LMFDB - Embedded newform 667.2.a.c.1.13

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			1.13
Root			$2.60496$ 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)

$f(q)$	$=$	$q+2.60496 q^{2} -1.02046 q^{3} +4.78583 q^{4} +1.68070 q^{5} -2.65826 q^{6} +2.80821 q^{7} +7.25699 q^{8} -1.95866 q^{9} +O(q^{10})$	\(q+2.60496 q^{2} -1.02046 q^{3} +4.78583 q^{4} +1.68070 q^{5} -2.65826 q^{6} +2.80821 q^{7} +7.25699 q^{8} -1.95866 q^{9} +4.37815 q^{10} -1.84810 q^{11} -4.88374 q^{12} -0.773187 q^{13} +7.31527 q^{14} -1.71508 q^{15} +9.33253 q^{16} -0.882567 q^{17} -5.10225 q^{18} -3.94266 q^{19} +8.04353 q^{20} -2.86566 q^{21} -4.81425 q^{22} -1.00000 q^{23} -7.40546 q^{24} -2.17526 q^{25} -2.01412 q^{26} +5.06011 q^{27} +13.4396 q^{28} +1.00000 q^{29} -4.46772 q^{30} +5.16975 q^{31} +9.79691 q^{32} +1.88591 q^{33} -2.29905 q^{34} +4.71974 q^{35} -9.37384 q^{36} +3.00050 q^{37} -10.2705 q^{38} +0.789005 q^{39} +12.1968 q^{40} +1.65149 q^{41} -7.46493 q^{42} -3.35090 q^{43} -8.84472 q^{44} -3.29192 q^{45} -2.60496 q^{46} -1.98916 q^{47} -9.52346 q^{48} +0.886016 q^{49} -5.66648 q^{50} +0.900622 q^{51} -3.70034 q^{52} +1.44385 q^{53} +13.1814 q^{54} -3.10610 q^{55} +20.3791 q^{56} +4.02332 q^{57} +2.60496 q^{58} +2.83981 q^{59} -8.20809 q^{60} +4.60276 q^{61} +13.4670 q^{62} -5.50033 q^{63} +6.85553 q^{64} -1.29949 q^{65} +4.91274 q^{66} -13.2444 q^{67} -4.22382 q^{68} +1.02046 q^{69} +12.2947 q^{70} -14.4949 q^{71} -14.2140 q^{72} -12.2449 q^{73} +7.81620 q^{74} +2.21976 q^{75} -18.8689 q^{76} -5.18986 q^{77} +2.05533 q^{78} -2.29854 q^{79} +15.6851 q^{80} +0.712362 q^{81} +4.30208 q^{82} +6.46906 q^{83} -13.7146 q^{84} -1.48333 q^{85} -8.72897 q^{86} -1.02046 q^{87} -13.4117 q^{88} +16.1242 q^{89} -8.57533 q^{90} -2.17127 q^{91} -4.78583 q^{92} -5.27551 q^{93} -5.18168 q^{94} -6.62640 q^{95} -9.99734 q^{96} +11.0455 q^{97} +2.30804 q^{98} +3.61982 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.60496	1.84199	0.920994	−	0.389578i	$-0.127379\pi$
$2$	2.60496	1.84199	0.920994	+	0.389578i	$0.127379\pi$
$3$	−1.02046	−0.589162	−0.294581	−	0.955627i	$-0.595180\pi$
$3$	−1.02046	−0.589162	−0.294581	+	0.955627i	$0.595180\pi$
$4$	4.78583	2.39292
$5$	1.68070	0.751630	0.375815	−	0.926695i	$-0.377363\pi$
$5$	1.68070	0.751630	0.375815	+	0.926695i	$0.377363\pi$
$6$	−2.65826	−1.08523
$7$	2.80821	1.06140	0.530701	−	0.847559i	$-0.321929\pi$
$7$	2.80821	1.06140	0.530701	+	0.847559i	$0.321929\pi$
$8$	7.25699	2.56573
$9$	−1.95866	−0.652888
$10$	4.37815	1.38449
$11$	−1.84810	−0.557225	−0.278612	−	0.960404i	$-0.589874\pi$
$11$	−1.84810	−0.557225	−0.278612	+	0.960404i	$0.589874\pi$
$12$	−4.88374	−1.40982
$13$	−0.773187	−0.214443	−0.107222	−	0.994235i	$-0.534195\pi$
$13$	−0.773187	−0.214443	−0.107222	+	0.994235i	$0.534195\pi$
$14$	7.31527	1.95509
$15$	−1.71508	−0.442832
$16$	9.33253	2.33313
$17$	−0.882567	−0.214054	−0.107027	−	0.994256i	$-0.534133\pi$
$17$	−0.882567	−0.214054	−0.107027	+	0.994256i	$0.534133\pi$
$18$	−5.10225	−1.20261
$19$	−3.94266	−0.904507	−0.452254	−	0.891889i	$-0.649380\pi$
$19$	−3.94266	−0.904507	−0.452254	+	0.891889i	$0.649380\pi$
$20$	8.04353	1.79859
$21$	−2.86566	−0.625337
$22$	−4.81425	−1.02640
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−7.40546	−1.51163
$25$	−2.17526	−0.435052
$26$	−2.01412	−0.395002
$27$	5.06011	0.973819
$28$	13.4396	2.53985
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−4.46772	−0.815690
$31$	5.16975	0.928514	0.464257	−	0.885700i	$-0.346321\pi$
$31$	5.16975	0.928514	0.464257	+	0.885700i	$0.346321\pi$
$32$	9.79691	1.73187
$33$	1.88591	0.328295
$34$	−2.29905	−0.394284
$35$	4.71974	0.797781
$36$	−9.37384	−1.56231
$37$	3.00050	0.493280	0.246640	−	0.969107i	$-0.420674\pi$
$37$	3.00050	0.493280	0.246640	+	0.969107i	$0.420674\pi$
$38$	−10.2705	−1.66609
$39$	0.789005	0.126342
$40$	12.1968	1.92848
$41$	1.65149	0.257920	0.128960	−	0.991650i	$-0.458836\pi$
$41$	1.65149	0.257920	0.128960	+	0.991650i	$0.458836\pi$
$42$	−7.46493	−1.15186
$43$	−3.35090	−0.511007	−0.255504	−	0.966808i	$-0.582241\pi$
$43$	−3.35090	−0.511007	−0.255504	+	0.966808i	$0.582241\pi$
$44$	−8.84472	−1.33339
$45$	−3.29192	−0.490730
$46$	−2.60496	−0.384081
$47$	−1.98916	−0.290148	−0.145074	−	0.989421i	$-0.546342\pi$
$47$	−1.98916	−0.290148	−0.145074	+	0.989421i	$0.546342\pi$
$48$	−9.52346	−1.37459
$49$	0.886016	0.126574
$50$	−5.66648	−0.801361
$51$	0.900622	0.126112
$52$	−3.70034	−0.513145
$53$	1.44385	0.198328	0.0991642	−	0.995071i	$-0.468383\pi$
$53$	1.44385	0.198328	0.0991642	+	0.995071i	$0.468383\pi$
$54$	13.1814	1.79376
$55$	−3.10610	−0.418827
$56$	20.3791	2.72327
$57$	4.02332	0.532901
$58$	2.60496	0.342048
$59$	2.83981	0.369711	0.184856	−	0.982766i	$-0.440818\pi$
$59$	2.83981	0.369711	0.184856	+	0.982766i	$0.440818\pi$
$60$	−8.20809	−1.05966
$61$	4.60276	0.589323	0.294661	−	0.955602i	$-0.404793\pi$
$61$	4.60276	0.589323	0.294661	+	0.955602i	$0.404793\pi$
$62$	13.4670	1.71031
$63$	−5.50033	−0.692977
$64$	6.85553	0.856942
$65$	−1.29949	−0.161182
$66$	4.91274	0.604716
$67$	−13.2444	−1.61806	−0.809032	−	0.587764i	$-0.800008\pi$
$67$	−13.2444	−1.61806	−0.809032	+	0.587764i	$0.800008\pi$
$68$	−4.22382	−0.512213
$69$	1.02046	0.122849
$70$	12.2947	1.46950
$71$	−14.4949	−1.72023	−0.860115	−	0.510099i	$-0.829609\pi$
$71$	−14.4949	−1.72023	−0.860115	+	0.510099i	$0.829609\pi$
$72$	−14.2140	−1.67514
$73$	−12.2449	−1.43316	−0.716579	−	0.697506i	$-0.754293\pi$
$73$	−12.2449	−1.43316	−0.716579	+	0.697506i	$0.754293\pi$
$74$	7.81620	0.908615
$75$	2.21976	0.256316
