LMFDB - Embedded newform 667.2.a.d.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} - 22 x^{14} + 68 x^{13} + 187 x^{12} - 597 x^{11} - 795 x^{10} + 2592 x^{9} + \cdots + 64 $ x^16 - 3x^15 - 22x^14 + 68x^13 + 187x^12 - 597x^11 - 795x^10 + 2592x^9 + 1860x^8 - 5877x^7 - 2496x^6 + 6612x^5 + 1842x^4 - 3011x^3 - 505x^2 + 336*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$1.88851$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.88851 q^{2} +0.985425 q^{3} +1.56646 q^{4} +3.37829 q^{5} +1.86098 q^{6} +1.01841 q^{7} -0.818750 q^{8} -2.02894 q^{9} +O(q^{10})$	\(q+1.88851 q^{2} +0.985425 q^{3} +1.56646 q^{4} +3.37829 q^{5} +1.86098 q^{6} +1.01841 q^{7} -0.818750 q^{8} -2.02894 q^{9} +6.37991 q^{10} -3.49970 q^{11} +1.54363 q^{12} +6.75636 q^{13} +1.92327 q^{14} +3.32905 q^{15} -4.67913 q^{16} +0.401525 q^{17} -3.83166 q^{18} -4.47325 q^{19} +5.29194 q^{20} +1.00356 q^{21} -6.60920 q^{22} +1.00000 q^{23} -0.806816 q^{24} +6.41281 q^{25} +12.7594 q^{26} -4.95564 q^{27} +1.59529 q^{28} -1.00000 q^{29} +6.28693 q^{30} -9.89960 q^{31} -7.19906 q^{32} -3.44869 q^{33} +0.758282 q^{34} +3.44047 q^{35} -3.17824 q^{36} +7.54484 q^{37} -8.44776 q^{38} +6.65789 q^{39} -2.76597 q^{40} +9.45431 q^{41} +1.89524 q^{42} -0.331050 q^{43} -5.48212 q^{44} -6.85433 q^{45} +1.88851 q^{46} -3.53155 q^{47} -4.61093 q^{48} -5.96285 q^{49} +12.1106 q^{50} +0.395673 q^{51} +10.5835 q^{52} -6.65867 q^{53} -9.35876 q^{54} -11.8230 q^{55} -0.833820 q^{56} -4.40805 q^{57} -1.88851 q^{58} +5.79376 q^{59} +5.21481 q^{60} -2.17367 q^{61} -18.6955 q^{62} -2.06628 q^{63} -4.23722 q^{64} +22.8249 q^{65} -6.51287 q^{66} +5.30065 q^{67} +0.628971 q^{68} +0.985425 q^{69} +6.49734 q^{70} +8.86081 q^{71} +1.66119 q^{72} -2.05083 q^{73} +14.2485 q^{74} +6.31934 q^{75} -7.00715 q^{76} -3.56411 q^{77} +12.5735 q^{78} -1.29928 q^{79} -15.8074 q^{80} +1.20340 q^{81} +17.8545 q^{82} -2.18842 q^{83} +1.57204 q^{84} +1.35647 q^{85} -0.625189 q^{86} -0.985425 q^{87} +2.86537 q^{88} +14.4156 q^{89} -12.9444 q^{90} +6.88072 q^{91} +1.56646 q^{92} -9.75531 q^{93} -6.66936 q^{94} -15.1119 q^{95} -7.09414 q^{96} -14.3144 q^{97} -11.2609 q^{98} +7.10066 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) $ 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * 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 $

$2$	1.88851	1.33538	0.667688	−	0.744441i	$-0.267284\pi$
$2$	1.88851	1.33538	0.667688	+	0.744441i	$0.267284\pi$
$3$	0.985425	0.568935	0.284468	−	0.958686i	$-0.408183\pi$
$3$	0.985425	0.568935	0.284468	+	0.958686i	$0.408183\pi$
$4$	1.56646	0.783228
$5$	3.37829	1.51081	0.755407	−	0.655255i	$-0.227439\pi$
$5$	3.37829	1.51081	0.755407	+	0.655255i	$0.227439\pi$
$6$	1.86098	0.759742
$7$	1.01841	0.384921	0.192461	−	0.981305i	$-0.438353\pi$
$7$	1.01841	0.384921	0.192461	+	0.981305i	$0.438353\pi$
$8$	−0.818750	−0.289472
$9$	−2.02894	−0.676313
$10$	6.37991	2.01751
$11$	−3.49970	−1.05520	−0.527599	−	0.849494i	$-0.676908\pi$
$11$	−3.49970	−1.05520	−0.527599	+	0.849494i	$0.676908\pi$
$12$	1.54363	0.445606
$13$	6.75636	1.87388	0.936938	−	0.349494i	$-0.113647\pi$
$13$	6.75636	1.87388	0.936938	+	0.349494i	$0.113647\pi$
$14$	1.92327	0.514015
$15$	3.32905	0.859556
$16$	−4.67913	−1.16978
$17$	0.401525	0.0973841	0.0486920	−	0.998814i	$-0.484495\pi$
$17$	0.401525	0.0973841	0.0486920	+	0.998814i	$0.484495\pi$
$18$	−3.83166	−0.903131
$19$	−4.47325	−1.02623	−0.513117	−	0.858319i	$-0.671509\pi$
$19$	−4.47325	−1.02623	−0.513117	+	0.858319i	$0.671509\pi$
$20$	5.29194	1.18331
$21$	1.00356	0.218995
$22$	−6.60920	−1.40909
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.806816	−0.164691
$25$	6.41281	1.28256
$26$	12.7594	2.50233
$27$	−4.95564	−0.953713
$28$	1.59529	0.301481
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	6.28693	1.14783
$31$	−9.89960	−1.77802	−0.889010	−	0.457887i	$-0.848606\pi$
$31$	−9.89960	−1.77802	−0.889010	+	0.457887i	$0.848606\pi$
$32$	−7.19906	−1.27263
$33$	−3.44869	−0.600339
$34$	0.758282	0.130044
$35$	3.44047	0.581545
$36$	−3.17824	−0.529707
$37$	7.54484	1.24036	0.620182	−	0.784458i	$-0.287059\pi$
$37$	7.54484	1.24036	0.620182	+	0.784458i	$0.287059\pi$
$38$	−8.44776	−1.37041
$39$	6.65789	1.06611
$40$	−2.76597	−0.437338
$41$	9.45431	1.47652	0.738258	−	0.674519i	$-0.235649\pi$
$41$	9.45431	1.47652	0.738258	+	0.674519i	$0.235649\pi$
$42$	1.89524	0.292441
$43$	−0.331050	−0.0504846	−0.0252423	−	0.999681i	$-0.508036\pi$
$43$	−0.331050	−0.0504846	−0.0252423	+	0.999681i	$0.508036\pi$
$44$	−5.48212	−0.826461
$45$	−6.85433	−1.02178
$46$	1.88851	0.278445
$47$	−3.53155	−0.515130	−0.257565	−	0.966261i	$-0.582920\pi$
$47$	−3.53155	−0.515130	−0.257565	+	0.966261i	$0.582920\pi$
$48$	−4.61093	−0.665530
$49$	−5.96285	−0.851835
$50$	12.1106	1.71270
$51$	0.395673	0.0554052
$52$	10.5835	1.46767
$53$	−6.65867	−0.914638	−0.457319	−	0.889303i	$-0.651190\pi$
$53$	−6.65867	−0.914638	−0.457319	+	0.889303i	$0.651190\pi$
$54$	−9.35876	−1.27357
$55$	−11.8230	−1.59421
$56$	−0.833820	−0.111424
$57$	−4.40805	−0.583861
$58$	−1.88851	−0.247973
$59$	5.79376	0.754283	0.377141	−	0.926156i	$-0.376907\pi$
$59$	5.79376	0.754283	0.377141	+	0.926156i	$0.376907\pi$
$60$	5.21481	0.673229
$61$	−2.17367	−0.278310	−0.139155	−	0.990271i	$-0.544439\pi$
$61$	−2.17367	−0.278310	−0.139155	+	0.990271i	$0.544439\pi$
$62$	−18.6955	−2.37433
$63$	−2.06628	−0.260327
$64$	−4.23722	−0.529653
$65$	22.8249	2.83108
$66$	−6.51287	−0.801679
$67$	5.30065	0.647577	0.323789	−	0.946129i	$-0.395043\pi$
$67$	5.30065	0.647577	0.323789	+	0.946129i	$0.395043\pi$
$68$	0.628971	0.0762740
$69$	0.985425	0.118631
$70$	6.49734	0.776581
$71$	8.86081	1.05158	0.525792	−	0.850613i	$-0.323769\pi$
$71$	8.86081	1.05158	0.525792	+	0.850613i	$0.323769\pi$
$72$	1.66119	0.195773
$73$	−2.05083	−0.240031	−0.120015	−	0.992772i	$-0.538294\pi$
$73$	−2.05083	−0.240031	−0.120015	+	0.992772i	$0.538294\pi$
