LMFDB - Embedded newform 667.2.a.c.1.4

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 58 x^{10} + 24 x^{9} - 298 x^{8} + 97 x^{7} + 641 x^{6} - 402 x^{5} + \cdots - 40 $ x^13 - 4x^12 - 11x^11 + 58x^10 + 24x^9 - 298x^8 + 97x^7 + 641x^6 - 402x^5 - 547x^4 + 352x^3 + 219x^2 - 88x - 40
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.806558$ 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)

$f(q)$	$=$	$q-0.806558 q^{2} +1.38777 q^{3} -1.34946 q^{4} +2.04515 q^{5} -1.11932 q^{6} +4.05430 q^{7} +2.70154 q^{8} -1.07409 q^{9} +O(q^{10})$	\(q-0.806558 q^{2} +1.38777 q^{3} -1.34946 q^{4} +2.04515 q^{5} -1.11932 q^{6} +4.05430 q^{7} +2.70154 q^{8} -1.07409 q^{9} -1.64953 q^{10} -3.00186 q^{11} -1.87275 q^{12} +1.84298 q^{13} -3.27003 q^{14} +2.83821 q^{15} +0.519985 q^{16} +7.58612 q^{17} +0.866313 q^{18} -2.21989 q^{19} -2.75986 q^{20} +5.62645 q^{21} +2.42117 q^{22} -1.00000 q^{23} +3.74912 q^{24} -0.817347 q^{25} -1.48647 q^{26} -5.65391 q^{27} -5.47114 q^{28} +1.00000 q^{29} -2.28918 q^{30} +2.91860 q^{31} -5.82247 q^{32} -4.16589 q^{33} -6.11864 q^{34} +8.29167 q^{35} +1.44944 q^{36} -4.19589 q^{37} +1.79047 q^{38} +2.55763 q^{39} +5.52506 q^{40} +7.56150 q^{41} -4.53805 q^{42} +1.21770 q^{43} +4.05090 q^{44} -2.19667 q^{45} +0.806558 q^{46} +2.01776 q^{47} +0.721621 q^{48} +9.43736 q^{49} +0.659237 q^{50} +10.5278 q^{51} -2.48703 q^{52} +4.03062 q^{53} +4.56020 q^{54} -6.13926 q^{55} +10.9528 q^{56} -3.08070 q^{57} -0.806558 q^{58} +4.61650 q^{59} -3.83006 q^{60} +6.09622 q^{61} -2.35402 q^{62} -4.35467 q^{63} +3.65619 q^{64} +3.76917 q^{65} +3.36003 q^{66} +3.87921 q^{67} -10.2372 q^{68} -1.38777 q^{69} -6.68771 q^{70} -14.7800 q^{71} -2.90169 q^{72} +6.28677 q^{73} +3.38423 q^{74} -1.13429 q^{75} +2.99566 q^{76} -12.1704 q^{77} -2.06288 q^{78} +8.58201 q^{79} +1.06345 q^{80} -4.62407 q^{81} -6.09879 q^{82} -2.36242 q^{83} -7.59269 q^{84} +15.5148 q^{85} -0.982147 q^{86} +1.38777 q^{87} -8.10962 q^{88} -9.84922 q^{89} +1.77174 q^{90} +7.47198 q^{91} +1.34946 q^{92} +4.05035 q^{93} -1.62744 q^{94} -4.54001 q^{95} -8.08026 q^{96} -16.9001 q^{97} -7.61177 q^{98} +3.22426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * 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 $

$2$	−0.806558	−0.570322	−0.285161	−	0.958480i	$-0.592047\pi$
$2$	−0.806558	−0.570322	−0.285161	+	0.958480i	$0.592047\pi$
$3$	1.38777	0.801231	0.400615	−	0.916246i	$-0.368796\pi$
$3$	1.38777	0.801231	0.400615	+	0.916246i	$0.368796\pi$
$4$	−1.34946	−0.674732
$5$	2.04515	0.914620	0.457310	−	0.889307i	$-0.348813\pi$
$5$	2.04515	0.914620	0.457310	+	0.889307i	$0.348813\pi$
$6$	−1.11932	−0.456960
$7$	4.05430	1.53238	0.766191	−	0.642613i	$-0.222150\pi$
$7$	4.05430	1.53238	0.766191	+	0.642613i	$0.222150\pi$
$8$	2.70154	0.955137
$9$	−1.07409	−0.358029
$10$	−1.64953	−0.521628
$11$	−3.00186	−0.905094	−0.452547	−	0.891741i	$-0.649484\pi$
$11$	−3.00186	−0.905094	−0.452547	+	0.891741i	$0.649484\pi$
$12$	−1.87275	−0.540616
$13$	1.84298	0.511150	0.255575	−	0.966789i	$-0.417735\pi$
$13$	1.84298	0.511150	0.255575	+	0.966789i	$0.417735\pi$
$14$	−3.27003	−0.873952
$15$	2.83821	0.732822
$16$	0.519985	0.129996
$17$	7.58612	1.83990	0.919952	−	0.392032i	$-0.128228\pi$
$17$	7.58612	1.83990	0.919952	+	0.392032i	$0.128228\pi$
$18$	0.866313	0.204192
$19$	−2.21989	−0.509278	−0.254639	−	0.967036i	$-0.581957\pi$
$19$	−2.21989	−0.509278	−0.254639	+	0.967036i	$0.581957\pi$
$20$	−2.75986	−0.617124
$21$	5.62645	1.22779
$22$	2.42117	0.516195
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.74912	0.765285
$25$	−0.817347	−0.163469
$26$	−1.48647	−0.291520
$27$	−5.65391	−1.08809
$28$	−5.47114	−1.03395
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−2.28918	−0.417945
$31$	2.91860	0.524195	0.262098	−	0.965041i	$-0.415586\pi$
$31$	2.91860	0.524195	0.262098	+	0.965041i	$0.415586\pi$
$32$	−5.82247	−1.02928
$33$	−4.16589	−0.725189
$34$	−6.11864	−1.04934
$35$	8.29167	1.40155
$36$	1.44944	0.241574
$37$	−4.19589	−0.689800	−0.344900	−	0.938639i	$-0.612087\pi$
$37$	−4.19589	−0.689800	−0.344900	+	0.938639i	$0.612087\pi$
$38$	1.79047	0.290452
$39$	2.55763	0.409549
$40$	5.52506	0.873588
$41$	7.56150	1.18091	0.590454	−	0.807071i	$-0.298949\pi$
$41$	7.56150	1.18091	0.590454	+	0.807071i	$0.298949\pi$
$42$	−4.53805	−0.700237
$43$	1.21770	0.185698	0.0928489	−	0.995680i	$-0.470403\pi$
$43$	1.21770	0.185698	0.0928489	+	0.995680i	$0.470403\pi$
$44$	4.05090	0.610696
$45$	−2.19667	−0.327461
$46$	0.806558	0.118920
$47$	2.01776	0.294321	0.147160	−	0.989113i	$-0.452987\pi$
$47$	2.01776	0.294321	0.147160	+	0.989113i	$0.452987\pi$
$48$	0.721621	0.104157
$49$	9.43736	1.34819
$50$	0.659237	0.0932303
$51$	10.5278	1.47419
$52$	−2.48703	−0.344889
$53$	4.03062	0.553649	0.276824	−	0.960921i	$-0.410718\pi$
$53$	4.03062	0.553649	0.276824	+	0.960921i	$0.410718\pi$
$54$	4.56020	0.620565
$55$	−6.13926	−0.827817
$56$	10.9528	1.46364
$57$	−3.08070	−0.408049
$58$	−0.806558	−0.105906
$59$	4.61650	0.601017	0.300509	−	0.953779i	$-0.402844\pi$
$59$	4.61650	0.601017	0.300509	+	0.953779i	$0.402844\pi$
$60$	−3.83006	−0.494459
$61$	6.09622	0.780541	0.390270	−	0.920700i	$-0.372382\pi$
$61$	6.09622	0.780541	0.390270	+	0.920700i	$0.372382\pi$
$62$	−2.35402	−0.298960
$63$	−4.35467	−0.548637
$64$	3.65619	0.457023
$65$	3.76917	0.467508
$66$	3.36003	0.413591
$67$	3.87921	0.473920	0.236960	−	0.971519i	$-0.423849\pi$
$67$	3.87921	0.473920	0.236960	+	0.971519i	$0.423849\pi$
$68$	−10.2372	−1.24144
$69$	−1.38777	−0.167068
$70$	−6.68771	−0.799334
$71$	−14.7800	−1.75406	−0.877031	−	0.480434i	$-0.840479\pi$
$71$	−14.7800	−1.75406	−0.877031	+	0.480434i	$0.840479\pi$
$72$	−2.90169	−0.341967
$73$	6.28677	0.735811	0.367906	−	0.929863i	$-0.380075\pi$
$73$	6.28677	0.735811	0.367906	+	0.929863i	$0.380075\pi$
$74$	3.38423	0.393408
$75$	−1.13429	−0.130977
$76$	2.99566	0.343626