$76$	−18.8689	−2.16441
$77$	−5.18986	−0.591439
$78$	2.05533	0.232720
$79$	−2.29854	−0.258606	−0.129303	−	0.991605i	$-0.541274\pi$
$79$	−2.29854	−0.258606	−0.129303	+	0.991605i	$0.541274\pi$
$80$	15.6851	1.75365
$81$	0.712362	0.0791514
$82$	4.30208	0.475085
$83$	6.46906	0.710072	0.355036	−	0.934853i	$-0.384469\pi$
$83$	6.46906	0.710072	0.355036	+	0.934853i	$0.384469\pi$
$84$	−13.7146	−1.49638
$85$	−1.48333	−0.160889
$86$	−8.72897	−0.941269
$87$	−1.02046	−0.109405
$88$	−13.4117	−1.42969
$89$	16.1242	1.70916	0.854582	−	0.519316i	$-0.173813\pi$
$89$	16.1242	1.70916	0.854582	+	0.519316i	$0.173813\pi$
$90$	−8.57533	−0.903919
$91$	−2.17127	−0.227611
$92$	−4.78583	−0.498958
$93$	−5.27551	−0.547045
$94$	−5.18168	−0.534449
$95$	−6.62640	−0.679855
$96$	−9.99734	−1.02035
$97$	11.0455	1.12150	0.560750	−	0.827985i	$-0.310513\pi$
$97$	11.0455	1.12150	0.560750	+	0.827985i	$0.310513\pi$
$98$	2.30804	0.233147
$99$	3.61982	0.363805
$100$	−10.4104	−1.04104
$101$	−4.27667	−0.425544	−0.212772	−	0.977102i	$-0.568249\pi$
$101$	−4.27667	−0.425544	−0.212772	+	0.977102i	$0.568249\pi$
$102$	2.34609	0.232297
$103$	−10.9818	−1.08207	−0.541036	−	0.840999i	$-0.681968\pi$
$103$	−10.9818	−1.08207	−0.541036	+	0.840999i	$0.681968\pi$
$104$	−5.61101	−0.550205
$105$	−4.81630	−0.470022
$106$	3.76118	0.365318
$107$	−3.61453	−0.349430	−0.174715	−	0.984619i	$-0.555900\pi$
$107$	−3.61453	−0.349430	−0.174715	+	0.984619i	$0.555900\pi$
$108$	24.2168	2.33027
$109$	11.3108	1.08338	0.541689	−	0.840579i	$-0.317785\pi$
$109$	11.3108	1.08338	0.541689	+	0.840579i	$0.317785\pi$
$110$	−8.09128	−0.771473
$111$	−3.06189	−0.290622
$112$	26.2077	2.47639
$113$	8.28187	0.779093	0.389546	−	0.921007i	$-0.372632\pi$
$113$	8.28187	0.779093	0.389546	+	0.921007i	$0.372632\pi$
$114$	10.4806	0.981597
$115$	−1.68070	−0.156726
$116$	4.78583	0.444353
$117$	1.51441	0.140008
$118$	7.39759	0.681003
$119$	−2.47843	−0.227197
$120$	−12.4463	−1.13619
$121$	−7.58451	−0.689501
$122$	11.9900	1.08553
$123$	−1.68528	−0.151957
$124$	24.7416	2.22186
$125$	−12.0594	−1.07863
$126$	−14.3282	−1.27645
$127$	14.2573	1.26514	0.632568	−	0.774505i	$-0.282001\pi$
$127$	14.2573	1.26514	0.632568	+	0.774505i	$0.282001\pi$
$128$	−1.73541	−0.153390
$129$	3.41945	0.301066
$130$	−3.38513	−0.296895
$131$	6.25663	0.546645	0.273322	−	0.961923i	$-0.411877\pi$
$131$	6.25663	0.546645	0.273322	+	0.961923i	$0.411877\pi$
$132$	9.02567	0.785584
$133$	−11.0718	−0.960046
$134$	−34.5013	−2.98045
$135$	8.50451	0.731951
$136$	−6.40478	−0.549205
$137$	9.16909	0.783369	0.391684	−	0.920100i	$-0.371893\pi$
$137$	9.16909	0.783369	0.391684	+	0.920100i	$0.371893\pi$
$138$	2.65826	0.226286
$139$	4.57593	0.388126	0.194063	−	0.980989i	$-0.437833\pi$
$139$	4.57593	0.388126	0.194063	+	0.980989i	$0.437833\pi$
$140$	22.5879	1.90902
$141$	2.02985	0.170944
$142$	−37.7587	−3.16864
$143$	1.42893	0.119493
$144$	−18.2793	−1.52327
$145$	1.68070	0.139574
$146$	−31.8975	−2.63986
$147$	−0.904143	−0.0745724
$148$	14.3599	1.18038
$149$	11.8201	0.968344	0.484172	−	0.874973i	$-0.339121\pi$
$149$	11.8201	0.968344	0.484172	+	0.874973i	$0.339121\pi$
$150$	5.78240	0.472131
$151$	−19.5875	−1.59401	−0.797003	−	0.603975i	$-0.793583\pi$
$151$	−19.5875	−1.59401	−0.797003	+	0.603975i	$0.793583\pi$
$152$	−28.6118	−2.32072
$153$	1.72865	0.139753
$154$	−13.5194	−1.08942
$155$	8.68878	0.697899
$156$	3.77605	0.302326
$157$	13.1463	1.04919	0.524595	−	0.851352i	$-0.324217\pi$
$157$	13.1463	1.04919	0.524595	+	0.851352i	$0.324217\pi$
$158$	−5.98761	−0.476348
$159$	−1.47339	−0.116848
$160$	16.4656	1.30172
$161$	−2.80821	−0.221318
$162$	1.85568	0.145796
$163$	−17.5673	−1.37598	−0.687988	−	0.725722i	$-0.741506\pi$
$163$	−17.5673	−1.37598	−0.687988	+	0.725722i	$0.741506\pi$
$164$	7.90377	0.617181
$165$	3.16965	0.246757
$166$	16.8517	1.30794
$167$	−2.69139	−0.208266	−0.104133	−	0.994563i	$-0.533207\pi$
$167$	−2.69139	−0.208266	−0.104133	+	0.994563i	$0.533207\pi$
$168$	−20.7960	−1.60445
$169$	−12.4022	−0.954014
$170$	−3.86401	−0.296356
$171$	7.72234	0.590542
$172$	−16.0368	−1.22280
$173$	4.04664	0.307661	0.153830	−	0.988097i	$-0.450839\pi$
$173$	4.04664	0.307661	0.153830	+	0.988097i	$0.450839\pi$
$174$	−2.65826	−0.201522
$175$	−6.10858	−0.461765
$176$	−17.2475	−1.30008
$177$	−2.89790	−0.217820
$178$	42.0030	3.14826
$179$	18.9925	1.41956	0.709782	−	0.704422i	$-0.248794\pi$
$179$	18.9925	1.41956	0.709782	+	0.704422i	$0.248794\pi$
$180$	−15.7546	−1.17428
$181$	−1.08134	−0.0803754	−0.0401877	−	0.999192i	$-0.512796\pi$
$181$	−1.08134	−0.0803754	−0.0401877	+	0.999192i	$0.512796\pi$
$182$	−5.65607	−0.419256
$183$	−4.69692	−0.347207
$184$	−7.25699	−0.534992
$185$	5.04293	0.370764
$186$	−13.7425	−1.00765
$187$	1.63108	0.119276
$188$	−9.51977	−0.694301
$189$	14.2098	1.03361
$190$	−17.2615	−1.25228
$191$	−8.42595	−0.609680	−0.304840	−	0.952404i	$-0.598603\pi$
$191$	−8.42595	−0.609680	−0.304840	+	0.952404i	$0.598603\pi$
$192$	−6.99579	−0.504877
$193$	−0.304423	−0.0219129	−0.0109564	−	0.999940i	$-0.503488\pi$
$193$	−0.304423	−0.0219129	−0.0109564	+	0.999940i	$0.503488\pi$
$194$	28.7731	2.06579
$195$	1.32608	0.0949624
$196$	4.24033	0.302880
$197$	−12.1145	−0.863119	−0.431560	−	0.902084i	$-0.642037\pi$
$197$	−12.1145	−0.863119	−0.431560	+	0.902084i	$0.642037\pi$
$198$	9.42949	0.670125
$199$	13.0890	0.927857	0.463928	−	0.885873i	$-0.346440\pi$
$199$	13.0890	0.927857	0.463928	+	0.885873i	$0.346440\pi$
$200$	−15.7859	−1.11623
$201$	13.5154	0.953302
$202$	−11.1406	−0.783847
$203$	2.80821	0.197097
$204$	4.31023	0.301776
$205$	2.77566	0.193860