$74$	14.2485	1.65635
$75$	6.31934	0.729695
$76$	−7.00715	−0.803775
$77$	−3.56411	−0.406168
$78$	12.5735	1.42366
$79$	−1.29928	−0.146181	−0.0730904	−	0.997325i	$-0.523286\pi$
$79$	−1.29928	−0.146181	−0.0730904	+	0.997325i	$0.523286\pi$
$80$	−15.8074	−1.76732
$81$	1.20340	0.133711
$82$	17.8545	1.97170
$83$	−2.18842	−0.240210	−0.120105	−	0.992761i	$-0.538323\pi$
$83$	−2.18842	−0.240210	−0.120105	+	0.992761i	$0.538323\pi$
$84$	1.57204	0.171523
$85$	1.35647	0.147129
$86$	−0.625189	−0.0674159
$87$	−0.985425	−0.105649
$88$	2.86537	0.305450
$89$	14.4156	1.52805	0.764025	−	0.645187i	$-0.223220\pi$
$89$	14.4156	1.52805	0.764025	+	0.645187i	$0.223220\pi$
$90$	−12.9444	−1.36446
$91$	6.88072	0.721295
$92$	1.56646	0.163314
$93$	−9.75531	−1.01158
$94$	−6.66936	−0.687892
$95$	−15.1119	−1.55045
$96$	−7.09414	−0.724042
$97$	−14.3144	−1.45341	−0.726704	−	0.686951i	$-0.758949\pi$
$97$	−14.3144	−1.45341	−0.726704	+	0.686951i	$0.758949\pi$
$98$	−11.2609	−1.13752
$99$	7.10066	0.713644
$100$	10.0454	1.00454
$101$	−0.807141	−0.0803135	−0.0401568	−	0.999193i	$-0.512786\pi$
$101$	−0.807141	−0.0803135	−0.0401568	+	0.999193i	$0.512786\pi$
$102$	0.747230	0.0739868
$103$	−4.43836	−0.437325	−0.218662	−	0.975801i	$-0.570169\pi$
$103$	−4.43836	−0.437325	−0.218662	+	0.975801i	$0.570169\pi$
$104$	−5.53177	−0.542434
$105$	3.39032	0.330862
$106$	−12.5749	−1.22139
$107$	−9.76581	−0.944096	−0.472048	−	0.881573i	$-0.656485\pi$
$107$	−9.76581	−0.944096	−0.472048	+	0.881573i	$0.656485\pi$
$108$	−7.76280	−0.746975
$109$	7.56403	0.724503	0.362251	−	0.932080i	$-0.382008\pi$
$109$	7.56403	0.724503	0.362251	+	0.932080i	$0.382008\pi$
$110$	−22.3278	−2.12887
$111$	7.43487	0.705687
$112$	−4.76525	−0.450274
$113$	−5.08324	−0.478191	−0.239096	−	0.970996i	$-0.576851\pi$
$113$	−5.08324	−0.478191	−0.239096	+	0.970996i	$0.576851\pi$
$114$	−8.32463	−0.779673
$115$	3.37829	0.315027
$116$	−1.56646	−0.145442
$117$	−13.7082	−1.26733
$118$	10.9415	1.00725
$119$	0.408915	0.0374852
$120$	−2.72566	−0.248817
$121$	1.24787	0.113443
$122$	−4.10499	−0.371648
$123$	9.31652	0.840042
$124$	−15.5073	−1.39260
$125$	4.77287	0.426899
$126$	−3.90219	−0.347635
$127$	0.260365	0.0231037	0.0115518	−	0.999933i	$-0.496323\pi$
$127$	0.260365	0.0231037	0.0115518	+	0.999933i	$0.496323\pi$
$128$	6.39610	0.565341
$129$	−0.326225	−0.0287225
$130$	43.1050	3.78056
$131$	0.831168	0.0726195	0.0363098	−	0.999341i	$-0.488440\pi$
$131$	0.831168	0.0726195	0.0363098	+	0.999341i	$0.488440\pi$
$132$	−5.40222	−0.470203
$133$	−4.55559	−0.395019
$134$	10.0103	0.864759
$135$	−16.7416	−1.44088
$136$	−0.328748	−0.0281899
$137$	−7.87284	−0.672622	−0.336311	−	0.941751i	$-0.609179\pi$
$137$	−7.87284	−0.672622	−0.336311	+	0.941751i	$0.609179\pi$
$138$	1.86098	0.158417
$139$	12.4717	1.05784	0.528920	−	0.848672i	$-0.322597\pi$
$139$	12.4717	1.05784	0.528920	+	0.848672i	$0.322597\pi$
$140$	5.38934	0.455483
$141$	−3.48008	−0.293076
$142$	16.7337	1.40426
$143$	−23.6452	−1.97731
$144$	9.49366	0.791138
$145$	−3.37829	−0.280551
$146$	−3.87300	−0.320532
$147$	−5.87594	−0.484639
$148$	11.8187	0.971488
$149$	−13.1304	−1.07568	−0.537841	−	0.843047i	$-0.680760\pi$
$149$	−13.1304	−1.07568	−0.537841	+	0.843047i	$0.680760\pi$
$150$	11.9341	0.974417
$151$	12.7125	1.03453	0.517266	−	0.855825i	$-0.326950\pi$
$151$	12.7125	1.03453	0.517266	+	0.855825i	$0.326950\pi$
$152$	3.66247	0.297066
$153$	−0.814669	−0.0658621
$154$	−6.73085	−0.542387
$155$	−33.4437	−2.68626
$156$	10.4293	0.835011
$157$	−13.4966	−1.07715	−0.538574	−	0.842578i	$-0.681037\pi$
$157$	−13.4966	−1.07715	−0.538574	+	0.842578i	$0.681037\pi$
$158$	−2.45370	−0.195206
$159$	−6.56162	−0.520370
$160$	−24.3205	−1.92270
$161$	1.01841	0.0802617
$162$	2.27263	0.178555
$163$	18.3806	1.43968	0.719841	−	0.694139i	$-0.244215\pi$
$163$	18.3806	1.43968	0.719841	+	0.694139i	$0.244215\pi$
$164$	14.8098	1.15645
$165$	−11.6506	−0.907002
$166$	−4.13284	−0.320771
$167$	−19.3127	−1.49446	−0.747229	−	0.664566i	$-0.768616\pi$
$167$	−19.3127	−1.49446	−0.747229	+	0.664566i	$0.768616\pi$
$168$	−0.821667	−0.0633930
$169$	32.6484	2.51141
$170$	2.56169	0.196473
$171$	9.07594	0.694055
$172$	−0.518575	−0.0395410
$173$	21.1572	1.60855	0.804277	−	0.594255i	$-0.202553\pi$
$173$	21.1572	1.60855	0.804277	+	0.594255i	$0.202553\pi$
$174$	−1.86098	−0.141081
$175$	6.53085	0.493686
$176$	16.3755	1.23435
$177$	5.70931	0.429138
$178$	27.2239	2.04052
$179$	−3.45804	−0.258466	−0.129233	−	0.991614i	$-0.541252\pi$
$179$	−3.45804	−0.258466	−0.129233	+	0.991614i	$0.541252\pi$
$180$	−10.7370	−0.800289
$181$	−23.5705	−1.75198	−0.875991	−	0.482328i	$-0.839791\pi$
$181$	−23.5705	−1.75198	−0.875991	+	0.482328i	$0.839791\pi$
$182$	12.9943	0.963200
$183$	−2.14199	−0.158340
$184$	−0.818750	−0.0603590
$185$	25.4886	1.87396
$186$	−18.4230	−1.35084
$187$	−1.40521	−0.102759
$188$	−5.53203	−0.403464
$189$	−5.04686	−0.367105
$190$	−28.5389	−2.07043
$191$	22.3003	1.61360	0.806798	−	0.590828i	$-0.201199\pi$
$191$	22.3003	1.61360	0.806798	+	0.590828i	$0.201199\pi$
$192$	−4.17546	−0.301338
$193$	11.5107	0.828561	0.414280	−	0.910149i	$-0.364033\pi$
$193$	11.5107	0.828561	0.414280	+	0.910149i	$0.364033\pi$
$194$	−27.0329	−1.94085
$195$	22.4922	1.61070
$196$	−9.34054	−0.667182
$197$	1.69924	0.121066	0.0605328	−	0.998166i	$-0.480720\pi$
$197$	1.69924	0.121066	0.0605328	+	0.998166i	$0.480720\pi$
$198$	13.4096	0.952982
$199$	−4.25008	−0.301280	−0.150640	−	0.988589i	$-0.548133\pi$
$199$	−4.25008	−0.301280	−0.150640	+	0.988589i	$0.548133\pi$
$200$	−5.25049	−0.371265
$201$	5.22339	0.368429
$202$	−1.52429	−0.107249
$203$	−1.01841	−0.0714781
$204$	0.619804	0.0433950
$205$	31.9394	2.23074
$206$	−8.38187	−0.583993
$207$	−2.02894	−0.141021
$208$	−31.6139	−2.19203
$209$	15.6550	1.08288
$210$	6.40265	0.441824
$211$	−11.2479	−0.774336	−0.387168	−	0.922009i	$-0.626547\pi$
$211$	−11.2479	−0.774336	−0.387168	+	0.922009i	$0.626547\pi$