$77$	−12.1704	−1.38695
$78$	−2.06288	−0.233575
$79$	8.58201	0.965552	0.482776	−	0.875744i	$-0.339629\pi$
$79$	8.58201	0.965552	0.482776	+	0.875744i	$0.339629\pi$
$80$	1.06345	0.118897
$81$	−4.62407	−0.513786
$82$	−6.09879	−0.673499
$83$	−2.36242	−0.259310	−0.129655	−	0.991559i	$-0.541387\pi$
$83$	−2.36242	−0.259310	−0.129655	+	0.991559i	$0.541387\pi$
$84$	−7.59269	−0.828431
$85$	15.5148	1.68281
$86$	−0.982147	−0.105908
$87$	1.38777	0.148785
$88$	−8.10962	−0.864489
$89$	−9.84922	−1.04402	−0.522008	−	0.852941i	$-0.674817\pi$
$89$	−9.84922	−1.04402	−0.522008	+	0.852941i	$0.674817\pi$
$90$	1.77174	0.186758
$91$	7.47198	0.783277
$92$	1.34946	0.140691
$93$	4.05035	0.420001
$94$	−1.62744	−0.167858
$95$	−4.54001	−0.465796
$96$	−8.08026	−0.824689
$97$	−16.9001	−1.71595	−0.857973	−	0.513695i	$-0.828276\pi$
$97$	−16.9001	−1.71595	−0.857973	+	0.513695i	$0.828276\pi$
$98$	−7.61177	−0.768905
$99$	3.22426	0.324050
$100$	1.10298	0.110298
$101$	14.9861	1.49118	0.745589	−	0.666407i	$-0.232168\pi$
$101$	14.9861	1.49118	0.745589	+	0.666407i	$0.232168\pi$
$102$	−8.49128	−0.840762
$103$	−18.3682	−1.80987	−0.904937	−	0.425546i	$-0.860082\pi$
$103$	−18.3682	−1.80987	−0.904937	+	0.425546i	$0.860082\pi$
$104$	4.97887	0.488218
$105$	11.5069	1.12296
$106$	−3.25093	−0.315758
$107$	12.2465	1.18392	0.591959	−	0.805968i	$-0.298355\pi$
$107$	12.2465	1.18392	0.591959	+	0.805968i	$0.298355\pi$
$108$	7.62975	0.734173
$109$	−12.4689	−1.19430	−0.597151	−	0.802129i	$-0.703701\pi$
$109$	−12.4689	−1.19430	−0.597151	+	0.802129i	$0.703701\pi$
$110$	4.95166	0.472123
$111$	−5.82294	−0.552689
$112$	2.10818	0.199204
$113$	−20.4069	−1.91972	−0.959862	−	0.280473i	$-0.909509\pi$
$113$	−20.4069	−1.91972	−0.959862	+	0.280473i	$0.909509\pi$
$114$	2.48476	0.232719
$115$	−2.04515	−0.190712
$116$	−1.34946	−0.125295
$117$	−1.97952	−0.183006
$118$	−3.72347	−0.342774
$119$	30.7564	2.81943
$120$	7.66752	0.699946
$121$	−1.98886	−0.180806
$122$	−4.91695	−0.445160
$123$	10.4936	0.946180
$124$	−3.93854	−0.353692
$125$	−11.8974	−1.06413
$126$	3.51230	0.312900
$127$	−9.90186	−0.878648	−0.439324	−	0.898329i	$-0.644782\pi$
$127$	−9.90186	−0.878648	−0.439324	+	0.898329i	$0.644782\pi$
$128$	8.69602	0.768626
$129$	1.68989	0.148787
$130$	−3.04005	−0.266630
$131$	16.9397	1.48003	0.740014	−	0.672591i	$-0.234819\pi$
$131$	16.9397	1.48003	0.740014	+	0.672591i	$0.234819\pi$
$132$	5.62173	0.489308
$133$	−9.00010	−0.780408
$134$	−3.12880	−0.270287
$135$	−11.5631	−0.995194
$136$	20.4942	1.75736
$137$	17.8614	1.52600	0.763002	−	0.646396i	$-0.223724\pi$
$137$	17.8614	1.52600	0.763002	+	0.646396i	$0.223724\pi$
$138$	1.11932	0.0952827
$139$	−9.50597	−0.806286	−0.403143	−	0.915137i	$-0.632082\pi$
$139$	−9.50597	−0.806286	−0.403143	+	0.915137i	$0.632082\pi$
$140$	−11.1893	−0.945670
$141$	2.80020	0.235819
$142$	11.9209	1.00038
$143$	−5.53235	−0.462638
$144$	−0.558510	−0.0465425
$145$	2.04515	0.169841
$146$	−5.07064	−0.419650
$147$	13.0969	1.08021
$148$	5.66221	0.465431
$149$	−15.2689	−1.25088	−0.625438	−	0.780274i	$-0.715080\pi$
$149$	−15.2689	−1.25088	−0.625438	+	0.780274i	$0.715080\pi$
$150$	0.914872	0.0746990
$151$	−10.5774	−0.860777	−0.430388	−	0.902644i	$-0.641623\pi$
$151$	−10.5774	−0.860777	−0.430388	+	0.902644i	$0.641623\pi$
$152$	−5.99711	−0.486430
$153$	−8.14815	−0.658739
$154$	9.81615	0.791008
$155$	5.96898	0.479440
$156$	−3.45143	−0.276336
$157$	−5.77058	−0.460543	−0.230271	−	0.973126i	$-0.573961\pi$
$157$	−5.77058	−0.460543	−0.230271	+	0.973126i	$0.573961\pi$
$158$	−6.92189	−0.550676
$159$	5.59359	0.443600
$160$	−11.9078	−0.941398
$161$	−4.05430	−0.319524
$162$	3.72958	0.293024
$163$	−16.3991	−1.28447	−0.642237	−	0.766506i	$-0.721994\pi$
$163$	−16.3991	−1.28447	−0.642237	+	0.766506i	$0.721994\pi$
$164$	−10.2040	−0.796797
$165$	−8.51989	−0.663273
$166$	1.90543	0.147890
$167$	−5.15361	−0.398799	−0.199399	−	0.979918i	$-0.563899\pi$
$167$	−5.15361	−0.398799	−0.199399	+	0.979918i	$0.563899\pi$
$168$	15.2001	1.17271
$169$	−9.60344	−0.738726
$170$	−12.5136	−0.959746
$171$	2.38436	0.182336
$172$	−1.64325	−0.125296
$173$	−7.04728	−0.535795	−0.267897	−	0.963447i	$-0.586329\pi$
$173$	−7.04728	−0.535795	−0.267897	+	0.963447i	$0.586329\pi$
$174$	−1.11932	−0.0848553
$175$	−3.31377	−0.250498
$176$	−1.56092	−0.117659
$177$	6.40665	0.481554
$178$	7.94397	0.595425
$179$	0.527490	0.0394265	0.0197132	−	0.999806i	$-0.493725\pi$
$179$	0.527490	0.0394265	0.0197132	+	0.999806i	$0.493725\pi$
$180$	2.96433	0.220948
$181$	−1.18927	−0.0883975	−0.0441988	−	0.999023i	$-0.514073\pi$
$181$	−1.18927	−0.0883975	−0.0441988	+	0.999023i	$0.514073\pi$
$182$	−6.02658	−0.446720
$183$	8.46017	0.625393
$184$	−2.70154	−0.199160
$185$	−8.58124	−0.630905
$186$	−3.26684	−0.239536
$187$	−22.7724	−1.66528
$188$	−2.72290	−0.198588
$189$	−22.9226	−1.66738
$190$	3.66178	0.265654
$191$	−3.48800	−0.252383	−0.126192	−	0.992006i	$-0.540275\pi$
$191$	−3.48800	−0.252383	−0.126192	+	0.992006i	$0.540275\pi$
$192$	5.07396	0.366181
$193$	0.0117890	0.000848590 0	0.000424295	−	1.00000i	$-0.499865\pi$
$193$	0.0117890	0.000848590 0	0.000424295		1.00000i	$0.499865\pi$
$194$	13.6309	0.978642
$195$	5.23075	0.374582
$196$	−12.7354	−0.909670
$197$	22.8749	1.62977	0.814886	−	0.579621i	$-0.196799\pi$
$197$	22.8749	1.62977	0.814886	+	0.579621i	$0.196799\pi$
$198$	−2.60055	−0.184813
$199$	−20.7363	−1.46995	−0.734977	−	0.678092i	$-0.762807\pi$
$199$	−20.7363	−1.46995	−0.734977	+	0.678092i	$0.762807\pi$
$200$	−2.20809	−0.156136
$201$	5.38345	0.379720
$202$	−12.0872	−0.850452
$203$	4.05430	0.284556
$204$	−14.2069	−0.994682
$205$	15.4644	1.08008
$206$	14.8150	1.03221
$207$	1.07409	0.0746542
$208$	0.958321	0.0664476
$209$	6.66379	0.460944
$210$	−9.28102	−0.640451
$211$	−10.8507	−0.746992	−0.373496	−	0.927632i	$-0.621841\pi$
$211$	−10.8507	−0.746992	−0.373496	+	0.927632i	$0.621841\pi$
$212$	−5.43918	−0.373565
