LMFDB - Embedded newform 667.2.a.d.1.8

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			1.8
Root			$-0.208883$ 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)

$f(q)$	$=$	$q-0.208883 q^{2} -2.00378 q^{3} -1.95637 q^{4} -2.17278 q^{5} +0.418556 q^{6} -2.92851 q^{7} +0.826420 q^{8} +1.01513 q^{9} +O(q^{10})$	\(q-0.208883 q^{2} -2.00378 q^{3} -1.95637 q^{4} -2.17278 q^{5} +0.418556 q^{6} -2.92851 q^{7} +0.826420 q^{8} +1.01513 q^{9} +0.453858 q^{10} -4.59858 q^{11} +3.92013 q^{12} -4.31724 q^{13} +0.611718 q^{14} +4.35378 q^{15} +3.74011 q^{16} -1.26240 q^{17} -0.212045 q^{18} +2.45596 q^{19} +4.25076 q^{20} +5.86810 q^{21} +0.960567 q^{22} +1.00000 q^{23} -1.65596 q^{24} -0.279016 q^{25} +0.901799 q^{26} +3.97723 q^{27} +5.72925 q^{28} -1.00000 q^{29} -0.909432 q^{30} -9.32607 q^{31} -2.43409 q^{32} +9.21454 q^{33} +0.263695 q^{34} +6.36302 q^{35} -1.98598 q^{36} +0.827308 q^{37} -0.513009 q^{38} +8.65080 q^{39} -1.79563 q^{40} +1.17569 q^{41} -1.22575 q^{42} +2.72597 q^{43} +8.99651 q^{44} -2.20567 q^{45} -0.208883 q^{46} +2.66809 q^{47} -7.49436 q^{48} +1.57619 q^{49} +0.0582818 q^{50} +2.52958 q^{51} +8.44611 q^{52} +6.56983 q^{53} -0.830778 q^{54} +9.99171 q^{55} -2.42018 q^{56} -4.92120 q^{57} +0.208883 q^{58} -6.48431 q^{59} -8.51759 q^{60} +9.91126 q^{61} +1.94806 q^{62} -2.97283 q^{63} -6.97178 q^{64} +9.38042 q^{65} -1.92476 q^{66} -12.7722 q^{67} +2.46972 q^{68} -2.00378 q^{69} -1.32913 q^{70} -14.5107 q^{71} +0.838927 q^{72} +12.5500 q^{73} -0.172811 q^{74} +0.559086 q^{75} -4.80476 q^{76} +13.4670 q^{77} -1.80701 q^{78} -10.5329 q^{79} -8.12645 q^{80} -11.0149 q^{81} -0.245582 q^{82} +0.738680 q^{83} -11.4802 q^{84} +2.74293 q^{85} -0.569410 q^{86} +2.00378 q^{87} -3.80036 q^{88} -13.5151 q^{89} +0.460727 q^{90} +12.6431 q^{91} -1.95637 q^{92} +18.6874 q^{93} -0.557320 q^{94} -5.33626 q^{95} +4.87737 q^{96} -14.4575 q^{97} -0.329240 q^{98} -4.66818 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.208883	−0.147703	−0.0738514	−	0.997269i	$-0.523529\pi$
$2$	−0.208883	−0.147703	−0.0738514	+	0.997269i	$0.523529\pi$
$3$	−2.00378	−1.15688	−0.578441	−	0.815724i	$-0.696339\pi$
$3$	−2.00378	−1.15688	−0.578441	+	0.815724i	$0.696339\pi$
$4$	−1.95637	−0.978184
$5$	−2.17278	−0.971698	−0.485849	−	0.874043i	$-0.661489\pi$
$5$	−2.17278	−0.971698	−0.485849	+	0.874043i	$0.661489\pi$
$6$	0.418556	0.170875
$7$	−2.92851	−1.10687	−0.553437	−	0.832891i	$-0.686684\pi$
$7$	−2.92851	−1.10687	−0.553437	+	0.832891i	$0.686684\pi$
$8$	0.826420	0.292183
$9$	1.01513	0.338378
$10$	0.453858	0.143523
$11$	−4.59858	−1.38652	−0.693262	−	0.720686i	$-0.743827\pi$
$11$	−4.59858	−1.38652	−0.693262	+	0.720686i	$0.743827\pi$
$12$	3.92013	1.13164
$13$	−4.31724	−1.19739	−0.598693	−	0.800978i	$-0.704313\pi$
$13$	−4.31724	−1.19739	−0.598693	+	0.800978i	$0.704313\pi$
$14$	0.611718	0.163488
$15$	4.35378	1.12414
$16$	3.74011	0.935028
$17$	−1.26240	−0.306178	−0.153089	−	0.988212i	$-0.548922\pi$
$17$	−1.26240	−0.306178	−0.153089	+	0.988212i	$0.548922\pi$
$18$	−0.212045	−0.0499794
$19$	2.45596	0.563435	0.281718	−	0.959497i	$-0.409096\pi$
$19$	2.45596	0.563435	0.281718	+	0.959497i	$0.409096\pi$
$20$	4.25076	0.950499
$21$	5.86810	1.28052
$22$	0.960567	0.204794
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.65596	−0.338022
$25$	−0.279016	−0.0558032
$26$	0.901799	0.176857
$27$	3.97723	0.765419
$28$	5.72925	1.08273
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−0.909432	−0.166039
$31$	−9.32607	−1.67501	−0.837505	−	0.546429i	$-0.815987\pi$
$31$	−9.32607	−1.67501	−0.837505	+	0.546429i	$0.815987\pi$
$32$	−2.43409	−0.430290
$33$	9.21454	1.60405
$34$	0.263695	0.0452233
$35$	6.36302	1.07555
$36$	−1.98598	−0.330996
$37$	0.827308	0.136009	0.0680043	−	0.997685i	$-0.478337\pi$
$37$	0.827308	0.136009	0.0680043	+	0.997685i	$0.478337\pi$
$38$	−0.513009	−0.0832210
$39$	8.65080	1.38524
$40$	−1.79563	−0.283914
$41$	1.17569	0.183612	0.0918058	−	0.995777i	$-0.470736\pi$
$41$	1.17569	0.183612	0.0918058	+	0.995777i	$0.470736\pi$
$42$	−1.22575	−0.189137
$43$	2.72597	0.415707	0.207853	−	0.978160i	$-0.433352\pi$
$43$	2.72597	0.415707	0.207853	+	0.978160i	$0.433352\pi$
$44$	8.99651	1.35628
$45$	−2.20567	−0.328801
$46$	−0.208883	−0.0307982
$47$	2.66809	0.389181	0.194590	−	0.980885i	$-0.437662\pi$
$47$	2.66809	0.389181	0.194590	+	0.980885i	$0.437662\pi$
$48$	−7.49436	−1.08172
$49$	1.57619	0.225170
$50$	0.0582818	0.00824229
$51$	2.52958	0.354212
$52$	8.44611	1.17126
$53$	6.56983	0.902435	0.451218	−	0.892414i	$-0.350990\pi$
$53$	6.56983	0.902435	0.451218	+	0.892414i	$0.350990\pi$
$54$	−0.830778	−0.113055
$55$	9.99171	1.34728
$56$	−2.42018	−0.323410
$57$	−4.92120	−0.651829
$58$	0.208883	0.0274277
$59$	−6.48431	−0.844185	−0.422092	−	0.906553i	$-0.638704\pi$
$59$	−6.48431	−0.844185	−0.422092	+	0.906553i	$0.638704\pi$
$60$	−8.51759	−1.09962
$61$	9.91126	1.26901	0.634503	−	0.772920i	$-0.281205\pi$
$61$	9.91126	1.26901	0.634503	+	0.772920i	$0.281205\pi$
$62$	1.94806	0.247404
$63$	−2.97283	−0.374542
$64$	−6.97178	−0.871473
$65$	9.38042	1.16350
$66$	−1.92476	−0.236922
$67$	−12.7722	−1.56037	−0.780187	−	0.625547i	$-0.784876\pi$
$67$	−12.7722	−1.56037	−0.780187	+	0.625547i	$0.784876\pi$
$68$	2.46972	0.299498
$69$	−2.00378	−0.241227
$70$	−1.32913	−0.158861
$71$	−14.5107	−1.72211	−0.861054	−	0.508514i	$-0.830195\pi$
$71$	−14.5107	−1.72211	−0.861054	+	0.508514i	$0.830195\pi$
$72$	0.838927	0.0988685
$73$	12.5500	1.46887	0.734436	−	0.678678i	$-0.237447\pi$
$73$	12.5500	1.46887	0.734436	+	0.678678i	$0.237447\pi$
$74$	−0.172811	−0.0200889
$75$	0.559086	0.0645577