$206$	−28.6073	−1.99316
$207$	1.95866	0.136137
$208$	−7.21579	−0.500325
$209$	7.28644	0.504014
$210$	−12.5463	−0.865775
$211$	20.5324	1.41351	0.706755	−	0.707458i	$-0.250158\pi$
$211$	20.5324	1.41351	0.706755	+	0.707458i	$0.250158\pi$
$212$	6.91004	0.474583
$213$	14.7915	1.01349
$214$	−9.41571	−0.643645
$215$	−5.63184	−0.384088
$216$	36.7212	2.49856
$217$	14.5177	0.985527
$218$	29.4642	1.99557
$219$	12.4954	0.844362
$220$	−14.8653	−1.00222
$221$	0.682389	0.0459025
$222$	−7.97611	−0.535321
$223$	4.71330	0.315626	0.157813	−	0.987469i	$-0.449556\pi$
$223$	4.71330	0.315626	0.157813	+	0.987469i	$0.449556\pi$
$224$	27.5117	1.83821
$225$	4.26061	0.284041
$226$	21.5740	1.43508
$227$	15.8873	1.05448	0.527240	−	0.849716i	$-0.323227\pi$
$227$	15.8873	1.05448	0.527240	+	0.849716i	$0.323227\pi$
$228$	19.2549	1.27519
$229$	24.2731	1.60401	0.802006	−	0.597316i	$-0.203766\pi$
$229$	24.2731	1.60401	0.802006	+	0.597316i	$0.203766\pi$
$230$	−4.37815	−0.288687
$231$	5.29603	0.348453
$232$	7.25699	0.476445
$233$	15.0023	0.982833	0.491416	−	0.870925i	$-0.336479\pi$
$233$	15.0023	0.982833	0.491416	+	0.870925i	$0.336479\pi$
$234$	3.94499	0.257892
$235$	−3.34317	−0.218084
$236$	13.5908	0.884688
$237$	2.34556	0.152361
$238$	−6.45621	−0.418494
$239$	3.22723	0.208752	0.104376	−	0.994538i	$-0.466715\pi$
$239$	3.22723	0.208752	0.104376	+	0.994538i	$0.466715\pi$
$240$	−16.0060	−1.03318
$241$	18.2846	1.17782	0.588909	−	0.808200i	$-0.299558\pi$
$241$	18.2846	1.17782	0.588909	+	0.808200i	$0.299558\pi$
$242$	−19.7574	−1.27005
$243$	−15.9073	−1.02045
$244$	22.0280	1.41020
$245$	1.48912	0.0951366
$246$	−4.39009	−0.279902
$247$	3.04841	0.193966
$248$	37.5168	2.38232
$249$	−6.60141	−0.418347
$250$	−31.4144	−1.98682
$251$	8.58591	0.541938	0.270969	−	0.962588i	$-0.412656\pi$
$251$	8.58591	0.541938	0.270969	+	0.962588i	$0.412656\pi$
$252$	−26.3237	−1.65824
$253$	1.84810	0.116189
$254$	37.1399	2.33036
$255$	1.51367	0.0947898
$256$	−18.2317	−1.13948
$257$	−3.17251	−0.197896	−0.0989478	−	0.995093i	$-0.531548\pi$
$257$	−3.17251	−0.197896	−0.0989478	+	0.995093i	$0.531548\pi$
$258$	8.90755	0.554560
$259$	8.42603	0.523568
$260$	−6.21915	−0.385695
$261$	−1.95866	−0.121238
$262$	16.2983	1.00691
$263$	0.895148	0.0551972	0.0275986	−	0.999619i	$-0.491214\pi$
$263$	0.895148	0.0551972	0.0275986	+	0.999619i	$0.491214\pi$
$264$	13.6861	0.842319
$265$	2.42668	0.149070
$266$	−28.8416	−1.76839
$267$	−16.4541	−1.00697
$268$	−63.3856	−3.87189
$269$	16.1610	0.985355	0.492677	−	0.870212i	$-0.336018\pi$
$269$	16.1610	0.985355	0.492677	+	0.870212i	$0.336018\pi$
$270$	22.1539	1.34824
$271$	−7.97606	−0.484511	−0.242255	−	0.970212i	$-0.577887\pi$
$271$	−7.97606	−0.484511	−0.242255	+	0.970212i	$0.577887\pi$
$272$	−8.23658	−0.499416
$273$	2.21569	0.134100
$274$	23.8852	1.44295
$275$	4.02011	0.242422
$276$	4.88374	0.293967
$277$	3.58237	0.215244	0.107622	−	0.994192i	$-0.465676\pi$
$277$	3.58237	0.215244	0.107622	+	0.994192i	$0.465676\pi$
$278$	11.9201	0.714922
$279$	−10.1258	−0.606216
$280$	34.2511	2.04689
$281$	4.75298	0.283539	0.141770	−	0.989900i	$-0.454721\pi$
$281$	4.75298	0.283539	0.141770	+	0.989900i	$0.454721\pi$
$282$	5.28769	0.314877
$283$	−11.3753	−0.676193	−0.338096	−	0.941111i	$-0.609783\pi$
$283$	−11.3753	−0.676193	−0.338096	+	0.941111i	$0.609783\pi$
$284$	−69.3703	−4.11637
$285$	6.76197	0.400544
$286$	3.72231	0.220105
$287$	4.63773	0.273757
$288$	−19.1889	−1.13071
$289$	−16.2211	−0.954181
$290$	4.37815	0.257094
$291$	−11.2715	−0.660745
$292$	−58.6021	−3.42943
$293$	−13.1847	−0.770257	−0.385128	−	0.922863i	$-0.625843\pi$
$293$	−13.1847	−0.770257	−0.385128	+	0.922863i	$0.625843\pi$
$294$	−2.35526	−0.137361
$295$	4.77285	0.277886
$296$	21.7746	1.26562
$297$	−9.35162	−0.542636
$298$	30.7910	1.78368
$299$	0.773187	0.0447146
$300$	10.6234	0.613344
$301$	−9.41001	−0.542384
$302$	−51.0247	−2.93614
$303$	4.36416	0.250715
$304$	−36.7949	−2.11033
$305$	7.73584	0.442953
$306$	4.50308	0.257424
$307$	−22.1761	−1.26566	−0.632829	−	0.774292i	$-0.718106\pi$
$307$	−22.1761	−1.26566	−0.632829	+	0.774292i	$0.718106\pi$
$308$	−24.8378	−1.41526
$309$	11.2065	0.637516
$310$	22.6339	1.28552
$311$	−31.3611	−1.77832	−0.889161	−	0.457594i	$-0.848711\pi$
$311$	−31.3611	−1.77832	−0.889161	+	0.457594i	$0.848711\pi$
$312$	5.72580	0.324160
$313$	21.5552	1.21837	0.609185	−	0.793028i	$-0.291497\pi$
$313$	21.5552	1.21837	0.609185	+	0.793028i	$0.291497\pi$
$314$	34.2457	1.93260
$315$	−9.24438	−0.520862
$316$	−11.0004	−0.618822
$317$	25.8705	1.45303	0.726515	−	0.687151i	$-0.241139\pi$
$317$	25.8705	1.45303	0.726515	+	0.687151i	$0.241139\pi$
$318$	−3.83813	−0.215232
$319$	−1.84810	−0.103474
$320$	11.5221	0.644103
$321$	3.68848	0.205871
$322$	−7.31527	−0.407664
$323$	3.47966	0.193613
$324$	3.40925	0.189403
$325$	1.68188	0.0932942
$326$	−45.7621	−2.53453
$327$	−11.5422	−0.638285
$328$	11.9849	0.661754
$329$	−5.58596	−0.307964
$330$	8.25681	0.454523
$331$	31.0454	1.70641	0.853205	−	0.521576i	$-0.174656\pi$
$331$	31.0454	1.70641	0.853205	+	0.521576i	$0.174656\pi$
$332$	30.9599	1.69914
$333$	−5.87698	−0.322057
$334$	−7.01098	−0.383624
$335$	−22.2599	−1.21619
$336$	−26.7438	−1.45899
$337$	21.2178	1.15581	0.577903	−	0.816105i	$-0.303871\pi$
$337$	21.2178	1.15581	0.577903	+	0.816105i	$0.303871\pi$
$338$	−32.3072	−1.75728
$339$	−8.45130	−0.459012
$340$	−7.09895	−0.384995
$341$	−9.55424	−0.517391
$342$	20.1164	1.08777
$343$	−17.1693	−0.927056
$344$	−24.3174	−1.31111
$345$	1.71508	0.0923368
$346$	10.5414	0.566707
$347$	−25.1938	−1.35248	−0.676238	−	0.736684i	$-0.736391\pi$