$213$	−20.5113	−1.40541
$214$	−9.87755	−0.675215
$215$	2.49039	0.169843
$216$	−15.2742	−1.03928
$217$	11.8329	0.803267
$218$	10.0569	0.681137
$219$	8.72461	0.589555
$220$	8.28471	0.558555
$221$	13.9810	0.940466
$222$	4.69654	0.315211
$223$	−7.03248	−0.470930	−0.235465	−	0.971883i	$-0.575661\pi$
$223$	−7.03248	−0.470930	−0.235465	+	0.971883i	$0.575661\pi$
$224$	−23.6060	−1.57725
$225$	0.877902	0.0585268
$226$	16.4594	1.09486
$227$	14.3071	0.949597	0.474798	−	0.880095i	$-0.342521\pi$
$227$	14.3071	0.949597	0.474798	+	0.880095i	$0.342521\pi$
$228$	4.15730	0.275324
$229$	6.10416	0.403374	0.201687	−	0.979450i	$-0.435358\pi$
$229$	6.10416	0.403374	0.201687	+	0.979450i	$0.435358\pi$
$230$	1.64953	0.108767
$231$	−16.8898	−1.11127
$232$	2.70154	0.177365
$233$	22.1337	1.45002	0.725012	−	0.688736i	$-0.241834\pi$
$233$	22.1337	1.45002	0.725012	+	0.688736i	$0.241834\pi$
$234$	1.59660	0.104373
$235$	4.12663	0.269192
$236$	−6.22981	−0.405526
$237$	11.9099	0.773630
$238$	−24.8068	−1.60799
$239$	−14.8240	−0.958882	−0.479441	−	0.877574i	$-0.659161\pi$
$239$	−14.8240	−0.958882	−0.479441	+	0.877574i	$0.659161\pi$
$240$	1.47583	0.0952642
$241$	−1.77555	−0.114373	−0.0571865	−	0.998364i	$-0.518213\pi$
$241$	−1.77555	−0.114373	−0.0571865	+	0.998364i	$0.518213\pi$
$242$	1.60413	0.103117
$243$	10.5446	0.676434
$244$	−8.22663	−0.526656
$245$	19.3008	1.23309
$246$	−8.46373	−0.539628
$247$	−4.09120	−0.260317
$248$	7.88469	0.500678
$249$	−3.27851	−0.207767
$250$	9.59591	0.606899
$251$	14.9548	0.943936	0.471968	−	0.881616i	$-0.343544\pi$
$251$	14.9548	0.943936	0.471968	+	0.881616i	$0.343544\pi$
$252$	5.87648	0.370183
$253$	3.00186	0.188725
$254$	7.98642	0.501113
$255$	21.5310	1.34832
$256$	−14.3262	−0.895388
$257$	2.91061	0.181559	0.0907794	−	0.995871i	$-0.471064\pi$
$257$	2.91061	0.181559	0.0907794	+	0.995871i	$0.471064\pi$
$258$	−1.36300	−0.0848565
$259$	−17.0114	−1.05704
$260$	−5.08636	−0.315443
$261$	−1.07409	−0.0664843
$262$	−13.6628	−0.844093
$263$	−30.6896	−1.89240	−0.946201	−	0.323580i	$-0.895114\pi$
$263$	−30.6896	−1.89240	−0.946201	+	0.323580i	$0.895114\pi$
$264$	−11.2543	−0.692655
$265$	8.24324	0.506378
$266$	7.25910	0.445084
$267$	−13.6685	−0.836497
$268$	−5.23485	−0.319769
$269$	−18.0587	−1.10106	−0.550530	−	0.834815i	$-0.685574\pi$
$269$	−18.0587	−1.10106	−0.550530	+	0.834815i	$0.685574\pi$
$270$	9.32631	0.567581
$271$	7.82283	0.475203	0.237601	−	0.971363i	$-0.423639\pi$
$271$	7.82283	0.475203	0.237601	+	0.971363i	$0.423639\pi$
$272$	3.94467	0.239181
$273$	10.3694	0.627585
$274$	−14.4063	−0.870315
$275$	2.45356	0.147955
$276$	1.87275	0.112726
$277$	19.2194	1.15478	0.577390	−	0.816469i	$-0.304071\pi$
$277$	19.2194	1.15478	0.577390	+	0.816469i	$0.304071\pi$
$278$	7.66711	0.459843
$279$	−3.13483	−0.187677
$280$	22.4002	1.33867
$281$	22.5950	1.34791	0.673953	−	0.738775i	$-0.264595\pi$
$281$	22.5950	1.34791	0.673953	+	0.738775i	$0.264595\pi$
$282$	−2.25852	−0.134493
$283$	−4.59462	−0.273122	−0.136561	−	0.990632i	$-0.543605\pi$
$283$	−4.59462	−0.273122	−0.136561	+	0.990632i	$0.543605\pi$
$284$	19.9451	1.18352
$285$	−6.30051	−0.373210
$286$	4.46216	0.263853
$287$	30.6566	1.80960
$288$	6.25384	0.368511
$289$	40.5492	2.38525
$290$	−1.64953	−0.0968640
$291$	−23.4535	−1.37487
$292$	−8.48378	−0.496476
$293$	6.38423	0.372971	0.186485	−	0.982458i	$-0.440290\pi$
$293$	6.38423	0.372971	0.186485	+	0.982458i	$0.440290\pi$
$294$	−10.5634	−0.616070
$295$	9.44145	0.549703
$296$	−11.3354	−0.658854
$297$	16.9722	0.984828
$298$	12.3152	0.713403
$299$	−1.84298	−0.106582
$300$	1.53069	0.0883743
$301$	4.93693	0.284560
$302$	8.53128	0.490920
$303$	20.7974	1.19478
$304$	−1.15431	−0.0662042
$305$	12.4677	0.713899
$306$	6.57195	0.375694
$307$	−11.3337	−0.646849	−0.323425	−	0.946254i	$-0.604834\pi$
$307$	−11.3337	−0.646849	−0.323425	+	0.946254i	$0.604834\pi$
$308$	16.4236	0.935819
$309$	−25.4909	−1.45013
$310$	−4.81432	−0.273435
$311$	−3.14192	−0.178162	−0.0890808	−	0.996024i	$-0.528393\pi$
$311$	−3.14192	−0.178162	−0.0890808	+	0.996024i	$0.528393\pi$
$312$	6.90954	0.391175
$313$	−14.5798	−0.824100	−0.412050	−	0.911161i	$-0.635187\pi$
$313$	−14.5798	−0.824100	−0.412050	+	0.911161i	$0.635187\pi$
$314$	4.65431	0.262658
$315$	−8.90598	−0.501795
$316$	−11.5811	−0.651489
$317$	−0.503716	−0.0282915	−0.0141458	−	0.999900i	$-0.504503\pi$
$317$	−0.503716	−0.0282915	−0.0141458	+	0.999900i	$0.504503\pi$
$318$	−4.51155	−0.252995
$319$	−3.00186	−0.168072
$320$	7.47746	0.418003
$321$	16.9954	0.948592
$322$	3.27003	0.182231
$323$	−16.8403	−0.937022
$324$	6.24003	0.346668
$325$	−1.50635	−0.0835573
$326$	13.2268	0.732564
$327$	−17.3040	−0.956911
$328$	20.4277	1.12793
$329$	8.18062	0.451012
$330$	6.87178	0.378279
$331$	21.9714	1.20766	0.603829	−	0.797114i	$-0.293641\pi$
$331$	21.9714	1.20766	0.603829	+	0.797114i	$0.293641\pi$
$332$	3.18801	0.174965
$333$	4.50675	0.246969
$334$	4.15669	0.227444
$335$	7.93357	0.433457
$336$	2.92567	0.159608
$337$	−9.59646	−0.522752	−0.261376	−	0.965237i	$-0.584176\pi$
$337$	−9.59646	−0.522752	−0.261376	+	0.965237i	$0.584176\pi$
$338$	7.74573	0.421312
$339$	−28.3202	−1.53814
$340$	−20.9366	−1.13545
$341$	−8.76120	−0.474446
$342$	−1.92312	−0.103990
$343$	9.88178	0.533566
$344$	3.28967	0.177367
$345$	−2.83821	−0.152804
$346$	5.68404	0.305576
$347$	−10.0974	−0.542059	−0.271029	−	0.962571i	$-0.587364\pi$
$347$	−10.0974	−0.542059	−0.271029	+	0.962571i	$0.587364\pi$
$348$	−1.87275	−0.100390
$349$	−9.00185	−0.481858	−0.240929	−	0.970543i	$-0.577452\pi$
$349$	−9.00185	−0.481858	−0.240929	+	0.970543i	$0.577452\pi$
$350$	2.67275	0.142864
$351$	−10.4200	−0.556179
$352$	17.4782	0.931592
$353$	−15.2438	−0.811344	−0.405672	−	0.914019i	$-0.632962\pi$
$353$	−15.2438	−0.811344	−0.405672	+	0.914019i	$0.632962\pi$
$354$	−5.16733	−0.274641
$355$	−30.2274	−1.60430
$356$	13.2912	0.704431
$357$	42.6829	2.25902
$358$	−0.425451	−0.0224858
