LMFDB - Embedded newform 5239.2.a.u.1.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5239,2,Mod(1,5239)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5239, 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("5239.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.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:	$41.8336256189$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.41
Character	$\chi$	$=$	5239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.48936 q^{2} -1.73680 q^{3} +0.218198 q^{4} -1.47351 q^{5} -2.58672 q^{6} -3.02295 q^{7} -2.65375 q^{8} +0.0164746 q^{9} +O(q^{10})$	\(q+1.48936 q^{2} -1.73680 q^{3} +0.218198 q^{4} -1.47351 q^{5} -2.58672 q^{6} -3.02295 q^{7} -2.65375 q^{8} +0.0164746 q^{9} -2.19459 q^{10} +0.0148607 q^{11} -0.378966 q^{12} -4.50226 q^{14} +2.55920 q^{15} -4.38879 q^{16} -5.48919 q^{17} +0.0245366 q^{18} +2.81790 q^{19} -0.321517 q^{20} +5.25026 q^{21} +0.0221329 q^{22} -7.41521 q^{23} +4.60903 q^{24} -2.82876 q^{25} +5.18179 q^{27} -0.659601 q^{28} -9.17591 q^{29} +3.81157 q^{30} -1.00000 q^{31} -1.22899 q^{32} -0.0258100 q^{33} -8.17539 q^{34} +4.45435 q^{35} +0.00359472 q^{36} +0.648559 q^{37} +4.19687 q^{38} +3.91033 q^{40} -10.3592 q^{41} +7.81953 q^{42} -11.7240 q^{43} +0.00324257 q^{44} -0.0242755 q^{45} -11.0439 q^{46} -4.10197 q^{47} +7.62244 q^{48} +2.13821 q^{49} -4.21305 q^{50} +9.53363 q^{51} +7.14159 q^{53} +7.71755 q^{54} -0.0218974 q^{55} +8.02214 q^{56} -4.89413 q^{57} -13.6663 q^{58} -10.7768 q^{59} +0.558412 q^{60} +7.53969 q^{61} -1.48936 q^{62} -0.0498018 q^{63} +6.94716 q^{64} -0.0384405 q^{66} -4.59520 q^{67} -1.19773 q^{68} +12.8787 q^{69} +6.63414 q^{70} +1.21134 q^{71} -0.0437193 q^{72} +6.27789 q^{73} +0.965939 q^{74} +4.91299 q^{75} +0.614860 q^{76} -0.0449231 q^{77} -11.0573 q^{79} +6.46693 q^{80} -9.04915 q^{81} -15.4286 q^{82} +11.5215 q^{83} +1.14560 q^{84} +8.08839 q^{85} -17.4612 q^{86} +15.9367 q^{87} -0.0394365 q^{88} +11.2734 q^{89} -0.0361550 q^{90} -1.61798 q^{92} +1.73680 q^{93} -6.10932 q^{94} -4.15222 q^{95} +2.13452 q^{96} -11.2239 q^{97} +3.18457 q^{98} +0.000244823 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) $ 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.48936	1.05314	0.526569	−	0.850132i	$-0.323478\pi$
$2$	1.48936	1.05314	0.526569	+	0.850132i	$0.323478\pi$
$3$	−1.73680	−1.00274	−0.501371	−	0.865232i	$-0.667171\pi$
$3$	−1.73680	−1.00274	−0.501371	+	0.865232i	$0.667171\pi$
$4$	0.218198	0.109099
$5$	−1.47351	−0.658975	−0.329488	−	0.944160i	$-0.606876\pi$
$5$	−1.47351	−0.658975	−0.329488	+	0.944160i	$0.606876\pi$
$6$	−2.58672	−1.05603
$7$	−3.02295	−1.14257	−0.571283	−	0.820753i	$-0.693554\pi$
$7$	−3.02295	−1.14257	−0.571283	+	0.820753i	$0.693554\pi$
$8$	−2.65375	−0.938241
$9$	0.0164746	0.00549152
$10$	−2.19459	−0.693991
$11$	0.0148607	0.00448066	0.00224033	−	0.999997i	$-0.499287\pi$
$11$	0.0148607	0.00448066	0.00224033	+	0.999997i	$0.499287\pi$
$12$	−0.378966	−0.109398
$13$	0	0
$13$	0	0
$14$	−4.50226	−1.20328
$15$	2.55920	0.660782
$16$	−4.38879	−1.09720
$17$	−5.48919	−1.33132	−0.665662	−	0.746253i	$-0.731851\pi$