$212$	−10.4305	−0.716371
$213$	8.73166	0.598284
$214$	−18.4428	−1.26072
$215$	−1.11838	−0.0762729
$216$	4.05743	0.276073
$217$	−10.0818	−0.684398
$218$	14.2847	0.967484
$219$	−2.02093	−0.136562
$220$	−18.5202	−1.24863
$221$	2.71285	0.182486
$222$	14.0408	0.942357
$223$	20.7869	1.39199	0.695997	−	0.718045i	$-0.254963\pi$
$223$	20.7869	1.39199	0.695997	+	0.718045i	$0.254963\pi$
$224$	−7.33157	−0.489861
$225$	−13.0112	−0.867413
$226$	−9.59974	−0.638565
$227$	11.3394	0.752625	0.376312	−	0.926493i	$-0.377192\pi$
$227$	11.3394	0.752625	0.376312	+	0.926493i	$0.377192\pi$
$228$	−6.90502	−0.457296
$229$	−0.135439	−0.00895004	−0.00447502	−	0.999990i	$-0.501424\pi$
$229$	−0.135439	−0.00895004	−0.00447502	+	0.999990i	$0.501424\pi$
$230$	6.37991	0.420679
$231$	−3.51217	−0.231084
$232$	0.818750	0.0537535
$233$	24.0364	1.57468	0.787338	−	0.616522i	$-0.211459\pi$
$233$	24.0364	1.57468	0.787338	+	0.616522i	$0.211459\pi$
$234$	−25.8881	−1.69236
$235$	−11.9306	−0.778266
$236$	9.07567	0.590776
$237$	−1.28035	−0.0831674
$238$	0.772239	0.0500568
$239$	29.4679	1.90612	0.953059	−	0.302785i	$-0.0979163\pi$
$239$	29.4679	1.90612	0.953059	+	0.302785i	$0.0979163\pi$
$240$	−15.5770	−1.00549
$241$	22.1913	1.42947	0.714733	−	0.699398i	$-0.246548\pi$
$241$	22.1913	1.42947	0.714733	+	0.699398i	$0.246548\pi$
$242$	2.35661	0.151488
$243$	16.0528	1.02979
$244$	−3.40496	−0.217980
$245$	−20.1442	−1.28697
$246$	17.5943	1.12177
$247$	−30.2229	−1.92304
$248$	8.10529	0.514687
$249$	−2.15652	−0.136664
$250$	9.01360	0.570070
$251$	−1.15155	−0.0726850	−0.0363425	−	0.999339i	$-0.511571\pi$
$251$	−1.15155	−0.0726850	−0.0363425	+	0.999339i	$0.511571\pi$
$252$	−3.23674	−0.203896
$253$	−3.49970	−0.220024
$254$	0.491701	0.0308521
$255$	1.33669	0.0837071
$256$	20.5535	1.28460
$257$	3.28749	0.205068	0.102534	−	0.994730i	$-0.467305\pi$
$257$	3.28749	0.205068	0.102534	+	0.994730i	$0.467305\pi$
$258$	−0.616077	−0.0383553
$259$	7.68371	0.477443
$260$	35.7542	2.21738
$261$	2.02894	0.125588
$262$	1.56967	0.0969743
$263$	−25.6739	−1.58312	−0.791559	−	0.611093i	$-0.790730\pi$
$263$	−25.6739	−1.58312	−0.791559	+	0.611093i	$0.790730\pi$
$264$	2.82361	0.173781
$265$	−22.4949	−1.38185
$266$	−8.60325	−0.527499
$267$	14.2055	0.869362
$268$	8.30323	0.507201
$269$	2.71824	0.165734	0.0828669	−	0.996561i	$-0.473592\pi$
$269$	2.71824	0.165734	0.0828669	+	0.996561i	$0.473592\pi$
$270$	−31.6166	−1.92412
$271$	−30.4113	−1.84736	−0.923678	−	0.383169i	$-0.874833\pi$
$271$	−30.4113	−1.84736	−0.923678	+	0.383169i	$0.874833\pi$
$272$	−1.87879	−0.113918
$273$	6.78043	0.410370
$274$	−14.8679	−0.898203
$275$	−22.4429	−1.35336
$276$	1.54363	0.0929153
$277$	−1.67444	−0.100607	−0.0503036	−	0.998734i	$-0.516019\pi$
$277$	−1.67444	−0.100607	−0.0503036	+	0.998734i	$0.516019\pi$
$278$	23.5530	1.41261
$279$	20.0857	1.20250
$280$	−2.81688	−0.168341
$281$	8.43741	0.503333	0.251667	−	0.967814i	$-0.419021\pi$
$281$	8.43741	0.503333	0.251667	+	0.967814i	$0.419021\pi$
$282$	−6.57216	−0.391366
$283$	−12.4094	−0.737662	−0.368831	−	0.929497i	$-0.620242\pi$
$283$	−12.4094	−0.737662	−0.368831	+	0.929497i	$0.620242\pi$
$284$	13.8801	0.823631
$285$	−14.8917	−0.882105
$286$	−44.6541	−2.64045
$287$	9.62833	0.568343
$288$	14.6064	0.860693
$289$	−16.8388	−0.990516
$290$	−6.37991	−0.374641
$291$	−14.1058	−0.826895
$292$	−3.21253	−0.187999
$293$	23.7307	1.38636	0.693181	−	0.720763i	$-0.256208\pi$
$293$	23.7307	1.38636	0.693181	+	0.720763i	$0.256208\pi$
$294$	−11.0967	−0.647176
$295$	19.5730	1.13958
$296$	−6.17734	−0.359050
$297$	17.3432	1.00636
$298$	−24.7968	−1.43644
$299$	6.75636	0.390730
$300$	9.89898	0.571518
$301$	−0.337143	−0.0194326
$302$	24.0077	1.38149
$303$	−0.795377	−0.0456932
$304$	20.9309	1.20047
$305$	−7.34328	−0.420475
$306$	−1.53851	−0.0879506
$307$	26.5915	1.51766	0.758829	−	0.651290i	$-0.225772\pi$
$307$	26.5915	1.51766	0.758829	+	0.651290i	$0.225772\pi$
$308$	−5.58303	−0.318122
$309$	−4.37367	−0.248809
$310$	−63.1586	−3.58717
$311$	5.43587	0.308240	0.154120	−	0.988052i	$-0.450746\pi$
$311$	5.43587	0.308240	0.154120	+	0.988052i	$0.450746\pi$
$312$	−5.45114	−0.308610
$313$	16.4961	0.932413	0.466207	−	0.884676i	$-0.345620\pi$
$313$	16.4961	0.932413	0.466207	+	0.884676i	$0.345620\pi$
$314$	−25.4885	−1.43840
$315$	−6.98049	−0.393306
$316$	−2.03527	−0.114493
$317$	−9.95220	−0.558971	−0.279486	−	0.960150i	$-0.590164\pi$
$317$	−9.95220	−0.558971	−0.279486	+	0.960150i	$0.590164\pi$
$318$	−12.3917	−0.694890
$319$	3.49970	0.195945
$320$	−14.3145	−0.800207
$321$	−9.62347	−0.537130
$322$	1.92327	0.107179
$323$	−1.79612	−0.0999388
$324$	1.88508	0.104726
$325$	43.3272	2.40336
$326$	34.7119	1.92252
$327$	7.45379	0.412195
$328$	−7.74072	−0.427409
$329$	−3.59656	−0.198285
$330$	−22.0023	−1.21119
$331$	−5.66600	−0.311432	−0.155716	−	0.987802i	$-0.549768\pi$
$331$	−5.66600	−0.311432	−0.155716	+	0.987802i	$0.549768\pi$
$332$	−3.42806	−0.188139
$333$	−15.3080	−0.838874
$334$	−36.4721	−1.99566
$335$	17.9071	0.978369
$336$	−4.69580	−0.256177
$337$	−0.573110	−0.0312193	−0.0156096	−	0.999878i	$-0.504969\pi$
$337$	−0.573110	−0.0312193	−0.0156096	+	0.999878i	$0.504969\pi$
$338$	61.6567	3.35368
$339$	−5.00915	−0.272060
$340$	2.12484	0.115236
$341$	34.6456	1.87616
$342$	17.1400	0.926824
$343$	−13.2014	−0.712811
$344$	0.271047	0.0146139
$345$	3.32905	0.179230
$346$	39.9555	2.14802
$347$	1.39354	0.0748090	0.0374045	−	0.999300i	$-0.488091\pi$
$347$	1.39354	0.0748090	0.0374045	+	0.999300i	$0.488091\pi$
$348$	−1.54363	−0.0827470
$349$	−8.04697	−0.430745	−0.215372	−	0.976532i	$-0.569096\pi$
$349$	−8.04697	−0.430745	−0.215372	+	0.976532i	$0.569096\pi$
$350$	12.3335	0.659256
$351$	−33.4821	−1.78714
$352$	25.1945	1.34287
$353$	29.3886	1.56420	0.782098	−	0.623155i	$-0.214150\pi$
$353$	29.3886	1.56420	0.782098	+	0.623155i	$0.214150\pi$
$354$	10.7821	0.573061
$355$	29.9343	1.58875
$356$	22.5814	1.19681