$359$	8.30291	0.438211	0.219105	−	0.975701i	$-0.429686\pi$
$359$	8.30291	0.438211	0.219105	+	0.975701i	$0.429686\pi$
$360$	−5.93439	−0.312770
$361$	−14.0721	−0.740636
$362$	0.959212	0.0504151
$363$	−2.76009	−0.144867
$364$	−10.0832	−0.528502
$365$	12.8574	0.672988
$366$	−6.82361	−0.356676
$367$	−26.7249	−1.39503	−0.697514	−	0.716571i	$-0.745711\pi$
$367$	−26.7249	−1.39503	−0.697514	+	0.716571i	$0.745711\pi$
$368$	−0.519985	−0.0271061
$369$	−8.12172	−0.422800
$370$	6.92126	0.359819
$371$	16.3414	0.848401
$372$	−5.46580	−0.283389
$373$	27.1260	1.40453	0.702265	−	0.711915i	$-0.252172\pi$
$373$	27.1260	1.40453	0.702265	+	0.711915i	$0.252172\pi$
$374$	18.3673	0.949749
$375$	−16.5108	−0.852616
$376$	5.45106	0.281117
$377$	1.84298	0.0949181
$378$	18.4884	0.950942
$379$	26.1448	1.34297	0.671483	−	0.741020i	$-0.265658\pi$
$379$	26.1448	1.34297	0.671483	+	0.741020i	$0.265658\pi$
$380$	6.12659	0.314287
$381$	−13.7415	−0.704000
$382$	2.81328	0.143940
$383$	9.77660	0.499561	0.249781	−	0.968302i	$-0.419642\pi$
$383$	9.77660	0.499561	0.249781	+	0.968302i	$0.419642\pi$
$384$	12.0681	0.615847
$385$	−24.8904	−1.26853
$386$	−0.00950850	−0.000483970 0
$387$	−1.30792	−0.0664853
$388$	22.8061	1.15780
$389$	33.3393	1.69037	0.845185	−	0.534474i	$-0.179490\pi$
$389$	33.3393	1.69037	0.845185	+	0.534474i	$0.179490\pi$
$390$	−4.21890	−0.213632
$391$	−7.58612	−0.383646
$392$	25.4954	1.28771
$393$	23.5085	1.18584
$394$	−18.4500	−0.929496
$395$	17.5515	0.883114
$396$	−4.35102	−0.218647
$397$	−3.29783	−0.165514	−0.0827568	−	0.996570i	$-0.526372\pi$
$397$	−3.29783	−0.165514	−0.0827568	+	0.996570i	$0.526372\pi$
$398$	16.7250	0.838348
$399$	−12.4901	−0.625287
$400$	−0.425009	−0.0212504
$401$	−6.69026	−0.334095	−0.167048	−	0.985949i	$-0.553423\pi$
$401$	−6.69026	−0.334095	−0.167048	+	0.985949i	$0.553423\pi$
$402$	−4.34207	−0.216563
$403$	5.37890	0.267942
$404$	−20.2233	−1.00615
$405$	−9.45694	−0.469919
$406$	−3.27003	−0.162289
$407$	12.5955	0.624334
$408$	28.4412	1.40805
$409$	−1.88547	−0.0932303	−0.0466151	−	0.998913i	$-0.514843\pi$
$409$	−1.88547	−0.0932303	−0.0466151	+	0.998913i	$0.514843\pi$
$410$	−12.4730	−0.615996
$411$	24.7876	1.22268
$412$	24.7873	1.22118
$413$	18.7167	0.920988
$414$	−0.866313	−0.0425770
$415$	−4.83152	−0.237170
$416$	−10.7307	−0.526115
$417$	−13.1921	−0.646021
$418$	−5.37473	−0.262887
$419$	−18.4700	−0.902316	−0.451158	−	0.892444i	$-0.648989\pi$
$419$	−18.4700	−0.902316	−0.451158	+	0.892444i	$0.648989\pi$
$420$	−15.5282	−0.757700
$421$	37.7969	1.84211	0.921054	−	0.389434i	$-0.127329\pi$
$421$	37.7969	1.84211	0.921054	+	0.389434i	$0.127329\pi$
$422$	8.75170	0.426026
$423$	−2.16725	−0.105375
$424$	10.8889	0.528810
$425$	−6.20049	−0.300768
$426$	16.5435	0.801536
$427$	24.7159	1.19609
$428$	−16.5263	−0.798828
$429$	−7.67764	−0.370680
$430$	−2.00864	−0.0968653
$431$	17.9306	0.863685	0.431843	−	0.901949i	$-0.357864\pi$
$431$	17.9306	0.863685	0.431843	+	0.901949i	$0.357864\pi$
$432$	−2.93995	−0.141448
$433$	−6.66248	−0.320178	−0.160089	−	0.987103i	$-0.551178\pi$
$433$	−6.66248	−0.320178	−0.160089	+	0.987103i	$0.551178\pi$
$434$	−9.54389	−0.458121
$435$	2.83821	0.136082
$436$	16.8263	0.805834
$437$	2.21989	0.106192
$438$	−7.03690	−0.336236
$439$	26.7654	1.27744	0.638721	−	0.769439i	$-0.279464\pi$
$439$	26.7654	1.27744	0.638721	+	0.769439i	$0.279464\pi$
$440$	−16.5854	−0.790679
$441$	−10.1365	−0.482693
$442$	−11.2765	−0.536369
$443$	−0.322044	−0.0153008	−0.00765040	−	0.999971i	$-0.502435\pi$
$443$	−0.322044	−0.0153008	−0.00765040	+	0.999971i	$0.502435\pi$
$444$	7.85786	0.372917
$445$	−20.1432	−0.954878
$446$	5.67210	0.268582
$447$	−21.1897	−1.00224
$448$	14.8233	0.700334
$449$	−37.4180	−1.76587	−0.882933	−	0.469499i	$-0.844435\pi$
$449$	−37.4180	−1.76587	−0.882933	+	0.469499i	$0.844435\pi$
$450$	−0.708079	−0.0333792
$451$	−22.6985	−1.06883
$452$	27.5385	1.29530
$453$	−14.6790	−0.689681
$454$	−11.5395	−0.541576
$455$	15.2813	0.716401
$456$	−8.32263	−0.389743
$457$	−7.20356	−0.336968	−0.168484	−	0.985704i	$-0.553887\pi$
$457$	−7.20356	−0.336968	−0.168484	+	0.985704i	$0.553887\pi$
$458$	−4.92335	−0.230053
$459$	−42.8912	−2.00199
$460$	2.75986	0.128679
$461$	2.27025	0.105736	0.0528681	−	0.998602i	$-0.483164\pi$
$461$	2.27025	0.105736	0.0528681	+	0.998602i	$0.483164\pi$
$462$	13.6226	0.633780
$463$	−14.6651	−0.681544	−0.340772	−	0.940146i	$-0.610688\pi$
$463$	−14.6651	−0.681544	−0.340772	+	0.940146i	$0.610688\pi$
$464$	0.519985	0.0241397
$465$	8.28358	0.384142
$466$	−17.8521	−0.826981
$467$	18.9504	0.876921	0.438461	−	0.898750i	$-0.355524\pi$
$467$	18.9504	0.876921	0.438461	+	0.898750i	$0.355524\pi$
$468$	2.67129	0.123480
$469$	15.7275	0.726227
$470$	−3.32837	−0.153526
$471$	−8.00826	−0.369001
$472$	12.4716	0.574054
$473$	−3.65537	−0.168074
$474$	−9.60600	−0.441218
$475$	1.81442	0.0832513
$476$	−41.5047	−1.90236
$477$	−4.32924	−0.198222
$478$	11.9564	0.546872
$479$	20.2734	0.926317	0.463158	−	0.886275i	$-0.346716\pi$
$479$	20.2734	0.926317	0.463158	+	0.886275i	$0.346716\pi$
$480$	−16.5254	−0.754277
$481$	−7.73293	−0.352591
$482$	1.43208	0.0652295
$483$	−5.62645	−0.256012
$484$	2.68390	0.121995
$485$	−34.5633	−1.56944
$486$	−8.50479	−0.385785
$487$	6.62022	0.299991	0.149995	−	0.988687i	$-0.452074\pi$
$487$	6.62022	0.299991	0.149995	+	0.988687i	$0.452074\pi$
$488$	16.4692	0.745524
$489$	−22.7582	−1.02916
$490$	−15.5672	−0.703256
$491$	−4.57913	−0.206653	−0.103327	−	0.994647i	$-0.532949\pi$
$491$	−4.57913	−0.206653	−0.103327	+	0.994647i	$0.532949\pi$
$492$	−14.1608	−0.638419
$493$	7.58612	0.341662
$494$	3.29979	0.148465
$495$	6.59410	0.296383
$496$	1.51763	0.0681435
$497$	−59.9225	−2.68789
$498$	2.64431	0.118494
$499$	−33.4375	−1.49687	−0.748435	−	0.663208i	$-0.769194\pi$
$499$	−33.4375	−1.49687	−0.748435	+	0.663208i	$0.769194\pi$
$500$	16.0551	0.718005
$501$	−7.15204	−0.319530