$347$	−25.1938	−1.35248	−0.676238	+	0.736684i	$0.736391\pi$
$348$	−4.88374	−0.261796
$349$	27.4503	1.46938	0.734691	−	0.678402i	$-0.237327\pi$
$349$	27.4503	1.46938	0.734691	+	0.678402i	$0.237327\pi$
$350$	−15.9126	−0.850566
$351$	−3.91241	−0.208829
$352$	−18.1057	−0.965038
$353$	15.5298	0.826567	0.413283	−	0.910602i	$-0.364382\pi$
$353$	15.5298	0.826567	0.413283	+	0.910602i	$0.364382\pi$
$354$	−7.54893	−0.401221
$355$	−24.3616	−1.29298
$356$	77.1679	4.08989
$357$	2.52913	0.133856
$358$	49.4747	2.61482
$359$	8.30533	0.438339	0.219169	−	0.975687i	$-0.429665\pi$
$359$	8.30533	0.438339	0.219169	+	0.975687i	$0.429665\pi$
$360$	−23.8894	−1.25908
$361$	−3.45547	−0.181867
$362$	−2.81685	−0.148050
$363$	7.73967	0.406228
$364$	−10.3913	−0.544653
$365$	−20.5800	−1.07720
$366$	−12.2353	−0.639550
$367$	−13.6556	−0.712815	−0.356407	−	0.934331i	$-0.615998\pi$
$367$	−13.6556	−0.712815	−0.356407	+	0.934331i	$0.615998\pi$
$368$	−9.33253	−0.486492
$369$	−3.23472	−0.168393
$370$	13.1367	0.682942
$371$	4.05463	0.210506
$372$	−25.2477	−1.30903
$373$	−33.1536	−1.71663	−0.858315	−	0.513124i	$-0.828488\pi$
$373$	−33.1536	−1.71663	−0.858315	+	0.513124i	$0.828488\pi$
$374$	4.24889	0.219705
$375$	12.3061	0.635487
$376$	−14.4353	−0.744443
$377$	−0.773187	−0.0398212
$378$	37.0161	1.90390
$379$	−19.4221	−0.997649	−0.498824	−	0.866703i	$-0.666235\pi$
$379$	−19.4221	−0.997649	−0.498824	+	0.866703i	$0.666235\pi$
$380$	−31.7129	−1.62684
$381$	−14.5490	−0.745369
$382$	−21.9493	−1.12302
$383$	10.5047	0.536764	0.268382	−	0.963313i	$-0.413511\pi$
$383$	10.5047	0.536764	0.268382	+	0.963313i	$0.413511\pi$
$384$	1.77092	0.0903716
$385$	−8.72257	−0.444543
$386$	−0.793011	−0.0403632
$387$	6.56329	0.333631
$388$	52.8619	2.68365
$389$	−17.3721	−0.880802	−0.440401	−	0.897801i	$-0.645164\pi$
$389$	−17.3721	−0.880802	−0.440401	+	0.897801i	$0.645164\pi$
$390$	3.45438	0.174919
$391$	0.882567	0.0446333
$392$	6.42981	0.324755
$393$	−6.38463	−0.322062
$394$	−31.5577	−1.58985
$395$	−3.86314	−0.194376
$396$	17.3238	0.870556
$397$	−12.6473	−0.634750	−0.317375	−	0.948300i	$-0.602801\pi$
$397$	−12.6473	−0.634750	−0.317375	+	0.948300i	$0.602801\pi$
$398$	34.0964	1.70910
$399$	11.2983	0.565622
$400$	−20.3007	−1.01503
$401$	−26.3988	−1.31829	−0.659146	−	0.752015i	$-0.729082\pi$
$401$	−26.3988	−1.31829	−0.659146	+	0.752015i	$0.729082\pi$
$402$	35.2071	1.75597
$403$	−3.99718	−0.199114
$404$	−20.4674	−1.01829
$405$	1.19726	0.0594925
$406$	7.31527	0.363051
$407$	−5.54525	−0.274868
$408$	6.53581	0.323571
$409$	9.29368	0.459543	0.229771	−	0.973245i	$-0.426202\pi$
$409$	9.29368	0.459543	0.229771	+	0.973245i	$0.426202\pi$
$410$	7.23049	0.357088
$411$	−9.35668	−0.461531
$412$	−52.5572	−2.58931
$413$	7.97476	0.392412
$414$	5.10225	0.250762
$415$	10.8725	0.533711
$416$	−7.57484	−0.371387
$417$	−4.66955	−0.228669
$418$	18.9809	0.928387
$419$	25.3396	1.23792	0.618961	−	0.785421i	$-0.287554\pi$
$419$	25.3396	1.23792	0.618961	+	0.785421i	$0.287554\pi$
$420$	−23.0500	−1.12472
$421$	−4.02340	−0.196089	−0.0980443	−	0.995182i	$-0.531259\pi$
$421$	−4.02340	−0.196089	−0.0980443	+	0.995182i	$0.531259\pi$
$422$	53.4862	2.60367
$423$	3.89609	0.189434
$424$	10.4780	0.508858
$425$	1.91981	0.0931247
$426$	38.5312	1.86684
$427$	12.9255	0.625508
$428$	−17.2985	−0.836156
$429$	−1.45816	−0.0704008
$430$	−14.6707	−0.707486
$431$	−35.5666	−1.71318	−0.856591	−	0.515996i	$-0.827422\pi$
$431$	−35.5666	−1.71318	−0.856591	+	0.515996i	$0.827422\pi$
$432$	47.2236	2.27205
$433$	30.5767	1.46942	0.734712	−	0.678380i	$-0.237317\pi$
$433$	30.5767	1.46942	0.734712	+	0.678380i	$0.237317\pi$
$434$	37.8181	1.81533
$435$	−1.71508	−0.0822318
$436$	54.1316	2.59243
$437$	3.94266	0.188603
$438$	32.5501	1.55530
$439$	−31.7051	−1.51320	−0.756600	−	0.653878i	$-0.773141\pi$
$439$	−31.7051	−1.51320	−0.756600	+	0.653878i	$0.773141\pi$
$440$	−22.5410	−1.07460
$441$	−1.73541	−0.0826385
$442$	1.77760	0.0845517
$443$	22.0093	1.04569	0.522846	−	0.852427i	$-0.324870\pi$
$443$	22.0093	1.04569	0.522846	+	0.852427i	$0.324870\pi$
$444$	−14.6537	−0.695433
$445$	27.0999	1.28466
$446$	12.2780	0.581379
$447$	−12.0620	−0.570511
$448$	19.2517	0.909559
$449$	2.97968	0.140620	0.0703098	−	0.997525i	$-0.477601\pi$
$449$	2.97968	0.140620	0.0703098	+	0.997525i	$0.477601\pi$
$450$	11.0987	0.523199
$451$	−3.05213	−0.143719
$452$	39.6356	1.86430
$453$	19.9882	0.939128
$454$	41.3859	1.94234
$455$	−3.64924	−0.171079
$456$	29.1972	1.36728
$457$	8.73038	0.408390	0.204195	−	0.978930i	$-0.434542\pi$
$457$	8.73038	0.408390	0.204195	+	0.978930i	$0.434542\pi$
$458$	63.2305	2.95457
$459$	−4.46589	−0.208450
$460$	−8.04353	−0.375031
$461$	−12.7674	−0.594639	−0.297319	−	0.954778i	$-0.596093\pi$
$461$	−12.7674	−0.594639	−0.297319	+	0.954778i	$0.596093\pi$
$462$	13.7960	0.641847
$463$	31.1939	1.44970	0.724851	−	0.688906i	$-0.241909\pi$
$463$	31.1939	1.44970	0.724851	+	0.688906i	$0.241909\pi$
$464$	9.33253	0.433252
$465$	−8.86653	−0.411176
$466$	39.0804	1.81037
$467$	22.5391	1.04299	0.521493	−	0.853256i	$-0.325375\pi$
$467$	22.5391	1.04299	0.521493	+	0.853256i	$0.325375\pi$
$468$	7.24773	0.335027
$469$	−37.1931	−1.71742
$470$	−8.70883	−0.401708
$471$	−13.4153	−0.618143
$472$	20.6085	0.948581
$473$	6.19281	0.284746
$474$	6.11010	0.280646
$475$	8.57631	0.393508
$476$	−11.8613	−0.543664
$477$	−2.82802	−0.129486
$478$	8.40682	0.384519
$479$	−24.5397	−1.12125	−0.560623	−	0.828071i	$-0.689438\pi$
$479$	−24.5397	−1.12125	−0.560623	+	0.828071i	$0.689438\pi$
$480$	−16.8025	−0.766925
$481$	−2.31995	−0.105781