$357$	0.402955	0.0213267
$358$	−6.53053	−0.345149
$359$	17.9826	0.949085	0.474542	−	0.880233i	$-0.342614\pi$
$359$	17.9826	0.949085	0.474542	+	0.880233i	$0.342614\pi$
$360$	5.61198	0.295777
$361$	1.00996	0.0531558
$362$	−44.5130	−2.33955
$363$	1.22968	0.0645415
$364$	10.7783	0.564939
$365$	−6.92827	−0.362642
$366$	−4.04516	−0.211444
$367$	7.56962	0.395131	0.197566	−	0.980290i	$-0.436696\pi$
$367$	7.56962	0.395131	0.197566	+	0.980290i	$0.436696\pi$
$368$	−4.67913	−0.243916
$369$	−19.1822	−0.998586
$370$	48.1354	2.50244
$371$	−6.78123	−0.352064
$372$	−15.2813	−0.792297
$373$	5.24304	0.271474	0.135737	−	0.990745i	$-0.456660\pi$
$373$	5.24304	0.271474	0.135737	+	0.990745i	$0.456660\pi$
$374$	−2.65376	−0.137222
$375$	4.70331	0.242878
$376$	2.89146	0.149116
$377$	−6.75636	−0.347970
$378$	−9.53102	−0.490223
$379$	−23.3251	−1.19813	−0.599064	−	0.800701i	$-0.704460\pi$
$379$	−23.3251	−1.19813	−0.599064	+	0.800701i	$0.704460\pi$
$380$	−23.6722	−1.21436
$381$	0.256570	0.0131445
$382$	42.1143	2.15476
$383$	23.0627	1.17845	0.589225	−	0.807969i	$-0.299433\pi$
$383$	23.0627	1.17845	0.589225	+	0.807969i	$0.299433\pi$
$384$	6.30288	0.321643
$385$	−12.0406	−0.613645
$386$	21.7381	1.10644
$387$	0.671679	0.0341434
$388$	−22.4229	−1.13835
$389$	−28.8661	−1.46357	−0.731786	−	0.681535i	$-0.761313\pi$
$389$	−28.8661	−1.46357	−0.731786	+	0.681535i	$0.761313\pi$
$390$	42.4767	2.15089
$391$	0.401525	0.0203060
$392$	4.88208	0.246582
$393$	0.819054	0.0413158
$394$	3.20902	0.161668
$395$	−4.38935	−0.220852
$396$	11.1229	0.558946
$397$	−14.8976	−0.747688	−0.373844	−	0.927492i	$-0.621960\pi$
$397$	−14.8976	−0.747688	−0.373844	+	0.927492i	$0.621960\pi$
$398$	−8.02631	−0.402322
$399$	−4.48919	−0.224741
$400$	−30.0064	−1.50032
$401$	−21.5622	−1.07677	−0.538384	−	0.842700i	$-0.680965\pi$
$401$	−21.5622	−1.07677	−0.538384	+	0.842700i	$0.680965\pi$
$402$	9.86440	0.491992
$403$	−66.8853	−3.33179
$404$	−1.26435	−0.0629038
$405$	4.06543	0.202013
$406$	−1.92327	−0.0954501
$407$	−26.4046	−1.30883
$408$	−0.323957	−0.0160382
$409$	−26.9456	−1.33237	−0.666187	−	0.745784i	$-0.732075\pi$
$409$	−26.9456	−1.33237	−0.666187	+	0.745784i	$0.732075\pi$
$410$	60.3177	2.97888
$411$	−7.75809	−0.382678
$412$	−6.95250	−0.342525
$413$	5.90040	0.290340
$414$	−3.83166	−0.188316
$415$	−7.39310	−0.362913
$416$	−48.6395	−2.38475
$417$	12.2900	0.601843
$418$	29.5646	1.44605
$419$	16.0755	0.785339	0.392670	−	0.919680i	$-0.371552\pi$
$419$	16.0755	0.785339	0.392670	+	0.919680i	$0.371552\pi$
$420$	5.31079	0.259140
$421$	39.0641	1.90387	0.951935	−	0.306300i	$-0.0990911\pi$
$421$	39.0641	1.90387	0.951935	+	0.306300i	$0.0990911\pi$
$422$	−21.2417	−1.03403
$423$	7.16530	0.348389
$424$	5.45178	0.264762
$425$	2.57490	0.124901
$426$	16.4898	0.798934
$427$	−2.21368	−0.107127
$428$	−15.2977	−0.739443
$429$	−23.3006	−1.12496
$430$	−2.11207	−0.101853
$431$	−15.7987	−0.760994	−0.380497	−	0.924782i	$-0.624247\pi$
$431$	−15.7987	−0.760994	−0.380497	+	0.924782i	$0.624247\pi$
$432$	23.1881	1.11564
$433$	−29.3863	−1.41222	−0.706108	−	0.708105i	$-0.749551\pi$
$433$	−29.3863	−1.41222	−0.706108	+	0.708105i	$0.749551\pi$
$434$	−19.0396	−0.913929
$435$	−3.32905	−0.159616
$436$	11.8487	0.567451
$437$	−4.47325	−0.213985
$438$	−3.81655	−0.182362
$439$	32.1319	1.53357	0.766785	−	0.641904i	$-0.221855\pi$
$439$	32.1319	1.53357	0.766785	+	0.641904i	$0.221855\pi$
$440$	9.68005	0.461478
$441$	12.0982	0.576107
$442$	5.12323	0.243687
$443$	31.6378	1.50316	0.751579	−	0.659644i	$-0.229293\pi$
$443$	31.6378	1.50316	0.751579	+	0.659644i	$0.229293\pi$
$444$	11.6464	0.552714
$445$	48.7000	2.30860
$446$	39.2562	1.85884
$447$	−12.9390	−0.611993
$448$	−4.31521	−0.203875
$449$	27.7325	1.30878	0.654389	−	0.756158i	$-0.272926\pi$
$449$	27.7325	1.30878	0.654389	+	0.756158i	$0.272926\pi$
$450$	−24.5717	−1.15832
$451$	−33.0872	−1.55802
$452$	−7.96268	−0.374533
$453$	12.5273	0.588582
$454$	21.4146	1.00504
$455$	23.2450	1.08974
$456$	3.60909	0.169011
$457$	−25.5701	−1.19612	−0.598058	−	0.801452i	$-0.704061\pi$
$457$	−25.5701	−1.19612	−0.598058	+	0.801452i	$0.704061\pi$
$458$	−0.255777	−0.0119517
$459$	−1.98981	−0.0928765
$460$	5.29194	0.246738
$461$	−33.2904	−1.55049	−0.775243	−	0.631663i	$-0.782373\pi$
$461$	−33.2904	−1.55049	−0.775243	+	0.631663i	$0.782373\pi$
$462$	−6.63275	−0.308583
$463$	0.701135	0.0325845	0.0162923	−	0.999867i	$-0.494814\pi$
$463$	0.701135	0.0325845	0.0162923	+	0.999867i	$0.494814\pi$
$464$	4.67913	0.217223
$465$	−32.9562	−1.52831
$466$	45.3928	2.10278
$467$	−23.6556	−1.09465	−0.547326	−	0.836919i	$-0.684354\pi$
$467$	−23.6556	−1.09465	−0.547326	+	0.836919i	$0.684354\pi$
$468$	−21.4734	−0.992606
$469$	5.39821	0.249266
$470$	−22.5310	−1.03928
$471$	−13.2999	−0.612828
$472$	−4.74363	−0.218343
$473$	1.15857	0.0532712
$474$	−2.41794	−0.111060
$475$	−28.6861	−1.31621
$476$	0.640548	0.0293595
$477$	13.5100	0.618581
$478$	55.6503	2.54538
$479$	−19.0403	−0.869976	−0.434988	−	0.900436i	$-0.643247\pi$
$479$	−19.0403	−0.869976	−0.434988	+	0.900436i	$0.643247\pi$
$480$	−23.9660	−1.09389
$481$	50.9757	2.32429
$482$	41.9084	1.90887
$483$	1.00356	0.0456637
$484$	1.95473	0.0888514
$485$	−48.3582	−2.19583
$486$	30.3158	1.37515
$487$	9.94987	0.450872	0.225436	−	0.974258i	$-0.427619\pi$
$487$	9.94987	0.450872	0.225436	+	0.974258i	$0.427619\pi$
$488$	1.77969	0.0805629
$489$	18.1127	0.819086
$490$	−38.0425	−1.71858
$491$	3.67131	0.165684	0.0828419	−	0.996563i	$-0.473600\pi$
$491$	3.67131	0.165684	0.0828419	+	0.996563i	$0.473600\pi$
$492$	14.5939	0.657945
$493$	−0.401525	−0.0180838
$494$	−57.0761	−2.56798
$495$	23.9881	1.07818
$496$	46.3215	2.07990
$497$	9.02391	0.404778
$498$	−4.07260	−0.182498
$499$	−11.2608	−0.504105	−0.252052	−	0.967714i	$-0.581106\pi$
$499$	−11.2608	−0.504105	−0.252052	+	0.967714i	$0.581106\pi$
$500$	7.47650	0.334359
$501$	−19.0312	−0.850250
$502$	−2.17470	−0.0970618