$76$	−4.80476	−0.551143
$77$	13.4670	1.53471
$78$	−1.80701	−0.204603
$79$	−10.5329	−1.18504	−0.592520	−	0.805556i	$-0.701867\pi$
$79$	−10.5329	−1.18504	−0.592520	+	0.805556i	$0.701867\pi$
$80$	−8.12645	−0.908564
$81$	−11.0149	−1.22388
$82$	−0.245582	−0.0271200
$83$	0.738680	0.0810807	0.0405403	−	0.999178i	$-0.487092\pi$
$83$	0.738680	0.0810807	0.0405403	+	0.999178i	$0.487092\pi$
$84$	−11.4802	−1.25259
$85$	2.74293	0.297512
$86$	−0.569410	−0.0614011
$87$	2.00378	0.214828
$88$	−3.80036	−0.405119
$89$	−13.5151	−1.43260	−0.716301	−	0.697791i	$-0.754166\pi$
$89$	−13.5151	−1.43260	−0.716301	+	0.697791i	$0.754166\pi$
$90$	0.460727	0.0485649
$91$	12.6431	1.32536
$92$	−1.95637	−0.203965
$93$	18.6874	1.93779
$94$	−0.557320	−0.0574831
$95$	−5.33626	−0.547489
$96$	4.87737	0.497795
$97$	−14.4575	−1.46794	−0.733969	−	0.679183i	$-0.762334\pi$
$97$	−14.4575	−1.46794	−0.733969	+	0.679183i	$0.762334\pi$
$98$	−0.329240	−0.0332582
$99$	−4.66818	−0.469169
$100$	0.545858	0.0545858
$101$	19.2513	1.91558	0.957788	−	0.287475i	$-0.0928159\pi$
$101$	19.2513	1.91558	0.957788	+	0.287475i	$0.0928159\pi$
$102$	−0.528387	−0.0523181
$103$	−0.772635	−0.0761300	−0.0380650	−	0.999275i	$-0.512119\pi$
$103$	−0.772635	−0.0761300	−0.0380650	+	0.999275i	$0.512119\pi$
$104$	−3.56785	−0.349856
$105$	−12.7501	−1.24428
$106$	−1.37233	−0.133292
$107$	−6.76133	−0.653643	−0.326821	−	0.945086i	$-0.605978\pi$
$107$	−6.76133	−0.653643	−0.326821	+	0.945086i	$0.605978\pi$
$108$	−7.78093	−0.748721
$109$	−2.76150	−0.264503	−0.132252	−	0.991216i	$-0.542221\pi$
$109$	−2.76150	−0.264503	−0.132252	+	0.991216i	$0.542221\pi$
$110$	−2.08710	−0.198997
$111$	−1.65774	−0.157346
$112$	−10.9530	−1.03496
$113$	−7.84074	−0.737595	−0.368797	−	0.929510i	$-0.620230\pi$
$113$	−7.84074	−0.737595	−0.368797	+	0.929510i	$0.620230\pi$
$114$	1.02796	0.0962770
$115$	−2.17278	−0.202613
$116$	1.95637	0.181644
$117$	−4.38258	−0.405169
$118$	1.35446	0.124689
$119$	3.69696	0.338900
$120$	3.59805	0.328455
$121$	10.1469	0.922448
$122$	−2.07030	−0.187436
$123$	−2.35582	−0.212417
$124$	18.2452	1.63847
$125$	11.4702	1.02592
$126$	0.620976	0.0553209
$127$	5.24649	0.465551	0.232775	−	0.972531i	$-0.425219\pi$
$127$	5.24649	0.465551	0.232775	+	0.972531i	$0.425219\pi$
$128$	6.32446	0.559009
$129$	−5.46225	−0.480924
$130$	−1.95941	−0.171852
$131$	1.54403	0.134903	0.0674513	−	0.997723i	$-0.478513\pi$
$131$	1.54403	0.134903	0.0674513	+	0.997723i	$0.478513\pi$
$132$	−18.0270	−1.56905
$133$	−7.19230	−0.623652
$134$	2.66790	0.230472
$135$	−8.64166	−0.743756
$136$	−1.04327	−0.0894600
$137$	2.21807	0.189503	0.0947514	−	0.995501i	$-0.469794\pi$
$137$	2.21807	0.189503	0.0947514	+	0.995501i	$0.469794\pi$
$138$	0.418556	0.0356299
$139$	−13.4409	−1.14004	−0.570020	−	0.821631i	$-0.693064\pi$
$139$	−13.4409	−1.14004	−0.570020	+	0.821631i	$0.693064\pi$
$140$	−12.4484	−1.05208
$141$	−5.34627	−0.450237
$142$	3.03105	0.254360
$143$	19.8532	1.66020
$144$	3.79672	0.316393
$145$	2.17278	0.180440
$146$	−2.62150	−0.216957
$147$	−3.15834	−0.260495
$148$	−1.61852	−0.133041
$149$	8.00649	0.655917	0.327958	−	0.944692i	$-0.393639\pi$
$149$	8.00649	0.655917	0.327958	+	0.944692i	$0.393639\pi$
$150$	−0.116784	−0.00953536
$151$	−22.0069	−1.79089	−0.895447	−	0.445169i	$-0.853144\pi$
$151$	−22.0069	−1.79089	−0.895447	+	0.445169i	$0.853144\pi$
$152$	2.02965	0.164626
$153$	−1.28151	−0.103604
$154$	−2.81303	−0.226681
$155$	20.2635	1.62760
$156$	−16.9241	−1.35502
$157$	5.27899	0.421309	0.210655	−	0.977561i	$-0.432440\pi$
$157$	5.27899	0.421309	0.210655	+	0.977561i	$0.432440\pi$
$158$	2.20014	0.175034
$159$	−13.1645	−1.04401
$160$	5.28874	0.418112
$161$	−2.92851	−0.230799
$162$	2.30083	0.180770
$163$	−5.41587	−0.424204	−0.212102	−	0.977248i	$-0.568031\pi$
$163$	−5.41587	−0.424204	−0.212102	+	0.977248i	$0.568031\pi$
$164$	−2.30008	−0.179606
$165$	−20.0212	−1.55865
$166$	−0.154298	−0.0119758
$167$	−1.28708	−0.0995975	−0.0497987	−	0.998759i	$-0.515858\pi$
$167$	−1.28708	−0.0995975	−0.0497987	+	0.998759i	$0.515858\pi$
$168$	4.84951	0.374148
$169$	5.63855	0.433734
$170$	−0.572952	−0.0439434
$171$	2.49313	0.190654
$172$	−5.33300	−0.406637
$173$	16.3837	1.24563	0.622816	−	0.782368i	$-0.285988\pi$
$173$	16.3837	1.24563	0.622816	+	0.782368i	$0.285988\pi$
$174$	−0.418556	−0.0317307
$175$	0.817102	0.0617671
$176$	−17.1992	−1.29644
$177$	12.9931	0.976623
$178$	2.82309	0.211599
$179$	20.9756	1.56779	0.783894	−	0.620894i	$-0.213230\pi$
$179$	20.9756	1.56779	0.783894	+	0.620894i	$0.213230\pi$
$180$	4.31510	0.321628
$181$	−6.02552	−0.447873	−0.223937	−	0.974604i	$-0.571891\pi$
$181$	−6.02552	−0.447873	−0.223937	+	0.974604i	$0.571891\pi$
$182$	−2.64093	−0.195759
$183$	−19.8600	−1.46809
$184$	0.826420	0.0609245
$185$	−1.79756	−0.132159
$186$	−3.90348	−0.286217
$187$	5.80526	0.424522
$188$	−5.21977	−0.380691
$189$	−11.6474	−0.847222
$190$	1.11466	0.0808657
$191$	10.4844	0.758624	0.379312	−	0.925269i	$-0.376161\pi$
$191$	10.4844	0.758624	0.379312	+	0.925269i	$0.376161\pi$
$192$	13.9699	1.00819
$193$	−13.9434	−1.00367	−0.501833	−	0.864965i	$-0.667341\pi$
$193$	−13.9434	−1.00367	−0.501833	+	0.864965i	$0.667341\pi$
$194$	3.01993	0.216819
$195$	−18.7963	−1.34603
$196$	−3.08361	−0.220258
$197$	18.5756	1.32345	0.661727	−	0.749745i	$-0.269824\pi$
$197$	18.5756	1.32345	0.661727	+	0.749745i	$0.269824\pi$
$198$	0.975105	0.0692977
$199$	−0.136543	−0.00967928	−0.00483964	−	0.999988i	$-0.501541\pi$
$199$	−0.136543	−0.00967928	−0.00483964	+	0.999988i	$0.501541\pi$
$200$	−0.230584	−0.0163048
$201$	25.5927	1.80517
$202$	−4.02128	−0.282936
$203$	2.92851	0.205541
