q^{20} + 11 q^{21} - 11 q^{22} - 5 q^{24} + 6 q^{25} + 12 q^{26} - 5 q^{27} - 11 q^{28} + q^{29} - q^{30} - 18 q^{31} + 5 q^{32} + 11 q^{33} + q^{34} - 11 q^{35} + 5 q^{36} - 10 q^{37} - 15 q^{38} - 12 q^{39} + q^{40} - 16 q^{41} + 11 q^{42} - 18 q^{43} - 11 q^{44} + q^{45} - 4 q^{47} - 5 q^{48} + 20 q^{49} + 6 q^{50} - q^{51} + 12 q^{52} + q^{53} - 5 q^{54} - 22 q^{55} - 11 q^{56} + 15 q^{57} + q^{58} + 2 q^{59} - q^{60} + q^{61} - 18 q^{62} - 11 q^{63} + 5 q^{64} - 24 q^{65} + 11 q^{66} - 29 q^{67} + q^{68} - 11 q^{70} - 11 q^{71} + 5 q^{72} - 8 q^{73} - 10 q^{74} - 6 q^{75} - 15 q^{76} + 11 q^{77} - 12 q^{78} - 40 q^{79} + q^{80} + 5 q^{81} - 16 q^{82} - 8 q^{83} + 11 q^{84} - 13 q^{85} - 18 q^{86} - q^{87} - 11 q^{88} - 2 q^{89} + q^{90} - 33 q^{91} + 18 q^{93} - 4 q^{94} - 3 q^{95} - 5 q^{96} - 17 q^{97} + 20 q^{98} - 11 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + q^5 - 5 * q^6 - 11 * q^7 + 5 * q^8 + 5 * q^9 + q^10 - 11 * q^11 - 5 * q^12 + 12 * q^13 - 11 * q^14 - q^15 + 5 * q^16 + q^17 + 5 * q^18 - 15 * q^19 + q^20 + 11 * q^21 - 11 * q^22 - 5 * q^24 + 6 * q^25 + 12 * q^26 - 5 * q^27 - 11 * q^28 + q^29 - q^30 - 18 * q^31 + 5 * q^32 + 11 * q^33 + q^34 - 11 * q^35 + 5 * q^36 - 10 * q^37 - 15 * q^38 - 12 * q^39 + q^40 - 16 * q^41 + 11 * q^42 - 18 * q^43 - 11 * q^44 + q^45 - 4 * q^47 - 5 * q^48 + 20 * q^49 + 6 * q^50 - q^51 + 12 * q^52 + q^53 - 5 * q^54 - 22 * q^55 - 11 * q^56 + 15 * q^57 + q^58 + 2 * q^59 - q^60 + q^61 - 18 * q^62 - 11 * q^63 + 5 * q^64 - 24 * q^65 + 11 * q^66 - 29 * q^67 + q^68 - 11 * q^70 - 11 * q^71 + 5 * q^72 - 8 * q^73 - 10 * q^74 - 6 * q^75 - 15 * q^76 + 11 * q^77 - 12 * q^78 - 40 * q^79 + q^80 + 5 * q^81 - 16 * q^82 - 8 * q^83 + 11 * q^84 - 13 * q^85 - 18 * q^86 - q^87 - 11 * q^88 - 2 * q^89 + q^90 - 33 * q^91 + 18 * q^93 - 4 * q^94 - 3 * q^95 - 5 * q^96 - 17 * q^97 + 20 * q^98 - 11 * q^99

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