$503$	34.4627	1.53661	0.768307	−	0.640082i	$-0.221099\pi$
$503$	34.4627	1.53661	0.768307	+	0.640082i	$0.221099\pi$
$504$	1.69177	0.0753574
$505$	−2.72675	−0.121339
$506$	−6.60920	−0.293815
$507$	32.1725	1.42883
$508$	0.407850	0.0180954
$509$	−8.04155	−0.356435	−0.178218	−	0.983991i	$-0.557033\pi$
$509$	−8.04155	−0.356435	−0.178218	+	0.983991i	$0.557033\pi$
$510$	2.52436	0.111780
$511$	−2.08857	−0.0923931
$512$	26.0233	1.15008
$513$	22.1678	0.978733
$514$	6.20844	0.273843
$515$	−14.9940	−0.660717
$516$	−0.511017	−0.0224962
$517$	12.3594	0.543564
$518$	14.5107	0.637565
$519$	20.8488	0.915163
$520$	−18.6879	−0.819518
$521$	24.0434	1.05336	0.526681	−	0.850063i	$-0.323436\pi$
$521$	24.0434	1.05336	0.526681	+	0.850063i	$0.323436\pi$
$522$	3.83166	0.167707
$523$	−17.5784	−0.768648	−0.384324	−	0.923198i	$-0.625565\pi$
$523$	−17.5784	−0.768648	−0.384324	+	0.923198i	$0.625565\pi$
$524$	1.30199	0.0568777
$525$	6.43566	0.280875
$526$	−48.4853	−2.11406
$527$	−3.97493	−0.173151
$528$	16.1368	0.702266
$529$	1.00000	0.0434783
$530$	−42.4817	−1.84529
$531$	−11.7552	−0.510131
$532$	−7.13613	−0.309390
$533$	63.8767	2.76681
$534$	26.8272	1.16092
$535$	−32.9917	−1.42635
$536$	−4.33990	−0.187455
$537$	−3.40764	−0.147050
$538$	5.13341	0.221317
$539$	20.8682	0.898855
$540$	−26.2249	−1.12854
$541$	−7.16409	−0.308008	−0.154004	−	0.988070i	$-0.549217\pi$
$541$	−7.16409	−0.308008	−0.154004	+	0.988070i	$0.549217\pi$
$542$	−57.4320	−2.46691
$543$	−23.2270	−0.996764
$544$	−2.89060	−0.123934
$545$	25.5535	1.09459
$546$	12.8049	0.547999
$547$	−21.2868	−0.910157	−0.455078	−	0.890451i	$-0.650389\pi$
$547$	−21.2868	−0.910157	−0.455078	+	0.890451i	$0.650389\pi$
$548$	−12.3325	−0.526816
$549$	4.41024	0.188225
$550$	−42.3835	−1.80724
$551$	4.47325	0.190567
$552$	−0.806816	−0.0343404
$553$	−1.32320	−0.0562681
$554$	−3.16219	−0.134348
$555$	25.1171	1.06616
$556$	19.5365	0.828530
$557$	−32.5538	−1.37935	−0.689674	−	0.724120i	$-0.742246\pi$
$557$	−32.5538	−1.37935	−0.689674	+	0.724120i	$0.742246\pi$
$558$	37.9319	1.60579
$559$	−2.23669	−0.0946019
$560$	−16.0984	−0.680281
$561$	−1.38473	−0.0584635
$562$	15.9341	0.672139
$563$	−30.1766	−1.27179	−0.635895	−	0.771775i	$-0.719369\pi$
$563$	−30.1766	−1.27179	−0.635895	+	0.771775i	$0.719369\pi$
$564$	−5.45140	−0.229545
$565$	−17.1726	−0.722459
$566$	−23.4352	−0.985056
$567$	1.22555	0.0514683
$568$	−7.25478	−0.304404
$569$	38.5718	1.61701	0.808507	−	0.588486i	$-0.200276\pi$
$569$	38.5718	1.61701	0.808507	+	0.588486i	$0.200276\pi$
$570$	−28.1230	−1.17794
$571$	−21.8563	−0.914657	−0.457328	−	0.889298i	$-0.651194\pi$
$571$	−21.8563	−0.914657	−0.457328	+	0.889298i	$0.651194\pi$
$572$	−37.0392	−1.54869
$573$	21.9753	0.918032
$574$	18.1832	0.758951
$575$	6.41281	0.267433
$576$	8.59706	0.358211
$577$	−27.1927	−1.13205	−0.566024	−	0.824389i	$-0.691519\pi$
$577$	−27.1927	−1.13205	−0.566024	+	0.824389i	$0.691519\pi$
$578$	−31.8001	−1.32271
$579$	11.3430	0.471398
$580$	−5.29194	−0.219736
$581$	−2.22870	−0.0924620
$582$	−26.6389	−1.10422
$583$	23.3033	0.965124
$584$	1.67911	0.0694822
$585$	−46.3103	−1.91470
$586$	44.8156	1.85132
$587$	−3.51905	−0.145247	−0.0726235	−	0.997359i	$-0.523137\pi$
$587$	−3.51905	−0.145247	−0.0726235	+	0.997359i	$0.523137\pi$
$588$	−9.20440	−0.379583
$589$	44.2834	1.82466
$590$	36.9637	1.52177
$591$	1.67447	0.0688785
$592$	−35.3033	−1.45096
$593$	−29.0267	−1.19198	−0.595991	−	0.802991i	$-0.703241\pi$
$593$	−29.0267	−1.19198	−0.595991	+	0.802991i	$0.703241\pi$
$594$	32.7528	1.34386
$595$	1.38143	0.0566332
$596$	−20.5681	−0.842504
$597$	−4.18814	−0.171409
$598$	12.7594	0.521772
$599$	−16.8393	−0.688037	−0.344018	−	0.938963i	$-0.611788\pi$
$599$	−16.8393	−0.688037	−0.344018	+	0.938963i	$0.611788\pi$
$600$	−5.17396	−0.211226
$601$	23.0837	0.941605	0.470802	−	0.882239i	$-0.343964\pi$
$601$	23.0837	0.941605	0.470802	+	0.882239i	$0.343964\pi$
$602$	−0.636697	−0.0259498
$603$	−10.7547	−0.437964
$604$	19.9136	0.810275
$605$	4.21566	0.171391
$606$	−1.50207	−0.0610176
$607$	−0.799035	−0.0324318	−0.0162159	−	0.999869i	$-0.505162\pi$
$607$	−0.799035	−0.0324318	−0.0162159	+	0.999869i	$0.505162\pi$
$608$	32.2032	1.30601
$609$	−1.00356	−0.0406664
$610$	−13.8678	−0.561492
$611$	−23.8604	−0.965290
$612$	−1.27614	−0.0515850
$613$	−30.9690	−1.25083	−0.625414	−	0.780293i	$-0.715070\pi$
$613$	−30.9690	−1.25083	−0.625414	+	0.780293i	$0.715070\pi$
$614$	50.2183	2.02664
$615$	31.4738	1.26915
$616$	2.91812	0.117574
$617$	0.964056	0.0388114	0.0194057	−	0.999812i	$-0.493823\pi$
$617$	0.964056	0.0388114	0.0194057	+	0.999812i	$0.493823\pi$
$618$	−8.25971	−0.332254
$619$	4.39765	0.176757	0.0883783	−	0.996087i	$-0.471832\pi$
$619$	4.39765	0.176757	0.0883783	+	0.996087i	$0.471832\pi$
$620$	−52.3881	−2.10395
$621$	−4.95564	−0.198863
$622$	10.2657	0.411616
$623$	14.6809	0.588179
$624$	−31.1531	−1.24712
$625$	−15.9399	−0.637597
$626$	31.1529	1.24512
$627$	15.4268	0.616089
$628$	−21.1419	−0.843653
$629$	3.02944	0.120792
$630$	−13.1827	−0.525212
$631$	−31.1332	−1.23939	−0.619696	−	0.784842i	$-0.712744\pi$
$631$	−31.1332	−1.23939	−0.619696	+	0.784842i	$0.712744\pi$
$632$	1.06379	0.0423152
$633$	−11.0839	−0.440547
$634$	−18.7948	−0.746437
$635$	0.879587	0.0349054
$636$	−10.2785	−0.407569
$637$	−40.2871	−1.59623
$638$	6.60920	0.261661
$639$	−17.9780	−0.711200
$640$	21.6079	0.854126
$641$	−16.9855	−0.670886	−0.335443	−	0.942060i	$-0.608886\pi$
$641$	−16.9855	−0.670886	−0.335443	+	0.942060i	$0.608886\pi$
$642$	−18.1740	−0.717270
$643$	−19.7097	−0.777273	−0.388637	−	0.921391i	$-0.627054\pi$
$643$	−19.7097	−0.777273	−0.388637	+	0.921391i	$0.627054\pi$
$644$	1.59529	0.0628632
$645$	−1.10208	−0.0433943
$646$	−3.39199	−0.133456
$647$	−39.6357	−1.55824	−0.779120	−	0.626875i	$-0.784334\pi$
$647$	−39.6357	−1.55824	−0.779120	+	0.626875i	$0.784334\pi$
$648$	−0.985284	−0.0387056
$649$	−20.2764	−0.795918
