LMFDB - Embedded newform 667.2.a.d.1.16

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			1.16
Root			$2.73896$ 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)

$f(q)$	$=$	$q+2.73896 q^{2} +1.50037 q^{3} +5.50188 q^{4} -1.91750 q^{5} +4.10945 q^{6} -0.472052 q^{7} +9.59151 q^{8} -0.748891 q^{9} +O(q^{10})$	\(q+2.73896 q^{2} +1.50037 q^{3} +5.50188 q^{4} -1.91750 q^{5} +4.10945 q^{6} -0.472052 q^{7} +9.59151 q^{8} -0.748891 q^{9} -5.25195 q^{10} -2.34056 q^{11} +8.25486 q^{12} +0.319606 q^{13} -1.29293 q^{14} -2.87696 q^{15} +15.2670 q^{16} -0.228054 q^{17} -2.05118 q^{18} +3.36342 q^{19} -10.5499 q^{20} -0.708253 q^{21} -6.41070 q^{22} +1.00000 q^{23} +14.3908 q^{24} -1.32319 q^{25} +0.875388 q^{26} -5.62472 q^{27} -2.59718 q^{28} -1.00000 q^{29} -7.87987 q^{30} -2.04991 q^{31} +22.6325 q^{32} -3.51171 q^{33} -0.624629 q^{34} +0.905161 q^{35} -4.12031 q^{36} -5.23336 q^{37} +9.21226 q^{38} +0.479527 q^{39} -18.3917 q^{40} +1.97999 q^{41} -1.93987 q^{42} -11.8584 q^{43} -12.8775 q^{44} +1.43600 q^{45} +2.73896 q^{46} +6.50673 q^{47} +22.9061 q^{48} -6.77717 q^{49} -3.62415 q^{50} -0.342165 q^{51} +1.75844 q^{52} -0.128482 q^{53} -15.4059 q^{54} +4.48804 q^{55} -4.52769 q^{56} +5.04637 q^{57} -2.73896 q^{58} +4.92843 q^{59} -15.8287 q^{60} +6.57063 q^{61} -5.61460 q^{62} +0.353516 q^{63} +31.4556 q^{64} -0.612846 q^{65} -9.61842 q^{66} +7.39486 q^{67} -1.25472 q^{68} +1.50037 q^{69} +2.47920 q^{70} +0.455585 q^{71} -7.18299 q^{72} +9.53772 q^{73} -14.3339 q^{74} -1.98527 q^{75} +18.5051 q^{76} +1.10487 q^{77} +1.31340 q^{78} -10.7528 q^{79} -29.2744 q^{80} -6.19249 q^{81} +5.42311 q^{82} +15.0544 q^{83} -3.89673 q^{84} +0.437293 q^{85} -32.4798 q^{86} -1.50037 q^{87} -22.4495 q^{88} -2.76934 q^{89} +3.93314 q^{90} -0.150871 q^{91} +5.50188 q^{92} -3.07562 q^{93} +17.8217 q^{94} -6.44936 q^{95} +33.9571 q^{96} -7.87806 q^{97} -18.5624 q^{98} +1.75283 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.73896	1.93673	0.968367	−	0.249529i	$-0.0802757\pi$
$2$	2.73896	1.93673	0.968367	+	0.249529i	$0.0802757\pi$
$3$	1.50037	0.866239	0.433119	−	0.901337i	$-0.357413\pi$
$3$	1.50037	0.866239	0.433119	+	0.901337i	$0.357413\pi$
$4$	5.50188	2.75094
$5$	−1.91750	−0.857533	−0.428766	−	0.903415i	$-0.641052\pi$
$5$	−1.91750	−0.857533	−0.428766	+	0.903415i	$0.641052\pi$
$6$	4.10945	1.67767
$7$	−0.472052	−0.178419	−0.0892095	−	0.996013i	$-0.528434\pi$
$7$	−0.472052	−0.178419	−0.0892095	+	0.996013i	$0.528434\pi$
$8$	9.59151	3.39111
$9$	−0.748891	−0.249630
$10$	−5.25195	−1.66081
$11$	−2.34056	−0.705707	−0.352853	−	0.935679i	$-0.614789\pi$
$11$	−2.34056	−0.705707	−0.352853	+	0.935679i	$0.614789\pi$
$12$	8.25486	2.38297
$13$	0.319606	0.0886428	0.0443214	−	0.999017i	$-0.485887\pi$
$13$	0.319606	0.0886428	0.0443214	+	0.999017i	$0.485887\pi$
$14$	−1.29293	−0.345550
$15$	−2.87696	−0.742828
$16$	15.2670	3.81674
$17$	−0.228054	−0.0553111	−0.0276556	−	0.999618i	$-0.508804\pi$
$17$	−0.228054	−0.0553111	−0.0276556	+	0.999618i	$0.508804\pi$
$18$	−2.05118	−0.483468
$19$	3.36342	0.771621	0.385811	−	0.922578i	$-0.373922\pi$
$19$	3.36342	0.771621	0.385811	+	0.922578i	$0.373922\pi$
$20$	−10.5499	−2.35902
$21$	−0.708253	−0.154553
$22$	−6.41070	−1.36677
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	14.3908	2.93751
$25$	−1.32319	−0.264637
$26$	0.875388	0.171678
$27$	−5.62472	−1.08248
$28$	−2.59718	−0.490820
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−7.87987	−1.43866
$31$	−2.04991	−0.368174	−0.184087	−	0.982910i	$-0.558933\pi$
$31$	−2.04991	−0.368174	−0.184087	+	0.982910i	$0.558933\pi$
$32$	22.6325	4.00090
$33$	−3.51171	−0.611310
$34$	−0.624629	−0.107123
$35$	0.905161	0.153000
$36$	−4.12031	−0.686719
$37$	−5.23336	−0.860359	−0.430180	−	0.902743i	$-0.641550\pi$
$37$	−5.23336	−0.860359	−0.430180	+	0.902743i	$0.641550\pi$
$38$	9.21226	1.49443
$39$	0.479527	0.0767859
$40$	−18.3917	−2.90799
$41$	1.97999	0.309222	0.154611	−	0.987975i	$-0.450587\pi$
$41$	1.97999	0.309222	0.154611	+	0.987975i	$0.450587\pi$
$42$	−1.93987	−0.299329
$43$	−11.8584	−1.80840	−0.904198	−	0.427114i	$-0.859530\pi$
$43$	−11.8584	−1.80840	−0.904198	+	0.427114i	$0.859530\pi$
$44$	−12.8775	−1.94136
$45$	1.43600	0.214066
$46$	2.73896	0.403837
$47$	6.50673	0.949104	0.474552	−	0.880227i	$-0.342610\pi$
$47$	6.50673	0.949104	0.474552	+	0.880227i	$0.342610\pi$
$48$	22.9061	3.30621
$49$	−6.77717	−0.968167
$50$	−3.62415	−0.512532
$51$	−0.342165	−0.0479127
$52$	1.75844	0.243851
$53$	−0.128482	−0.0176484	−0.00882420	−	0.999961i	$-0.502809\pi$
$53$	−0.128482	−0.0176484	−0.00882420	+	0.999961i	$0.502809\pi$
$54$	−15.4059	−2.09647
$55$	4.48804	0.605167
$56$	−4.52769	−0.605038
$57$	5.04637	0.668408
$58$	−2.73896	−0.359643
$59$	4.92843	0.641627	0.320814	−	0.947142i	$-0.396044\pi$
$59$	4.92843	0.641627	0.320814	+	0.947142i	$0.396044\pi$
$60$	−15.8287	−2.04348
$61$	6.57063	0.841283	0.420641	−	0.907227i	$-0.361805\pi$
$61$	6.57063	0.841283	0.420641	+	0.907227i	$0.361805\pi$
$62$	−5.61460	−0.713055
$63$	0.353516	0.0445388
$64$	31.4556	3.93194
$65$	−0.612846	−0.0760141
$66$	−9.61842	−1.18395
$67$	7.39486	0.903426	0.451713	−	0.892163i	$-0.350813\pi$
$67$	7.39486	0.903426	0.451713	+	0.892163i	$0.350813\pi$
$68$	−1.25472	−0.152158
$69$	1.50037	0.180623
$70$	2.47920	0.296321
$71$	0.455585	0.0540680	0.0270340	−	0.999635i	$-0.491394\pi$
$71$	0.455585	0.0540680	0.0270340	+	0.999635i	$0.491394\pi$
$72$	−7.18299	−0.846524
$73$	9.53772	1.11631	0.558153	−	0.829738i	$-0.311510\pi$
$73$	9.53772	1.11631	0.558153	+	0.829738i	$0.311510\pi$
$74$	−14.3339	−1.66629