$17$	−5.48919	−1.33132	−0.665662	+	0.746253i	$0.731851\pi$
$18$	0.0245366	0.00578333
$19$	2.81790	0.646471	0.323236	−	0.946319i	$-0.395229\pi$
$19$	2.81790	0.646471	0.323236	+	0.946319i	$0.395229\pi$
$20$	−0.321517	−0.0718935
$21$	5.25026	1.14570
$22$	0.0221329	0.00471876
$23$	−7.41521	−1.54618	−0.773089	−	0.634297i	$-0.781290\pi$
$23$	−7.41521	−1.54618	−0.773089	+	0.634297i	$0.781290\pi$
$24$	4.60903	0.940814
$25$	−2.82876	−0.565752
$26$	0	0
$27$	5.18179	0.997235
$28$	−0.659601	−0.124653
$29$	−9.17591	−1.70392	−0.851962	−	0.523603i	$-0.824587\pi$
$29$	−9.17591	−1.70392	−0.851962	+	0.523603i	$0.824587\pi$
$30$	3.81157	0.695894
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.22899	−0.217257
$33$	−0.0258100	−0.00449295
$34$	−8.17539	−1.40207
$35$	4.45435	0.752923
$36$	0.00359472	0.000599119 0
$37$	0.648559	0.106622	0.0533112	−	0.998578i	$-0.483022\pi$
$37$	0.648559	0.106622	0.0533112	+	0.998578i	$0.483022\pi$
$38$	4.19687	0.680823
$39$	0	0
$40$	3.91033	0.618278
$41$	−10.3592	−1.61784	−0.808920	−	0.587919i	$-0.799947\pi$
$41$	−10.3592	−1.61784	−0.808920	+	0.587919i	$0.799947\pi$
$42$	7.81953	1.20658
$43$	−11.7240	−1.78789	−0.893944	−	0.448178i	$-0.852073\pi$
$43$	−11.7240	−1.78789	−0.893944	+	0.448178i	$0.852073\pi$
$44$	0.00324257	0.000488836 0
$45$	−0.0242755	−0.00361878
$46$	−11.0439	−1.62834
$47$	−4.10197	−0.598334	−0.299167	−	0.954201i	$-0.596709\pi$
$47$	−4.10197	−0.598334	−0.299167	+	0.954201i	$0.596709\pi$
$48$	7.62244	1.10020
$49$	2.13821	0.305459
$50$	−4.21305	−0.595815
$51$	9.53363	1.33497
$52$	0	0
$53$	7.14159	0.980973	0.490487	−	0.871449i	$-0.336819\pi$
$53$	7.14159	0.980973	0.490487	+	0.871449i	$0.336819\pi$
$54$	7.71755	1.05023
$55$	−0.0218974	−0.00295265
$56$	8.02214	1.07200
$57$	−4.89413	−0.648244
$58$	−13.6663	−1.79447
$59$	−10.7768	−1.40301	−0.701507	−	0.712662i	$-0.747489\pi$
$59$	−10.7768	−1.40301	−0.701507	+	0.712662i	$0.747489\pi$
$60$	0.558412	0.0720906
$61$	7.53969	0.965358	0.482679	−	0.875797i	$-0.339664\pi$
$61$	7.53969	0.965358	0.482679	+	0.875797i	$0.339664\pi$
$62$	−1.48936	−0.189149
$63$	−0.0498018	−0.00627443
$64$	6.94716	0.868394
$65$	0	0
$66$	−0.0384405	−0.00473170
$67$	−4.59520	−0.561393	−0.280697	−	0.959797i	$-0.590565\pi$
$67$	−4.59520	−0.561393	−0.280697	+	0.959797i	$0.590565\pi$
$68$	−1.19773	−0.145246
$69$	12.8787	1.55042
$70$	6.63414	0.792932
$71$	1.21134	0.143759	0.0718797	−	0.997413i	$-0.477100\pi$
$71$	1.21134	0.143759	0.0718797	+	0.997413i	$0.477100\pi$
$72$	−0.0437193	−0.00515237
$73$	6.27789	0.734771	0.367386	−	0.930069i	$-0.380253\pi$
$73$	6.27789	0.734771	0.367386	+	0.930069i	$0.380253\pi$
$74$	0.965939	0.112288
$75$	4.91299	0.567303
$76$	0.614860	0.0705293
$77$	−0.0449231	−0.00511946
$78$	0	0
$79$	−11.0573	−1.24404	−0.622021	−	0.783001i	$-0.713688\pi$
$79$	−11.0573	−1.24404	−0.622021	+	0.783001i	$0.713688\pi$
$80$	6.46693	0.723025
$81$	−9.04915	−1.00546
$82$	−15.4286	−1.70381
$83$	11.5215	1.26464	0.632322	−	0.774705i	$-0.282102\pi$
$83$	11.5215	1.26464	0.632322	+	0.774705i	$0.282102\pi$
$84$	1.14560	0.124995
$85$	8.08839	0.877309
$86$	−17.4612	−1.88289
$87$	15.9367	1.70860
$88$	−0.0394365	−0.00420394