$502$	−12.0619	−0.538348
$503$	−26.2354	−1.16978	−0.584890	−	0.811112i	$-0.698862\pi$
$503$	−26.2354	−1.16978	−0.584890	+	0.811112i	$0.698862\pi$
$504$	−11.7643	−0.524024
$505$	30.6490	1.36386
$506$	−2.42117	−0.107634
$507$	−13.3274	−0.591890
$508$	13.3622	0.592853
$509$	11.3542	0.503266	0.251633	−	0.967823i	$-0.419032\pi$
$509$	11.3542	0.503266	0.251633	+	0.967823i	$0.419032\pi$
$510$	−17.3660	−0.768978
$511$	25.4885	1.12754
$512$	−5.83712	−0.257967
$513$	12.5510	0.554142
$514$	−2.34757	−0.103547
$515$	−37.5658	−1.65535
$516$	−2.28045	−0.100391
$517$	−6.05703	−0.266388
$518$	13.7207	0.602852
$519$	−9.78002	−0.429295
$520$	10.1825	0.446534
$521$	1.35393	0.0593168	0.0296584	−	0.999560i	$-0.490558\pi$
$521$	1.35393	0.0593168	0.0296584	+	0.999560i	$0.490558\pi$
$522$	0.866313	0.0379175
$523$	−34.4624	−1.50694	−0.753468	−	0.657484i	$-0.771621\pi$
$523$	−34.4624	−1.50694	−0.753468	+	0.657484i	$0.771621\pi$
$524$	−22.8595	−0.998623
$525$	−4.59876	−0.200706
$526$	24.7529	1.07928
$527$	22.1408	0.964469
$528$	−2.16620	−0.0942719
$529$	1.00000	0.0434783
$530$	−6.64865	−0.288799
$531$	−4.95853	−0.215182
$532$	12.1453	0.526566
$533$	13.9357	0.603621
$534$	11.0244	0.477073
$535$	25.0461	1.08284
$536$	10.4798	0.452659
$537$	0.732036	0.0315897
$538$	14.5654	0.627959
$539$	−28.3296	−1.22024
$540$	15.6040	0.671490
$541$	31.8239	1.36822	0.684109	−	0.729380i	$-0.260191\pi$
$541$	31.8239	1.36822	0.684109	+	0.729380i	$0.260191\pi$
$542$	−6.30956	−0.271019
$543$	−1.65043	−0.0708268
$544$	−44.1699	−1.89377
$545$	−25.5008	−1.09233
$546$	−8.36353	−0.357926
$547$	−32.5223	−1.39056	−0.695278	−	0.718741i	$-0.744719\pi$
$547$	−32.5223	−1.39056	−0.695278	+	0.718741i	$0.744719\pi$
$548$	−24.1034	−1.02965
$549$	−6.54787	−0.279456
$550$	−1.97894	−0.0843821
$551$	−2.21989	−0.0945705
$552$	−3.74912	−0.159573
$553$	34.7941	1.47959
$554$	−15.5015	−0.658597
$555$	−11.9088	−0.505501
$556$	12.8280	0.544027
$557$	13.1453	0.556985	0.278492	−	0.960438i	$-0.410165\pi$
$557$	13.1453	0.556985	0.278492	+	0.960438i	$0.410165\pi$
$558$	2.52842	0.107036
$559$	2.24420	0.0949194
$560$	4.31155	0.182196
$561$	−31.6030	−1.33428
$562$	−18.2242	−0.768740
$563$	0.527928	0.0222495	0.0111247	−	0.999938i	$-0.496459\pi$
$563$	0.527928	0.0222495	0.0111247	+	0.999938i	$0.496459\pi$
$564$	−3.77877	−0.159115
$565$	−41.7353	−1.75582
$566$	3.70582	0.155767
$567$	−18.7474	−0.787316
$568$	−39.9287	−1.67537
$569$	33.0756	1.38660	0.693301	−	0.720648i	$-0.256156\pi$
$569$	33.0756	1.38660	0.693301	+	0.720648i	$0.256156\pi$
$570$	5.08172	0.212850
$571$	30.1395	1.26130	0.630648	−	0.776069i	$-0.282789\pi$
$571$	30.1395	1.26130	0.630648	+	0.776069i	$0.282789\pi$
$572$	7.46571	0.312157
$573$	−4.84056	−0.202217
$574$	−24.7263	−1.03206
$575$	0.817347	0.0340857
$576$	−3.92706	−0.163628
$577$	33.4063	1.39072	0.695362	−	0.718660i	$-0.255244\pi$
$577$	33.4063	1.39072	0.695362	+	0.718660i	$0.255244\pi$
$578$	−32.7052	−1.36036
$579$	0.0163604	0.000679917 0
$580$	−2.75986	−0.114597
$581$	−9.57798	−0.397362
$582$	18.9166	0.784118
$583$	−12.0993	−0.501104
$584$	16.9839	0.702801
$585$	−4.04842	−0.167381
$586$	−5.14925	−0.212714
$587$	−22.3434	−0.922210	−0.461105	−	0.887346i	$-0.652547\pi$
$587$	−22.3434	−0.922210	−0.461105	+	0.887346i	$0.652547\pi$
$588$	−17.6738	−0.728856
$589$	−6.47896	−0.266961
$590$	−7.61508	−0.313508
$591$	31.7452	1.30582
$592$	−2.18180	−0.0896715
$593$	25.0660	1.02934	0.514668	−	0.857389i	$-0.327915\pi$
$593$	25.0660	1.02934	0.514668	+	0.857389i	$0.327915\pi$
$594$	−13.6891	−0.561669
$595$	62.9016	2.57871
$596$	20.6048	0.844007
$597$	−28.7772	−1.17777
$598$	1.48647	0.0607861
$599$	3.08054	0.125868	0.0629338	−	0.998018i	$-0.479954\pi$
$599$	3.08054	0.125868	0.0629338	+	0.998018i	$0.479954\pi$
$600$	−3.06433	−0.125101
$601$	1.72624	0.0704146	0.0352073	−	0.999380i	$-0.488791\pi$
$601$	1.72624	0.0704146	0.0352073	+	0.999380i	$0.488791\pi$
$602$	−3.98192	−0.162291
$603$	−4.16661	−0.169677
$604$	14.2738	0.580794
$605$	−4.06753	−0.165368
$606$	−16.7743	−0.681408
$607$	−15.5236	−0.630085	−0.315043	−	0.949078i	$-0.602019\pi$
$607$	−15.5236	−0.630085	−0.315043	+	0.949078i	$0.602019\pi$
$608$	12.9252	0.524188
$609$	5.62645	0.227995
$610$	−10.0559	−0.407152
$611$	3.71869	0.150442
$612$	10.9956	0.444473
$613$	19.2422	0.777185	0.388592	−	0.921410i	$-0.372961\pi$
$613$	19.2422	0.777185	0.388592	+	0.921410i	$0.372961\pi$
$614$	9.14129	0.368912
$615$	21.4611	0.865396
$616$	−32.8789	−1.32473
$617$	35.7408	1.43887	0.719435	−	0.694560i	$-0.244401\pi$
$617$	35.7408	1.43887	0.719435	+	0.694560i	$0.244401\pi$
$618$	20.5599	0.827039
$619$	−1.95266	−0.0784838	−0.0392419	−	0.999230i	$-0.512494\pi$
$619$	−1.95266	−0.0784838	−0.0392419	+	0.999230i	$0.512494\pi$
$620$	−8.05492	−0.323494
$621$	5.65391	0.226883
$622$	2.53414	0.101610
$623$	−39.9317	−1.59983
$624$	1.32993	0.0532399
$625$	−20.2452	−0.809808
$626$	11.7595	0.470003
$627$	9.24782	0.369322
$628$	7.78720	0.310743
$629$	−31.8305	−1.26917
$630$	7.18318	0.286185
$631$	−19.3286	−0.769459	−0.384729	−	0.923029i	$-0.625705\pi$
$631$	−19.3286	−0.769459	−0.384729	+	0.923029i	$0.625705\pi$
$632$	23.1846	0.922235
$633$	−15.0583	−0.598513
$634$	0.406276	0.0161353
$635$	−20.2508	−0.803630
$636$	−7.54835	−0.299311
$637$	17.3928	0.689129
$638$	2.42117	0.0958550
$639$	15.8750	0.628005
$640$	17.7847	0.703002
$641$	10.7786	0.425727	0.212864	−	0.977082i	$-0.431721\pi$
$641$	10.7786	0.425727	0.212864	+	0.977082i	$0.431721\pi$
$642$	−13.7078	−0.541003
$643$	−27.2439	−1.07439	−0.537197	−	0.843457i	$-0.680517\pi$
$643$	−27.2439	−1.07439	−0.537197	+	0.843457i	$0.680517\pi$
$644$	5.47114	0.215593
$645$	3.45609	0.136084
$646$	13.5827	0.534404
$647$	21.8677	0.859706	0.429853	−	0.902899i	$-0.358565\pi$
$647$	21.8677	0.859706	0.429853	+	0.902899i	$0.358565\pi$
$648$	−12.4921	−0.490736
$649$	−13.8581	−0.543977
$650$	1.21496	0.0476546