$75$	−1.98527	−0.229239
$76$	18.5051	2.12268
$77$	1.10487	0.125911
$78$	1.31340	0.148714
$79$	−10.7528	−1.20979	−0.604893	−	0.796307i	$-0.706784\pi$
$79$	−10.7528	−1.20979	−0.604893	+	0.796307i	$0.706784\pi$
$80$	−29.2744	−3.27298
$81$	−6.19249	−0.688054
$82$	5.42311	0.598882
$83$	15.0544	1.65243	0.826215	−	0.563355i	$-0.190490\pi$
$83$	15.0544	1.65243	0.826215	+	0.563355i	$0.190490\pi$
$84$	−3.89673	−0.425168
$85$	0.437293	0.0474311
$86$	−32.4798	−3.50238
$87$	−1.50037	−0.160857
$88$	−22.4495	−2.39313
$89$	−2.76934	−0.293550	−0.146775	−	0.989170i	$-0.546889\pi$
$89$	−2.76934	−0.293550	−0.146775	+	0.989170i	$0.546889\pi$
$90$	3.93314	0.414590
$91$	−0.150871	−0.0158156
$92$	5.50188	0.573611
$93$	−3.07562	−0.318927
$94$	17.8217	1.83816
$95$	−6.44936	−0.661690
$96$	33.9571	3.46574
$97$	−7.87806	−0.799896	−0.399948	−	0.916538i	$-0.630972\pi$
$97$	−7.87806	−0.799896	−0.399948	+	0.916538i	$0.630972\pi$
$98$	−18.5624	−1.87508
$99$	1.75283	0.176166
$100$	−7.28002	−0.728002
$101$	12.8819	1.28180	0.640900	−	0.767625i	$-0.278562\pi$
$101$	12.8819	1.28180	0.640900	+	0.767625i	$0.278562\pi$
$102$	−0.937174	−0.0927941
$103$	3.80646	0.375062	0.187531	−	0.982259i	$-0.439951\pi$
$103$	3.80646	0.375062	0.187531	+	0.982259i	$0.439951\pi$
$104$	3.06551	0.300598
$105$	1.35808	0.132535
$106$	−0.351908	−0.0341803
$107$	8.57347	0.828829	0.414414	−	0.910088i	$-0.363986\pi$
$107$	8.57347	0.828829	0.414414	+	0.910088i	$0.363986\pi$
$108$	−30.9466	−2.97783
$109$	−9.57100	−0.916736	−0.458368	−	0.888763i	$-0.651566\pi$
$109$	−9.57100	−0.916736	−0.458368	+	0.888763i	$0.651566\pi$
$110$	12.2925	1.17205
$111$	−7.85198	−0.745277
$112$	−7.20680	−0.680979
$113$	10.1083	0.950912	0.475456	−	0.879740i	$-0.342283\pi$
$113$	10.1083	0.950912	0.475456	+	0.879740i	$0.342283\pi$
$114$	13.8218	1.29453
$115$	−1.91750	−0.178808
$116$	−5.50188	−0.510837
$117$	−0.239350	−0.0221279
$118$	13.4988	1.24266
$119$	0.107653	0.00986856
$120$	−27.5944	−2.51901
$121$	−5.52176	−0.501978
$122$	17.9967	1.62934
$123$	2.97072	0.267861
$124$	−11.2783	−1.01283
$125$	12.1247	1.08447
$126$	0.968264	0.0862598
$127$	11.6804	1.03646	0.518232	−	0.855240i	$-0.326590\pi$
$127$	11.6804	1.03646	0.518232	+	0.855240i	$0.326590\pi$
$128$	40.8904	3.61423
$129$	−17.7920	−1.56650
$130$	−1.67856	−0.147219
$131$	−7.44339	−0.650332	−0.325166	−	0.945657i	$-0.605420\pi$
$131$	−7.44339	−0.650332	−0.325166	+	0.945657i	$0.605420\pi$
$132$	−19.3210	−1.68168
$133$	−1.58771	−0.137672
$134$	20.2542	1.74970
$135$	10.7854	0.928261
$136$	−2.18738	−0.187566
$137$	11.7505	1.00392	0.501958	−	0.864892i	$-0.332613\pi$
$137$	11.7505	1.00392	0.501958	+	0.864892i	$0.332613\pi$
$138$	4.10945	0.349819
$139$	21.6918	1.83987	0.919935	−	0.392070i	$-0.128241\pi$
$139$	21.6918	1.83987	0.919935	+	0.392070i	$0.128241\pi$
$140$	4.98009	0.420895
$141$	9.76250	0.822151
$142$	1.24783	0.104715
$143$	−0.748059	−0.0625558
$144$	−11.4333	−0.952774
$145$	1.91750	0.159240
$146$	26.1234	2.16199
$147$	−10.1683	−0.838664
$148$	−28.7933	−2.36680
$149$	8.78218	0.719464	0.359732	−	0.933056i	$-0.382868\pi$
$149$	8.78218	0.719464	0.359732	+	0.933056i	$0.382868\pi$
$150$	−5.43757	−0.443975
$151$	16.0772	1.30835	0.654174	−	0.756344i	$-0.273017\pi$
$151$	16.0772	1.30835	0.654174	+	0.756344i	$0.273017\pi$
$152$	32.2602	2.61665
$153$	0.170787	0.0138073
$154$	3.02619	0.243857
$155$	3.93070	0.315721
$156$	2.63830	0.211233
$157$	−16.9632	−1.35381	−0.676907	−	0.736069i	$-0.736680\pi$
$157$	−16.9632	−1.35381	−0.676907	+	0.736069i	$0.736680\pi$
$158$	−29.4515	−2.34303
$159$	−0.192771	−0.0152877
$160$	−43.3979	−3.43090
$161$	−0.472052	−0.0372029
$162$	−16.9610	−1.33258
$163$	−20.2343	−1.58487	−0.792435	−	0.609957i	$-0.791187\pi$
$163$	−20.2343	−1.58487	−0.792435	+	0.609957i	$0.791187\pi$
$164$	10.8937	0.850653
$165$	6.73371	0.524219
$166$	41.2332	3.20032
$167$	−17.3251	−1.34065	−0.670327	−	0.742066i	$-0.733846\pi$
$167$	−17.3251	−1.34065	−0.670327	+	0.742066i	$0.733846\pi$
$168$	−6.79321	−0.524108
$169$	−12.8979	−0.992142
$170$	1.19773	0.0918615
$171$	−2.51883	−0.192620
$172$	−65.2438	−4.97479
$173$	−17.0135	−1.29351	−0.646755	−	0.762698i	$-0.723874\pi$
$173$	−17.0135	−1.29351	−0.646755	+	0.762698i	$0.723874\pi$
$174$	−4.10945	−0.311536
$175$	0.624613	0.0472163
$176$	−35.7333	−2.69350
$177$	7.39447	0.555803
$178$	−7.58511	−0.568528
$179$	−7.06258	−0.527882	−0.263941	−	0.964539i	$-0.585022\pi$
$179$	−7.06258	−0.527882	−0.263941	+	0.964539i	$0.585022\pi$
$180$	7.90070	0.588884
$181$	14.6788	1.09106	0.545532	−	0.838090i	$-0.316328\pi$
$181$	14.6788	1.09106	0.545532	+	0.838090i	$0.316328\pi$
$182$	−0.413229	−0.0306306
$183$	9.85837	0.728752
$184$	9.59151	0.707095
$185$	10.0350	0.737786
$186$	−8.42398	−0.617676
$187$	0.533774	0.0390334
$188$	35.7993	2.61093
$189$	2.65516	0.193135
$190$	−17.6645	−1.28152
$191$	20.2462	1.46497	0.732483	−	0.680785i	$-0.238361\pi$
$191$	20.2462	1.46497	0.732483	+	0.680785i	$0.238361\pi$
$192$	47.1950	3.40600
$193$	−10.4593	−0.752880	−0.376440	−	0.926441i	$-0.622852\pi$
$193$	−10.4593	−0.752880	−0.376440	+	0.926441i	$0.622852\pi$
$194$	−21.5777	−1.54919
$195$	−0.919495	−0.0658464
$196$	−37.2872	−2.66337
$197$	1.06522	0.0758938	0.0379469	−	0.999280i	$-0.487918\pi$
$197$	1.06522	0.0758938	0.0379469	+	0.999280i	$0.487918\pi$
$198$	4.80092	0.341186
$199$	10.6750	0.756728	0.378364	−	0.925657i	$-0.376487\pi$
$199$	10.6750	0.756728	0.378364	+	0.925657i	$0.376487\pi$
$200$	−12.6914	−0.897414
$201$	11.0950	0.782583
$202$	35.2830	2.48250
$203$	0.472052	0.0331316
$204$	−1.88255	−0.131805
$205$	−3.79663	−0.265168
$206$	10.4257	0.726396