$204$	−4.94878	−0.346484
$205$	−2.55451	−0.178415
$206$	0.161391	0.0112446
$207$	1.01513	0.0705567
$208$	−16.1469	−1.11959
$209$	−11.2939	−0.781216
$210$	2.66328	0.183784
$211$	14.8993	1.02571	0.512855	−	0.858475i	$-0.328588\pi$
$211$	14.8993	1.02571	0.512855	+	0.858475i	$0.328588\pi$
$212$	−12.8530	−0.882748
$213$	29.0763	1.99228
$214$	1.41233	0.0965449
$215$	−5.92294	−0.403941
$216$	3.28686	0.223643
$217$	27.3115	1.85403
$218$	0.576831	0.0390679
$219$	−25.1475	−1.69931
$220$	−19.5475	−1.31789
$221$	5.45009	0.366613
$222$	0.346275	0.0232405
$223$	17.3060	1.15889	0.579446	−	0.815010i	$-0.303269\pi$
$223$	17.3060	1.15889	0.579446	+	0.815010i	$0.303269\pi$
$224$	7.12825	0.476276
$225$	−0.283239	−0.0188826
$226$	1.63780	0.108945
$227$	−17.3405	−1.15093	−0.575466	−	0.817826i	$-0.695179\pi$
$227$	−17.3405	−1.15093	−0.575466	+	0.817826i	$0.695179\pi$
$228$	9.62767	0.637608
$229$	−15.5502	−1.02759	−0.513793	−	0.857914i	$-0.671760\pi$
$229$	−15.5502	−1.02759	−0.513793	+	0.857914i	$0.671760\pi$
$230$	0.453858	0.0299265
$231$	−26.9849	−1.77548
$232$	−0.826420	−0.0542571
$233$	25.9588	1.70062	0.850310	−	0.526283i	$-0.176415\pi$
$233$	25.9588	1.70062	0.850310	+	0.526283i	$0.176415\pi$
$234$	0.915448	0.0598447
$235$	−5.79718	−0.378166
$236$	12.6857	0.825768
$237$	21.1055	1.37095
$238$	−0.772234	−0.0500565
$239$	20.9393	1.35445	0.677227	−	0.735774i	$-0.263182\pi$
$239$	20.9393	1.35445	0.677227	+	0.735774i	$0.263182\pi$
$240$	16.2836	1.05110
$241$	20.7478	1.33648	0.668240	−	0.743945i	$-0.267048\pi$
$241$	20.7478	1.33648	0.668240	+	0.743945i	$0.267048\pi$
$242$	−2.11952	−0.136248
$243$	10.1397	0.650465
$244$	−19.3901	−1.24132
$245$	−3.42472	−0.218797
$246$	0.492092	0.0313746
$247$	−10.6030	−0.674650
$248$	−7.70724	−0.489410
$249$	−1.48015	−0.0938009
$250$	−2.39592	−0.151532
$251$	−14.9000	−0.940477	−0.470239	−	0.882539i	$-0.655832\pi$
$251$	−14.9000	−0.940477	−0.470239	+	0.882539i	$0.655832\pi$
$252$	5.81596	0.366371
$253$	−4.59858	−0.289110
$254$	−1.09590	−0.0687632
$255$	−5.49622	−0.344187
$256$	12.6225	0.788905
$257$	16.9623	1.05808	0.529040	−	0.848597i	$-0.322552\pi$
$257$	16.9623	1.05808	0.529040	+	0.848597i	$0.322552\pi$
$258$	1.14097	0.0710338
$259$	−2.42278	−0.150544
$260$	−18.3516	−1.13811
$261$	−1.01513	−0.0628353
$262$	−0.322523	−0.0199255
$263$	−13.9517	−0.860297	−0.430148	−	0.902758i	$-0.641539\pi$
$263$	−13.9517	−0.860297	−0.430148	+	0.902758i	$0.641539\pi$
$264$	7.61508	0.468676
$265$	−14.2748	−0.876895
$266$	1.50235	0.0921152
$267$	27.0814	1.65735
$268$	24.9871	1.52633
$269$	−18.8640	−1.15016	−0.575080	−	0.818097i	$-0.695029\pi$
$269$	−18.8640	−1.15016	−0.575080	+	0.818097i	$0.695029\pi$
$270$	1.80510	0.109855
$271$	−9.87245	−0.599709	−0.299854	−	0.953985i	$-0.596938\pi$
$271$	−9.87245	−0.599709	−0.299854	+	0.953985i	$0.596938\pi$
$272$	−4.72152	−0.286284
$273$	−25.3340	−1.53328
$274$	−0.463319	−0.0279901
$275$	1.28308	0.0773724
$276$	3.92013	0.235964
$277$	−25.9762	−1.56076	−0.780380	−	0.625306i	$-0.784974\pi$
$277$	−25.9762	−1.56076	−0.780380	+	0.625306i	$0.784974\pi$
$278$	2.80757	0.168387
$279$	−9.46721	−0.566787
$280$	5.25853	0.314257
$281$	4.88210	0.291242	0.145621	−	0.989340i	$-0.453482\pi$
$281$	4.88210	0.291242	0.145621	+	0.989340i	$0.453482\pi$
$282$	1.11675	0.0665013
$283$	19.1452	1.13807	0.569033	−	0.822315i	$-0.307318\pi$
$283$	19.1452	1.13807	0.569033	+	0.822315i	$0.307318\pi$
$284$	28.3883	1.68454
$285$	10.6927	0.633381
$286$	−4.14700	−0.245217
$287$	−3.44302	−0.203235
$288$	−2.47092	−0.145601
$289$	−15.4063	−0.906255
$290$	−0.453858	−0.0266515
$291$	28.9697	1.69823
$292$	−24.5525	−1.43683
$293$	12.6416	0.738532	0.369266	−	0.929324i	$-0.379609\pi$
$293$	12.6416	0.738532	0.369266	+	0.929324i	$0.379609\pi$
$294$	0.659724	0.0384759
$295$	14.0890	0.820293
$296$	0.683704	0.0397395
$297$	−18.2896	−1.06127
$298$	−1.67242	−0.0968808
$299$	−4.31724	−0.249672
$300$	−1.09378	−0.0631493
$301$	−7.98304	−0.460135
$302$	4.59687	0.264520
$303$	−38.5754	−2.21610
$304$	9.18555	0.526827
$305$	−21.5350	−1.23309
$306$	0.267686	0.0153026
$307$	−17.3116	−0.988023	−0.494011	−	0.869455i	$-0.664470\pi$
$307$	−17.3116	−0.988023	−0.494011	+	0.869455i	$0.664470\pi$
$308$	−26.3464	−1.50123
$309$	1.54819	0.0880735
$310$	−4.23271	−0.240402
$311$	13.5016	0.765608	0.382804	−	0.923830i	$-0.374959\pi$
$311$	13.5016	0.765608	0.382804	+	0.923830i	$0.374959\pi$
$312$	7.14919	0.404743
$313$	−16.3551	−0.924446	−0.462223	−	0.886764i	$-0.652948\pi$
$313$	−16.3551	−0.924446	−0.462223	+	0.886764i	$0.652948\pi$
$314$	−1.10269	−0.0622286
$315$	6.45932	0.363942
$316$	20.6062	1.15919
$317$	12.0251	0.675399	0.337699	−	0.941254i	$-0.390351\pi$
$317$	12.0251	0.675399	0.337699	+	0.941254i	$0.390351\pi$
$318$	2.74984	0.154204
$319$	4.59858	0.257471
$320$	15.1482	0.846808
$321$	13.5482	0.756188
$322$	0.611718	0.0340897
$323$	−3.10041	−0.172511
$324$	21.5492	1.19718
$325$	1.20458	0.0668180
$326$	1.13129	0.0626561
$327$	5.53343	0.305999
$328$	0.971612	0.0536483
$329$	−7.81354	−0.430774
$330$	4.18209	0.230217
$331$	9.26937	0.509491	0.254745	−	0.967008i	$-0.418008\pi$
$331$	9.26937	0.509491	0.254745	+	0.967008i	$0.418008\pi$
$332$	−1.44513	−0.0793118
$333$	0.839829	0.0460223
$334$	0.268850	0.0147108
$335$	27.7512	1.51621
$336$	21.9473	1.19732
$337$	−19.4356	−1.05873	−0.529363	−	0.848395i	$-0.677569\pi$
$337$	−19.4356	−1.05873	−0.529363	+	0.848395i	$0.677569\pi$
$338$	−1.17780	−0.0640638
$339$	15.7111	0.853311
$340$	−5.36617	−0.291021
$341$	42.8866	2.32244
$342$	−0.520773	−0.0281602
$343$	15.8837	0.857639
$344$	2.25280	0.121463