$651$	16.4213	0.643602
$652$	22.1300	0.866676
$653$	−37.1875	−1.45526	−0.727631	−	0.685969i	$-0.759378\pi$
$653$	−37.1875	−1.45526	−0.727631	+	0.685969i	$0.759378\pi$
$654$	13.9566	0.545748
$655$	34.6443	1.35366
$656$	3.93187	0.153514
$657$	−6.75254	−0.263442
$658$	−6.59814	−0.257222
$659$	0.0830271	0.00323428	0.00161714	−	0.999999i	$-0.499485\pi$
$659$	0.0830271	0.00323428	0.00161714	+	0.999999i	$0.499485\pi$
$660$	11.4973	0.447532
$661$	11.9274	0.463921	0.231960	−	0.972725i	$-0.425486\pi$
$661$	11.9274	0.463921	0.231960	+	0.972725i	$0.425486\pi$
$662$	−17.7212	−0.688754
$663$	19.4025	0.753530
$664$	−6.38218	−0.247676
$665$	−18.4066	−0.713777
$666$	−3.63496	−0.140852
$667$	−1.00000	−0.0387202
$668$	6.95462	0.269082
$669$	−9.75949	−0.377324
$670$	−6.39888	−0.247210
$671$	−18.3000	−0.706463
$672$	−32.7598	−1.26374
$673$	7.06226	0.272230	0.136115	−	0.990693i	$-0.456538\pi$
$673$	7.06226	0.272230	0.136115	+	0.990693i	$0.456538\pi$
$674$	7.74010	0.298137
$675$	4.62120	0.177870
$676$	12.9595	0.498442
$677$	−17.6531	−0.678464	−0.339232	−	0.940703i	$-0.610167\pi$
$677$	−17.6531	−0.678464	−0.339232	+	0.940703i	$0.610167\pi$
$678$	22.8419	0.877237
$679$	−68.5181	−2.62948
$680$	41.9137	1.60732
$681$	19.8550	0.760846
$682$	7.06641	0.270587
$683$	30.2672	1.15814	0.579072	−	0.815277i	$-0.303415\pi$
$683$	30.2672	1.15814	0.579072	+	0.815277i	$0.303415\pi$
$684$	−3.21760	−0.123028
$685$	36.5294	1.39572
$686$	−7.97023	−0.304305
$687$	8.47118	0.323196
$688$	0.633187	0.0241400
$689$	7.42834	0.282997
$690$	2.28918	0.0871475
$691$	7.10897	0.270438	0.135219	−	0.990816i	$-0.456826\pi$
$691$	7.10897	0.270438	0.135219	+	0.990816i	$0.456826\pi$
$692$	9.51006	0.361518
$693$	13.0721	0.496568
$694$	8.14417	0.309148
$695$	−19.4412	−0.737446
$696$	3.74912	0.142110
$697$	57.3625	2.17276
$698$	7.26051	0.274814
$699$	30.7165	1.16180
$700$	4.47182	0.169019
$701$	38.2389	1.44426	0.722131	−	0.691756i	$-0.243163\pi$
$701$	38.2389	1.44426	0.722131	+	0.691756i	$0.243163\pi$
$702$	8.40434	0.317201
$703$	9.31441	0.351300
$704$	−10.9753	−0.413649
$705$	5.72683	0.215685
$706$	12.2950	0.462727
$707$	60.7583	2.28505
$708$	−8.64555	−0.324920
$709$	16.8926	0.634413	0.317207	−	0.948356i	$-0.397255\pi$
$709$	16.8926	0.634413	0.317207	+	0.948356i	$0.397255\pi$
$710$	24.3801	0.914969
$711$	−9.21783	−0.345696
$712$	−26.6080	−0.997178
$713$	−2.91860	−0.109302
$714$	−34.4262	−1.28837
$715$	−11.3145	−0.423138
$716$	−0.711829	−0.0266023
$717$	−20.5723	−0.768286
$718$	−6.69677	−0.249921
$719$	−44.6469	−1.66505	−0.832524	−	0.553989i	$-0.813105\pi$
$719$	−44.6469	−1.66505	−0.832524	+	0.553989i	$0.813105\pi$
$720$	−1.14224	−0.0425687
$721$	−74.4702	−2.77342
$722$	11.3500	0.422401
$723$	−2.46406	−0.0916392
$724$	1.60487	0.0596447
$725$	−0.817347	−0.0303555
$726$	2.22617	0.0826209
$727$	53.7250	1.99255	0.996274	−	0.0862392i	$-0.0274849\pi$
$727$	53.7250	1.99255	0.996274	+	0.0862392i	$0.0274849\pi$
$728$	20.1858	0.748137
$729$	28.5057	1.05577
$730$	−10.3702	−0.383820
$731$	9.23763	0.341666
$732$	−11.4167	−0.421973
$733$	11.9235	0.440403	0.220202	−	0.975454i	$-0.429328\pi$
$733$	11.9235	0.440403	0.220202	+	0.975454i	$0.429328\pi$
$734$	21.5552	0.795616
$735$	26.7852	0.987986
$736$	5.82247	0.214619
$737$	−11.6448	−0.428942
$738$	6.55063	0.241132
$739$	−31.0283	−1.14139	−0.570697	−	0.821161i	$-0.693327\pi$
$739$	−31.0283	−1.14139	−0.570697	+	0.821161i	$0.693327\pi$
$740$	11.5801	0.425692
$741$	−5.67766	−0.208574
$742$	−13.1802	−0.483862
$743$	−37.1174	−1.36171	−0.680853	−	0.732420i	$-0.738391\pi$
$743$	−37.1174	−1.36171	−0.680853	+	0.732420i	$0.738391\pi$
$744$	10.9422	0.401159
$745$	−31.2272	−1.14408
$746$	−21.8787	−0.801035
$747$	2.53745	0.0928405
$748$	30.7306	1.12362
$749$	49.6512	1.81422
$750$	13.3169	0.486266
$751$	−7.93504	−0.289554	−0.144777	−	0.989464i	$-0.546246\pi$
$751$	−7.93504	−0.289554	−0.144777	+	0.989464i	$0.546246\pi$
$752$	1.04921	0.0382606
$753$	20.7538	0.756310
$754$	−1.48647	−0.0541339
$755$	−21.6324	−0.787284
$756$	30.9333	1.12503
$757$	26.9655	0.980077	0.490038	−	0.871701i	$-0.336983\pi$
$757$	26.9655	0.980077	0.490038	+	0.871701i	$0.336983\pi$
$758$	−21.0873	−0.765924
$759$	4.16589	0.151212
$760$	−12.2650	−0.444899
$761$	−16.1655	−0.586000	−0.293000	−	0.956112i	$-0.594654\pi$
$761$	−16.1655	−0.586000	−0.293000	+	0.956112i	$0.594654\pi$
$762$	11.0833	0.401507
$763$	−50.5526	−1.83013
$764$	4.70694	0.170291
$765$	−16.6642	−0.602496
$766$	−7.88539	−0.284911
$767$	8.50810	0.307210
$768$	−19.8815	−0.717413
$769$	47.1411	1.69995	0.849976	−	0.526821i	$-0.176616\pi$
$769$	47.1411	1.69995	0.849976	+	0.526821i	$0.176616\pi$
$770$	20.0755	0.723472
$771$	4.03926	0.145471
$772$	−0.0159088	−0.000572571 0
$773$	−29.2704	−1.05278	−0.526391	−	0.850243i	$-0.676455\pi$
$773$	−29.2704	−1.05278	−0.526391	+	0.850243i	$0.676455\pi$
$774$	1.05491	0.0379180
$775$	−2.38551	−0.0856899
$776$	−45.6562	−1.63896
$777$	−23.6080	−0.846931
$778$	−26.8901	−0.964056
$779$	−16.7857	−0.601410
$780$	−7.05871	−0.252742
$781$	44.3674	1.58759
$782$	6.11864	0.218802
$783$	−5.65391	−0.202054
$784$	4.90729	0.175260
$785$	−11.8017	−0.421222
$786$	−18.9609	−0.676314
$787$	−41.1128	−1.46551	−0.732756	−	0.680491i	$-0.761767\pi$
$787$	−41.1128	−1.46551	−0.732756	+	0.680491i	$0.761767\pi$
$788$	−30.8689	−1.09966
$789$	−42.5902	−1.51625
$790$	−14.1563	−0.503659
$791$	−82.7359	−2.94175
$792$	8.71044	0.309512
$793$	11.2352	0.398973
$794$	2.65989	0.0943961
$795$	11.4397	0.405726
$796$	27.9829	0.991826
$797$	−5.29125	−0.187426	−0.0937128	−	0.995599i	$-0.529874\pi$
$797$	−5.29125	−0.187426	−0.0937128	+	0.995599i	$0.529874\pi$
$798$	10.0740	0.356615
$799$	15.3070	0.541522
$800$	4.75898	0.168255
$801$	10.5789	0.373788
$802$	5.39608	0.190542
$803$	−18.8720	−0.665978
$804$	−7.26478	−0.256209
$805$	−8.29167	−0.292243
$806$	−4.33839	−0.152813
$807$	−25.0614	−0.882203