$650$	81.8238	3.20939
$651$	−9.93487	−0.389378
$652$	28.7925	1.12760
$653$	−16.4740	−0.644676	−0.322338	−	0.946625i	$-0.604469\pi$
$653$	−16.4740	−0.644676	−0.322338	+	0.946625i	$0.604469\pi$
$654$	14.0765	0.550436
$655$	2.80792	0.109715
$656$	−44.2379	−1.72720
$657$	4.16100	0.162336
$658$	−6.79212	−0.264784
$659$	−3.96397	−0.154414	−0.0772072	−	0.997015i	$-0.524600\pi$
$659$	−3.96397	−0.154414	−0.0772072	+	0.997015i	$0.524600\pi$
$660$	−18.2502	−0.710389
$661$	−35.7093	−1.38893	−0.694464	−	0.719527i	$-0.744359\pi$
$661$	−35.7093	−1.38893	−0.694464	+	0.719527i	$0.744359\pi$
$662$	−10.7003	−0.415878
$663$	2.67331	0.103823
$664$	1.79177	0.0695340
$665$	−15.3901	−0.596801
$666$	−28.9093	−1.12021
$667$	−1.00000	−0.0387202
$668$	−30.2524	−1.17050
$669$	20.4839	0.791955
$670$	33.8177	1.30649
$671$	7.60718	0.293672
$672$	−7.22471	−0.278699
$673$	1.02454	0.0394930	0.0197465	−	0.999805i	$-0.493714\pi$
$673$	1.02454	0.0394930	0.0197465	+	0.999805i	$0.493714\pi$
$674$	−1.08232	−0.0416895
$675$	−31.7796	−1.22320
$676$	51.1423	1.96701
$677$	43.9314	1.68842	0.844210	−	0.536012i	$-0.180070\pi$
$677$	43.9314	1.68842	0.844210	+	0.536012i	$0.180070\pi$
$678$	−9.45982	−0.363302
$679$	−14.5779	−0.559448
$680$	−1.11061	−0.0425898
$681$	11.1742	0.428195
$682$	65.4284	2.50538
$683$	−40.0801	−1.53362	−0.766811	−	0.641872i	$-0.778158\pi$
$683$	−40.0801	−1.53362	−0.766811	+	0.641872i	$0.778158\pi$
$684$	14.2171	0.543603
$685$	−26.5967	−1.01621
$686$	−24.9310	−0.951871
$687$	−0.133465	−0.00509200
$688$	1.54902	0.0590559
$689$	−44.9884	−1.71392
$690$	6.28693	0.239339
$691$	44.0624	1.67621	0.838107	−	0.545506i	$-0.183662\pi$
$691$	44.0624	1.67621	0.838107	+	0.545506i	$0.183662\pi$
$692$	33.1419	1.25986
$693$	7.23136	0.274697
$694$	2.63170	0.0998981
$695$	42.1331	1.59820
$696$	0.806816	0.0305823
$697$	3.79614	0.143789
$698$	−15.1968	−0.575206
$699$	23.6860	0.895888
$700$	10.2303	0.386669
$701$	29.4338	1.11170	0.555850	−	0.831283i	$-0.312393\pi$
$701$	29.4338	1.11170	0.555850	+	0.831283i	$0.312393\pi$
$702$	−63.2311	−2.38651
$703$	−33.7500	−1.27290
$704$	14.8290	0.558888
$705$	−11.7567	−0.442783
$706$	55.5005	2.08879
$707$	−0.821998	−0.0309144
$708$	8.94339	0.336113
$709$	16.1042	0.604805	0.302403	−	0.953180i	$-0.402211\pi$
$709$	16.1042	0.604805	0.302403	+	0.953180i	$0.402211\pi$
$710$	56.5312	2.12158
$711$	2.63616	0.0988638
$712$	−11.8028	−0.442327
$713$	−9.89960	−0.370743
$714$	0.760984	0.0284791
$715$	−79.8802	−2.98735
$716$	−5.41687	−0.202438
$717$	29.0384	1.08446
$718$	33.9602	1.26738
$719$	28.4321	1.06034	0.530168	−	0.847892i	$-0.322129\pi$
$719$	28.4321	1.06034	0.530168	+	0.847892i	$0.322129\pi$
$720$	32.0723	1.19526
$721$	−4.52005	−0.168336
$722$	1.90732	0.0709830
$723$	21.8678	0.813274
$724$	−36.9222	−1.37220
$725$	−6.41281	−0.238166
$726$	2.32226	0.0861871
$727$	−35.0847	−1.30122	−0.650609	−	0.759413i	$-0.725486\pi$
$727$	−35.0847	−1.30122	−0.650609	+	0.759413i	$0.725486\pi$
$728$	−5.63359	−0.208795
$729$	12.2086	0.452171
$730$	−13.0841	−0.484264
$731$	−0.132925	−0.00491639
$732$	−3.35533	−0.124017
$733$	−12.7050	−0.469272	−0.234636	−	0.972083i	$-0.575390\pi$
$733$	−12.7050	−0.469272	−0.234636	+	0.972083i	$0.575390\pi$
$734$	14.2953	0.527648
$735$	−19.8506	−0.732200
$736$	−7.19906	−0.265361
$737$	−18.5506	−0.683322
$738$	−36.2257	−1.33349
$739$	−5.70101	−0.209715	−0.104858	−	0.994487i	$-0.533439\pi$
$739$	−5.70101	−0.209715	−0.104858	+	0.994487i	$0.533439\pi$
$740$	39.9268	1.46774
$741$	−29.7824	−1.09408
$742$	−12.8064	−0.470138
$743$	37.2440	1.36635	0.683176	−	0.730254i	$-0.260598\pi$
$743$	37.2440	1.36635	0.683176	+	0.730254i	$0.260598\pi$
$744$	7.98716	0.292823
$745$	−44.3581	−1.62516
$746$	9.90151	0.362520
$747$	4.44016	0.162457
$748$	−2.20121	−0.0804841
$749$	−9.94556	−0.363403
$750$	8.88223	0.324333
$751$	−36.3339	−1.32584	−0.662921	−	0.748689i	$-0.730684\pi$
$751$	−36.3339	−1.32584	−0.662921	+	0.748689i	$0.730684\pi$
$752$	16.5246	0.602590
$753$	−1.13476	−0.0413531
$754$	−12.7594	−0.464671
$755$	42.9466	1.56299
$756$	−7.90568	−0.287527
$757$	45.1215	1.63997	0.819985	−	0.572385i	$-0.193982\pi$
$757$	45.1215	1.63997	0.819985	+	0.572385i	$0.193982\pi$
$758$	−44.0495	−1.59995
$759$	−3.44869	−0.125179
$760$	12.3729	0.448811
$761$	27.4473	0.994965	0.497483	−	0.867474i	$-0.334258\pi$
$761$	27.4473	0.994965	0.497483	+	0.867474i	$0.334258\pi$
$762$	0.484534	0.0175528
$763$	7.70326	0.278877
$764$	34.9325	1.26381
$765$	−2.75218	−0.0995054
$766$	43.5541	1.57367
$767$	39.1447	1.41343
$768$	20.2540	0.730852
$769$	−24.9929	−0.901268	−0.450634	−	0.892709i	$-0.648802\pi$
$769$	−24.9929	−0.901268	−0.450634	+	0.892709i	$0.648802\pi$
$770$	−22.7387	−0.819447
$771$	3.23957	0.116670
$772$	18.0311	0.648952
$773$	51.8934	1.86648	0.933238	−	0.359258i	$-0.116970\pi$
$773$	51.8934	1.86648	0.933238	+	0.359258i	$0.116970\pi$
$774$	1.26847	0.0455942
$775$	−63.4842	−2.28042
$776$	11.7199	0.420721
$777$	7.57172	0.271634
$778$	−54.5139	−1.95442
$779$	−42.2915	−1.51525
$780$	35.2331	1.26155
$781$	−31.0101	−1.10963
$782$	0.758282	0.0271161
$783$	4.95564	0.177100
$784$	27.9009	0.996462
$785$	−45.5955	−1.62737
$786$	1.54679	0.0551721
$787$	−37.6250	−1.34118	−0.670592	−	0.741826i	$-0.733960\pi$
$787$	−37.6250	−1.34118	−0.670592	+	0.741826i	$0.733960\pi$
$788$	2.66178	0.0948221
$789$	−25.2997	−0.900692
$790$	−8.28931	−0.294920
$791$	−5.17681	−0.184066
$792$	−5.81367	−0.206580
$793$	−14.6861	−0.521519
$794$	−28.1342	−0.998444
$795$	−22.1670	−0.786183
$796$	−6.65757	−0.235971
$797$	−38.1785	−1.35235	−0.676175	−	0.736741i	$-0.736364\pi$
$797$	−38.1785	−1.35235	−0.676175	+	0.736741i	$0.736364\pi$
$798$	−8.47786	−0.300113
$799$	−1.41801	−0.0501655
$800$	−46.1662	−1.63222
$801$	−29.2483	−1.03344
$802$	−40.7204	−1.43789
$803$	7.17726	0.253280
$804$	8.18221	0.288564
$805$	3.44047	0.121261
$806$	−126.313	−4.44919
$807$	2.67862	0.0942918