$89$	11.2734	1.19498	0.597488	−	0.801878i	$-0.296165\pi$
$89$	11.2734	1.19498	0.597488	+	0.801878i	$0.296165\pi$
$90$	−0.0361550	−0.00381107
$91$	0	0
$92$	−1.61798	−0.168687
$93$	1.73680	0.180098
$94$	−6.10932	−0.630129
$95$	−4.15222	−0.426008
$96$	2.13452	0.217853
$97$	−11.2239	−1.13961	−0.569807	−	0.821779i	$-0.692982\pi$
$97$	−11.2239	−1.13961	−0.569807	+	0.821779i	$0.692982\pi$
$98$	3.18457	0.321691
$99$	0.000244823 0	2.46057e−5 0
$100$	−0.617229	−0.0617229
$101$	5.54053	0.551304	0.275652	−	0.961258i	$-0.411106\pi$
$101$	5.54053	0.551304	0.275652	+	0.961258i	$0.411106\pi$
$102$	14.1990	1.40591
$103$	7.91033	0.779428	0.389714	−	0.920936i	$-0.372574\pi$
$103$	7.91033	0.779428	0.389714	+	0.920936i	$0.372574\pi$
$104$	0	0
$105$	−7.73632	−0.754988
$106$	10.6364	1.03310
$107$	15.2904	1.47818	0.739091	−	0.673606i	$-0.235256\pi$
$107$	15.2904	1.47818	0.739091	+	0.673606i	$0.235256\pi$
$108$	1.13066	0.108797
$109$	−6.69369	−0.641139	−0.320570	−	0.947225i	$-0.603874\pi$
$109$	−6.69369	−0.641139	−0.320570	+	0.947225i	$0.603874\pi$
$110$	−0.0326132	−0.00310954
$111$	−1.12642	−0.106915
$112$	13.2671	1.25362
$113$	9.47556	0.891385	0.445693	−	0.895186i	$-0.352957\pi$
$113$	9.47556	0.891385	0.445693	+	0.895186i	$0.352957\pi$
$114$	−7.28913	−0.682690
$115$	10.9264	1.01889
$116$	−2.00217	−0.185896
$117$	0	0
$118$	−16.0505	−1.47757
$119$	16.5935	1.52113
$120$	−6.79146	−0.619973
$121$	−10.9998	−0.999980
$122$	11.2293	1.01665
$123$	17.9919	1.62228
$124$	−0.218198	−0.0195948
$125$	11.5358	1.03179
$126$	−0.0741728	−0.00660784
$127$	2.64258	0.234491	0.117245	−	0.993103i	$-0.462594\pi$
$127$	2.64258	0.234491	0.117245	+	0.993103i	$0.462594\pi$
$128$	12.8048	1.13180
$129$	20.3622	1.79279
$130$	0	0
$131$	9.70918	0.848295	0.424148	−	0.905593i	$-0.360574\pi$
$131$	9.70918	0.848295	0.424148	+	0.905593i	$0.360574\pi$
$132$	−0.00563170	−0.000490176 0
$133$	−8.51837	−0.738636
$134$	−6.84392	−0.591224
$135$	−7.63543	−0.657153
$136$	14.5669	1.24910
$137$	−22.8463	−1.95189	−0.975945	−	0.218015i	$-0.930042\pi$
$137$	−22.8463	−1.95189	−0.975945	+	0.218015i	$0.930042\pi$
$138$	19.1811	1.63280
$139$	8.04037	0.681975	0.340988	−	0.940068i	$-0.389239\pi$
$139$	8.04037	0.681975	0.340988	+	0.940068i	$0.389239\pi$
$140$	0.971931	0.0821431
$141$	7.12431	0.599975
$142$	1.80412	0.151398
$143$	0	0
$144$	−0.0723033	−0.00602528
$145$	13.5208	1.12284
$146$	9.35005	0.773815
$147$	−3.71365	−0.306297
$148$	0.141514	0.0116324
$149$	5.57570	0.456779	0.228390	−	0.973570i	$-0.426654\pi$
$149$	5.57570	0.456779	0.228390	+	0.973570i	$0.426654\pi$
$150$	7.31722	0.597448
$151$	−8.89929	−0.724214	−0.362107	−	0.932136i	$-0.617943\pi$
$151$	−8.89929	−0.724214	−0.362107	+	0.932136i	$0.617943\pi$
$152$	−7.47800	−0.606546
$153$	−0.0904320	−0.00731100
$154$	−0.0669067	−0.00539149
$155$	1.47351	0.118355
$156$	0	0
$157$	−3.26511	−0.260584	−0.130292	−	0.991476i	$-0.541591\pi$
$157$	−3.26511	−0.260584	−0.130292	+	0.991476i	$0.541591\pi$
$158$	−16.4683	−1.31015
$159$	−12.4035	−0.983663
$160$	1.81094	0.143167
$161$	22.4158	1.76661
$162$	−13.4775	−1.05889
$163$	−1.36071	−0.106579	−0.0532894	−	0.998579i	$-0.516971\pi$