$207$	−0.748891	−0.0520515
$208$	4.87941	0.338326
$209$	−7.87230	−0.544538
$210$	3.71971	0.256685
$211$	−18.6423	−1.28339	−0.641695	−	0.766960i	$-0.721769\pi$
$211$	−18.6423	−1.28339	−0.641695	+	0.766960i	$0.721769\pi$
$212$	−0.706895	−0.0485497
$213$	0.683547	0.0468358
$214$	23.4824	1.60522
$215$	22.7386	1.55076
$216$	−53.9496	−3.67080
$217$	0.967663	0.0656892
$218$	−26.2146	−1.77547
$219$	14.3101	0.966988
$220$	24.6926	1.66478
$221$	−0.0728874	−0.00490294
$222$	−21.5062	−1.44340
$223$	−19.7223	−1.32070	−0.660350	−	0.750958i	$-0.729592\pi$
$223$	−19.7223	−1.32070	−0.660350	+	0.750958i	$0.729592\pi$
$224$	−10.6837	−0.713837
$225$	0.990923	0.0660615
$226$	27.6863	1.84166
$227$	−3.83497	−0.254536	−0.127268	−	0.991868i	$-0.540621\pi$
$227$	−3.83497	−0.254536	−0.127268	+	0.991868i	$0.540621\pi$
$228$	27.7645	1.83875
$229$	8.27021	0.546511	0.273255	−	0.961941i	$-0.411900\pi$
$229$	8.27021	0.546511	0.273255	+	0.961941i	$0.411900\pi$
$230$	−5.25195	−0.346304
$231$	1.65771	0.109069
$232$	−9.59151	−0.629713
$233$	21.3381	1.39790	0.698951	−	0.715169i	$-0.253650\pi$
$233$	21.3381	1.39790	0.698951	+	0.715169i	$0.253650\pi$
$234$	−0.655570	−0.0428559
$235$	−12.4767	−0.813888
$236$	27.1157	1.76508
$237$	−16.1332	−1.04796
$238$	0.294858	0.0191128
$239$	−2.68311	−0.173556	−0.0867781	−	0.996228i	$-0.527657\pi$
$239$	−2.68311	−0.173556	−0.0867781	+	0.996228i	$0.527657\pi$
$240$	−43.9224	−2.83518
$241$	−17.1681	−1.10590	−0.552948	−	0.833216i	$-0.686497\pi$
$241$	−17.1681	−1.10590	−0.552948	+	0.833216i	$0.686497\pi$
$242$	−15.1239	−0.972199
$243$	7.58314	0.486459
$244$	36.1508	2.31432
$245$	12.9952	0.830235
$246$	8.13666	0.518775
$247$	1.07497	0.0683987
$248$	−19.6617	−1.24852
$249$	22.5871	1.43140
$250$	33.2091	2.10033
$251$	−24.7244	−1.56059	−0.780295	−	0.625411i	$-0.784931\pi$
$251$	−24.7244	−1.56059	−0.780295	+	0.625411i	$0.784931\pi$
$252$	1.94500	0.122524
$253$	−2.34056	−0.147150
$254$	31.9920	2.00736
$255$	0.656102	0.0410867
$256$	49.0859	3.06787
$257$	−25.0454	−1.56229	−0.781145	−	0.624350i	$-0.785364\pi$
$257$	−25.0454	−1.56229	−0.781145	+	0.624350i	$0.785364\pi$
$258$	−48.7316	−3.03390
$259$	2.47042	0.153504
$260$	−3.37180	−0.209110
$261$	0.748891	0.0463552
$262$	−20.3871	−1.25952
$263$	15.6651	0.965950	0.482975	−	0.875634i	$-0.339556\pi$
$263$	15.6651	0.965950	0.482975	+	0.875634i	$0.339556\pi$
$264$	−33.6826	−2.07302
$265$	0.246365	0.0151341
$266$	−4.34867	−0.266634
$267$	−4.15504	−0.254284
$268$	40.6857	2.48527
$269$	13.0997	0.798701	0.399350	−	0.916798i	$-0.369236\pi$
$269$	13.0997	0.798701	0.399350	+	0.916798i	$0.369236\pi$
$270$	29.5408	1.79779
$271$	16.3884	0.995525	0.497762	−	0.867313i	$-0.334155\pi$
$271$	16.3884	0.995525	0.497762	+	0.867313i	$0.334155\pi$
$272$	−3.48168	−0.211108
$273$	−0.226362	−0.0137001
$274$	32.1842	1.94432
$275$	3.09700	0.186756
$276$	8.25486	0.496884
$277$	14.7704	0.887465	0.443732	−	0.896159i	$-0.353654\pi$
$277$	14.7704	0.887465	0.443732	+	0.896159i	$0.353654\pi$
$278$	59.4128	3.56334
$279$	1.53516	0.0919074
$280$	8.68186	0.518840
$281$	−32.4768	−1.93740	−0.968700	−	0.248233i	$-0.920150\pi$
$281$	−32.4768	−1.93740	−0.968700	+	0.248233i	$0.920150\pi$
$282$	26.7391	1.59229
$283$	−9.21618	−0.547845	−0.273922	−	0.961752i	$-0.588321\pi$
$283$	−9.21618	−0.547845	−0.273922	+	0.961752i	$0.588321\pi$
$284$	2.50658	0.148738
$285$	−9.67642	−0.573182
$286$	−2.04890	−0.121154
$287$	−0.934659	−0.0551712
$288$	−16.9493	−0.998746
$289$	−16.9480	−0.996941
$290$	5.25195	0.308405
$291$	−11.8200	−0.692901
$292$	52.4754	3.07089
$293$	11.9851	0.700177	0.350088	−	0.936717i	$-0.386152\pi$
$293$	11.9851	0.700177	0.350088	+	0.936717i	$0.386152\pi$
$294$	−27.8504	−1.62427
$295$	−9.45028	−0.550217
$296$	−50.1958	−2.91757
$297$	13.1650	0.763912
$298$	24.0540	1.39341
$299$	0.319606	0.0184833
$300$	−10.9227	−0.630623
$301$	5.59781	0.322652
$302$	44.0349	2.53392
$303$	19.3276	1.11034
$304$	51.3491	2.94508
$305$	−12.5992	−0.721428
$306$	0.467779	0.0267412
$307$	−15.0754	−0.860398	−0.430199	−	0.902734i	$-0.641557\pi$
$307$	−15.0754	−0.860398	−0.430199	+	0.902734i	$0.641557\pi$
$308$	6.07886	0.346375
$309$	5.71110	0.324893
$310$	10.7660	0.611468
$311$	−10.6937	−0.606384	−0.303192	−	0.952929i	$-0.598052\pi$
$311$	−10.6937	−0.606384	−0.303192	+	0.952929i	$0.598052\pi$
$312$	4.59939	0.260389
$313$	34.4367	1.94647	0.973237	−	0.229802i	$-0.0738080\pi$
$313$	34.4367	1.94647	0.973237	+	0.229802i	$0.0738080\pi$
$314$	−46.4615	−2.62198
$315$	−0.677867	−0.0381935
$316$	−59.1607	−3.32805
$317$	−29.2559	−1.64317	−0.821587	−	0.570084i	$-0.806911\pi$
$317$	−29.2559	−1.64317	−0.821587	+	0.570084i	$0.806911\pi$
$318$	−0.527991	−0.0296083
$319$	2.34056	0.131046
$320$	−60.3161	−3.37177
$321$	12.8634	0.717964
$322$	−1.29293	−0.0720522
$323$	−0.767040	−0.0426792
$324$	−34.0704	−1.89280
$325$	−0.422899	−0.0234582
$326$	−55.4207	−3.06947
$327$	−14.3600	−0.794112
$328$	18.9911	1.04861
$329$	−3.07152	−0.169338
$330$	18.4433	1.01527
$331$	−24.9937	−1.37378	−0.686889	−	0.726763i	$-0.741024\pi$
$331$	−24.9937	−1.37378	−0.686889	+	0.726763i	$0.741024\pi$
$332$	82.8273	4.54574
$333$	3.91922	0.214772
$334$	−47.4526	−2.59649
$335$	−14.1797	−0.774718
$336$	−10.8129	−0.589890
$337$	−1.08292	−0.0589902	−0.0294951	−	0.999565i	$-0.509390\pi$
$337$	−1.08292	−0.0589902	−0.0294951	+	0.999565i	$0.509390\pi$
$338$	−35.3267	−1.92152
$339$	15.1662	0.823717
$340$	2.40594	0.130480
$341$	4.79794	0.259823
$342$	−6.89898	−0.373054
$343$	6.50354	0.351158
$344$	−113.740	−6.13247
$345$	−2.87696	−0.154890
$346$	−46.5992	−2.50519