$808$	40.4856	1.42428
$809$	−51.6941	−1.81747	−0.908734	−	0.417375i	$-0.862950\pi$
$809$	−51.6941	−1.81747	−0.908734	+	0.417375i	$0.862950\pi$
$810$	7.62757	0.268005
$811$	−52.2658	−1.83530	−0.917650	−	0.397390i	$-0.869916\pi$
$811$	−52.2658	−1.83530	−0.917650	+	0.397390i	$0.869916\pi$
$812$	−5.47114	−0.191999
$813$	10.8563	0.380747
$814$	−10.1590	−0.356071
$815$	−33.5386	−1.17481
$816$	5.47430	0.191639
$817$	−2.70316	−0.0945718
$818$	1.52074	0.0531713
$819$	−8.02556	−0.280436
$820$	−20.8687	−0.728767
$821$	−47.3575	−1.65279	−0.826394	−	0.563093i	$-0.809611\pi$
$821$	−47.3575	−1.65279	−0.826394	+	0.563093i	$0.809611\pi$
$822$	−19.9926	−0.697323
$823$	40.3942	1.40805	0.704027	−	0.710174i	$-0.251384\pi$
$823$	40.3942	1.40805	0.704027	+	0.710174i	$0.251384\pi$
$824$	−49.6224	−1.72868
$825$	3.40498	0.118546
$826$	−15.0961	−0.525260
$827$	−18.6652	−0.649053	−0.324526	−	0.945877i	$-0.605205\pi$
$827$	−18.6652	−0.649053	−0.324526	+	0.945877i	$0.605205\pi$
$828$	−1.44944	−0.0503716
$829$	5.05460	0.175553	0.0877767	−	0.996140i	$-0.472024\pi$
$829$	5.05460	0.175553	0.0877767	+	0.996140i	$0.472024\pi$
$830$	3.89690	0.135263
$831$	26.6721	0.925245
$832$	6.73827	0.233607
$833$	71.5929	2.48055
$834$	10.6402	0.368440
$835$	−10.5399	−0.364749
$836$	−8.99255	−0.311014
$837$	−16.5015	−0.570374
$838$	14.8971	0.514611
$839$	11.3499	0.391841	0.195920	−	0.980620i	$-0.437231\pi$
$839$	11.3499	0.391841	0.195920	+	0.980620i	$0.437231\pi$
$840$	31.0864	1.07258
$841$	1.00000	0.0344828
$842$	−30.4854	−1.05060
$843$	31.3567	1.07998
$844$	14.6426	0.504019
$845$	−19.6405	−0.675654
$846$	1.74801	0.0600980
$847$	−8.06344	−0.277063
$848$	2.09586	0.0719723
$849$	−6.37628	−0.218833
$850$	5.00105	0.171535
$851$	4.19589	0.143833
$852$	27.6792	0.948275
$853$	6.25961	0.214325	0.107162	−	0.994242i	$-0.465824\pi$
$853$	6.25961	0.214325	0.107162	+	0.994242i	$0.465824\pi$
$854$	−19.9348	−0.682155
$855$	4.87637	0.166768
$856$	33.0845	1.13080
$857$	47.0510	1.60723	0.803615	−	0.595149i	$-0.202907\pi$
$857$	47.0510	1.60723	0.803615	+	0.595149i	$0.202907\pi$
$858$	6.19246	0.211407
$859$	−25.1552	−0.858284	−0.429142	−	0.903237i	$-0.641184\pi$
$859$	−25.1552	−0.858284	−0.429142	+	0.903237i	$0.641184\pi$
$860$	−3.36069	−0.114599
$861$	42.5444	1.44991
$862$	−14.4620	−0.492579
$863$	40.7578	1.38741	0.693705	−	0.720259i	$-0.255977\pi$
$863$	40.7578	1.38741	0.693705	+	0.720259i	$0.255977\pi$
$864$	32.9197	1.11995
$865$	−14.4128	−0.490049
$866$	5.37367	0.182605
$867$	56.2730	1.91113
$868$	−15.9680	−0.541990
$869$	−25.7620	−0.873915
$870$	−2.28918	−0.0776104
$871$	7.14928	0.242244
$872$	−33.6851	−1.14072
$873$	18.1522	0.614358
$874$	−1.79047	−0.0605635
$875$	−48.2355	−1.63066
$876$	−11.7736	−0.397792
$877$	−40.6135	−1.37142	−0.685710	−	0.727875i	$-0.740508\pi$
$877$	−40.6135	−1.37142	−0.685710	+	0.727875i	$0.740508\pi$
$878$	−21.5878	−0.728553
$879$	8.85987	0.298836
$880$	−3.19232	−0.107613
$881$	−31.5751	−1.06379	−0.531896	−	0.846809i	$-0.678520\pi$
$881$	−31.5751	−1.06379	−0.531896	+	0.846809i	$0.678520\pi$
$882$	8.17571	0.275290
$883$	17.2242	0.579641	0.289820	−	0.957081i	$-0.406404\pi$
$883$	17.2242	0.579641	0.289820	+	0.957081i	$0.406404\pi$
$884$	−18.8669	−0.634563
$885$	13.1026	0.440439
$886$	0.259747	0.00872638
$887$	16.1007	0.540608	0.270304	−	0.962775i	$-0.412876\pi$
$887$	16.1007	0.540608	0.270304	+	0.962775i	$0.412876\pi$
$888$	−15.7309	−0.527894
$889$	−40.1451	−1.34642
$890$	16.2466	0.544588
$891$	13.8808	0.465024
$892$	9.49009	0.317752
$893$	−4.47921	−0.149891
$894$	17.0907	0.571600
$895$	1.07880	0.0360603
$896$	35.2563	1.17783
$897$	−2.55763	−0.0853968
$898$	30.1798	1.00711
$899$	2.91860	0.0973406
$900$	−1.18470	−0.0394899
$901$	30.5768	1.01866
$902$	18.3077	0.609579
$903$	6.85134	0.227998
$904$	−55.1301	−1.83360
$905$	−2.43223	−0.0808502
$906$	11.8395	0.393340
$907$	1.20503	0.0400124	0.0200062	−	0.999800i	$-0.493631\pi$
$907$	1.20503	0.0400124	0.0200062	+	0.999800i	$0.493631\pi$
$908$	−19.3070	−0.640724
$909$	−16.0964	−0.533885
$910$	−12.3253	−0.408579
$911$	28.2695	0.936610	0.468305	−	0.883567i	$-0.344865\pi$
$911$	28.2695	0.936610	0.468305	+	0.883567i	$0.344865\pi$
$912$	−1.60192	−0.0530449
$913$	7.09166	0.234700
$914$	5.81008	0.192180
$915$	17.3023	0.571998
$916$	−8.23734	−0.272169
$917$	68.6787	2.26797
$918$	34.5942	1.14178
$919$	25.7108	0.848122	0.424061	−	0.905634i	$-0.360604\pi$
$919$	25.7108	0.848122	0.424061	+	0.905634i	$0.360604\pi$
$920$	−5.52506	−0.182156
$921$	−15.7286	−0.518275
$922$	−1.83109	−0.0603038
$923$	−27.2392	−0.896588
$924$	22.7922	0.749807
$925$	3.42950	0.112761
$926$	11.8282	0.388700
$927$	19.7291	0.647987
$928$	−5.82247	−0.191132
$929$	−30.0952	−0.987390	−0.493695	−	0.869635i	$-0.664354\pi$
$929$	−30.0952	−0.987390	−0.493695	+	0.869635i	$0.664354\pi$
$930$	−6.68118	−0.219085
$931$	−20.9499	−0.686605
$932$	−29.8686	−0.978379
$933$	−4.36026	−0.142749
$934$	−15.2846	−0.500128
$935$	−46.5731	−1.52310
$936$	−5.34774	−0.174796
$937$	−58.4410	−1.90918	−0.954592	−	0.297915i	$-0.903709\pi$
$937$	−58.4410	−1.90918	−0.954592	+	0.297915i	$0.903709\pi$
$938$	−12.6851	−0.414183
$939$	−20.2335	−0.660294
$940$	−5.56875	−0.181633
$941$	14.8023	0.482540	0.241270	−	0.970458i	$-0.422436\pi$
$941$	14.8023	0.482540	0.241270	+	0.970458i	$0.422436\pi$
$942$	6.45912	0.210449
$943$	−7.56150	−0.246236
$944$	2.40051	0.0781300
$945$	−46.8803	−1.52502
$946$	2.94826	0.0958563
$947$	51.8728	1.68564	0.842819	−	0.538196i	$-0.180894\pi$
$947$	51.8728	1.68564	0.842819	+	0.538196i	$0.180894\pi$
$948$	−16.0720	−0.521993
$949$	11.5864	0.376110
$950$	−1.46343	−0.0474801
$951$	−0.699043	−0.0226680
$952$	83.0895	2.69295
$953$	27.8978	0.903697	0.451849	−	0.892095i	$-0.350765\pi$
$953$	27.8978	0.903697	0.451849	+	0.892095i	$0.350765\pi$
$954$	3.49178	0.113051
$955$	−7.13350	−0.230835
$956$	20.0044	0.646989
$957$	−4.16589	−0.134664