$163$	−1.36071	−0.106579	−0.0532894	+	0.998579i	$0.516971\pi$
$164$	−2.26036	−0.176505
$165$	0.0380314	0.00296074
$166$	17.1596	1.33184
$167$	−18.7783	−1.45311	−0.726554	−	0.687109i	$-0.758879\pi$
$167$	−18.7783	−1.45311	−0.726554	+	0.687109i	$0.758879\pi$
$168$	−13.9329	−1.07494
$169$	0	0
$170$	12.0465	0.923928
$171$	0.0464237	0.00355011
$172$	−2.55815	−0.195057
$173$	11.2727	0.857050	0.428525	−	0.903530i	$-0.359033\pi$
$173$	11.2727	0.857050	0.428525	+	0.903530i	$0.359033\pi$
$174$	23.7356	1.79939
$175$	8.55119	0.646409
$176$	−0.0652203	−0.00491617
$177$	18.7171	1.40686
$178$	16.7901	1.25847
$179$	14.9317	1.11605	0.558025	−	0.829824i	$-0.311559\pi$
$179$	14.9317	1.11605	0.558025	+	0.829824i	$0.311559\pi$
$180$	−0.00529686	−0.000394805 0
$181$	−14.5736	−1.08325	−0.541625	−	0.840620i	$-0.682191\pi$
$181$	−14.5736	−1.08325	−0.541625	+	0.840620i	$0.682191\pi$
$182$	0	0
$183$	−13.0949	−0.968005
$184$	19.6781	1.45069
$185$	−0.955660	−0.0702615
$186$	2.58672	0.189668
$187$	−0.0815731	−0.00596522
$188$	−0.895042	−0.0652777
$189$	−15.6643	−1.13941
$190$	−6.18415	−0.448645
$191$	−12.2048	−0.883109	−0.441555	−	0.897234i	$-0.645573\pi$
$191$	−12.2048	−0.883109	−0.441555	+	0.897234i	$0.645573\pi$
$192$	−12.0658	−0.870776
$193$	−18.5167	−1.33286	−0.666431	−	0.745567i	$-0.732179\pi$
$193$	−18.5167	−1.33286	−0.666431	+	0.745567i	$0.732179\pi$
$194$	−16.7164	−1.20017
$195$	0	0
$196$	0.466554	0.0333253
$197$	19.6853	1.40252	0.701261	−	0.712904i	$-0.252621\pi$
$197$	19.6853	1.40252	0.701261	+	0.712904i	$0.252621\pi$
$198$	0.000364630 0	2.59132e−5 0
$199$	−20.1620	−1.42924	−0.714622	−	0.699511i	$-0.753401\pi$
$199$	−20.1620	−1.42924	−0.714622	+	0.699511i	$0.753401\pi$
$200$	7.50681	0.530812
$201$	7.98095	0.562933
$202$	8.25186	0.580599
$203$	27.7383	1.94685
$204$	2.08022	0.145644
$205$	15.2645	1.06612
$206$	11.7813	0.820845
$207$	−0.122162	−0.00849088
$208$	0	0
$209$	0.0418759	0.00289662
$210$	−11.5222	−0.795106
$211$	11.7347	0.807851	0.403925	−	0.914792i	$-0.367646\pi$
$211$	11.7347	0.807851	0.403925	+	0.914792i	$0.367646\pi$
$212$	1.55828	0.107023
$213$	−2.10385	−0.144154
$214$	22.7730	1.55673
$215$	17.2754	1.17817
$216$	−13.7512	−0.935648
$217$	3.02295	0.205211
$218$	−9.96933	−0.675208
$219$	−10.9034	−0.736786
$220$	−0.00477797	−0.000322131 0
$221$	0	0
$222$	−1.67764	−0.112596
$223$	−7.27192	−0.486964	−0.243482	−	0.969905i	$-0.578290\pi$
$223$	−7.27192	−0.486964	−0.243482	+	0.969905i	$0.578290\pi$
$224$	3.71518	0.248231
$225$	−0.0466026	−0.00310684
$226$	14.1125	0.938752
$227$	−18.9330	−1.25662	−0.628312	−	0.777961i	$-0.716254\pi$
$227$	−18.9330	−1.25662	−0.628312	+	0.777961i	$0.716254\pi$
$228$	−1.06789	−0.0707227
$229$	−24.6280	−1.62746	−0.813732	−	0.581240i	$-0.802568\pi$
$229$	−24.6280	−1.62746	−0.813732	+	0.581240i	$0.802568\pi$
$230$	16.2734	1.07304
$231$	0.0780224	0.00513350
$232$	24.3506	1.59869
$233$	6.62438	0.433977	0.216989	−	0.976174i	$-0.430377\pi$
$233$	6.62438	0.433977	0.216989	+	0.976174i	$0.430377\pi$
$234$	0	0
$235$	6.04431	0.394287
$236$	−2.35147	−0.153067
$237$	19.2043	1.24745
$238$	24.7138	1.60196
$239$	−1.99612	−0.129118	−0.0645590	−	0.997914i	$-0.520564\pi$