$347$	−10.6720	−0.572904	−0.286452	−	0.958095i	$-0.592476\pi$
$347$	−10.6720	−0.572904	−0.286452	+	0.958095i	$0.592476\pi$
$348$	−8.25486	−0.442507
$349$	35.6630	1.90900	0.954498	−	0.298216i	$-0.0963916\pi$
$349$	35.6630	1.90900	0.954498	+	0.298216i	$0.0963916\pi$
$350$	1.71079	0.0914455
$351$	−1.79770	−0.0959539
$352$	−52.9728	−2.82346
$353$	−2.01254	−0.107117	−0.0535584	−	0.998565i	$-0.517056\pi$
$353$	−2.01254	−0.107117	−0.0535584	+	0.998565i	$0.517056\pi$
$354$	20.2531	1.07644
$355$	−0.873586	−0.0463651
$356$	−15.2366	−0.807538
$357$	0.161520	0.00854853
$358$	−19.3441	−1.02237
$359$	−1.80858	−0.0954531	−0.0477265	−	0.998860i	$-0.515198\pi$
$359$	−1.80858	−0.0954531	−0.0477265	+	0.998860i	$0.515198\pi$
$360$	13.7734	0.725922
$361$	−7.68742	−0.404601
$362$	40.2045	2.11310
$363$	−8.28468	−0.434833
$364$	−0.830074	−0.0435077
$365$	−18.2886	−0.957269
$366$	27.0017	1.41140
$367$	−26.7995	−1.39892	−0.699460	−	0.714672i	$-0.746576\pi$
$367$	−26.7995	−1.39892	−0.699460	+	0.714672i	$0.746576\pi$
$368$	15.2670	0.795845
$369$	−1.48280	−0.0771913
$370$	27.4854	1.42890
$371$	0.0606504	0.00314881
$372$	−16.9217	−0.877349
$373$	10.4556	0.541369	0.270685	−	0.962668i	$-0.412750\pi$
$373$	10.4556	0.541369	0.270685	+	0.962668i	$0.412750\pi$
$374$	1.46198	0.0755974
$375$	18.1916	0.939408
$376$	62.4094	3.21852
$377$	−0.319606	−0.0164606
$378$	7.27238	0.374051
$379$	36.1379	1.85628	0.928140	−	0.372231i	$-0.121407\pi$
$379$	36.1379	1.85628	0.928140	+	0.372231i	$0.121407\pi$
$380$	−35.4836	−1.82027
$381$	17.5248	0.897825
$382$	55.4535	2.83725
$383$	5.70146	0.291331	0.145666	−	0.989334i	$-0.453468\pi$
$383$	5.70146	0.291331	0.145666	+	0.989334i	$0.453468\pi$
$384$	61.3507	3.13079
$385$	−2.11859	−0.107973
$386$	−28.6477	−1.45813
$387$	8.88068	0.451430
$388$	−43.3442	−2.20047
$389$	34.8012	1.76449	0.882245	−	0.470790i	$-0.156031\pi$
$389$	34.8012	1.76449	0.882245	+	0.470790i	$0.156031\pi$
$390$	−2.51846	−0.127527
$391$	−0.228054	−0.0115332
$392$	−65.0032	−3.28316
$393$	−11.1678	−0.563343
$394$	2.91759	0.146986
$395$	20.6185	1.03743
$396$	9.64385	0.484622
$397$	9.47664	0.475619	0.237809	−	0.971312i	$-0.423571\pi$
$397$	9.47664	0.475619	0.237809	+	0.971312i	$0.423571\pi$
$398$	29.2382	1.46558
$399$	−2.38215	−0.119257
$400$	−20.2010	−1.01005
$401$	−13.3593	−0.667132	−0.333566	−	0.942727i	$-0.608252\pi$
$401$	−13.3593	−0.667132	−0.333566	+	0.942727i	$0.608252\pi$
$402$	30.3888	1.51566
$403$	−0.655163	−0.0326360
$404$	70.8748	3.52615
$405$	11.8741	0.590029
$406$	1.29293	0.0641671
$407$	12.2490	0.607161
$408$	−3.28188	−0.162477
$409$	11.0887	0.548302	0.274151	−	0.961687i	$-0.411603\pi$
$409$	11.0887	0.548302	0.274151	+	0.961687i	$0.411603\pi$
$410$	−10.3988	−0.513561
$411$	17.6301	0.869631
$412$	20.9427	1.03177
$413$	−2.32648	−0.114479
$414$	−2.05118	−0.100810
$415$	−28.8668	−1.41701
$416$	7.23349	0.354651
$417$	32.5457	1.59377
$418$	−21.5619	−1.05463
$419$	−22.8227	−1.11496	−0.557480	−	0.830190i	$-0.688232\pi$
$419$	−22.8227	−1.11496	−0.557480	+	0.830190i	$0.688232\pi$
$420$	7.47198	0.364595
$421$	−7.94252	−0.387095	−0.193547	−	0.981091i	$-0.561999\pi$
$421$	−7.94252	−0.387095	−0.193547	+	0.981091i	$0.561999\pi$
$422$	−51.0605	−2.48559
$423$	−4.87283	−0.236925
$424$	−1.23234	−0.0598477
$425$	0.301758	0.0146374
$426$	1.87220	0.0907086
$427$	−3.10168	−0.150101
$428$	47.1702	2.28006
$429$	−1.12236	−0.0541883
$430$	62.2800	3.00341
$431$	−6.31249	−0.304062	−0.152031	−	0.988376i	$-0.548581\pi$
$431$	−6.31249	−0.304062	−0.152031	+	0.988376i	$0.548581\pi$
$432$	−85.8724	−4.13154
$433$	15.9635	0.767155	0.383578	−	0.923509i	$-0.374692\pi$
$433$	15.9635	0.767155	0.383578	+	0.923509i	$0.374692\pi$
$434$	2.65039	0.127223
$435$	2.87696	0.137940
$436$	−52.6585	−2.52189
$437$	3.36342	0.160894
$438$	39.1948	1.87280
$439$	−10.3550	−0.494216	−0.247108	−	0.968988i	$-0.579480\pi$
$439$	−10.3550	−0.494216	−0.247108	+	0.968988i	$0.579480\pi$
$440$	43.0470	2.05219
$441$	5.07536	0.241684
$442$	−0.199635	−0.00949569
$443$	−16.3370	−0.776196	−0.388098	−	0.921618i	$-0.626868\pi$
$443$	−16.3370	−0.776196	−0.388098	+	0.921618i	$0.626868\pi$
$444$	−43.2007	−2.05021
$445$	5.31022	0.251729
$446$	−54.0184	−2.55785
$447$	13.1765	0.623228
$448$	−14.8487	−0.701534
$449$	13.9838	0.659938	0.329969	−	0.943992i	$-0.392962\pi$
$449$	13.9838	0.659938	0.329969	+	0.943992i	$0.392962\pi$
$450$	2.71409	0.127944
$451$	−4.63429	−0.218220
$452$	55.6149	2.61590
$453$	24.1218	1.13334
$454$	−10.5038	−0.492969
$455$	0.289295	0.0135624
$456$	48.4023	2.26665
$457$	10.2930	0.481485	0.240743	−	0.970589i	$-0.422609\pi$
$457$	10.2930	0.481485	0.240743	+	0.970589i	$0.422609\pi$
$458$	22.6518	1.05845
$459$	1.28274	0.0598731
$460$	−10.5499	−0.491890
$461$	31.6586	1.47449	0.737244	−	0.675626i	$-0.236127\pi$
$461$	31.6586	1.47449	0.737244	+	0.675626i	$0.236127\pi$
$462$	4.54040	0.211239
$463$	9.21454	0.428236	0.214118	−	0.976808i	$-0.431312\pi$
$463$	9.21454	0.428236	0.214118	+	0.976808i	$0.431312\pi$
$464$	−15.2670	−0.708751
$465$	5.89750	0.273490
$466$	58.4440	2.70737
$467$	15.9397	0.737601	0.368801	−	0.929509i	$-0.379768\pi$
$467$	15.9397	0.737601	0.368801	+	0.929509i	$0.379768\pi$
$468$	−1.31688	−0.0608727
$469$	−3.49076	−0.161188
$470$	−34.1731	−1.57629
$471$	−25.4511	−1.17273
$472$	47.2711	2.17583
$473$	27.7554	1.27620
$474$	−44.1881	−2.02963
$475$	−4.45043	−0.204200
$476$	0.592296	0.0271478
$477$	0.0962193	0.00440558
$478$	−7.34894	−0.336132
$479$	−9.02738	−0.412471	−0.206236	−	0.978502i	$-0.566121\pi$
$479$	−9.02738	−0.412471	−0.206236	+	0.978502i	$0.566121\pi$
$480$	−65.1129	−2.97198