$345$	4.35378	0.234400
$346$	−3.42229	−0.183983
$347$	21.2447	1.14047	0.570237	−	0.821480i	$-0.306851\pi$
$347$	21.2447	1.14047	0.570237	+	0.821480i	$0.306851\pi$
$348$	−3.92013	−0.210141
$349$	17.4225	0.932605	0.466303	−	0.884625i	$-0.345586\pi$
$349$	17.4225	0.932605	0.466303	+	0.884625i	$0.345586\pi$
$350$	−0.170679	−0.00912317
$351$	−17.1707	−0.916502
$352$	11.1933	0.596607
$353$	28.1837	1.50007	0.750033	−	0.661401i	$-0.230038\pi$
$353$	28.1837	1.50007	0.750033	+	0.661401i	$0.230038\pi$
$354$	−2.71405	−0.144250
$355$	31.5287	1.67337
$356$	26.4406	1.40135
$357$	−7.40790	−0.392068
$358$	−4.38145	−0.231567
$359$	5.28283	0.278817	0.139408	−	0.990235i	$-0.455480\pi$
$359$	5.28283	0.278817	0.139408	+	0.990235i	$0.455480\pi$
$360$	−1.82281	−0.0960703
$361$	−12.9683	−0.682541
$362$	1.25863	0.0661522
$363$	−20.3322	−1.06716
$364$	−24.7345	−1.29644
$365$	−27.2685	−1.42730
$366$	4.14842	0.216841
$367$	10.9920	0.573777	0.286889	−	0.957964i	$-0.407379\pi$
$367$	10.9920	0.573777	0.286889	+	0.957964i	$0.407379\pi$
$368$	3.74011	0.194967
$369$	1.19348	0.0621302
$370$	0.375481	0.0195203
$371$	−19.2398	−0.998882
$372$	−36.5594	−1.89552
$373$	12.7343	0.659360	0.329680	−	0.944093i	$-0.393059\pi$
$373$	12.7343	0.659360	0.329680	+	0.944093i	$0.393059\pi$
$374$	−1.21262	−0.0627032
$375$	−22.9837	−1.18687
$376$	2.20496	0.113712
$377$	4.31724	0.222349
$378$	2.43294	0.125137
$379$	−30.5469	−1.56909	−0.784545	−	0.620072i	$-0.787103\pi$
$379$	−30.5469	−1.56909	−0.784545	+	0.620072i	$0.787103\pi$
$380$	10.4397	0.535545
$381$	−10.5128	−0.538588
$382$	−2.19001	−0.112051
$383$	3.76472	0.192368	0.0961840	−	0.995364i	$-0.469336\pi$
$383$	3.76472	0.192368	0.0961840	+	0.995364i	$0.469336\pi$
$384$	−12.6728	−0.646708
$385$	−29.2609	−1.49127
$386$	2.91254	0.148244
$387$	2.76723	0.140666
$388$	28.2842	1.43591
$389$	−24.8291	−1.25888	−0.629442	−	0.777048i	$-0.716716\pi$
$389$	−24.8291	−1.25888	−0.629442	+	0.777048i	$0.716716\pi$
$390$	3.92623	0.198813
$391$	−1.26240	−0.0638424
$392$	1.30259	0.0657909
$393$	−3.09390	−0.156067
$394$	−3.88013	−0.195478
$395$	22.8856	1.15150
$396$	9.13267	0.458934
$397$	8.76026	0.439665	0.219832	−	0.975538i	$-0.429449\pi$
$397$	8.76026	0.439665	0.219832	+	0.975538i	$0.429449\pi$
$398$	0.0285216	0.00142966
$399$	14.4118	0.721492
$400$	−1.04355	−0.0521775
$401$	−24.0076	−1.19888	−0.599440	−	0.800419i	$-0.704610\pi$
$401$	−24.0076	−1.19888	−0.599440	+	0.800419i	$0.704610\pi$
$402$	−5.34589	−0.266629
$403$	40.2628	2.00564
$404$	−37.6626	−1.87379
$405$	23.9330	1.18924
$406$	−0.611718	−0.0303590
$407$	−3.80444	−0.188579
$408$	2.09049	0.103495
$409$	−23.1751	−1.14593	−0.572967	−	0.819579i	$-0.694208\pi$
$409$	−23.1751	−1.14593	−0.572967	+	0.819579i	$0.694208\pi$
$410$	0.533596	0.0263524
$411$	−4.44453	−0.219233
$412$	1.51156	0.0744692
$413$	18.9894	0.934406
$414$	−0.212045	−0.0104214
$415$	−1.60499	−0.0787859
$416$	10.5085	0.515223
$417$	26.9325	1.31889
$418$	2.35911	0.115388
$419$	−3.47063	−0.169551	−0.0847757	−	0.996400i	$-0.527017\pi$
$419$	−3.47063	−0.169551	−0.0847757	+	0.996400i	$0.527017\pi$
$420$	24.9439	1.21714
$421$	28.1704	1.37294	0.686471	−	0.727157i	$-0.259159\pi$
$421$	28.1704	1.37294	0.686471	+	0.727157i	$0.259159\pi$
$422$	−3.11221	−0.151500
$423$	2.70847	0.131690
$424$	5.42944	0.263677
$425$	0.352230	0.0170857
$426$	−6.07356	−0.294265
$427$	−29.0252	−1.40463
$428$	13.2277	0.639383
$429$	−39.7814	−1.92066
$430$	1.23720	0.0596633
$431$	−13.0279	−0.627534	−0.313767	−	0.949500i	$-0.601591\pi$
$431$	−13.0279	−0.627534	−0.313767	+	0.949500i	$0.601591\pi$
$432$	14.8753	0.715688
$433$	40.0693	1.92561	0.962803	−	0.270205i	$-0.0870916\pi$
$433$	40.0693	1.92561	0.962803	+	0.270205i	$0.0870916\pi$
$434$	−5.70492	−0.273845
$435$	−4.35378	−0.208748
$436$	5.40250	0.258733
$437$	2.45596	0.117484
$438$	5.25290	0.250993
$439$	−18.4542	−0.880773	−0.440387	−	0.897808i	$-0.645159\pi$
$439$	−18.4542	−0.880773	−0.440387	+	0.897808i	$0.645159\pi$
$440$	8.25735	0.393654
$441$	1.60004	0.0761926
$442$	−1.13843	−0.0541498
$443$	−1.02292	−0.0486004	−0.0243002	−	0.999705i	$-0.507736\pi$
$443$	−1.02292	−0.0486004	−0.0243002	+	0.999705i	$0.507736\pi$
$444$	3.24316	0.153913
$445$	29.3655	1.39206
$446$	−3.61493	−0.171172
$447$	−16.0432	−0.758819
$448$	20.4169	0.964610
$449$	−21.1061	−0.996059	−0.498029	−	0.867160i	$-0.665943\pi$
$449$	−21.1061	−0.996059	−0.498029	+	0.867160i	$0.665943\pi$
$450$	0.0591639	0.00278901
$451$	−5.40649	−0.254582
$452$	15.3394	0.721503
$453$	44.0969	2.07185
$454$	3.62215	0.169996
$455$	−27.4707	−1.28785
$456$	−4.06697	−0.190454
$457$	−18.0078	−0.842367	−0.421184	−	0.906975i	$-0.638385\pi$
$457$	−18.0078	−0.842367	−0.421184	+	0.906975i	$0.638385\pi$
$458$	3.24818	0.151777
$459$	−5.02087	−0.234354
$460$	4.25076	0.198193
$461$	−10.1715	−0.473734	−0.236867	−	0.971542i	$-0.576121\pi$
$461$	−10.1715	−0.473734	−0.236867	+	0.971542i	$0.576121\pi$
$462$	5.63670	0.262243
$463$	3.24020	0.150585	0.0752924	−	0.997161i	$-0.476011\pi$
$463$	3.24020	0.150585	0.0752924	+	0.997161i	$0.476011\pi$
$464$	−3.74011	−0.173630
$465$	−40.6036	−1.88295
$466$	−5.42237	−0.251186
$467$	−5.43944	−0.251707	−0.125854	−	0.992049i	$-0.540167\pi$
$467$	−5.43944	−0.251707	−0.125854	+	0.992049i	$0.540167\pi$
$468$	8.57393	0.396330
$469$	37.4036	1.72714
$470$	1.21093	0.0558563
$471$	−10.5779	−0.487406
$472$	−5.35876	−0.246657
$473$	−12.5356	−0.576387
$474$	−4.40860	−0.202494
$475$	−0.685251	−0.0314415
$476$	−7.23262	−0.331506
$477$	6.66926	0.305364
$478$	−4.37388	−0.200057
$479$	−4.68933	−0.214261	−0.107131	−	0.994245i	$-0.534166\pi$