$239$	−1.99612	−0.129118	−0.0645590	+	0.997914i	$0.520564\pi$
$240$	−11.2318	−0.725008
$241$	−0.174812	−0.0112606	−0.00563030	−	0.999984i	$-0.501792\pi$
$241$	−0.174812	−0.0112606	−0.00563030	+	0.999984i	$0.501792\pi$
$242$	−16.3826	−1.05312
$243$	0.171207	0.0109829
$244$	1.64514	0.105320
$245$	−3.15069	−0.201290
$246$	26.7965	1.70848
$247$	0	0
$248$	2.65375	0.168513
$249$	−20.0105	−1.26811
$250$	17.1809	1.08662
$251$	4.88412	0.308283	0.154142	−	0.988049i	$-0.450739\pi$
$251$	4.88412	0.308283	0.154142	+	0.988049i	$0.450739\pi$
$252$	−0.0108666	−0.000684534 0
$253$	−0.110195	−0.00692791
$254$	3.93575	0.246951
$255$	−14.0479	−0.879715
$256$	5.17669	0.323543
$257$	−7.36620	−0.459491	−0.229745	−	0.973251i	$-0.573789\pi$
$257$	−7.36620	−0.459491	−0.229745	+	0.973251i	$0.573789\pi$
$258$	30.3267	1.88806
$259$	−1.96056	−0.121823
$260$	0	0
$261$	−0.151169	−0.00935714
$262$	14.4605	0.893372
$263$	−24.0474	−1.48283	−0.741414	−	0.671048i	$-0.765845\pi$
$263$	−24.0474	−1.48283	−0.741414	+	0.671048i	$0.765845\pi$
$264$	0.0684933	0.00421547
$265$	−10.5232	−0.646437
$266$	−12.6869	−0.777886
$267$	−19.5796	−1.19825
$268$	−1.00266	−0.0612474
$269$	0.351556	0.0214348	0.0107174	−	0.999943i	$-0.496588\pi$
$269$	0.351556	0.0214348	0.0107174	+	0.999943i	$0.496588\pi$
$270$	−11.3719	−0.692073
$271$	−18.4751	−1.12228	−0.561142	−	0.827720i	$-0.689638\pi$
$271$	−18.4751	−1.12228	−0.561142	+	0.827720i	$0.689638\pi$
$272$	24.0909	1.46072
$273$	0	0
$274$	−34.0264	−2.05561
$275$	−0.0420373	−0.00253494
$276$	2.81012	0.169149
$277$	2.16088	0.129835	0.0649173	−	0.997891i	$-0.479322\pi$
$277$	2.16088	0.129835	0.0649173	+	0.997891i	$0.479322\pi$
$278$	11.9750	0.718214
$279$	−0.0164746	−0.000986307 0
$280$	−11.8207	−0.706424
$281$	−1.03090	−0.0614984	−0.0307492	−	0.999527i	$-0.509789\pi$
$281$	−1.03090	−0.0614984	−0.0307492	+	0.999527i	$0.509789\pi$
$282$	10.6107	0.631856
$283$	−0.921960	−0.0548048	−0.0274024	−	0.999624i	$-0.508724\pi$
$283$	−0.921960	−0.0548048	−0.0274024	+	0.999624i	$0.508724\pi$
$284$	0.264312	0.0156840
$285$	7.21157	0.427176
$286$	0	0
$287$	31.3154	1.84849
$288$	−0.0202471	−0.00119307
$289$	13.1312	0.772424
$290$	20.1374	1.18251
$291$	19.4936	1.14274
$292$	1.36982	0.0801628
$293$	−11.9255	−0.696696	−0.348348	−	0.937365i	$-0.613257\pi$
$293$	−11.9255	−0.696696	−0.348348	+	0.937365i	$0.613257\pi$
$294$	−5.53097	−0.322573
$295$	15.8797	0.924552
$296$	−1.72111	−0.100038
$297$	0.0770049	0.00446828
$298$	8.30424	0.481052
$299$	0	0
$300$	1.07200	0.0618922
$301$	35.4409	2.04278
$302$	−13.2543	−0.762697
$303$	−9.62280	−0.552815
$304$	−12.3672	−0.709306
$305$	−11.1098	−0.636147
$306$	−0.134686	−0.00769949
$307$	−19.8887	−1.13511	−0.567555	−	0.823336i	$-0.692110\pi$
$307$	−19.8887	−1.13511	−0.567555	+	0.823336i	$0.692110\pi$
$308$	−0.00980212	−0.000558528 0
$309$	−13.7387	−0.781565
$310$	2.19459	0.124645
$311$	21.6135	1.22559	0.612795	−	0.790242i	$-0.290045\pi$
$311$	21.6135	1.22559	0.612795	+	0.790242i	$0.290045\pi$
$312$	0	0
$313$	−9.00482	−0.508982	−0.254491	−	0.967075i	$-0.581908\pi$
$313$	−9.00482	−0.508982	−0.254491	+	0.967075i	$0.581908\pi$