$958$	−16.3517	−0.528299
$959$	72.4156	2.33842
$960$	10.3770	0.334917
$961$	−22.4818	−0.725219
$962$	6.23705	0.201091
$963$	−13.1539	−0.423877
$964$	2.39604	0.0771712
$965$	0.0241103	0.000776138 0
$966$	4.53805	0.146009
$967$	36.0174	1.15824	0.579120	−	0.815242i	$-0.303396\pi$
$967$	36.0174	1.15824	0.579120	+	0.815242i	$0.303396\pi$
$968$	−5.37298	−0.172694
$969$	−23.3706	−0.750771
$970$	27.8773	0.895086
$971$	10.4186	0.334347	0.167174	−	0.985927i	$-0.446536\pi$
$971$	10.4186	0.334347	0.167174	+	0.985927i	$0.446536\pi$
$972$	−14.2295	−0.456412
$973$	−38.5401	−1.23554
$974$	−5.33959	−0.171091
$975$	−2.09047	−0.0669487
$976$	3.16994	0.101467
$977$	1.30072	0.0416137	0.0208068	−	0.999784i	$-0.493376\pi$
$977$	1.30072	0.0416137	0.0208068	+	0.999784i	$0.493376\pi$
$978$	18.3558	0.586953
$979$	29.5659	0.944932
$980$	−26.0458	−0.832003
$981$	13.3927	0.427595
$982$	3.69333	0.117859
$983$	17.6168	0.561887	0.280944	−	0.959724i	$-0.409353\pi$
$983$	17.6168	0.561887	0.280944	+	0.959724i	$0.409353\pi$
$984$	28.3490	0.903732
$985$	46.7828	1.49062
$986$	−6.11864	−0.194857
$987$	11.3528	0.361365
$988$	5.52094	0.175644
$989$	−1.21770	−0.0387207
$990$	−5.31852	−0.169034
$991$	19.6932	0.625576	0.312788	−	0.949823i	$-0.398737\pi$
$991$	19.6932	0.625576	0.312788	+	0.949823i	$0.398737\pi$
$992$	−16.9934	−0.539542
$993$	30.4913	0.967612
$994$	48.3310	1.53297
$995$	−42.4088	−1.34445
$996$	4.42423	0.140187
$997$	50.3107	1.59336	0.796678	−	0.604404i	$-0.206589\pi$
$997$	50.3107	1.59336	0.796678	+	0.604404i	$0.206589\pi$
$998$	26.9693	0.853698
$999$	23.7232	0.750568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.4	✓	13
3.2	odd	2		6003.2.a.o.1.10		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.4	✓	13	1.1	even	1	trivial
6003.2.a.o.1.10		13	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)

\(f(q)\)	\(=\)	\(q-0.806558 q^{2} +1.38777 q^{3} -1.34946 q^{4} +2.04515 q^{5} -1.11932 q^{6} +4.05430 q^{7} +2.70154 q^{8} -1.07409 q^{9} +O(q^{10})\)	\(q-0.806558 q^{2} +1.38777 q^{3} -1.34946 q^{4} +2.04515 q^{5} -1.11932 q^{6} +4.05430 q^{7} +2.70154 q^{8} -1.07409 q^{9} -1.64953 q^{10} -3.00186 q^{11} -1.87275 q^{12} +1.84298 q^{13} -3.27003 q^{14} +2.83821 q^{15} +0.519985 q^{16} +7.58612 q^{17} +0.866313 q^{18} -2.21989 q^{19} -2.75986 q^{20} +5.62645 q^{21} +2.42117 q^{22} -1.00000 q^{23} +3.74912 q^{24} -0.817347 q^{25} -1.48647 q^{26} -5.65391 q^{27} -5.47114 q^{28} +1.00000 q^{29} -2.28918 q^{30} +2.91860 q^{31} -5.82247 q^{32} -4.16589 q^{33} -6.11864 q^{34} +8.29167 q^{35} +1.44944 q^{36} -4.19589 q^{37} +1.79047 q^{38} +2.55763 q^{39} +5.52506 q^{40} +7.56150 q^{41} -4.53805 q^{42} +1.21770 q^{43} +4.05090 q^{44} -2.19667 q^{45} +0.806558 q^{46} +2.01776 q^{47} +0.721621 q^{48} +9.43736 q^{49} +0.659237 q^{50} +10.5278 q^{51} -2.48703 q^{52} +4.03062 q^{53} +4.56020 q^{54} -6.13926 q^{55} +10.9528 q^{56} -3.08070 q^{57} -0.806558 q^{58} +4.61650 q^{59} -3.83006 q^{60} +6.09622 q^{61} -2.35402 q^{62} -4.35467 q^{63} +3.65619 q^{64} +3.76917 q^{65} +3.36003 q^{66} +3.87921 q^{67} -10.2372 q^{68} -1.38777 q^{69} -6.68771 q^{70} -14.7800 q^{71} -2.90169 q^{72} +6.28677 q^{73} +3.38423 q^{74} -1.13429 q^{75} +2.99566 q^{76} -12.1704 q^{77} -2.06288 q^{78} +8.58201 q^{79} +1.06345 q^{80} -4.62407 q^{81} -6.09879 q^{82} -2.36242 q^{83} -7.59269 q^{84} +15.5148 q^{85} -0.982147 q^{86} +1.38777 q^{87} -8.10962 q^{88} -9.84922 q^{89} +1.77174 q^{90} +7.47198 q^{91} +1.34946 q^{92} +4.05035 q^{93} -1.62744 q^{94} -4.54001 q^{95} -8.08026 q^{96} -16.9001 q^{97} -7.61177 q^{98} +3.22426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9} + 10 q^{10} + 10 q^{11} + 3 q^{12} + 7 q^{13} - 12 q^{14} + 8 q^{15} + 2 q^{16} + 26 q^{17} + 7 q^{18} + 25 q^{20} + 11 q^{21} - 15 q^{22} - 13 q^{23} + 10 q^{24} + 19 q^{25} - 15 q^{26} + 12 q^{27} + 5 q^{28} + 13 q^{29} + 7 q^{30} - 6 q^{31} + 16 q^{32} + 3 q^{33} + 11 q^{34} + q^{35} - 22 q^{36} + 15 q^{37} + 8 q^{38} - 4 q^{39} + 14 q^{40} + 9 q^{41} - 34 q^{42} + q^{43} + 29 q^{44} + 16 q^{45} - 4 q^{46} + 15 q^{47} - 15 q^{48} + 4 q^{49} + 31 q^{50} - 14 q^{51} - 8 q^{52} + 43 q^{53} - 35 q^{54} - 3 q^{55} - 5 q^{56} + 6 q^{57} + 4 q^{58} - 9 q^{59} + 3 q^{60} + 20 q^{61} + 11 q^{62} + 21 q^{63} - 16 q^{64} - 25 q^{65} - q^{66} + q^{67} + 21 q^{68} - 3 q^{69} - 2 q^{70} + 17 q^{71} - 59 q^{72} + 26 q^{73} + 11 q^{74} - 43 q^{75} + 8 q^{76} + 17 q^{77} - 10 q^{78} + 5 q^{79} + 10 q^{80} - 3 q^{81} - 25 q^{82} + 4 q^{83} - 78 q^{84} + 20 q^{85} - 13 q^{86} + 3 q^{87} - 32 q^{88} + 48 q^{89} + 17 q^{90} - 9 q^{91} - 12 q^{92} - 8 q^{93} - 65 q^{94} + 8 q^{95} + 8 q^{96} + 30 q^{97} + 2 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 3 * q^3 + 12 * q^4 + 16 * q^5 + q^7 + 6 * q^8 + 14 * q^9 + 10 * q^10 + 10 * q^11 + 3 * q^12 + 7 * q^13 - 12 * q^14 + 8 * q^15 + 2 * q^16 + 26 * q^17 + 7 * q^18 + 25 * q^20 + 11 * q^21 - 15 * q^22 - 13 * q^23 + 10 * q^24 + 19 * q^25 - 15 * q^26 + 12 * q^27 + 5 * q^28 + 13 * q^29 + 7 * q^30 - 6 * q^31 + 16 * q^32 + 3 * q^33 + 11 * q^34 + q^35 - 22 * q^36 + 15 * q^37 + 8 * q^38 - 4 * q^39 + 14 * q^40 + 9 * q^41 - 34 * q^42 + q^43 + 29 * q^44 + 16 * q^45 - 4 * q^46 + 15 * q^47 - 15 * q^48 + 4 * q^49 + 31 * q^50 - 14 * q^51 - 8 * q^52 + 43 * q^53 - 35 * q^54 - 3 * q^55 - 5 * q^56 + 6 * q^57 + 4 * q^58 - 9 * q^59 + 3 * q^60 + 20 * q^61 + 11 * q^62 + 21 * q^63 - 16 * q^64 - 25 * q^65 - q^66 + q^67 + 21 * q^68 - 3 * q^69 - 2 * q^70 + 17 * q^71 - 59 * q^72 + 26 * q^73 + 11 * q^74 - 43 * q^75 + 8 * q^76 + 17 * q^77 - 10 * q^78 + 5 * q^79 + 10 * q^80 - 3 * q^81 - 25 * q^82 + 4 * q^83 - 78 * q^84 + 20 * q^85 - 13 * q^86 + 3 * q^87 - 32 * q^88 + 48 * q^89 + 17 * q^90 - 9 * q^91 - 12 * q^92 - 8 * q^93 - 65 * q^94 + 8 * q^95 + 8 * q^96 + 30 * q^97 + 2 * q^98 + 4 * q^99

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