$808$	0.660846	0.0232485
$809$	−9.95680	−0.350063	−0.175031	−	0.984563i	$-0.556003\pi$
$809$	−9.95680	−0.350063	−0.175031	+	0.984563i	$0.556003\pi$
$810$	7.67759	0.269763
$811$	4.54658	0.159652	0.0798260	−	0.996809i	$-0.474564\pi$
$811$	4.54658	0.159652	0.0798260	+	0.996809i	$0.474564\pi$
$812$	−1.59529	−0.0559837
$813$	−29.9681	−1.05103
$814$	−49.8653	−1.74778
$815$	62.0950	2.17509
$816$	−1.85140	−0.0648120
$817$	1.48087	0.0518090
$818$	−50.8870	−1.77922
$819$	−13.9606	−0.487821
$820$	50.0316	1.74718
$821$	−15.7070	−0.548178	−0.274089	−	0.961704i	$-0.588376\pi$
$821$	−15.7070	−0.548178	−0.274089	+	0.961704i	$0.588376\pi$
$822$	−14.6512	−0.511019
$823$	−8.97215	−0.312750	−0.156375	−	0.987698i	$-0.549981\pi$
$823$	−8.97215	−0.312750	−0.156375	+	0.987698i	$0.549981\pi$
$824$	3.63391	0.126593
$825$	−22.1158	−0.769972
$826$	11.1429	0.387712
$827$	7.63258	0.265411	0.132705	−	0.991156i	$-0.457634\pi$
$827$	7.63258	0.265411	0.132705	+	0.991156i	$0.457634\pi$
$828$	−3.17824	−0.110452
$829$	17.0943	0.593710	0.296855	−	0.954923i	$-0.404062\pi$
$829$	17.0943	0.593710	0.296855	+	0.954923i	$0.404062\pi$
$830$	−13.9619	−0.484625
$831$	−1.65003	−0.0572390
$832$	−28.6282	−0.992504
$833$	−2.39423	−0.0829552
$834$	23.2097	0.803686
$835$	−65.2437	−2.25785
$836$	24.5229	0.848142
$837$	49.0589	1.69572
$838$	30.3587	1.04872
$839$	1.90631	0.0658131	0.0329066	−	0.999458i	$-0.489524\pi$
$839$	1.90631	0.0658131	0.0329066	+	0.999458i	$0.489524\pi$
$840$	−2.77582	−0.0957751
$841$	1.00000	0.0344828
$842$	73.7729	2.54238
$843$	8.31443	0.286364
$844$	−17.6193	−0.606482
$845$	110.296	3.79428
$846$	13.5317	0.465230
$847$	1.27084	0.0436665
$848$	31.1568	1.06993
$849$	−12.2285	−0.419682
$850$	4.86272	0.166790
$851$	7.54484	0.258634
$852$	13.6778	0.468593
$853$	2.96457	0.101505	0.0507524	−	0.998711i	$-0.483838\pi$
$853$	2.96457	0.101505	0.0507524	+	0.998711i	$0.483838\pi$
$854$	−4.18055	−0.143055
$855$	30.6611	1.04859
$856$	7.99575	0.273289
$857$	−28.4481	−0.971767	−0.485883	−	0.874024i	$-0.661502\pi$
$857$	−28.4481	−0.971767	−0.485883	+	0.874024i	$0.661502\pi$
$858$	−44.0033	−1.50225
$859$	−23.2912	−0.794685	−0.397342	−	0.917670i	$-0.630067\pi$
$859$	−23.2912	−0.794685	−0.397342	+	0.917670i	$0.630067\pi$
$860$	−1.75189	−0.0597391
$861$	9.48800	0.323350
$862$	−29.8359	−1.01621
$863$	−16.4751	−0.560819	−0.280410	−	0.959880i	$-0.590470\pi$
$863$	−16.4751	−0.560819	−0.280410	+	0.959880i	$0.590470\pi$
$864$	35.6760	1.21372
$865$	71.4751	2.43023
$866$	−55.4962	−1.88584
$867$	−16.5934	−0.563540
$868$	−15.7927	−0.536040
$869$	4.54709	0.154250
$870$	−6.28693	−0.213147
$871$	35.8131	1.21348
$872$	−6.19305	−0.209723
$873$	29.0430	0.982958
$874$	−8.44776	−0.285750
$875$	4.86073	0.164322
$876$	−3.16571	−0.106959
$877$	18.0348	0.608992	0.304496	−	0.952514i	$-0.401512\pi$
$877$	18.0348	0.608992	0.304496	+	0.952514i	$0.401512\pi$
$878$	60.6812	2.04789
$879$	23.3848	0.788751
$880$	55.3212	1.86488
$881$	−16.4853	−0.555404	−0.277702	−	0.960667i	$-0.589573\pi$
$881$	−16.4853	−0.555404	−0.277702	+	0.960667i	$0.589573\pi$
$882$	22.8476	0.769319
$883$	12.6634	0.426159	0.213079	−	0.977035i	$-0.431651\pi$
$883$	12.6634	0.426159	0.213079	+	0.977035i	$0.431651\pi$
$884$	4.24956	0.142928
$885$	19.2877	0.648348
$886$	59.7482	2.00728
$887$	−28.5832	−0.959730	−0.479865	−	0.877342i	$-0.659314\pi$
$887$	−28.5832	−0.959730	−0.479865	+	0.877342i	$0.659314\pi$
$888$	−6.08730	−0.204276
$889$	0.265157	0.00889309
$890$	91.9702	3.08285
$891$	−4.21154	−0.141092
$892$	32.5618	1.09025
$893$	15.7975	0.528644
$894$	−24.4354	−0.817241
$895$	−11.6822	−0.390494
$896$	6.51383	0.217612
$897$	6.65789	0.222300
$898$	52.3730	1.74771
$899$	9.89960	0.330170
$900$	−20.3815	−0.679382
$901$	−2.67362	−0.0890712
$902$	−62.4854	−2.08054
$903$	−0.332229	−0.0110559
$904$	4.16190	0.138423
$905$	−79.6279	−2.64692
$906$	23.6578	0.785978
$907$	20.5563	0.682560	0.341280	−	0.939962i	$-0.389140\pi$
$907$	20.5563	0.682560	0.341280	+	0.939962i	$0.389140\pi$
$908$	17.7627	0.589477
$909$	1.63764	0.0543171
$910$	43.8984	1.45522
$911$	19.0030	0.629598	0.314799	−	0.949158i	$-0.398063\pi$
$911$	19.0030	0.629598	0.314799	+	0.949158i	$0.398063\pi$
$912$	20.6258	0.682990
$913$	7.65879	0.253469
$914$	−48.2892	−1.59727
$915$	−7.23625	−0.239223
$916$	−0.212159	−0.00700993
$917$	0.846467	0.0279528
$918$	−3.75777	−0.124025
$919$	−47.2700	−1.55930	−0.779648	−	0.626219i	$-0.784602\pi$
$919$	−47.2700	−1.55930	−0.779648	+	0.626219i	$0.784602\pi$
$920$	−2.76597	−0.0911913
$921$	26.2040	0.863450
$922$	−62.8690	−2.07048
$923$	59.8668	1.97054
$924$	−5.50165	−0.180991
$925$	48.3836	1.59084
$926$	1.32410	0.0435126
$927$	9.00516	0.295768
$928$	7.19906	0.236321
$929$	21.7873	0.714819	0.357409	−	0.933948i	$-0.383660\pi$
$929$	21.7873	0.714819	0.357409	+	0.933948i	$0.383660\pi$
$930$	−62.2380	−2.04087
$931$	26.6733	0.874182
$932$	37.6519	1.23333
$933$	5.35664	0.175369
$934$	−44.6738	−1.46177
$935$	−4.74722	−0.155251
$936$	11.2236	0.366855
$937$	−46.4247	−1.51663	−0.758314	−	0.651890i	$-0.773976\pi$
$937$	−46.4247	−1.51663	−0.758314	+	0.651890i	$0.773976\pi$
$938$	10.1946	0.332864
$939$	16.2556	0.530483
$940$	−18.6888	−0.609560
$941$	25.3015	0.824806	0.412403	−	0.911001i	$-0.364690\pi$
$941$	25.3015	0.824806	0.412403	+	0.911001i	$0.364690\pi$
$942$	−25.1170	−0.818356
$943$	9.45431	0.307875
$944$	−27.1097	−0.882346
$945$	−17.0497	−0.554627
$946$	2.18797	0.0711371
$947$	−35.7859	−1.16288	−0.581442	−	0.813588i	$-0.697511\pi$
$947$	−35.7859	−1.16288	−0.581442	+	0.813588i	$0.697511\pi$
$948$	−2.00561	−0.0651390
$949$	−13.8561	−0.449788
$950$	−54.1739	−1.75763
$951$	−9.80715	−0.318019
$952$	−0.334799	−0.0108509
$953$	52.7262	1.70797	0.853984	−	0.520299i	$-0.174179\pi$
$953$	52.7262	1.70797	0.853984	+	0.520299i	$0.174179\pi$
$954$	25.5138	0.826039
$955$	75.3369	2.43784
$956$	46.1601	1.49293
$957$	3.44869	0.111480