$482$	47.6308	2.16952
$483$	2.86566	0.130392
$484$	−36.2982	−1.64992
$485$	18.5641	0.842953
$486$	−41.4378	−1.87966
$487$	−23.2452	−1.05334	−0.526671	−	0.850069i	$-0.676560\pi$
$487$	−23.2452	−1.05334	−0.526671	+	0.850069i	$0.676560\pi$
$488$	33.4022	1.51205
$489$	17.9267	0.810673
$490$	3.87911	0.175240
$491$	−5.76174	−0.260024	−0.130012	−	0.991512i	$-0.541502\pi$
$491$	−5.76174	−0.260024	−0.130012	+	0.991512i	$0.541502\pi$
$492$	−8.06547	−0.363619
$493$	−0.882567	−0.0397488
$494$	7.94100	0.357282
$495$	6.08381	0.273447
$496$	48.2468	2.16635
$497$	−40.7047	−1.82586
$498$	−17.1964	−0.770590
$499$	−30.8637	−1.38165	−0.690825	−	0.723022i	$-0.742752\pi$
$499$	−30.8637	−1.38165	−0.690825	+	0.723022i	$0.742752\pi$
$500$	−57.7144	−2.58107
$501$	2.74646	0.122703
$502$	22.3660	0.998243
$503$	35.6442	1.58930	0.794648	−	0.607071i	$-0.207656\pi$
$503$	35.6442	1.58930	0.794648	+	0.607071i	$0.207656\pi$
$504$	−39.9159	−1.77799
$505$	−7.18778	−0.319852
$506$	4.81425	0.214019
$507$	12.6559	0.562069
$508$	68.2333	3.02736
$509$	−3.06341	−0.135783	−0.0678917	−	0.997693i	$-0.521627\pi$
$509$	−3.06341	−0.135783	−0.0678917	+	0.997693i	$0.521627\pi$
$510$	3.94306	0.174602
$511$	−34.3862	−1.52116
$512$	−44.0222	−1.94553
$513$	−19.9503	−0.880826
$514$	−8.26427	−0.364521
$515$	−18.4571	−0.813318
$516$	16.3649	0.720426
$517$	3.67617	0.161678
$518$	21.9495	0.964406
$519$	−4.12943	−0.181262
$520$	−9.43040	−0.413550
$521$	30.5468	1.33828	0.669140	−	0.743136i	$-0.266663\pi$
$521$	30.5468	1.33828	0.669140	+	0.743136i	$0.266663\pi$
$522$	−5.10225	−0.223319
$523$	−25.4624	−1.11339	−0.556696	−	0.830716i	$-0.687931\pi$
$523$	−25.4624	−1.11339	−0.556696	+	0.830716i	$0.687931\pi$
$524$	29.9432	1.30807
$525$	6.23355	0.272055
$526$	2.33183	0.101672
$527$	−4.56265	−0.198752
$528$	17.6003	0.765957
$529$	1.00000	0.0434783
$530$	6.32140	0.274584
$531$	−5.56223	−0.241380
$532$	−52.9877	−2.29731
$533$	−1.27691	−0.0553093
$534$	−42.8623	−1.85483
$535$	−6.07492	−0.262642
$536$	−96.1147	−4.15152
$537$	−19.3810	−0.836353
$538$	42.0989	1.81501
$539$	−1.63745	−0.0705300
$540$	40.7011	1.75150
$541$	9.43243	0.405532	0.202766	−	0.979227i	$-0.435007\pi$
$541$	9.43243	0.405532	0.202766	+	0.979227i	$0.435007\pi$
$542$	−20.7773	−0.892463
$543$	1.10346	0.0473541
$544$	−8.64643	−0.370712
$545$	19.0100	0.814299
$546$	5.77179	0.247010
$547$	41.5690	1.77736	0.888681	−	0.458527i	$-0.151623\pi$
$547$	41.5690	1.77736	0.888681	+	0.458527i	$0.151623\pi$
$548$	43.8817	1.87454
$549$	−9.01526	−0.384762
$550$	10.4722	0.446538
$551$	−3.94266	−0.167963
$552$	7.40546	0.315197
$553$	−6.45477	−0.274485
$554$	9.33195	0.396477
$555$	−5.14610	−0.218440
$556$	21.8997	0.928752
$557$	29.1407	1.23473	0.617366	−	0.786676i	$-0.288200\pi$
$557$	29.1407	1.23473	0.617366	+	0.786676i	$0.288200\pi$
$558$	−26.3774	−1.11664
$559$	2.59087	0.109582
$560$	44.0471	1.86133
$561$	−1.66444	−0.0702729
$562$	12.3813	0.522276
$563$	28.9802	1.22137	0.610685	−	0.791873i	$-0.290894\pi$
$563$	28.9802	1.22137	0.610685	+	0.791873i	$0.290894\pi$
$564$	9.71453	0.409056
$565$	13.9193	0.585590
$566$	−29.6323	−1.24554
$567$	2.00046	0.0840114
$568$	−105.190	−4.41365
$569$	−34.2223	−1.43467	−0.717337	−	0.696726i	$-0.754639\pi$
$569$	−34.2223	−1.43467	−0.717337	+	0.696726i	$0.754639\pi$
$570$	17.6147	0.737798
$571$	−26.0169	−1.08877	−0.544386	−	0.838835i	$-0.683237\pi$
$571$	−26.0169	−1.08877	−0.544386	+	0.838835i	$0.683237\pi$
$572$	6.83862	0.285937
$573$	8.59833	0.359200
$574$	12.0811	0.504256
$575$	2.17526	0.0907147
$576$	−13.4277	−0.559487
$577$	−28.2981	−1.17806	−0.589032	−	0.808110i	$-0.700491\pi$
$577$	−28.2981	−1.17806	−0.589032	+	0.808110i	$0.700491\pi$
$578$	−42.2553	−1.75759
$579$	0.310651	0.0129102
$580$	8.04353	0.333989
$581$	18.1665	0.753672
$582$	−29.3617	−1.21708
$583$	−2.66839	−0.110513
$584$	−88.8612	−3.67710
$585$	2.54527	0.105234
$586$	−34.3456	−1.41880
$587$	17.1615	0.708331	0.354165	−	0.935183i	$-0.384765\pi$
$587$	17.1615	0.708331	0.354165	+	0.935183i	$0.384765\pi$
$588$	−4.32708	−0.178446
$589$	−20.3825	−0.839848
$590$	12.4331	0.511863
$591$	12.3623	0.508517
$592$	28.0023	1.15089
$593$	−17.0152	−0.698731	−0.349365	−	0.936987i	$-0.613603\pi$
$593$	−17.0152	−0.698731	−0.349365	+	0.936987i	$0.613603\pi$
$594$	−24.3606	−0.999528
$595$	−4.16548	−0.170768
$596$	56.5692	2.31717
$597$	−13.3568	−0.546658
$598$	2.01412	0.0823636
$599$	−6.72206	−0.274656	−0.137328	−	0.990526i	$-0.543851\pi$
$599$	−6.72206	−0.274656	−0.137328	+	0.990526i	$0.543851\pi$
$600$	16.1088	0.657639
$601$	−45.1047	−1.83986	−0.919930	−	0.392082i	$-0.871755\pi$
$601$	−45.1047	−1.83986	−0.919930	+	0.392082i	$0.871755\pi$
$602$	−24.5127	−0.999064
$603$	25.9414	1.05642
$604$	−93.7424	−3.81432
$605$	−12.7472	−0.518249
$606$	11.3685	0.461813
$607$	−22.7337	−0.922732	−0.461366	−	0.887210i	$-0.652640\pi$
$607$	−22.7337	−0.922732	−0.461366	+	0.887210i	$0.652640\pi$
$608$	−38.6258	−1.56648
$609$	−2.86566	−0.116122
$610$	20.1516	0.815913
$611$	1.53799	0.0622204
$612$	8.27304	0.334418
$613$	−25.6809	−1.03724	−0.518620	−	0.855005i	$-0.673554\pi$
$613$	−25.6809	−1.03724	−0.518620	+	0.855005i	$0.673554\pi$
$614$	−57.7679	−2.33132
$615$	−2.83244	−0.114215
$616$	−37.6628	−1.51748
$617$	22.8029	0.918009	0.459004	−	0.888434i	$-0.348206\pi$
$617$	22.8029	0.918009	0.459004	+	0.888434i	$0.348206\pi$
$618$	29.1925	1.17430
$619$	17.3140	0.695909	0.347955	−	0.937511i	$-0.386876\pi$
$619$	17.3140	0.695909	0.347955	+	0.937511i	$0.386876\pi$
$620$	41.5830	1.67001
$621$	−5.06011	−0.203055
$622$	−81.6944	−3.27565