$481$	−1.67261	−0.0762647
$482$	−47.0227	−2.14183
$483$	−0.708253	−0.0322266
$484$	−30.3801	−1.38091
$485$	15.1062	0.685937
$486$	20.7699	0.942142
$487$	−34.8413	−1.57881	−0.789405	−	0.613873i	$-0.789611\pi$
$487$	−34.8413	−1.57881	−0.789405	+	0.613873i	$0.789611\pi$
$488$	63.0222	2.85288
$489$	−30.3589	−1.37288
$490$	35.5934	1.60794
$491$	−2.35939	−0.106478	−0.0532388	−	0.998582i	$-0.516954\pi$
$491$	−2.35939	−0.106478	−0.0532388	+	0.998582i	$0.516954\pi$
$492$	16.3445	0.736869
$493$	0.228054	0.0102710
$494$	2.94429	0.132470
$495$	−3.36105	−0.151068
$496$	−31.2958	−1.40522
$497$	−0.215060	−0.00964677
$498$	61.8651	2.77224
$499$	−20.0500	−0.897559	−0.448780	−	0.893643i	$-0.648141\pi$
$499$	−20.0500	−0.897559	−0.448780	+	0.893643i	$0.648141\pi$
$500$	66.7088	2.98331
$501$	−25.9940	−1.16133
$502$	−67.7191	−3.02245
$503$	−18.8490	−0.840434	−0.420217	−	0.907424i	$-0.638046\pi$
$503$	−18.8490	−0.840434	−0.420217	+	0.907424i	$0.638046\pi$
$504$	3.39075	0.151036
$505$	−24.7011	−1.09918
$506$	−6.41070	−0.284991
$507$	−19.3515	−0.859432
$508$	64.2640	2.85125
$509$	9.07142	0.402084	0.201042	−	0.979583i	$-0.435567\pi$
$509$	9.07142	0.402084	0.201042	+	0.979583i	$0.435567\pi$
$510$	1.79703	0.0795740
$511$	−4.50230	−0.199170
$512$	52.6633	2.32741
$513$	−18.9183	−0.835263
$514$	−68.5983	−3.02574
$515$	−7.29890	−0.321628
$516$	−97.8898	−4.30936
$517$	−15.2294	−0.669789
$518$	6.76637	0.297297
$519$	−25.5265	−1.12049
$520$	−5.87811	−0.257772
$521$	14.2415	0.623933	0.311967	−	0.950093i	$-0.399012\pi$
$521$	14.2415	0.623933	0.311967	+	0.950093i	$0.399012\pi$
$522$	2.05118	0.0897777
$523$	33.1353	1.44891	0.724454	−	0.689324i	$-0.242092\pi$
$523$	33.1353	1.44891	0.724454	+	0.689324i	$0.242092\pi$
$524$	−40.9526	−1.78902
$525$	0.937151	0.0409006
$526$	42.9059	1.87079
$527$	0.467489	0.0203641
$528$	−53.6131	−2.33321
$529$	1.00000	0.0434783
$530$	0.674783	0.0293107
$531$	−3.69086	−0.160170
$532$	−8.73539	−0.378727
$533$	0.632817	0.0274104
$534$	−11.3805	−0.492481
$535$	−16.4396	−0.710748
$536$	70.9279	3.06362
$537$	−10.5965	−0.457272
$538$	35.8794	1.54687
$539$	15.8624	0.683242
$540$	59.3401	2.55359
$541$	28.2274	1.21359	0.606796	−	0.794858i	$-0.292455\pi$
$541$	28.2274	1.21359	0.606796	+	0.794858i	$0.292455\pi$
$542$	44.8871	1.92807
$543$	22.0236	0.945122
$544$	−5.16143	−0.221294
$545$	18.3524	0.786131
$546$	−0.619996	−0.0265334
$547$	−19.2164	−0.821633	−0.410817	−	0.911718i	$-0.634756\pi$
$547$	−19.2164	−0.821633	−0.410817	+	0.911718i	$0.634756\pi$
$548$	64.6501	2.76171
$549$	−4.92069	−0.210010
$550$	8.48256	0.361697
$551$	−3.36342	−0.143286
$552$	14.3908	0.612513
$553$	5.07589	0.215849
$554$	40.4554	1.71878
$555$	15.0562	0.639099
$556$	119.346	5.06138
$557$	−7.31679	−0.310022	−0.155011	−	0.987913i	$-0.549541\pi$
$557$	−7.31679	−0.310022	−0.155011	+	0.987913i	$0.549541\pi$
$558$	4.20473	0.178000
$559$	−3.79003	−0.160301
$560$	13.8191	0.583962
$561$	0.800859	0.0338123
$562$	−88.9524	−3.75223
$563$	−23.8300	−1.00431	−0.502157	−	0.864776i	$-0.667460\pi$
$563$	−23.8300	−1.00431	−0.502157	+	0.864776i	$0.667460\pi$
$564$	53.7122	2.26169
$565$	−19.3827	−0.815438
$566$	−25.2427	−1.06103
$567$	2.92318	0.122762
$568$	4.36975	0.183351
$569$	−2.37588	−0.0996022	−0.0498011	−	0.998759i	$-0.515859\pi$
$569$	−2.37588	−0.0996022	−0.0498011	+	0.998759i	$0.515859\pi$
$570$	−26.5033	−1.11010
$571$	−3.18919	−0.133463	−0.0667317	−	0.997771i	$-0.521257\pi$
$571$	−3.18919	−0.133463	−0.0667317	+	0.997771i	$0.521257\pi$
$572$	−4.11573	−0.172087
$573$	30.3768	1.26901
$574$	−2.55999	−0.106852
$575$	−1.32319	−0.0551807
$576$	−23.5568	−0.981533
$577$	−33.9831	−1.41473	−0.707367	−	0.706846i	$-0.750117\pi$
$577$	−33.9831	−1.41473	−0.707367	+	0.706846i	$0.750117\pi$
$578$	−46.4198	−1.93081
$579$	−15.6929	−0.652174
$580$	10.5499	0.438060
$581$	−7.10644	−0.294825
$582$	−32.3745	−1.34197
$583$	0.300721	0.0124546
$584$	91.4811	3.78552
$585$	0.458955	0.0189754
$586$	32.8267	1.35606
$587$	16.7339	0.690682	0.345341	−	0.938477i	$-0.387763\pi$
$587$	16.7339	0.690682	0.345341	+	0.938477i	$0.387763\pi$
$588$	−55.9446	−2.30711
$589$	−6.89469	−0.284091
$590$	−25.8839	−1.06562
$591$	1.59822	0.0657421
$592$	−79.8975	−3.28377
$593$	32.3693	1.32925	0.664623	−	0.747178i	$-0.268592\pi$
$593$	32.3693	1.32925	0.664623	+	0.747178i	$0.268592\pi$
$594$	36.0584	1.47950
$595$	−0.206425	−0.00846261
$596$	48.3185	1.97920
$597$	16.0164	0.655507
$598$	0.875388	0.0357973
$599$	21.6112	0.883010	0.441505	−	0.897259i	$-0.354445\pi$
$599$	21.6112	0.883010	0.441505	+	0.897259i	$0.354445\pi$
$600$	−19.0417	−0.777375
$601$	−12.1545	−0.495793	−0.247897	−	0.968786i	$-0.579739\pi$
$601$	−12.1545	−0.495793	−0.247897	+	0.968786i	$0.579739\pi$
$602$	15.3321	0.624892
$603$	−5.53795	−0.225523
$604$	88.4551	3.59919
$605$	10.5880	0.430463
$606$	52.9376	2.15044
$607$	−8.60603	−0.349308	−0.174654	−	0.984630i	$-0.555881\pi$
$607$	−8.60603	−0.349308	−0.174654	+	0.984630i	$0.555881\pi$
$608$	76.1226	3.08718
$609$	0.708253	0.0286999
$610$	−34.5086	−1.39721
$611$	2.07959	0.0841313
$612$	0.939652	0.0379832
$613$	−15.7991	−0.638120	−0.319060	−	0.947735i	$-0.603367\pi$
$613$	−15.7991	−0.638120	−0.319060	+	0.947735i	$0.603367\pi$
$614$	−41.2909	−1.66636
$615$	−5.69636	−0.229699
$616$	10.5974	0.426980
$617$	−20.9455	−0.843235	−0.421617	−	0.906774i	$-0.638537\pi$
$617$	−20.9455	−0.843235	−0.421617	+	0.906774i	$0.638537\pi$
$618$	15.6425	0.629232
$619$	−39.3700	−1.58242	−0.791208	−	0.611547i	$-0.790547\pi$
$619$	−39.3700	−1.58242	−0.791208	+	0.611547i	$0.790547\pi$
$620$	21.6262	0.868531
$621$	−5.62472	−0.225712