$314$	−4.86292	−0.274431
$315$	0.0733835	0.00413469
$316$	−2.41268	−0.135724
$317$	23.6803	1.33002	0.665009	−	0.746835i	$-0.268428\pi$
$317$	23.6803	1.33002	0.665009	+	0.746835i	$0.268428\pi$
$318$	−18.4733	−1.03593
$319$	−0.136360	−0.00763471
$320$	−10.2367	−0.572250
$321$	−26.5564	−1.48223
$322$	33.3852	1.86049
$323$	−15.4680	−0.860662
$324$	−1.97451	−0.109695
$325$	0	0
$326$	−2.02658	−0.112242
$327$	11.6256	0.642897
$328$	27.4908	1.51792
$329$	12.4001	0.683637
$330$	0.0566425	0.00311807
$331$	16.0402	0.881649	0.440824	−	0.897593i	$-0.354686\pi$
$331$	16.0402	0.881649	0.440824	+	0.897593i	$0.354686\pi$
$332$	2.51396	0.137971
$333$	0.0106847	0.000585520 0
$334$	−27.9677	−1.53032
$335$	6.77109	0.369944
$336$	−23.0422	−1.25706
$337$	−9.13159	−0.497430	−0.248715	−	0.968577i	$-0.580008\pi$
$337$	−9.13159	−0.497430	−0.248715	+	0.968577i	$0.580008\pi$
$338$	0	0
$339$	−16.4571	−0.893830
$340$	1.76487	0.0957135
$341$	−0.0148607	−0.000804751 0
$342$	0.0691417	0.00373876
$343$	14.6969	0.793559
$344$	31.1125	1.67747
$345$	−18.9770	−1.02169
$346$	16.7892	0.902591
$347$	−13.6337	−0.731898	−0.365949	−	0.930635i	$-0.619256\pi$
$347$	−13.6337	−0.731898	−0.365949	+	0.930635i	$0.619256\pi$
$348$	3.47736	0.186406
$349$	−2.92909	−0.156791	−0.0783954	−	0.996922i	$-0.524980\pi$
$349$	−2.92909	−0.156791	−0.0783954	+	0.996922i	$0.524980\pi$
$350$	12.7358	0.680758
$351$	0	0
$352$	−0.0182637	−0.000973457 0
$353$	−10.2558	−0.545859	−0.272929	−	0.962034i	$-0.587992\pi$
$353$	−10.2558	−0.545859	−0.272929	+	0.962034i	$0.587992\pi$
$354$	27.8765	1.48162
$355$	−1.78492	−0.0947339
$356$	2.45983	0.130371
$357$	−28.8197	−1.52530
$358$	22.2387	1.17535
$359$	28.6543	1.51232	0.756159	−	0.654388i	$-0.227073\pi$
$359$	28.6543	1.51232	0.756159	+	0.654388i	$0.227073\pi$
$360$	0.0644210	0.00339529
$361$	−11.0594	−0.582075
$362$	−21.7054	−1.14081
$363$	19.1044	1.00272
$364$	0	0
$365$	−9.25055	−0.484196
$366$	−19.5031	−1.01944
$367$	1.08930	0.0568611	0.0284305	−	0.999596i	$-0.490949\pi$
$367$	1.08930	0.0568611	0.0284305	+	0.999596i	$0.490949\pi$
$368$	32.5438	1.69646
$369$	−0.170664	−0.00888440
$370$	−1.42332	−0.0739951
$371$	−21.5887	−1.12083
$372$	0.378966	0.0196485
$373$	−30.9995	−1.60509	−0.802546	−	0.596591i	$-0.796522\pi$
$373$	−30.9995	−1.60509	−0.802546	+	0.596591i	$0.796522\pi$
$374$	−0.121492	−0.00628219
$375$	−20.0353	−1.03462
$376$	10.8856	0.561382
$377$	0	0
$378$	−23.3298	−1.19995
$379$	−2.17422	−0.111682	−0.0558411	−	0.998440i	$-0.517784\pi$
$379$	−2.17422	−0.111682	−0.0558411	+	0.998440i	$0.517784\pi$
$380$	−0.906005	−0.0464771
$381$	−4.58963	−0.235134
$382$	−18.1774	−0.930035
$383$	−19.2592	−0.984098	−0.492049	−	0.870568i	$-0.663752\pi$
$383$	−19.2592	−0.984098	−0.492049	+	0.870568i	$0.663752\pi$
$384$	−22.2394	−1.13490
$385$	0.0661947	0.00337360
$386$	−27.5781	−1.40369
$387$	−0.193147	−0.00981823
$388$	−2.44903	−0.124331
$389$	34.7613	1.76247	0.881235	−	0.472679i	$-0.156713\pi$
$389$	34.7613	1.76247	0.881235	+	0.472679i	$0.156713\pi$
$390$	0	0
$391$	40.7035	2.05847
$392$	−5.67428	−0.286594
$393$	−16.8629	−0.850621
$394$	29.3186	1.47705
$395$	16.2931	0.819792