$623$	45.2801	1.81411
$624$	7.36341	0.294772
$625$	−9.39192	−0.375677
$626$	56.1504	2.24422
$627$	−7.43551	−0.296946
$628$	62.9161	2.51063
$629$	−2.64814	−0.105588
$630$	−24.0813	−0.959421
$631$	−4.67782	−0.186221	−0.0931105	−	0.995656i	$-0.529681\pi$
$631$	−4.67782	−0.186221	−0.0931105	+	0.995656i	$0.529681\pi$
$632$	−16.6805	−0.663513
$633$	−20.9525	−0.832787
$634$	67.3916	2.67646
$635$	23.9623	0.950913
$636$	−7.05140	−0.279606
$637$	−0.685056	−0.0271429
$638$	−4.81425	−0.190598
$639$	28.3907	1.12312
$640$	−2.91670	−0.115293
$641$	−27.9708	−1.10478	−0.552390	−	0.833586i	$-0.686284\pi$
$641$	−27.9708	−1.10478	−0.552390	+	0.833586i	$0.686284\pi$
$642$	9.60834	0.379211
$643$	−29.9724	−1.18199	−0.590997	−	0.806673i	$-0.701266\pi$
$643$	−29.9724	−1.18199	−0.590997	+	0.806673i	$0.701266\pi$
$644$	−13.4396	−0.529594
$645$	5.74706	0.226290
$646$	9.06438	0.356633
$647$	−2.35510	−0.0925886	−0.0462943	−	0.998928i	$-0.514741\pi$
$647$	−2.35510	−0.0925886	−0.0462943	+	0.998928i	$0.514741\pi$
$648$	5.16961	0.203081
$649$	−5.24826	−0.206012
$650$	4.38125	0.171847
$651$	−14.8147	−0.580635
$652$	−84.0741	−3.29260
$653$	5.15341	0.201668	0.100834	−	0.994903i	$-0.467849\pi$
$653$	5.15341	0.201668	0.100834	+	0.994903i	$0.467849\pi$
$654$	−30.0670	−1.17571
$655$	10.5155	0.410875
$656$	15.4126	0.601761
$657$	23.9837	0.935692
$658$	−14.5512	−0.567266
$659$	20.5225	0.799444	0.399722	−	0.916636i	$-0.369107\pi$
$659$	20.5225	0.799444	0.399722	+	0.916636i	$0.369107\pi$
$660$	15.1694	0.590468
$661$	−12.3073	−0.478697	−0.239348	−	0.970934i	$-0.576934\pi$
$661$	−12.3073	−0.478697	−0.239348	+	0.970934i	$0.576934\pi$
$662$	80.8721	3.14318
$663$	−0.696350	−0.0270440
$664$	46.9459	1.82186
$665$	−18.6083	−0.721599
$666$	−15.3093	−0.593224
$667$	−1.00000	−0.0387202
$668$	−12.8806	−0.498364
$669$	−4.80973	−0.185955
$670$	−57.9861	−2.24020
$671$	−8.50638	−0.328385
$672$	−28.0746	−1.08300
$673$	6.69894	0.258225	0.129113	−	0.991630i	$-0.458787\pi$
$673$	6.69894	0.258225	0.129113	+	0.991630i	$0.458787\pi$
$674$	55.2716	2.12898
$675$	−11.0071	−0.423662
$676$	−59.3548	−2.28288
$677$	19.1249	0.735030	0.367515	−	0.930018i	$-0.380209\pi$
$677$	19.1249	0.735030	0.367515	+	0.930018i	$0.380209\pi$
$678$	−22.0153	−0.845494
$679$	31.0180	1.19036
$680$	−10.7645	−0.412799
$681$	−16.2124	−0.621259
$682$	−24.8884	−0.953028
$683$	7.36478	0.281805	0.140903	−	0.990023i	$-0.455000\pi$
$683$	7.36478	0.281805	0.140903	+	0.990023i	$0.455000\pi$
$684$	36.9578	1.41312
$685$	15.4105	0.588803
$686$	−44.7254	−1.70763
$687$	−24.7697	−0.945022
$688$	−31.2724	−1.19225
$689$	−1.11637	−0.0425302
$690$	4.46772	0.170083
$691$	−49.1019	−1.86792	−0.933961	−	0.357374i	$-0.883672\pi$
$691$	−49.1019	−1.86792	−0.933961	+	0.357374i	$0.883672\pi$
$692$	19.3666	0.736206
$693$	10.1652	0.386144
$694$	−65.6290	−2.49124
$695$	7.69075	0.291727
$696$	−7.40546	−0.280703
$697$	−1.45755	−0.0552088
$698$	71.5071	2.70658
$699$	−15.3092	−0.579048
$700$	−29.2347	−1.10497
$701$	36.2294	1.36837	0.684183	−	0.729310i	$-0.260159\pi$
$701$	36.2294	1.36837	0.684183	+	0.729310i	$0.260159\pi$
$702$	−10.1917	−0.384660
$703$	−11.8300	−0.446175
$704$	−12.6697	−0.477509
$705$	3.41156	0.128487
$706$	40.4545	1.52253
$707$	−12.0098	−0.451674
$708$	−13.8689	−0.521225
$709$	−45.7281	−1.71735	−0.858677	−	0.512518i	$-0.828713\pi$
$709$	−45.7281	−1.71735	−0.858677	+	0.512518i	$0.828713\pi$
$710$	−63.4609	−2.38165
$711$	4.50207	0.168841
$712$	117.013	4.38526
$713$	−5.16975	−0.193609
$714$	6.58830	0.246561
$715$	2.40160	0.0898147
$716$	90.8947	3.39690
$717$	−3.29326	−0.122989
$718$	21.6351	0.807414
$719$	33.7657	1.25925	0.629624	−	0.776900i	$-0.283209\pi$
$719$	33.7657	1.25925	0.629624	+	0.776900i	$0.283209\pi$
$720$	−30.7219	−1.14494
$721$	−30.8392	−1.14851
$722$	−9.00137	−0.334996
$723$	−18.6587	−0.693925
$724$	−5.17512	−0.192332
$725$	−2.17526	−0.0807872
$726$	20.1616	0.748266
$727$	−27.4791	−1.01914	−0.509571	−	0.860429i	$-0.670196\pi$
$727$	−27.4791	−1.01914	−0.509571	+	0.860429i	$0.670196\pi$
$728$	−15.7569	−0.583988
$729$	14.0956	0.522060
$730$	−53.6100	−1.98420
$731$	2.95739	0.109383
$732$	−22.4787	−0.830836
$733$	−15.6367	−0.577554	−0.288777	−	0.957396i	$-0.593249\pi$
$733$	−15.6367	−0.577554	−0.288777	+	0.957396i	$0.593249\pi$
$734$	−35.5723	−1.31300
$735$	−1.51959	−0.0560509
$736$	−9.79691	−0.361119
$737$	24.4771	0.901625
$738$	−8.42633	−0.310178
$739$	4.37819	0.161054	0.0805271	−	0.996752i	$-0.474340\pi$
$739$	4.37819	0.161054	0.0805271	+	0.996752i	$0.474340\pi$
$740$	24.1346	0.887207
$741$	−3.11078	−0.114277
$742$	10.5622	0.387750
$743$	−7.80342	−0.286280	−0.143140	−	0.989702i	$-0.545720\pi$
$743$	−7.80342	−0.286280	−0.143140	+	0.989702i	$0.545720\pi$
$744$	−38.2844	−1.40357
$745$	19.8661	0.727836
$746$	−86.3640	−3.16201
$747$	−12.6707	−0.463598
$748$	7.80606	0.285418
$749$	−10.1503	−0.370885
$750$	32.0571	1.17056
$751$	36.6586	1.33769	0.668845	−	0.743402i	$-0.266789\pi$
$751$	36.6586	1.33769	0.668845	+	0.743402i	$0.266789\pi$
$752$	−18.5639	−0.676954
$753$	−8.76157	−0.319289
$754$	−2.01412	−0.0733501
$755$	−32.9206	−1.19810
$756$	68.0059	2.47335
$757$	−15.5724	−0.565989	−0.282994	−	0.959122i	$-0.591328\pi$
$757$	−15.5724	−0.565989	−0.282994	+	0.959122i	$0.591328\pi$
$758$	−50.5940	−1.83766
$759$	−1.88591	−0.0684543
$760$	−48.0878	−1.74433
$761$	27.3332	0.990827	0.495414	−	0.868657i	$-0.335017\pi$
$761$	27.3332	0.990827	0.495414	+	0.868657i	$0.335017\pi$
$762$	−37.8997	−1.37296
$763$	31.7630	1.14990
$764$	−40.3252	−1.45891
$765$	2.90534	0.105043
$766$	27.3643	0.988713