$622$	−29.2896	−1.17441
$623$	1.30727	0.0523749
$624$	7.32092	0.293072
$625$	−16.6332	−0.665330
$626$	94.3205	3.76981
$627$	−11.8114	−0.471700
$628$	−93.3297	−3.72426
$629$	1.19349	0.0475874
$630$	−1.85665	−0.0739707
$631$	−30.9614	−1.23256	−0.616278	−	0.787529i	$-0.711360\pi$
$631$	−30.9614	−1.23256	−0.616278	+	0.787529i	$0.711360\pi$
$632$	−103.136	−4.10252
$633$	−27.9704	−1.11172
$634$	−80.1305	−3.18239
$635$	−22.3971	−0.888802
$636$	−1.06060	−0.0420557
$637$	−2.16602	−0.0858210
$638$	6.41070	0.253802
$639$	−0.341184	−0.0134970
$640$	−78.4074	−3.09932
$641$	11.3484	0.448236	0.224118	−	0.974562i	$-0.428050\pi$
$641$	11.3484	0.448236	0.224118	+	0.974562i	$0.428050\pi$
$642$	35.2322	1.39051
$643$	−7.98456	−0.314880	−0.157440	−	0.987529i	$-0.550324\pi$
$643$	−7.98456	−0.314880	−0.157440	+	0.987529i	$0.550324\pi$
$644$	−2.59718	−0.102343
$645$	34.1163	1.34333
$646$	−2.10089	−0.0826584
$647$	7.76293	0.305192	0.152596	−	0.988289i	$-0.451237\pi$
$647$	7.76293	0.305192	0.152596	+	0.988289i	$0.451237\pi$
$648$	−59.3953	−2.33327
$649$	−11.5353	−0.452801
$650$	−1.15830	−0.0454323
$651$	1.45185	0.0569026
$652$	−111.327	−4.35988
$653$	41.7182	1.63256	0.816279	−	0.577658i	$-0.196033\pi$
$653$	41.7182	1.63256	0.816279	+	0.577658i	$0.196033\pi$
$654$	−39.3315	−1.53798
$655$	14.2727	0.557681
$656$	30.2284	1.18022
$657$	−7.14271	−0.278664
$658$	−8.41276	−0.327963
$659$	−50.7906	−1.97852	−0.989261	−	0.146158i	$-0.953309\pi$
$659$	−50.7906	−1.97852	−0.989261	+	0.146158i	$0.953309\pi$
$660$	37.0481	1.44210
$661$	−4.51998	−0.175807	−0.0879035	−	0.996129i	$-0.528017\pi$
$661$	−4.51998	−0.175807	−0.0879035	+	0.996129i	$0.528017\pi$
$662$	−68.4566	−2.66064
$663$	−0.109358	−0.00424711
$664$	144.394	5.60357
$665$	3.04444	0.118058
$666$	10.7346	0.415956
$667$	−1.00000	−0.0387202
$668$	−95.3205	−3.68806
$669$	−29.5907	−1.14404
$670$	−38.8375	−1.50042
$671$	−15.3790	−0.593699
$672$	−16.0295	−0.618353
$673$	−11.8316	−0.456075	−0.228038	−	0.973652i	$-0.573231\pi$
$673$	−11.8316	−0.456075	−0.228038	+	0.973652i	$0.573231\pi$
$674$	−2.96606	−0.114248
$675$	7.44256	0.286464
$676$	−70.9625	−2.72933
$677$	16.4707	0.633022	0.316511	−	0.948589i	$-0.397489\pi$
$677$	16.4707	0.633022	0.316511	+	0.948589i	$0.397489\pi$
$678$	41.5396	1.59532
$679$	3.71886	0.142717
$680$	4.19430	0.160844
$681$	−5.75388	−0.220489
$682$	13.1413	0.503208
$683$	−22.6484	−0.866615	−0.433308	−	0.901246i	$-0.642654\pi$
$683$	−22.6484	−0.866615	−0.433308	+	0.901246i	$0.642654\pi$
$684$	−13.8583	−0.529886
$685$	−22.5317	−0.860891
$686$	17.8129	0.680101
$687$	12.4084	0.473409
$688$	−181.042	−6.90217
$689$	−0.0410638	−0.00156440
$690$	−7.87987	−0.299982
$691$	15.3540	0.584095	0.292048	−	0.956404i	$-0.405663\pi$
$691$	15.3540	0.584095	0.292048	+	0.956404i	$0.405663\pi$
$692$	−93.6061	−3.55837
$693$	−0.827426	−0.0314313
$694$	−29.2302	−1.10956
$695$	−41.5940	−1.57775
$696$	−14.3908	−0.545482
$697$	−0.451544	−0.0171034
$698$	97.6794	3.69722
$699$	32.0150	1.21092
$700$	3.43655	0.129889
$701$	33.3510	1.25965	0.629824	−	0.776737i	$-0.283127\pi$
$701$	33.3510	1.25965	0.629824	+	0.776737i	$0.283127\pi$
$702$	−4.92381	−0.185837
$703$	−17.6020	−0.663871
$704$	−73.6237	−2.77480
$705$	−18.7196	−0.705022
$706$	−5.51227	−0.207457
$707$	−6.08094	−0.228697
$708$	40.6835	1.52898
$709$	−26.9569	−1.01239	−0.506194	−	0.862420i	$-0.668948\pi$
$709$	−26.9569	−1.01239	−0.506194	+	0.862420i	$0.668948\pi$
$710$	−2.39271	−0.0897970
$711$	8.05269	0.301999
$712$	−26.5622	−0.995459
$713$	−2.04991	−0.0767696
$714$	0.442395	0.0165562
$715$	1.43440	0.0536437
$716$	−38.8575	−1.45217
$717$	−4.02566	−0.150341
$718$	−4.95361	−0.184867
$719$	−15.0402	−0.560905	−0.280453	−	0.959868i	$-0.590485\pi$
$719$	−15.0402	−0.560905	−0.280453	+	0.959868i	$0.590485\pi$
$720$	21.9233	0.817035
$721$	−1.79685	−0.0669182
$722$	−21.0555	−0.783605
$723$	−25.7585	−0.957970
$724$	80.7608	3.00145
$725$	1.32319	0.0491419
$726$	−22.6914	−0.842156
$727$	−40.9075	−1.51718	−0.758588	−	0.651571i	$-0.774110\pi$
$727$	−40.9075	−1.51718	−0.758588	+	0.651571i	$0.774110\pi$
$728$	−1.44708	−0.0536323
$729$	29.9550	1.10944
$730$	−50.0917	−1.85398
$731$	2.70436	0.100024
$732$	54.2396	2.00475
$733$	4.31515	0.159384	0.0796918	−	0.996820i	$-0.474606\pi$
$733$	4.31515	0.159384	0.0796918	+	0.996820i	$0.474606\pi$
$734$	−73.4026	−2.70934
$735$	19.4976	0.719182
$736$	22.6325	0.834245
$737$	−17.3081	−0.637554
$738$	−4.06132	−0.149499
$739$	14.2442	0.523980	0.261990	−	0.965071i	$-0.415621\pi$
$739$	14.2442	0.523980	0.261990	+	0.965071i	$0.415621\pi$
$740$	55.2113	2.02961
$741$	1.61285	0.0592496
$742$	0.166119	0.00609841
$743$	−24.3012	−0.891523	−0.445762	−	0.895152i	$-0.647067\pi$
$743$	−24.3012	−0.891523	−0.445762	+	0.895152i	$0.647067\pi$
$744$	−29.4998	−1.08152
$745$	−16.8398	−0.616964
$746$	28.6374	1.04849
$747$	−11.2741	−0.412497
$748$	2.93676	0.107379
$749$	−4.04713	−0.147879
$750$	49.8259	1.81938
$751$	2.73017	0.0996254	0.0498127	−	0.998759i	$-0.484138\pi$
$751$	2.73017	0.0996254	0.0498127	+	0.998759i	$0.484138\pi$
$752$	99.3380	3.62248
$753$	−37.0957	−1.35184
$754$	−0.875388	−0.0318797
$755$	−30.8281	−1.12195
$756$	14.6084	0.531302
$757$	12.1676	0.442241	0.221120	−	0.975247i	$-0.429029\pi$
$757$	12.1676	0.442241	0.221120	+	0.975247i	$0.429029\pi$
$758$	98.9802	3.59512
$759$	−3.51171	−0.127467
$760$	−61.8591	−2.24386
$761$	−11.9905	−0.434655	−0.217328	−	0.976099i	$-0.569734\pi$
$761$	−11.9905	−0.434655	−0.217328	+	0.976099i	$0.569734\pi$
$762$	47.9998	1.73885
$763$	4.51801	0.163563
$764$	111.392	4.03004
$765$	−0.327485	−0.0118402