$396$	5.34199e−5 0	2.68445e−6 0
$397$	−11.1808	−0.561147	−0.280573	−	0.959833i	$-0.590525\pi$
$397$	−11.1808	−0.561147	−0.280573	+	0.959833i	$0.590525\pi$
$398$	−30.0285	−1.50519
$399$	14.7947	0.740662
$400$	12.4148	0.620741
$401$	−12.8807	−0.643231	−0.321616	−	0.946870i	$-0.604226\pi$
$401$	−12.8807	−0.643231	−0.321616	+	0.946870i	$0.604226\pi$
$402$	11.8865	0.592846
$403$	0	0
$404$	1.20893	0.0601467
$405$	13.3340	0.662574
$406$	41.3124	2.05030
$407$	0.00963803	0.000477739 0
$408$	−25.2998	−1.25253
$409$	−25.5483	−1.26328	−0.631641	−	0.775261i	$-0.717618\pi$
$409$	−25.5483	−1.26328	−0.631641	+	0.775261i	$0.717618\pi$
$410$	22.7343	1.12277
$411$	39.6794	1.95724
$412$	1.72602	0.0850347
$413$	32.5776	1.60304
$414$	−0.181944	−0.00894206
$415$	−16.9770	−0.833369
$416$	0	0
$417$	−13.9645	−0.683845
$418$	0.0623684	0.00305054
$419$	10.0768	0.492283	0.246141	−	0.969234i	$-0.420837\pi$
$419$	10.0768	0.492283	0.246141	+	0.969234i	$0.420837\pi$
$420$	−1.68805	−0.0823684
$421$	7.59436	0.370126	0.185063	−	0.982727i	$-0.440751\pi$
$421$	7.59436	0.370126	0.185063	+	0.982727i	$0.440751\pi$
$422$	17.4772	0.850778
$423$	−0.0675783	−0.00328577
$424$	−18.9520	−0.920390
$425$	15.5276	0.753199
$426$	−3.13340	−0.151814
$427$	−22.7921	−1.10299
$428$	3.33634	0.161268
$429$	0	0
$430$	25.7293	1.24078
$431$	−11.4938	−0.553638	−0.276819	−	0.960922i	$-0.589280\pi$
$431$	−11.4938	−0.553638	−0.276819	+	0.960922i	$0.589280\pi$
$432$	−22.7418	−1.09416
$433$	−4.87226	−0.234146	−0.117073	−	0.993123i	$-0.537351\pi$
$433$	−4.87226	−0.234146	−0.117073	+	0.993123i	$0.537351\pi$
$434$	4.50226	0.216116
$435$	−23.4830	−1.12592
$436$	−1.46055	−0.0699476
$437$	−20.8953	−0.999560
$438$	−16.2392	−0.775937
$439$	6.23788	0.297718	0.148859	−	0.988858i	$-0.452440\pi$
$439$	6.23788	0.297718	0.148859	+	0.988858i	$0.452440\pi$
$440$	0.0581102	0.00277029
$441$	0.0352262	0.00167744
$442$	0	0
$443$	−17.0172	−0.808510	−0.404255	−	0.914646i	$-0.632469\pi$
$443$	−17.0172	−0.808510	−0.404255	+	0.914646i	$0.632469\pi$
$444$	−0.245782	−0.0116643
$445$	−16.6115	−0.787460
$446$	−10.8305	−0.512840
$447$	−9.68388	−0.458032
$448$	−21.0009	−0.992199
$449$	0.0740650	0.00349534	0.00174767	−	0.999998i	$-0.499444\pi$
$449$	0.0740650	0.00349534	0.00174767	+	0.999998i	$0.499444\pi$
$450$	−0.0694081	−0.00327193
$451$	−0.153945	−0.00724900
$452$	2.06755	0.0972492
$453$	15.4563	0.726200
$454$	−28.1980	−1.32340
$455$	0	0
$456$	12.9878	0.608209
$457$	−26.7775	−1.25260	−0.626299	−	0.779583i	$-0.715431\pi$
$457$	−26.7775	−1.25260	−0.626299	+	0.779583i	$0.715431\pi$
$458$	−36.6800	−1.71394
$459$	−28.4438	−1.32764
$460$	2.38412	0.111160
$461$	−31.7676	−1.47956	−0.739782	−	0.672847i	$-0.765071\pi$
$461$	−31.7676	−1.47956	−0.739782	+	0.672847i	$0.765071\pi$
$462$	0.116204	0.00540628
$463$	−3.48674	−0.162042	−0.0810212	−	0.996712i	$-0.525818\pi$
$463$	−3.48674	−0.162042	−0.0810212	+	0.996712i	$0.525818\pi$
$464$	40.2711	1.86954
$465$	−2.55920	−0.118680
$466$	9.86609	0.457038
$467$	−38.6293	−1.78755	−0.893774	−	0.448517i	$-0.851952\pi$
$467$	−38.6293	−1.78755	−0.893774	+	0.448517i	$0.851952\pi$
$468$	0	0
$469$	13.8911	0.641429