$767$	−2.19570	−0.0792822
$768$	18.6047	0.671341
$769$	23.2168	0.837219	0.418610	−	0.908166i	$-0.362518\pi$
$769$	23.2168	0.837219	0.418610	+	0.908166i	$0.362518\pi$
$770$	−22.7220	−0.818843
$771$	3.23741	0.116593
$772$	−1.45692	−0.0524356
$773$	−7.03205	−0.252925	−0.126463	−	0.991971i	$-0.540362\pi$
$773$	−7.03205	−0.252925	−0.126463	+	0.991971i	$0.540362\pi$
$774$	17.0971	0.614543
$775$	−11.2456	−0.403952
$776$	80.1570	2.87747
$777$	−8.59841	−0.308466
$778$	−45.2538	−1.62243
$779$	−6.51127	−0.233290
$780$	6.34638	0.227237
$781$	26.7881	0.958555
$782$	2.29905	0.0822140
$783$	5.06011	0.180834
$784$	8.26877	0.295313
$785$	22.0950	0.788603
$786$	−16.6317	−0.593234
$787$	−38.4072	−1.36907	−0.684535	−	0.728980i	$-0.739995\pi$
$787$	−38.4072	−1.36907	−0.684535	+	0.728980i	$0.739995\pi$
$788$	−57.9778	−2.06537
$789$	−0.913461	−0.0325201
$790$	−10.0633	−0.358038
$791$	23.2572	0.826931
$792$	26.2690	0.933428
$793$	−3.55879	−0.126376
$794$	−32.9457	−1.16920
$795$	−2.47632	−0.0878261
$796$	62.6419	2.22028
$797$	29.2736	1.03693	0.518463	−	0.855100i	$-0.326504\pi$
$797$	29.2736	1.03693	0.518463	+	0.855100i	$0.326504\pi$
$798$	29.4316	1.04187
$799$	1.75556	0.0621074
$800$	−21.3108	−0.753452
$801$	−31.5820	−1.11589
$802$	−68.7678	−2.42828
$803$	22.6299	0.798591
$804$	64.6824	2.28117
$805$	−4.71974	−0.166349
$806$	−10.4125	−0.366765
$807$	−16.4917	−0.580534
$808$	−31.0357	−1.09183
$809$	−53.7604	−1.89011	−0.945057	−	0.326905i	$-0.893994\pi$
$809$	−53.7604	−1.89011	−0.945057	+	0.326905i	$0.893994\pi$
$810$	3.11883	0.109584
$811$	−15.2539	−0.535636	−0.267818	−	0.963470i	$-0.586303\pi$
$811$	−15.2539	−0.535636	−0.267818	+	0.963470i	$0.586303\pi$
$812$	13.4396	0.471637
$813$	8.13923	0.285455
$814$	−14.4452	−0.506303
$815$	−29.5253	−1.03423
$816$	8.40509	0.294237
$817$	13.2114	0.462210
$818$	24.2097	0.846472
$819$	4.25279	0.148604
$820$	13.2838	0.463892
$821$	32.7377	1.14256	0.571278	−	0.820757i	$-0.306448\pi$
$821$	32.7377	1.14256	0.571278	+	0.820757i	$0.306448\pi$
$822$	−24.3738	−0.850134
$823$	−34.5678	−1.20496	−0.602479	−	0.798135i	$-0.705820\pi$
$823$	−34.5678	−1.20496	−0.602479	+	0.798135i	$0.705820\pi$
$824$	−79.6950	−2.77631
$825$	−4.10236	−0.142826
$826$	20.7740	0.722818
$827$	45.1215	1.56903	0.784513	−	0.620112i	$-0.212913\pi$
$827$	45.1215	1.56903	0.784513	+	0.620112i	$0.212913\pi$
$828$	9.37384	0.325764
$829$	−48.9447	−1.69992	−0.849960	−	0.526847i	$-0.823374\pi$
$829$	−48.9447	−1.69992	−0.849960	+	0.526847i	$0.823374\pi$
$830$	28.3225	0.983089
$831$	−3.65566	−0.126814
$832$	−5.30061	−0.183766
$833$	−0.781968	−0.0270936
$834$	−12.1640	−0.421205
$835$	−4.52341	−0.156539
$836$	34.8717	1.20606
$837$	26.1595	0.904205
$838$	66.0088	2.28024
$839$	−54.6452	−1.88656	−0.943281	−	0.331995i	$-0.892278\pi$
$839$	−54.6452	−1.88656	−0.943281	+	0.331995i	$0.892278\pi$
$840$	−34.9518	−1.20595
$841$	1.00000	0.0344828
$842$	−10.4808	−0.361193
$843$	−4.85022	−0.167051
$844$	98.2648	3.38241
$845$	−20.8443	−0.717065
$846$	10.1492	0.348936
$847$	−21.2989	−0.731837
$848$	13.4748	0.462726
$849$	11.6080	0.398387
$850$	5.00104	0.171534
$851$	−3.00050	−0.102856
$852$	70.7895	2.42521
$853$	−18.9241	−0.647948	−0.323974	−	0.946066i	$-0.605019\pi$
$853$	−18.9241	−0.647948	−0.323974	+	0.946066i	$0.605019\pi$
$854$	33.6704	1.15218
$855$	12.9789	0.443869
$856$	−26.2306	−0.896543
$857$	14.1409	0.483046	0.241523	−	0.970395i	$-0.422353\pi$
$857$	14.1409	0.483046	0.241523	+	0.970395i	$0.422353\pi$
$858$	−3.79846	−0.129677
$859$	55.3730	1.88930	0.944652	−	0.328075i	$-0.106400\pi$
$859$	55.3730	1.88930	0.944652	+	0.328075i	$0.106400\pi$
$860$	−26.9530	−0.919091
$861$	−4.73261	−0.161287
$862$	−92.6496	−3.15566
$863$	−9.62971	−0.327799	−0.163900	−	0.986477i	$-0.552407\pi$
$863$	−9.62971	−0.327799	−0.163900	+	0.986477i	$0.552407\pi$
$864$	49.5735	1.68652
$865$	6.80117	0.231247
$866$	79.6512	2.70666
$867$	16.5529	0.562167
$868$	69.4794	2.35828
$869$	4.24794	0.144101
$870$	−4.46772	−0.151470
$871$	10.2404	0.346983
$872$	82.0824	2.77966
$873$	−21.6344	−0.732214
$874$	10.2705	0.347404
$875$	−33.8654	−1.14486
$876$	59.8010	2.02049
$877$	6.67453	0.225383	0.112691	−	0.993630i	$-0.464053\pi$
$877$	6.67453	0.225383	0.112691	+	0.993630i	$0.464053\pi$
$878$	−82.5905	−2.78730
$879$	13.4544	0.453806
$880$	−28.9878	−0.977178
$881$	−56.9064	−1.91722	−0.958612	−	0.284715i	$-0.908101\pi$
$881$	−56.9064	−1.91722	−0.958612	+	0.284715i	$0.908101\pi$
$882$	−4.52068	−0.152219
$883$	8.65659	0.291318	0.145659	−	0.989335i	$-0.453470\pi$
$883$	8.65659	0.291318	0.145659	+	0.989335i	$0.453470\pi$
$884$	3.26580	0.109841
$885$	−4.87049	−0.163720
$886$	57.3334	1.92615
$887$	21.9095	0.735648	0.367824	−	0.929895i	$-0.380103\pi$
$887$	21.9095	0.735648	0.367824	+	0.929895i	$0.380103\pi$
$888$	−22.2201	−0.745658
$889$	40.0376	1.34282
$890$	70.5943	2.36633
$891$	−1.31652	−0.0441051
$892$	22.5571	0.755267
$893$	7.84256	0.262441
$894$	−31.4210	−1.05087
$895$	31.9205	1.06699
$896$	−4.87339	−0.162809
$897$	−0.789005	−0.0263441
$898$	7.76194	0.259019
$899$	5.16975	0.172421
$900$	20.3906	0.679685
$901$	−1.27430	−0.0424530
$902$	−7.95069	−0.264729
$903$	9.60252	0.319552
$904$	60.1015	1.99895
$905$	−1.81740	−0.0604126
$906$	52.0685	1.72986
$907$	−50.4844	−1.67631	−0.838153	−	0.545435i	$-0.816365\pi$
$907$	−50.4844	−1.67631	−0.838153	+	0.545435i	$0.816365\pi$
$908$	76.0342	2.52328
$909$	8.37656	0.277833
$910$	−9.50614	−0.315125
$911$	17.2002	0.569867	0.284933	−	0.958547i	$-0.408029\pi$
$911$	17.2002	0.569867	0.284933	+	0.958547i	$0.408029\pi$