$479$	−4.68933	−0.214261	−0.107131	+	0.994245i	$0.534166\pi$
$480$	−10.5975	−0.483706
$481$	−3.57169	−0.162855
$482$	−4.33386	−0.197402
$483$	5.86810	0.267008
$484$	−19.8511	−0.902324
$485$	31.4130	1.42639
$486$	−2.11802	−0.0960756
$487$	−29.7281	−1.34711	−0.673555	−	0.739137i	$-0.735234\pi$
$487$	−29.7281	−1.34711	−0.673555	+	0.739137i	$0.735234\pi$
$488$	8.19086	0.370783
$489$	10.8522	0.490754
$490$	0.715366	0.0323170
$491$	−13.0284	−0.587963	−0.293981	−	0.955811i	$-0.594980\pi$
$491$	−13.0284	−0.587963	−0.293981	+	0.955811i	$0.594980\pi$
$492$	4.60885	0.207783
$493$	1.26240	0.0568557
$494$	2.21478	0.0996477
$495$	10.1429	0.455891
$496$	−34.8805	−1.56618
$497$	42.4949	1.90616
$498$	0.309179	0.0138547
$499$	−12.5718	−0.562791	−0.281396	−	0.959592i	$-0.590797\pi$
$499$	−12.5718	−0.562791	−0.281396	+	0.959592i	$0.590797\pi$
$500$	−22.4398	−1.00354
$501$	2.57903	0.115223
$502$	3.11236	0.138911
$503$	12.4114	0.553398	0.276699	−	0.960957i	$-0.410759\pi$
$503$	12.4114	0.553398	0.276699	+	0.960957i	$0.410759\pi$
$504$	−2.45681	−0.109435
$505$	−41.8289	−1.86136
$506$	0.960567	0.0427024
$507$	−11.2984	−0.501780
$508$	−10.2641	−0.455394
$509$	−5.93930	−0.263255	−0.131627	−	0.991299i	$-0.542020\pi$
$509$	−5.93930	−0.263255	−0.131627	+	0.991299i	$0.542020\pi$
$510$	1.14807	0.0508374
$511$	−36.7530	−1.62586
$512$	−15.2856	−0.675532
$513$	9.76792	0.431264
$514$	−3.54315	−0.156281
$515$	1.67877	0.0739754
$516$	10.6862	0.470432
$517$	−12.2694	−0.539609
$518$	0.506079	0.0222358
$519$	−32.8294	−1.44105
$520$	7.75216	0.339955
$521$	27.9546	1.22471	0.612356	−	0.790582i	$-0.290222\pi$
$521$	27.9546	1.22471	0.612356	+	0.790582i	$0.290222\pi$
$522$	0.212045	0.00928095
$523$	−8.64009	−0.377805	−0.188902	−	0.981996i	$-0.560493\pi$
$523$	−8.64009	−0.377805	−0.188902	+	0.981996i	$0.560493\pi$
$524$	−3.02069	−0.131960
$525$	−1.63729	−0.0714573
$526$	2.91427	0.127068
$527$	11.7732	0.512851
$528$	34.4634	1.49983
$529$	1.00000	0.0434783
$530$	2.98177	0.129520
$531$	−6.58244	−0.285654
$532$	14.0708	0.610046
$533$	−5.07573	−0.219854
$534$	−5.65685	−0.244796
$535$	14.6909	0.635143
$536$	−10.5552	−0.455915
$537$	−42.0305	−1.81375
$538$	3.94038	0.169882
$539$	−7.24823	−0.312203
$540$	16.9063	0.727530
$541$	30.7792	1.32330	0.661651	−	0.749812i	$-0.269856\pi$
$541$	30.7792	1.32330	0.661651	+	0.749812i	$0.269856\pi$
$542$	2.06219	0.0885787
$543$	12.0738	0.518137
$544$	3.07280	0.131745
$545$	6.00013	0.257017
$546$	5.29185	0.226470
$547$	−12.1559	−0.519750	−0.259875	−	0.965642i	$-0.583681\pi$
$547$	−12.1559	−0.519750	−0.259875	+	0.965642i	$0.583681\pi$
$548$	−4.33937	−0.185369
$549$	10.0613	0.429404
$550$	−0.268013	−0.0114281
$551$	−2.45596	−0.104627
$552$	−1.65596	−0.0704825
$553$	30.8456	1.31169
$554$	5.42600	0.230529
$555$	3.60192	0.152893
$556$	26.2953	1.11517
$557$	1.41177	0.0598186	0.0299093	−	0.999553i	$-0.490478\pi$
$557$	1.41177	0.0598186	0.0299093	+	0.999553i	$0.490478\pi$
$558$	1.97754	0.0837161
$559$	−11.7687	−0.497761
$560$	23.7984	1.00567
$561$	−11.6325	−0.491123
$562$	−1.01979	−0.0430172
$563$	−8.37310	−0.352884	−0.176442	−	0.984311i	$-0.556459\pi$
$563$	−8.37310	−0.352884	−0.176442	+	0.984311i	$0.556459\pi$
$564$	10.4593	0.440414
$565$	17.0362	0.716719
$566$	−3.99912	−0.168096
$567$	32.2573	1.35468
$568$	−11.9920	−0.503171
$569$	−23.8853	−1.00132	−0.500662	−	0.865643i	$-0.666910\pi$
$569$	−23.8853	−1.00132	−0.500662	+	0.865643i	$0.666910\pi$
$570$	−2.23353	−0.0935521
$571$	28.4095	1.18890	0.594450	−	0.804133i	$-0.297370\pi$
$571$	28.4095	1.18890	0.594450	+	0.804133i	$0.297370\pi$
$572$	−38.8401	−1.62399
$573$	−21.0084	−0.877639
$574$	0.719189	0.0300184
$575$	−0.279016	−0.0116358
$576$	−7.07729	−0.294887
$577$	15.3659	0.639692	0.319846	−	0.947470i	$-0.396369\pi$
$577$	15.3659	0.639692	0.319846	+	0.947470i	$0.396369\pi$
$578$	3.21813	0.133857
$579$	27.9395	1.16112
$580$	−4.25076	−0.176503
$581$	−2.16323	−0.0897461
$582$	−6.05128	−0.250834
$583$	−30.2119	−1.25125
$584$	10.3716	0.429180
$585$	9.52239	0.393702
$586$	−2.64063	−0.109083
$587$	20.7449	0.856234	0.428117	−	0.903723i	$-0.359177\pi$
$587$	20.7449	0.856234	0.428117	+	0.903723i	$0.359177\pi$
$588$	6.17887	0.254812
$589$	−22.9044	−0.943760
$590$	−2.94296	−0.121160
$591$	−37.2214	−1.53108
$592$	3.09422	0.127172
$593$	33.9653	1.39479	0.697393	−	0.716689i	$-0.254343\pi$
$593$	33.9653	1.39479	0.697393	+	0.716689i	$0.254343\pi$
$594$	3.82040	0.156753
$595$	−8.03269	−0.329308
$596$	−15.6636	−0.641607
$597$	0.273602	0.0111978
$598$	0.901799	0.0368773
$599$	−1.65402	−0.0675816	−0.0337908	−	0.999429i	$-0.510758\pi$
$599$	−1.65402	−0.0675816	−0.0337908	+	0.999429i	$0.510758\pi$
$600$	0.462040	0.0188627
$601$	−32.2924	−1.31724	−0.658618	−	0.752477i	$-0.728859\pi$
$601$	−32.2924	−1.31724	−0.658618	+	0.752477i	$0.728859\pi$
$602$	1.66752	0.0679632
$603$	−12.9655	−0.527996
$604$	43.0535	1.75182
$605$	−22.0471	−0.896341
$606$	8.05776	0.327324
$607$	−36.4463	−1.47931	−0.739654	−	0.672987i	$-0.765011\pi$
$607$	−36.4463	−1.47931	−0.739654	+	0.672987i	$0.765011\pi$
$608$	−5.97801	−0.242440
$609$	−5.86810	−0.237787
$610$	4.49831	0.182131
$611$	−11.5188	−0.466000
$612$	2.50710	0.101344
$613$	23.8712	0.964150	0.482075	−	0.876130i	$-0.339883\pi$
$613$	23.8712	0.964150	0.482075	+	0.876130i	$0.339883\pi$
$614$	3.61610	0.145934
$615$	5.11869	0.206405
$616$	11.1294	0.448416
$617$	−30.4325	−1.22517	−0.612583	−	0.790406i	$-0.709869\pi$
$617$	−30.4325	−1.22517	−0.612583	+	0.790406i	$0.709869\pi$
$618$	−0.323391	−0.0130087
$619$	7.67468	0.308472	0.154236	−	0.988034i	$-0.450708\pi$
$619$	7.67468	0.308472	0.154236	+	0.988034i	$0.450708\pi$