$766$	15.6161	0.564231
$767$	1.57516	0.0568757
$768$	73.6470	2.65751
$769$	−13.6001	−0.490434	−0.245217	−	0.969468i	$-0.578859\pi$
$769$	−13.6001	−0.490434	−0.245217	+	0.969468i	$0.578859\pi$
$770$	−5.80272	−0.209116
$771$	−37.5774	−1.35332
$772$	−57.5461	−2.07113
$773$	−25.6026	−0.920860	−0.460430	−	0.887696i	$-0.652305\pi$
$773$	−25.6026	−0.920860	−0.460430	+	0.887696i	$0.652305\pi$
$774$	24.3238	0.874301
$775$	2.71241	0.0974326
$776$	−75.5625	−2.71253
$777$	3.70654	0.132972
$778$	95.3190	3.41735
$779$	6.65953	0.238603
$780$	−5.05895	−0.181140
$781$	−1.06633	−0.0381562
$782$	−0.624629	−0.0223367
$783$	5.62472	0.201011
$784$	−103.467	−3.69524
$785$	32.5270	1.16094
$786$	−30.5882	−1.09105
$787$	−5.97177	−0.212871	−0.106435	−	0.994320i	$-0.533944\pi$
$787$	−5.97177	−0.212871	−0.106435	+	0.994320i	$0.533944\pi$
$788$	5.86071	0.208779
$789$	23.5034	0.836743
$790$	56.4733	2.00923
$791$	−4.77166	−0.169661
$792$	16.8123	0.597397
$793$	2.10001	0.0745737
$794$	25.9561	0.921148
$795$	0.369639	0.0131097
$796$	58.7324	2.08171
$797$	−36.2551	−1.28422	−0.642111	−	0.766612i	$-0.721941\pi$
$797$	−36.2551	−1.28422	−0.642111	+	0.766612i	$0.721941\pi$
$798$	−6.52461	−0.230969
$799$	−1.48388	−0.0524960
$800$	−29.9470	−1.05879
$801$	2.07394	0.0732789
$802$	−36.5906	−1.29206
$803$	−22.3236	−0.787784
$804$	61.0435	2.15284
$805$	0.905161	0.0319027
$806$	−1.79446	−0.0632072
$807$	19.6543	0.691865
$808$	123.557	4.34672
$809$	32.3249	1.13648	0.568242	−	0.822862i	$-0.307624\pi$
$809$	32.3249	1.13648	0.568242	+	0.822862i	$0.307624\pi$
$810$	32.5227	1.14273
$811$	−23.8825	−0.838628	−0.419314	−	0.907841i	$-0.637729\pi$
$811$	−23.8825	−0.838628	−0.419314	+	0.907841i	$0.637729\pi$
$812$	2.59718	0.0911430
$813$	24.5887	0.862362
$814$	33.5495	1.17591
$815$	38.7992	1.35908
$816$	−5.22381	−0.182870
$817$	−39.8849	−1.39540
$818$	30.3715	1.06192
$819$	0.112986	0.00394804
$820$	−20.8886	−0.729463
$821$	−26.6795	−0.931121	−0.465560	−	0.885016i	$-0.654147\pi$
$821$	−26.6795	−0.931121	−0.465560	+	0.885016i	$0.654147\pi$
$822$	48.2882	1.68424
$823$	50.7284	1.76828	0.884141	−	0.467221i	$-0.154745\pi$
$823$	50.7284	1.76828	0.884141	+	0.467221i	$0.154745\pi$
$824$	36.5097	1.27188
$825$	4.64665	0.161776
$826$	−6.37212	−0.221715
$827$	−19.1478	−0.665833	−0.332917	−	0.942956i	$-0.608033\pi$
$827$	−19.1478	−0.665833	−0.332917	+	0.942956i	$0.608033\pi$
$828$	−4.12031	−0.143191
$829$	2.03854	0.0708015	0.0354007	−	0.999373i	$-0.488729\pi$
$829$	2.03854	0.0708015	0.0354007	+	0.999373i	$0.488729\pi$
$830$	−79.0648	−2.74438
$831$	22.1610	0.768756
$832$	10.0534	0.348539
$833$	1.54556	0.0535504
$834$	89.1411	3.08671
$835$	33.2208	1.14965
$836$	−43.3125	−1.49799
$837$	11.5302	0.398540
$838$	−62.5103	−2.15938
$839$	−14.4289	−0.498142	−0.249071	−	0.968485i	$-0.580125\pi$
$839$	−14.4289	−0.498142	−0.249071	+	0.968485i	$0.580125\pi$
$840$	13.0260	0.449440
$841$	1.00000	0.0344828
$842$	−21.7542	−0.749700
$843$	−48.7271	−1.67825
$844$	−102.568	−3.53053
$845$	24.7317	0.850795
$846$	−13.3465	−0.458861
$847$	2.60656	0.0895625
$848$	−1.96153	−0.0673594
$849$	−13.8277	−0.474564
$850$	0.826501	0.0283487
$851$	−5.23336	−0.179397
$852$	3.76079	0.128843
$853$	15.7135	0.538021	0.269011	−	0.963137i	$-0.413303\pi$
$853$	15.7135	0.538021	0.269011	+	0.963137i	$0.413303\pi$
$854$	−8.49537	−0.290706
$855$	4.82987	0.165178
$856$	82.2325	2.81065
$857$	−20.1784	−0.689281	−0.344640	−	0.938735i	$-0.611999\pi$
$857$	−20.1784	−0.689281	−0.344640	+	0.938735i	$0.611999\pi$
$858$	−3.07411	−0.104948
$859$	35.7174	1.21866	0.609331	−	0.792916i	$-0.291438\pi$
$859$	35.7174	1.21866	0.609331	+	0.792916i	$0.291438\pi$
$860$	125.105	4.26605
$861$	−1.40233	−0.0477914
$862$	−17.2896	−0.588887
$863$	−7.63686	−0.259962	−0.129981	−	0.991516i	$-0.541492\pi$
$863$	−7.63686	−0.259962	−0.129981	+	0.991516i	$0.541492\pi$
$864$	−127.302	−4.33089
$865$	32.6234	1.10923
$866$	43.7232	1.48578
$867$	−25.4283	−0.863589
$868$	5.32397	0.180707
$869$	25.1676	0.853754
$870$	7.87987	0.267153
$871$	2.36344	0.0800822
$872$	−91.8003	−3.10875
$873$	5.89981	0.199678
$874$	9.21226	0.311609
$875$	−5.72350	−0.193490
$876$	78.7326	2.66013
$877$	−39.3917	−1.33016	−0.665082	−	0.746771i	$-0.731603\pi$
$877$	−39.3917	−1.33016	−0.665082	+	0.746771i	$0.731603\pi$
$878$	−28.3618	−0.957165
$879$	17.9821	0.606520
$880$	68.5186	2.30976
$881$	14.0836	0.474487	0.237243	−	0.971450i	$-0.423756\pi$
$881$	14.0836	0.474487	0.237243	+	0.971450i	$0.423756\pi$
$882$	13.9012	0.468077
$883$	20.7640	0.698763	0.349381	−	0.936981i	$-0.386392\pi$
$883$	20.7640	0.698763	0.349381	+	0.936981i	$0.386392\pi$
$884$	−0.401018	−0.0134877
$885$	−14.1789	−0.476619
$886$	−44.7464	−1.50329
$887$	55.5503	1.86520	0.932598	−	0.360918i	$-0.117536\pi$
$887$	55.5503	1.86520	0.932598	+	0.360918i	$0.117536\pi$
$888$	−75.3123	−2.52731
$889$	−5.51374	−0.184925
$890$	14.5445	0.487531
$891$	14.4939	0.485564
$892$	−108.510	−3.63317
$893$	21.8849	0.732349
$894$	36.0899	1.20703
$895$	13.5425	0.452676
$896$	−19.3024	−0.644848
$897$	0.479527	0.0160110
$898$	38.3011	1.27813
$899$	2.04991	0.0683682
$900$	5.45194	0.181731
$901$	0.0293009	0.000976153 0
$902$	−12.6931	−0.422635
$903$	8.39878	0.279494
$904$	96.9541	3.22465
$905$	−28.1466	−0.935623
$906$	66.0686	2.19498
$907$	−4.42952	−0.147080	−0.0735399	−	0.997292i	$-0.523430\pi$
$907$	−4.42952	−0.147080	−0.0735399	+	0.997292i	$0.523430\pi$
$908$	−21.0996	−0.700214
$909$	−9.64715	−0.319976
$910$	0.792367	0.0262667
$911$	−1.22958	−0.0407377	−0.0203689	−	0.999793i	$-0.506484\pi$
$911$	−1.22958	−0.0407377	−0.0203689	+	0.999793i	$0.506484\pi$