$958$	−35.9578	−1.16174
$959$	−8.01775	−0.258907
$960$	−14.1059	−0.455266
$961$	67.0021	2.16136
$962$	96.2679	3.10380
$963$	19.8142	0.638504
$964$	34.7617	1.11960
$965$	38.8865	1.25180
$966$	1.89524	0.0609782
$967$	41.7909	1.34391	0.671953	−	0.740594i	$-0.265456\pi$
$967$	41.7909	1.34391	0.671953	+	0.740594i	$0.265456\pi$
$968$	−1.02169	−0.0328384
$969$	−1.76994	−0.0568587
$970$	−91.3247	−2.93226
$971$	13.6739	0.438818	0.219409	−	0.975633i	$-0.429587\pi$
$971$	13.6739	0.438818	0.219409	+	0.975633i	$0.429587\pi$
$972$	25.1460	0.806558
$973$	12.7013	0.407185
$974$	18.7904	0.602083
$975$	42.6958	1.36736
$976$	10.1709	0.325562
$977$	−40.2771	−1.28858	−0.644289	−	0.764783i	$-0.722846\pi$
$977$	−40.2771	−1.28858	−0.644289	+	0.764783i	$0.722846\pi$
$978$	34.2060	1.09379
$979$	−50.4502	−1.61240
$980$	−31.5550	−1.00799
$981$	−15.3469	−0.489990
$982$	6.93329	0.221250
$983$	18.2202	0.581136	0.290568	−	0.956854i	$-0.406156\pi$
$983$	18.2202	0.581136	0.290568	+	0.956854i	$0.406156\pi$
$984$	−7.62789	−0.243168
$985$	5.74051	0.182908
$986$	−0.758282	−0.0241486
$987$	−3.54414	−0.112811
$988$	−47.3428	−1.50618
$989$	−0.331050	−0.0105268
$990$	45.3016	1.43978
$991$	42.8019	1.35965	0.679824	−	0.733376i	$-0.262056\pi$
$991$	42.8019	1.35965	0.679824	+	0.733376i	$0.262056\pi$
$992$	71.2678	2.26276
$993$	−5.58342	−0.177185
$994$	17.0417	0.540530
$995$	−14.3580	−0.455179
$996$	−3.37810	−0.107039
$997$	−14.4707	−0.458291	−0.229145	−	0.973392i	$-0.573593\pi$
$997$	−14.4707	−0.458291	−0.229145	+	0.973392i	$0.573593\pi$
$998$	−21.2662	−0.673169
$999$	−37.3895	−1.18295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.12	✓	16
3.2	odd	2		6003.2.a.q.1.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.12	✓	16	1.1	even	1	trivial
6003.2.a.q.1.5		16	3.2	odd	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+1.88851 q^{2} +0.985425 q^{3} +1.56646 q^{4} +3.37829 q^{5} +1.86098 q^{6} +1.01841 q^{7} -0.818750 q^{8} -2.02894 q^{9} +O(q^{10})\)	\(q+1.88851 q^{2} +0.985425 q^{3} +1.56646 q^{4} +3.37829 q^{5} +1.86098 q^{6} +1.01841 q^{7} -0.818750 q^{8} -2.02894 q^{9} +6.37991 q^{10} -3.49970 q^{11} +1.54363 q^{12} +6.75636 q^{13} +1.92327 q^{14} +3.32905 q^{15} -4.67913 q^{16} +0.401525 q^{17} -3.83166 q^{18} -4.47325 q^{19} +5.29194 q^{20} +1.00356 q^{21} -6.60920 q^{22} +1.00000 q^{23} -0.806816 q^{24} +6.41281 q^{25} +12.7594 q^{26} -4.95564 q^{27} +1.59529 q^{28} -1.00000 q^{29} +6.28693 q^{30} -9.89960 q^{31} -7.19906 q^{32} -3.44869 q^{33} +0.758282 q^{34} +3.44047 q^{35} -3.17824 q^{36} +7.54484 q^{37} -8.44776 q^{38} +6.65789 q^{39} -2.76597 q^{40} +9.45431 q^{41} +1.89524 q^{42} -0.331050 q^{43} -5.48212 q^{44} -6.85433 q^{45} +1.88851 q^{46} -3.53155 q^{47} -4.61093 q^{48} -5.96285 q^{49} +12.1106 q^{50} +0.395673 q^{51} +10.5835 q^{52} -6.65867 q^{53} -9.35876 q^{54} -11.8230 q^{55} -0.833820 q^{56} -4.40805 q^{57} -1.88851 q^{58} +5.79376 q^{59} +5.21481 q^{60} -2.17367 q^{61} -18.6955 q^{62} -2.06628 q^{63} -4.23722 q^{64} +22.8249 q^{65} -6.51287 q^{66} +5.30065 q^{67} +0.628971 q^{68} +0.985425 q^{69} +6.49734 q^{70} +8.86081 q^{71} +1.66119 q^{72} -2.05083 q^{73} +14.2485 q^{74} +6.31934 q^{75} -7.00715 q^{76} -3.56411 q^{77} +12.5735 q^{78} -1.29928 q^{79} -15.8074 q^{80} +1.20340 q^{81} +17.8545 q^{82} -2.18842 q^{83} +1.57204 q^{84} +1.35647 q^{85} -0.625189 q^{86} -0.985425 q^{87} +2.86537 q^{88} +14.4156 q^{89} -12.9444 q^{90} +6.88072 q^{91} +1.56646 q^{92} -9.75531 q^{93} -6.66936 q^{94} -15.1119 q^{95} -7.09414 q^{96} -14.3144 q^{97} -11.2609 q^{98} +7.10066 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9} - 14 q^{10} + 4 q^{11} + 3 q^{12} + 15 q^{13} + 8 q^{14} + 8 q^{15} + 23 q^{16} + 20 q^{17} + 2 q^{18} - 4 q^{19} + 25 q^{20} + 5 q^{21} + 13 q^{22} + 16 q^{23} - 24 q^{24} + 30 q^{25} + 25 q^{26} + 8 q^{27} - 13 q^{28} - 16 q^{29} - 45 q^{30} - 19 q^{32} + q^{33} - 23 q^{34} + 5 q^{35} + 37 q^{36} + 5 q^{37} + 38 q^{38} - 10 q^{39} - 20 q^{40} + 7 q^{41} + 14 q^{42} - 17 q^{43} - 21 q^{44} + 48 q^{45} + 3 q^{46} + 29 q^{47} + 35 q^{48} + 31 q^{49} - 44 q^{50} - 14 q^{51} + 20 q^{52} + 63 q^{53} - 13 q^{54} + q^{55} - 19 q^{56} - 22 q^{57} - 3 q^{58} + 11 q^{59} - 3 q^{60} + 33 q^{62} - 33 q^{63} + 29 q^{64} + 53 q^{65} - 43 q^{66} - 13 q^{67} + 63 q^{68} + 5 q^{69} - 46 q^{70} - 23 q^{71} + 46 q^{72} - 38 q^{73} - 47 q^{74} + 37 q^{75} - 56 q^{76} + 97 q^{77} - 24 q^{78} - 27 q^{79} + 8 q^{80} + 40 q^{81} + 9 q^{82} + 36 q^{83} + 22 q^{84} + 6 q^{85} - 11 q^{86} - 5 q^{87} - 24 q^{88} - 16 q^{89} - 95 q^{90} - 47 q^{91} + 21 q^{92} + 62 q^{93} + 37 q^{94} - 12 q^{95} - 74 q^{96} - 30 q^{97} - 27 q^{98} - 42 q^{99}+O(q^{100}) \) 16 * q + 3 * q^2 + 5 * q^3 + 21 * q^4 + 16 * q^5 + 6 * q^6 + q^7 + 9 * q^8 + 23 * q^9 - 14 * q^10 + 4 * q^11 + 3 * q^12 + 15 * q^13 + 8 * q^14 + 8 * q^15 + 23 * q^16 + 20 * q^17 + 2 * q^18 - 4 * q^19 + 25 * q^20 + 5 * q^21 + 13 * q^22 + 16 * q^23 - 24 * q^24 + 30 * q^25 + 25 * q^26 + 8 * q^27 - 13 * q^28 - 16 * q^29 - 45 * q^30 - 19 * q^32 + q^33 - 23 * q^34 + 5 * q^35 + 37 * q^36 + 5 * q^37 + 38 * q^38 - 10 * q^39 - 20 * q^40 + 7 * q^41 + 14 * q^42 - 17 * q^43 - 21 * q^44 + 48 * q^45 + 3 * q^46 + 29 * q^47 + 35 * q^48 + 31 * q^49 - 44 * q^50 - 14 * q^51 + 20 * q^52 + 63 * q^53 - 13 * q^54 + q^55 - 19 * q^56 - 22 * q^57 - 3 * q^58 + 11 * q^59 - 3 * q^60 + 33 * q^62 - 33 * q^63 + 29 * q^64 + 53 * q^65 - 43 * q^66 - 13 * q^67 + 63 * q^68 + 5 * q^69 - 46 * q^70 - 23 * q^71 + 46 * q^72 - 38 * q^73 - 47 * q^74 + 37 * q^75 - 56 * q^76 + 97 * q^77 - 24 * q^78 - 27 * q^79 + 8 * q^80 + 40 * q^81 + 9 * q^82 + 36 * q^83 + 22 * q^84 + 6 * q^85 - 11 * q^86 - 5 * q^87 - 24 * q^88 - 16 * q^89 - 95 * q^90 - 47 * q^91 + 21 * q^92 + 62 * q^93 + 37 * q^94 - 12 * q^95 - 74 * q^96 - 30 * q^97 - 27 * q^98 - 42 * q^99

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