$912$	37.5477	1.24333
$913$	−11.9555	−0.395670
$914$	22.7423	0.752249
$915$	−7.89410	−0.260971
$916$	116.167	3.83827
$917$	17.5699	0.580210
$918$	−11.6335	−0.383962
$919$	−12.9679	−0.427771	−0.213886	−	0.976859i	$-0.568612\pi$
$919$	−12.9679	−0.427771	−0.213886	+	0.976859i	$0.568612\pi$
$920$	−12.1968	−0.402116
$921$	22.6298	0.745677
$922$	−33.2587	−1.09532
$923$	11.2073	0.368892
$924$	25.3459	0.833820
$925$	−6.52688	−0.214603
$926$	81.2588	2.67033
$927$	21.5097	0.706472
$928$	9.79691	0.321599
$929$	−47.6705	−1.56402	−0.782010	−	0.623266i	$-0.785805\pi$
$929$	−47.6705	−1.56402	−0.782010	+	0.623266i	$0.785805\pi$
$930$	−23.0970	−0.757380
$931$	−3.49326	−0.114487
$932$	71.7985	2.35184
$933$	32.0026	1.04772
$934$	58.7136	1.92117
$935$	2.74134	0.0896515
$936$	10.9901	0.359222
$937$	−12.0522	−0.393727	−0.196863	−	0.980431i	$-0.563076\pi$
$937$	−12.0522	−0.393727	−0.196863	+	0.980431i	$0.563076\pi$
$938$	−96.8866	−3.16346
$939$	−21.9962	−0.717817
$940$	−15.9998	−0.521857
$941$	15.0969	0.492146	0.246073	−	0.969251i	$-0.420860\pi$
$941$	15.0969	0.492146	0.246073	+	0.969251i	$0.420860\pi$
$942$	−34.9463	−1.13861
$943$	−1.65149	−0.0537800
$944$	26.5026	0.862585
$945$	23.8824	0.776894
$946$	16.1320	0.524498
$947$	15.8760	0.515900	0.257950	−	0.966158i	$-0.416953\pi$
$947$	15.8760	0.515900	0.257950	+	0.966158i	$0.416953\pi$
$948$	11.2255	0.364586
$949$	9.46760	0.307331
$950$	22.3410	0.724837
$951$	−26.3997	−0.856069
$952$	−17.9859	−0.582927
$953$	24.7437	0.801528	0.400764	−	0.916181i	$-0.368745\pi$
$953$	24.7437	0.801528	0.400764	+	0.916181i	$0.368745\pi$
$954$	−7.36690	−0.238512
$955$	−14.1615	−0.458254
$956$	15.4450	0.499527
$957$	1.88591	0.0609629
$958$	−63.9250	−2.06532
$959$	25.7487	0.831469
$960$	−11.7578	−0.379481
$961$	−4.27369	−0.137861
$962$	−6.04339	−0.194847
$963$	7.07965	0.228138
$964$	87.5072	2.81842
$965$	−0.511643	−0.0164704
$966$	7.46493	0.240180
$967$	4.50132	0.144753	0.0723763	−	0.997377i	$-0.476942\pi$
$967$	4.50132	0.144753	0.0723763	+	0.997377i	$0.476942\pi$
$968$	−55.0407	−1.76908
$969$	−3.55084	−0.114070
$970$	48.3588	1.55271
$971$	−9.14396	−0.293444	−0.146722	−	0.989178i	$-0.546872\pi$
$971$	−9.14396	−0.293444	−0.146722	+	0.989178i	$0.546872\pi$
$972$	−76.1295	−2.44186
$973$	12.8502	0.411957
$974$	−60.5530	−1.94024
$975$	−1.71629	−0.0549654
$976$	42.9554	1.37497
$977$	26.5953	0.850858	0.425429	−	0.904992i	$-0.360123\pi$
$977$	26.5953	0.850858	0.425429	+	0.904992i	$0.360123\pi$
$978$	46.6984	1.49325
$979$	−29.7993	−0.952389
$980$	7.12670	0.227654
$981$	−22.1541	−0.707325
$982$	−15.0091	−0.478961
$983$	−14.8855	−0.474773	−0.237387	−	0.971415i	$-0.576291\pi$
$983$	−14.8855	−0.474773	−0.237387	+	0.971415i	$0.576291\pi$
$984$	−12.2301	−0.389880
$985$	−20.3607	−0.648746
$986$	−2.29905	−0.0732168
$987$	5.70024	0.181441
$988$	14.5892	0.464144
$989$	3.35090	0.106552
$990$	15.8481	0.503686
$991$	−14.8656	−0.472222	−0.236111	−	0.971726i	$-0.575873\pi$
$991$	−14.8656	−0.472222	−0.236111	+	0.971726i	$0.575873\pi$
$992$	50.6476	1.60806
$993$	−31.6805	−1.00535
$994$	−106.034	−3.36320
$995$	21.9987	0.697405
$996$	−31.5932	−1.00107
$997$	−3.64966	−0.115586	−0.0577930	−	0.998329i	$-0.518406\pi$
$997$	−3.64966	−0.115586	−0.0577930	+	0.998329i	$0.518406\pi$
$998$	−80.3989	−2.54498
$999$	15.1829	0.480365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.c.1.13	✓	13
3.2	odd	2		6003.2.a.o.1.1		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.c.1.13	✓	13	1.1	even	1	trivial
6003.2.a.o.1.1		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)

\(f(q)\)	\(=\)	\(q+2.60496 q^{2} -1.02046 q^{3} +4.78583 q^{4} +1.68070 q^{5} -2.65826 q^{6} +2.80821 q^{7} +7.25699 q^{8} -1.95866 q^{9} +O(q^{10})\)	\(q+2.60496 q^{2} -1.02046 q^{3} +4.78583 q^{4} +1.68070 q^{5} -2.65826 q^{6} +2.80821 q^{7} +7.25699 q^{8} -1.95866 q^{9} +4.37815 q^{10} -1.84810 q^{11} -4.88374 q^{12} -0.773187 q^{13} +7.31527 q^{14} -1.71508 q^{15} +9.33253 q^{16} -0.882567 q^{17} -5.10225 q^{18} -3.94266 q^{19} +8.04353 q^{20} -2.86566 q^{21} -4.81425 q^{22} -1.00000 q^{23} -7.40546 q^{24} -2.17526 q^{25} -2.01412 q^{26} +5.06011 q^{27} +13.4396 q^{28} +1.00000 q^{29} -4.46772 q^{30} +5.16975 q^{31} +9.79691 q^{32} +1.88591 q^{33} -2.29905 q^{34} +4.71974 q^{35} -9.37384 q^{36} +3.00050 q^{37} -10.2705 q^{38} +0.789005 q^{39} +12.1968 q^{40} +1.65149 q^{41} -7.46493 q^{42} -3.35090 q^{43} -8.84472 q^{44} -3.29192 q^{45} -2.60496 q^{46} -1.98916 q^{47} -9.52346 q^{48} +0.886016 q^{49} -5.66648 q^{50} +0.900622 q^{51} -3.70034 q^{52} +1.44385 q^{53} +13.1814 q^{54} -3.10610 q^{55} +20.3791 q^{56} +4.02332 q^{57} +2.60496 q^{58} +2.83981 q^{59} -8.20809 q^{60} +4.60276 q^{61} +13.4670 q^{62} -5.50033 q^{63} +6.85553 q^{64} -1.29949 q^{65} +4.91274 q^{66} -13.2444 q^{67} -4.22382 q^{68} +1.02046 q^{69} +12.2947 q^{70} -14.4949 q^{71} -14.2140 q^{72} -12.2449 q^{73} +7.81620 q^{74} +2.21976 q^{75} -18.8689 q^{76} -5.18986 q^{77} +2.05533 q^{78} -2.29854 q^{79} +15.6851 q^{80} +0.712362 q^{81} +4.30208 q^{82} +6.46906 q^{83} -13.7146 q^{84} -1.48333 q^{85} -8.72897 q^{86} -1.02046 q^{87} -13.4117 q^{88} +16.1242 q^{89} -8.57533 q^{90} -2.17127 q^{91} -4.78583 q^{92} -5.27551 q^{93} -5.18168 q^{94} -6.62640 q^{95} -9.99734 q^{96} +11.0455 q^{97} +2.30804 q^{98} +3.61982 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 3 q^{3} + 12 q^{4} + 16 q^{5} + q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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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