$912$	77.0427	2.55114
$913$	−35.2357	−1.16613
$914$	28.1920	0.932510
$915$	−18.9034	−0.624929
$916$	45.5017	1.50342
$917$	3.51367	0.116032
$918$	3.51336	0.115958
$919$	−8.29213	−0.273532	−0.136766	−	0.990603i	$-0.543671\pi$
$919$	−8.29213	−0.273532	−0.136766	+	0.990603i	$0.543671\pi$
$920$	−18.3917	−0.606357
$921$	−22.6187	−0.745310
$922$	86.7116	2.85569
$923$	0.145608	0.00479274
$924$	9.12053	0.300044
$925$	6.92471	0.227683
$926$	25.2382	0.829380
$927$	−2.85063	−0.0936269
$928$	−22.6325	−0.742949
$929$	15.6905	0.514790	0.257395	−	0.966306i	$-0.417136\pi$
$929$	15.6905	0.514790	0.257395	+	0.966306i	$0.417136\pi$
$930$	16.1530	0.529678
$931$	−22.7944	−0.747058
$932$	117.399	3.84555
$933$	−16.0445	−0.525274
$934$	43.6581	1.42854
$935$	−1.02351	−0.0334725
$936$	−2.29573	−0.0750383
$937$	−5.91998	−0.193397	−0.0966986	−	0.995314i	$-0.530828\pi$
$937$	−5.91998	−0.193397	−0.0966986	+	0.995314i	$0.530828\pi$
$938$	−9.56105	−0.312179
$939$	51.6677	1.68611
$940$	−68.6452	−2.23896
$941$	−7.94486	−0.258995	−0.129498	−	0.991580i	$-0.541336\pi$
$941$	−7.94486	−0.258995	−0.129498	+	0.991580i	$0.541336\pi$
$942$	−69.7095	−2.27126
$943$	1.97999	0.0644773
$944$	75.2422	2.44892
$945$	−5.09128	−0.165619
$946$	76.0210	2.47165
$947$	48.2636	1.56836	0.784179	−	0.620535i	$-0.213085\pi$
$947$	48.2636	1.56836	0.784179	+	0.620535i	$0.213085\pi$
$948$	−88.7629	−2.88289
$949$	3.04832	0.0989525
$950$	−12.1895	−0.395481
$951$	−43.8946	−1.42338
$952$	1.03256	0.0334654
$953$	58.0127	1.87922	0.939608	−	0.342252i	$-0.111190\pi$
$953$	58.0127	1.87922	0.939608	+	0.342252i	$0.111190\pi$
$954$	0.263540	0.00853244
$955$	−38.8222	−1.25626
$956$	−14.7622	−0.477443
$957$	3.51171	0.113517
$958$	−24.7256	−0.798848
$959$	−5.54687	−0.179118
$960$	−90.4964	−2.92076
$961$	−26.7979	−0.864448
$962$	−4.58122	−0.147704
$963$	−6.42060	−0.206901
$964$	−94.4570	−3.04226
$965$	20.0558	0.645619
$966$	−1.93987	−0.0624144
$967$	42.8336	1.37744	0.688718	−	0.725030i	$-0.258174\pi$
$967$	42.8336	1.37744	0.688718	+	0.725030i	$0.258174\pi$
$968$	−52.9620	−1.70226
$969$	−1.15084	−0.0369704
$970$	41.3752	1.32848
$971$	54.8657	1.76072	0.880362	−	0.474303i	$-0.157300\pi$
$971$	54.8657	1.76072	0.880362	+	0.474303i	$0.157300\pi$
$972$	41.7216	1.33822
$973$	−10.2396	−0.328268
$974$	−95.4288	−3.05774
$975$	−0.634504	−0.0203204
$976$	100.313	3.21096
$977$	−0.842056	−0.0269398	−0.0134699	−	0.999909i	$-0.504288\pi$
$977$	−0.842056	−0.0269398	−0.0134699	+	0.999909i	$0.504288\pi$
$978$	−83.1516	−2.65890
$979$	6.48182	0.207160
$980$	71.4982	2.28393
$981$	7.16764	0.228845
$982$	−6.46226	−0.206219
$983$	−26.6803	−0.850969	−0.425485	−	0.904966i	$-0.639896\pi$
$983$	−26.6803	−0.850969	−0.425485	+	0.904966i	$0.639896\pi$
$984$	28.4937	0.908344
$985$	−2.04256	−0.0650814
$986$	0.624629	0.0198922
$987$	−4.60841	−0.146687
$988$	5.91436	0.188161
$989$	−11.8584	−0.377077
$990$	−9.20577	−0.292579
$991$	−59.7070	−1.89665	−0.948327	−	0.317294i	$-0.897226\pi$
$991$	−59.7070	−1.89665	−0.948327	+	0.317294i	$0.897226\pi$
$992$	−46.3945	−1.47303
$993$	−37.4998	−1.19002
$994$	−0.589041	−0.0186832
$995$	−20.4693	−0.648919
$996$	124.272	3.93770
$997$	54.7306	1.73333	0.866667	−	0.498887i	$-0.166258\pi$
$997$	54.7306	1.73333	0.866667	+	0.498887i	$0.166258\pi$
$998$	−54.9159	−1.73833
$999$	29.4362	0.931320

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.d.1.16	✓	16
3.2	odd	2		6003.2.a.q.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.d.1.16	✓	16	1.1	even	1	trivial
6003.2.a.q.1.1		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)

\(f(q)\)	\(=\)	\(q+2.73896 q^{2} +1.50037 q^{3} +5.50188 q^{4} -1.91750 q^{5} +4.10945 q^{6} -0.472052 q^{7} +9.59151 q^{8} -0.748891 q^{9} +O(q^{10})\)	\(q+2.73896 q^{2} +1.50037 q^{3} +5.50188 q^{4} -1.91750 q^{5} +4.10945 q^{6} -0.472052 q^{7} +9.59151 q^{8} -0.748891 q^{9} -5.25195 q^{10} -2.34056 q^{11} +8.25486 q^{12} +0.319606 q^{13} -1.29293 q^{14} -2.87696 q^{15} +15.2670 q^{16} -0.228054 q^{17} -2.05118 q^{18} +3.36342 q^{19} -10.5499 q^{20} -0.708253 q^{21} -6.41070 q^{22} +1.00000 q^{23} +14.3908 q^{24} -1.32319 q^{25} +0.875388 q^{26} -5.62472 q^{27} -2.59718 q^{28} -1.00000 q^{29} -7.87987 q^{30} -2.04991 q^{31} +22.6325 q^{32} -3.51171 q^{33} -0.624629 q^{34} +0.905161 q^{35} -4.12031 q^{36} -5.23336 q^{37} +9.21226 q^{38} +0.479527 q^{39} -18.3917 q^{40} +1.97999 q^{41} -1.93987 q^{42} -11.8584 q^{43} -12.8775 q^{44} +1.43600 q^{45} +2.73896 q^{46} +6.50673 q^{47} +22.9061 q^{48} -6.77717 q^{49} -3.62415 q^{50} -0.342165 q^{51} +1.75844 q^{52} -0.128482 q^{53} -15.4059 q^{54} +4.48804 q^{55} -4.52769 q^{56} +5.04637 q^{57} -2.73896 q^{58} +4.92843 q^{59} -15.8287 q^{60} +6.57063 q^{61} -5.61460 q^{62} +0.353516 q^{63} +31.4556 q^{64} -0.612846 q^{65} -9.61842 q^{66} +7.39486 q^{67} -1.25472 q^{68} +1.50037 q^{69} +2.47920 q^{70} +0.455585 q^{71} -7.18299 q^{72} +9.53772 q^{73} -14.3339 q^{74} -1.98527 q^{75} +18.5051 q^{76} +1.10487 q^{77} +1.31340 q^{78} -10.7528 q^{79} -29.2744 q^{80} -6.19249 q^{81} +5.42311 q^{82} +15.0544 q^{83} -3.89673 q^{84} +0.437293 q^{85} -32.4798 q^{86} -1.50037 q^{87} -22.4495 q^{88} -2.76934 q^{89} +3.93314 q^{90} -0.150871 q^{91} +5.50188 q^{92} -3.07562 q^{93} +17.8217 q^{94} -6.44936 q^{95} +33.9571 q^{96} -7.87806 q^{97} -18.5624 q^{98} +1.75283 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 3 q^{2} + 5 q^{3} + 21 q^{4} + 16 q^{5} + 6 q^{6} + q^{7} + 9 q^{8} + 23 q^{9}+O(q^{10}) \) 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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