$620$	−39.6429	−1.59210
$621$	3.97723	0.159601
$622$	−2.82027	−0.113082
$623$	39.5793	1.58571
$624$	32.3549	1.29523
$625$	−23.5271	−0.941083
$626$	3.41631	0.136543
$627$	22.6305	0.903776
$628$	−10.3276	−0.412118
$629$	−1.04440	−0.0416428
$630$	−1.34925	−0.0537552
$631$	−31.9475	−1.27181	−0.635905	−	0.771768i	$-0.719373\pi$
$631$	−31.9475	−1.27181	−0.635905	+	0.771768i	$0.719373\pi$
$632$	−8.70457	−0.346249
$633$	−29.8549	−1.18663
$634$	−2.51185	−0.0997583
$635$	−11.3995	−0.452375
$636$	25.7546	1.02124
$637$	−6.80478	−0.269615
$638$	−0.960567	−0.0380292
$639$	−14.7303	−0.582724
$640$	−13.7417	−0.543188
$641$	−26.4345	−1.04410	−0.522050	−	0.852915i	$-0.674833\pi$
$641$	−26.4345	−1.04410	−0.522050	+	0.852915i	$0.674833\pi$
$642$	−2.83000	−0.111691
$643$	−39.7892	−1.56913	−0.784567	−	0.620045i	$-0.787114\pi$
$643$	−39.7892	−1.56913	−0.784567	+	0.620045i	$0.787114\pi$
$644$	5.72925	0.225764
$645$	11.8683	0.467313
$646$	0.647623	0.0254804
$647$	−1.75466	−0.0689827	−0.0344914	−	0.999405i	$-0.510981\pi$
$647$	−1.75466	−0.0689827	−0.0344914	+	0.999405i	$0.510981\pi$
$648$	−9.10293	−0.357597
$649$	29.8186	1.17048
$650$	−0.251616	−0.00986920
$651$	−54.7262	−2.14489
$652$	10.5954	0.414949
$653$	10.5358	0.412298	0.206149	−	0.978521i	$-0.433907\pi$
$653$	10.5358	0.412298	0.206149	+	0.978521i	$0.433907\pi$
$654$	−1.15584	−0.0451970
$655$	−3.35484	−0.131085
$656$	4.39720	0.171682
$657$	12.7400	0.497034
$658$	1.63212	0.0636266
$659$	2.47246	0.0963134	0.0481567	−	0.998840i	$-0.484665\pi$
$659$	2.47246	0.0963134	0.0481567	+	0.998840i	$0.484665\pi$
$660$	39.1688	1.52464
$661$	−49.7697	−1.93582	−0.967908	−	0.251304i	$-0.919141\pi$
$661$	−49.7697	−1.93582	−0.967908	+	0.251304i	$0.919141\pi$
$662$	−1.93622	−0.0752533
$663$	−10.9208	−0.424128
$664$	0.610460	0.0236904
$665$	15.6273	0.606001
$666$	−0.175426	−0.00679763
$667$	−1.00000	−0.0387202
$668$	2.51801	0.0974246
$669$	−34.6773	−1.34070
$670$	−5.79677	−0.223949
$671$	−45.5777	−1.75951
$672$	−14.2835	−0.550996
$673$	8.06121	0.310737	0.155368	−	0.987857i	$-0.450344\pi$
$673$	8.06121	0.310737	0.155368	+	0.987857i	$0.450344\pi$
$674$	4.05978	0.156377
$675$	−1.10971	−0.0427128
$676$	−11.0311	−0.424272
$677$	−3.26890	−0.125634	−0.0628170	−	0.998025i	$-0.520008\pi$
$677$	−3.26890	−0.125634	−0.0628170	+	0.998025i	$0.520008\pi$
$678$	−3.28179	−0.126036
$679$	42.3390	1.62482
$680$	2.26681	0.0869281
$681$	34.7466	1.33149
$682$	−8.95831	−0.343031
$683$	−41.6175	−1.59245	−0.796225	−	0.605001i	$-0.793173\pi$
$683$	−41.6175	−1.59245	−0.796225	+	0.605001i	$0.793173\pi$
$684$	−4.87747	−0.186495
$685$	−4.81939	−0.184140
$686$	−3.31784	−0.126676
$687$	31.1592	1.18880
$688$	10.1954	0.388697
$689$	−28.3635	−1.08056
$690$	−0.909432	−0.0346215
$691$	8.77968	0.333995	0.166997	−	0.985957i	$-0.446593\pi$
$691$	8.77968	0.333995	0.166997	+	0.985957i	$0.446593\pi$
$692$	−32.0526	−1.21846
$693$	13.6708	0.519311
$694$	−4.43766	−0.168451
$695$	29.2041	1.10777
$696$	1.65596	0.0627691
$697$	−1.48419	−0.0562178
$698$	−3.63927	−0.137748
$699$	−52.0158	−1.96742
$700$	−1.59855	−0.0604196
$701$	−44.9376	−1.69727	−0.848635	−	0.528979i	$-0.822575\pi$
$701$	−44.9376	−1.69727	−0.848635	+	0.528979i	$0.822575\pi$
$702$	3.58667	0.135370
$703$	2.03183	0.0766320
$704$	32.0603	1.20832
$705$	11.6163	0.437494
$706$	−5.88710	−0.221564
$707$	−56.3777	−2.12030
$708$	−25.4193	−0.955317
$709$	−25.8244	−0.969857	−0.484928	−	0.874554i	$-0.661154\pi$
$709$	−25.8244	−0.969857	−0.484928	+	0.874554i	$0.661154\pi$
$710$	−6.58582	−0.247161
$711$	−10.6923	−0.400992
$712$	−11.1692	−0.418583
$713$	−9.32607	−0.349264
$714$	1.54739	0.0579095
$715$	−43.1366	−1.61322
$716$	−41.0359	−1.53359
$717$	−41.9578	−1.56694
$718$	−1.10350	−0.0411821
$719$	41.6399	1.55291	0.776453	−	0.630175i	$-0.217017\pi$
$719$	41.6399	1.55291	0.776453	+	0.630175i	$0.217017\pi$
$720$	−8.24944	−0.307438
$721$	2.26267	0.0842663
$722$	2.70886	0.100813
$723$	−41.5739	−1.54615
$724$	11.7881	0.438102
$725$	0.279016	0.0103624
$726$	4.24706	0.157623
$727$	32.6375	1.21046	0.605229	−	0.796051i	$-0.293081\pi$
$727$	32.6375	1.21046	0.605229	+	0.796051i	$0.293081\pi$
$728$	10.4485	0.387247
$729$	12.7269	0.471366
$730$	5.69594	0.210816
$731$	−3.44127	−0.127280
$732$	38.8534	1.43606
$733$	−26.9747	−0.996333	−0.498167	−	0.867081i	$-0.665993\pi$
$733$	−26.9747	−0.996333	−0.498167	+	0.867081i	$0.665993\pi$
$734$	−2.29604	−0.0847485
$735$	6.86238	0.253123
$736$	−2.43409	−0.0897216
$737$	58.7340	2.16349
$738$	−0.249299	−0.00917680
$739$	3.39525	0.124896	0.0624482	−	0.998048i	$-0.480109\pi$
$739$	3.39525	0.124896	0.0624482	+	0.998048i	$0.480109\pi$
$740$	3.51669	0.129276
$741$	21.2460	0.780491
$742$	4.01888	0.147538
$743$	−25.1497	−0.922652	−0.461326	−	0.887231i	$-0.652626\pi$
$743$	−25.1497	−0.922652	−0.461326	+	0.887231i	$0.652626\pi$
$744$	15.4436	0.566191
$745$	−17.3964	−0.637353
$746$	−2.65999	−0.0973893
$747$	0.749860	0.0274359
$748$	−11.3572	−0.415261
$749$	19.8006	0.723500
$750$	4.80091	0.175304
$751$	29.1407	1.06336	0.531679	−	0.846946i	$-0.321561\pi$
$751$	29.1407	1.06336	0.531679	+	0.846946i	$0.321561\pi$
$752$	9.97895	0.363895
$753$	29.8563	1.08802
$754$	−0.901799	−0.0328416
$755$	47.8161	1.74021
$756$	22.7866	0.828739
$757$	−20.9561	−0.761664	−0.380832	−	0.924644i	$-0.624362\pi$
$757$	−20.9561	−0.761664	−0.380832	+	0.924644i	$0.624362\pi$
$758$	6.38074	0.231759
$759$	9.21454	0.334467
$760$	−4.40999	−0.159967
$761$	11.2717	0.408600	0.204300	−	0.978908i	$-0.434508\pi$
$761$	11.2717	0.408600	0.204300	+	0.978908i	$0.434508\pi$
$762$	2.19595	0.0795510
$763$	8.08708	0.292772
$764$	−20.5113	−0.742073
$765$	2.78444	0.100672
$766$	−0.786387	−0.0284133
$767$	27.9943	1.01082
$768$	−25.2927	−0.912671
$769$	13.8381	0.499016	0.249508	−	0.968373i	$-0.419731\pi$
$769$	13.8381	0.499016	0.249508	+	0.968373i	$0.419731\pi$
$770$	6.11211	0.220265
$771$	−33.9887	−1.22407
$772$	27.2784	0.981770
$773$	50.3010	1.80920	0.904600	−	0.426262i	$-0.140170\pi$
$773$	50.3010	1.80920	0.904600	+	0.426262i	$0.140170\pi$
$774$	−0.578028	−0.0207768
$775$	2.60212	0.0934709
$776$	−11.9480	−0.428907
$777$	4.85472	0.174162
$778$	5.18638	0.185941
$779$	2.88744	0.103453
$780$	36.7725	1.31667
$781$	66.7288	2.38774
$782$	0.263695	0.00942971
$783$	−3.97723	−0.142135
$784$	5.89512	0.210540
$785$	−11.4701	−0.409385
$786$	0.646264	0.0230515
$787$	−26.6673	−0.950585	−0.475293	−	0.879828i	$-0.657658\pi$
$787$	−26.6673	−0.950585	−0.475293	+	0.879828i	$0.657658\pi$
$788$	−36.3406	−1.29458
$789$	27.9561	0.995262
$790$	−4.78043	−0.170080
$791$	22.9617	0.816425
$792$	−3.85787	−0.137084
$793$	−42.7893	−1.51949
$794$	−1.82987	−0.0649397
$795$	28.6036	1.01446
$796$	0.267129	0.00946812
$797$	40.0029	1.41698	0.708488	−	0.705723i	$-0.249378\pi$
$797$	40.0029	1.41698	0.708488	+	0.705723i	$0.249378\pi$
$798$	−3.01038	−0.106566
$799$	−3.36820	−0.119158
$800$	0.679149	0.0240115
$801$	−13.7197	−0.484761
$802$	5.01478	0.177078
$803$	−57.7124	−2.03663
$804$	−50.0687	−1.76579
$805$	6.36302	0.224267
$806$	−8.41024	−0.296238
$807$	37.7993	1.33060
$808$	15.9097	0.559700
$809$	−7.09107	−0.249309	−0.124654	−	0.992200i	$-0.539782\pi$
$809$	−7.09107	−0.249309	−0.124654	+	0.992200i	$0.539782\pi$
$810$	−4.99921	−0.175654
$811$	51.5801	1.81122	0.905611	−	0.424110i	$-0.139413\pi$
$811$	51.5801	1.81122	0.905611	+	0.424110i	$0.139413\pi$
$812$	−5.72925	−0.201057
$813$	19.7822	0.693793
$814$	0.794685	0.0278537
$815$	11.7675	0.412198
$816$	9.46089	0.331198
$817$	6.69487	0.234224
$818$	4.84089	0.169258
$819$	12.8344	0.448472
$820$	4.99757	0.174523
$821$	−1.86996	−0.0652619	−0.0326310	−	0.999467i	$-0.510389\pi$
$821$	−1.86996	−0.0652619	−0.0326310	+	0.999467i	$0.510389\pi$
$822$	0.928389	0.0323813
$823$	−16.8983	−0.589039	−0.294520	−	0.955645i	$-0.595160\pi$
$823$	−16.8983	−0.589039	−0.294520	+	0.955645i	$0.595160\pi$
$824$	−0.638521	−0.0222439
$825$	−2.57100	−0.0895108
$826$	−3.96657	−0.138014
$827$	−19.5305	−0.679143	−0.339571	−	0.940580i	$-0.610282\pi$
$827$	−19.5305	−0.679143	−0.339571	+	0.940580i	$0.610282\pi$
$828$	−1.98598	−0.0690175
$829$	47.9451	1.66520	0.832601	−	0.553874i	$-0.186851\pi$
$829$	47.9451	1.66520	0.832601	+	0.553874i	$0.186851\pi$
$830$	0.335256	0.0116369
$831$	52.0506	1.80562
$832$	30.0988	1.04349
$833$	−1.98978	−0.0689419
$834$	−5.62576	−0.194804
$835$	2.79655	0.0967787
$836$	22.0950	0.764173
$837$	−37.0919	−1.28209
$838$	0.724957	0.0250432
$839$	−33.9625	−1.17251	−0.586257	−	0.810125i	$-0.699399\pi$
$839$	−33.9625	−1.17251	−0.586257	+	0.810125i	$0.699399\pi$
$840$	−10.5369	−0.363559
$841$	1.00000	0.0344828
$842$	−5.88433	−0.202788
$843$	−9.78266	−0.336933
$844$	−29.1485	−1.00333
$845$	−12.2513	−0.421459
$846$	−0.565755	−0.0194510
$847$	−29.7154	−1.02103
$848$	24.5719	0.843802
$849$	−38.3628	−1.31661
$850$	−0.0735751	−0.00252360
$851$	0.827308	0.0283598
$852$	−56.8840	−1.94881
$853$	16.2359	0.555907	0.277954	−	0.960595i	$-0.410344\pi$
$853$	16.2359	0.555907	0.277954	+	0.960595i	$0.410344\pi$
$854$	6.06289	0.207468
$855$	−5.41702	−0.185258
$856$	−5.58770	−0.190984
$857$	5.97287	0.204029	0.102015	−	0.994783i	$-0.467471\pi$
$857$	5.97287	0.204029	0.102015	+	0.994783i	$0.467471\pi$
$858$	8.30967	0.283687
$859$	14.6467	0.499738	0.249869	−	0.968280i	$-0.419612\pi$
$859$	14.6467	0.499738	0.249869	+	0.968280i	$0.419612\pi$
$860$	11.5875	0.395129
$861$	6.89905	0.235119
$862$	2.72132	0.0926886
$863$	12.5656	0.427740	0.213870	−	0.976862i	$-0.431393\pi$
$863$	12.5656	0.427740	0.213870	+	0.976862i	$0.431393\pi$
$864$	−9.68093	−0.329352
$865$	−35.5983	−1.21038
$866$	−8.36980	−0.284417
$867$	30.8709	1.04843
$868$	−53.4313	−1.81358
$869$	48.4362	1.64309
$870$	0.909432	0.0308326
$871$	55.1407	1.86837
$872$	−2.28215	−0.0772835
$873$	−14.6763	−0.496718
$874$	−0.513009	−0.0173528
$875$	−33.5905	−1.13557
$876$	49.1978	1.66224
$877$	6.56496	0.221683	0.110842	−	0.993838i	$-0.464645\pi$
$877$	6.56496	0.221683	0.110842	+	0.993838i	$0.464645\pi$
$878$	3.85479	0.130093
$879$	−25.3310	−0.854395
$880$	37.3701	1.25975
$881$	−53.0308	−1.78665	−0.893326	−	0.449409i	$-0.851635\pi$
$881$	−53.0308	−1.78665	−0.893326	+	0.449409i	$0.851635\pi$
$882$	−0.334223	−0.0112539
$883$	35.8060	1.20497	0.602484	−	0.798131i	$-0.294178\pi$
$883$	35.8060	1.20497	0.602484	+	0.798131i	$0.294178\pi$
$884$	−10.6624	−0.358615
$885$	−28.2312	−0.948982
$886$	0.213671	0.00717842
$887$	52.8011	1.77289	0.886444	−	0.462836i	$-0.153168\pi$
$887$	52.8011	1.77289	0.886444	+	0.462836i	$0.153168\pi$
$888$	−1.36999	−0.0459739
$889$	−15.3644	−0.515306
$890$	−6.13396	−0.205611
$891$	50.6529	1.69694
$892$	−33.8568	−1.13361
$893$	6.55272	0.219278
$894$	3.35117	0.112080
$895$	−45.5754	−1.52342
$896$	−18.5213	−0.618752
$897$	8.65080	0.288842
$898$	4.40872	0.147121
$899$	9.32607	0.311042
$900$	0.554119	0.0184706
$901$	−8.29377	−0.276305
$902$	1.12933	0.0376025
$903$	15.9963	0.532322
$904$	−6.47974	−0.215513
$905$	13.0921	0.435198
$906$	−9.21112	−0.306019
$907$	26.8599	0.891869	0.445934	−	0.895066i	$-0.352871\pi$
$907$	26.8599	0.891869	0.445934	+	0.895066i	$0.352871\pi$
$908$	33.9245	1.12582
$909$	19.5427	0.648189
$910$	5.73817	0.190218
$911$	−11.1798	−0.370404	−0.185202	−	0.982701i	$-0.559294\pi$
$911$	−11.1798	−0.370404	−0.185202	+	0.982701i	$0.559294\pi$
$912$	−18.4058	−0.609478
$913$	−3.39688	−0.112420
$914$	3.76152	0.124420
$915$	43.1514	1.42654
$916$	30.4219	1.00517
$917$	−4.52172	−0.149320
$918$	1.04878	0.0346148
$919$	0.391772	0.0129234	0.00646169	−	0.999979i	$-0.497943\pi$
$919$	0.391772	0.0129234	0.00646169	+	0.999979i	$0.497943\pi$
$920$	−1.79563	−0.0592002
$921$	34.6886	1.14303
$922$	2.12466	0.0699719
$923$	62.6463	2.06203
$924$	52.7924	1.73674
$925$	−0.230832	−0.00758971
$926$	−0.676824	−0.0222418
$927$	−0.784329	−0.0257607
$928$	2.43409	0.0799028
$929$	44.8143	1.47031	0.735155	−	0.677899i	$-0.237109\pi$
$929$	44.8143	1.47031	0.735155	+	0.677899i	$0.237109\pi$
$930$	8.48142	0.278117
$931$	3.87105	0.126869
$932$	−50.7850	−1.66352
$933$	−27.0543	−0.885718
$934$	1.13621	0.0371779
$935$	−12.6136	−0.412507
$936$	−3.62185	−0.118384
$937$	12.2061	0.398757	0.199378	−	0.979923i	$-0.436108\pi$
$937$	12.2061	0.398757	0.199378	+	0.979923i	$0.436108\pi$
$938$	−7.81299	−0.255103
$939$	32.7720	1.06948
$940$	11.3414	0.369916
$941$	−16.0893	−0.524496	−0.262248	−	0.965000i	$-0.584464\pi$
$941$	−16.0893	−0.524496	−0.262248	+	0.965000i	$0.584464\pi$
$942$	2.20956	0.0719912
$943$	1.17569	0.0382857
$944$	−24.2520	−0.789336
$945$	25.3072	0.823244
$946$	2.61848	0.0851340
$947$	−50.1187	−1.62864	−0.814320	−	0.580417i	$-0.802890\pi$
$947$	−50.1187	−1.62864	−0.814320	+	0.580417i	$0.802890\pi$
$948$	−41.2902	−1.34104
$949$	−54.1816	−1.75881
$950$	0.143138	0.00464400
$951$	−24.0957	−0.781357
$952$	3.05524	0.0990209
$953$	−9.59489	−0.310809	−0.155405	−	0.987851i	$-0.549668\pi$
$953$	−9.59489	−0.310809	−0.155405	+	0.987851i	$0.549668\pi$
$954$	−1.39310	−0.0451032
$955$	−22.7803	−0.737153
$956$	−40.9650	−1.32490
$957$	−9.21454	−0.297864
$958$	0.979524	0.0316470
$959$	−6.49566	−0.209756
$960$	−30.3536	−0.979658
$961$	55.9755	1.80566
$962$	0.746066	0.0240541
$963$	−6.86366	−0.221178
$964$	−40.5902	−1.30732
$965$	30.2959	0.975260
$966$	−1.22575	−0.0394378
$967$	49.4455	1.59006	0.795030	−	0.606570i	$-0.207455\pi$
$967$	49.4455	1.59006	0.795030	+	0.606570i	$0.207455\pi$
$968$	8.38562	0.269524
$969$	6.21253	0.199575
$970$	−6.56166	−0.210682
$971$	−34.1533	−1.09603	−0.548016	−	0.836468i	$-0.684617\pi$
$971$	−34.1533	−1.09603	−0.548016	+	0.836468i	$0.684617\pi$
$972$	−19.8371	−0.636274
$973$	39.3617	1.26188
$974$	6.20971	0.198972
$975$	−2.41371	−0.0773006
$976$	37.0692	1.18656
$977$	36.6513	1.17258	0.586289	−	0.810102i	$-0.300588\pi$
$977$	36.6513	1.17258	0.586289	+	0.810102i	$0.300588\pi$
$978$	−2.26685	−0.0724858
$979$	62.1505	1.98634
$980$	6.70000	0.214024
$981$	−2.80329	−0.0895022
$982$	2.72141	0.0868438
$983$	9.56101	0.304949	0.152474	−	0.988307i	$-0.451276\pi$
$983$	9.56101	0.304949	0.152474	+	0.988307i	$0.451276\pi$
$984$	−1.94690	−0.0620648
$985$	−40.3607	−1.28600
$986$	−0.263695	−0.00839776
$987$	15.6566	0.498355
$988$	20.7433	0.659932
$989$	2.72597	0.0866808
$990$	−2.11869	−0.0673364
$991$	21.0473	0.668589	0.334294	−	0.942469i	$-0.391502\pi$
$991$	21.0473	0.668589	0.334294	+	0.942469i	$0.391502\pi$
$992$	22.7004	0.720740
$993$	−18.5738	−0.589421
$994$	−8.87648	−0.281545
$995$	0.296678	0.00940534
$996$	2.89572	0.0917545
$997$	−4.20896	−0.133299	−0.0666496	−	0.997776i	$-0.521231\pi$
$997$	−4.20896	−0.133299	−0.0666496	+	0.997776i	$0.521231\pi$
$998$	2.62604	0.0831259
$999$	3.29040	0.104104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.8	✓	16
3.2	odd	2		6003.2.a.q.1.9		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.8	✓	16	1.1	even	1	trivial
6003.2.a.q.1.9		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)

\(f(q)\)	\(=\)	\(q-0.208883 q^{2} -2.00378 q^{3} -1.95637 q^{4} -2.17278 q^{5} +0.418556 q^{6} -2.92851 q^{7} +0.826420 q^{8} +1.01513 q^{9} +O(q^{10})\)	\(q-0.208883 q^{2} -2.00378 q^{3} -1.95637 q^{4} -2.17278 q^{5} +0.418556 q^{6} -2.92851 q^{7} +0.826420 q^{8} +1.01513 q^{9} +0.453858 q^{10} -4.59858 q^{11} +3.92013 q^{12} -4.31724 q^{13} +0.611718 q^{14} +4.35378 q^{15} +3.74011 q^{16} -1.26240 q^{17} -0.212045 q^{18} +2.45596 q^{19} +4.25076 q^{20} +5.86810 q^{21} +0.960567 q^{22} +1.00000 q^{23} -1.65596 q^{24} -0.279016 q^{25} +0.901799 q^{26} +3.97723 q^{27} +5.72925 q^{28} -1.00000 q^{29} -0.909432 q^{30} -9.32607 q^{31} -2.43409 q^{32} +9.21454 q^{33} +0.263695 q^{34} +6.36302 q^{35} -1.98598 q^{36} +0.827308 q^{37} -0.513009 q^{38} +8.65080 q^{39} -1.79563 q^{40} +1.17569 q^{41} -1.22575 q^{42} +2.72597 q^{43} +8.99651 q^{44} -2.20567 q^{45} -0.208883 q^{46} +2.66809 q^{47} -7.49436 q^{48} +1.57619 q^{49} +0.0582818 q^{50} +2.52958 q^{51} +8.44611 q^{52} +6.56983 q^{53} -0.830778 q^{54} +9.99171 q^{55} -2.42018 q^{56} -4.92120 q^{57} +0.208883 q^{58} -6.48431 q^{59} -8.51759 q^{60} +9.91126 q^{61} +1.94806 q^{62} -2.97283 q^{63} -6.97178 q^{64} +9.38042 q^{65} -1.92476 q^{66} -12.7722 q^{67} +2.46972 q^{68} -2.00378 q^{69} -1.32913 q^{70} -14.5107 q^{71} +0.838927 q^{72} +12.5500 q^{73} -0.172811 q^{74} +0.559086 q^{75} -4.80476 q^{76} +13.4670 q^{77} -1.80701 q^{78} -10.5329 q^{79} -8.12645 q^{80} -11.0149 q^{81} -0.245582 q^{82} +0.738680 q^{83} -11.4802 q^{84} +2.74293 q^{85} -0.569410 q^{86} +2.00378 q^{87} -3.80036 q^{88} -13.5151 q^{89} +0.460727 q^{90} +12.6431 q^{91} -1.95637 q^{92} +18.6874 q^{93} -0.557320 q^{94} -5.33626 q^{95} +4.87737 q^{96} -14.4575 q^{97} -0.329240 q^{98} -4.66818 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 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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