$470$	9.00217	0.415239
$471$	5.67083	0.261298
$472$	28.5988	1.31637
$473$	−0.174226	−0.00801093
$474$	28.6021	1.31374
$475$	−7.97117	−0.365742
$476$	3.62067	0.165953
$477$	0.117655	0.00538704
$478$	−2.97294	−0.135979
$479$	−7.32951	−0.334894	−0.167447	−	0.985881i	$-0.553552\pi$
$479$	−7.32951	−0.334894	−0.167447	+	0.985881i	$0.553552\pi$
$480$	−3.14524	−0.143560
$481$	0	0
$482$	−0.260358	−0.0118590
$483$	−38.9318	−1.77146
$484$	−2.40013	−0.109097
$485$	16.5385	0.750977
$486$	0.254989	0.0115665
$487$	31.4911	1.42700	0.713499	−	0.700656i	$-0.247109\pi$
$487$	31.4911	1.42700	0.713499	+	0.700656i	$0.247109\pi$
$488$	−20.0084	−0.905739
$489$	2.36327	0.106871
$490$	−4.69251	−0.211986
$491$	−8.42612	−0.380266	−0.190133	−	0.981758i	$-0.560892\pi$
$491$	−8.42612	−0.380266	−0.190133	+	0.981758i	$0.560892\pi$
$492$	3.92580	0.176989
$493$	50.3683	2.26848
$494$	0	0
$495$	−0.000360750 0	−1.62145e−5 0
$496$	4.38879	0.197062
$497$	−3.66181	−0.164255
$498$	−29.8028	−1.33550
$499$	−18.6200	−0.833545	−0.416772	−	0.909011i	$-0.636839\pi$
$499$	−18.6200	−0.833545	−0.416772	+	0.909011i	$0.636839\pi$
$500$	2.51708	0.112567
$501$	32.6142	1.45709
$502$	7.27422	0.324664
$503$	23.9128	1.06622	0.533110	−	0.846046i	$-0.321023\pi$
$503$	23.9128	1.06622	0.533110	+	0.846046i	$0.321023\pi$
$504$	0.132161	0.00588693
$505$	−8.16405	−0.363295
$506$	−0.164120	−0.00729604
$507$	0	0
$508$	0.576605	0.0255827
$509$	−5.73109	−0.254026	−0.127013	−	0.991901i	$-0.540539\pi$
$509$	−5.73109	−0.254026	−0.127013	+	0.991901i	$0.540539\pi$
$510$	−20.9224	−0.926461
$511$	−18.9777	−0.839525
$512$	−17.8997	−0.791061
$513$	14.6018	0.644684
$514$	−10.9709	−0.483907
$515$	−11.6560	−0.513623
$516$	4.44299	0.195592
$517$	−0.0609581	−0.00268094
$518$	−2.91998	−0.128297
$519$	−19.5785	−0.859400
$520$	0	0
$521$	43.1259	1.88938	0.944691	−	0.327963i	$-0.106362\pi$
$521$	43.1259	1.88938	0.944691	+	0.327963i	$0.106362\pi$
$522$	−0.225146	−0.00985436
$523$	27.7934	1.21532	0.607661	−	0.794196i	$-0.292108\pi$
$523$	27.7934	1.21532	0.607661	+	0.794196i	$0.292108\pi$
$524$	2.11852	0.0925481
$525$	−14.8517	−0.648182
$526$	−35.8153	−1.56162
$527$	5.48919	0.239113
$528$	0.113275	0.00492965
$529$	31.9854	1.39067
$530$	−15.6729	−0.680787
$531$	−0.177542	−0.00770469
$532$	−1.85869	−0.0805845
$533$	0	0
$534$	−29.1611	−1.26193
$535$	−22.5306	−0.974085
$536$	12.1945	0.526722
$537$	−25.9334	−1.11911
$538$	0.523594	0.0225738
$539$	0.0317753	0.00136866
$540$	−1.66604	−0.0716947
$541$	25.5474	1.09837	0.549185	−	0.835701i	$-0.314938\pi$
$541$	25.5474	1.09837	0.549185	+	0.835701i	$0.314938\pi$
$542$	−27.5161	−1.18192
$543$	25.3115	1.08622
$544$	6.74618	0.289240
$545$	9.86324	0.422495
$546$	0	0
$547$	−20.8410	−0.891098	−0.445549	−	0.895258i	$-0.646992\pi$
$547$	−20.8410	−0.891098	−0.445549	+	0.895258i	$0.646992\pi$
$548$	−4.98501	−0.212949
$549$	0.124213	0.00530128
$550$	−0.0626087	−0.00266965
$551$	−25.8568	−1.10154
$552$	−34.1769	−1.45467
$553$	33.4256	1.42140
$554$	3.21833	0.136734
$555$	1.65979	0.0704542
$556$	1.75439	0.0744028
$557$	−3.00369	−0.127270	−0.0636352	−	0.997973i	$-0.520269\pi$
$557$	−3.00369	−0.127270	−0.0636352	+	0.997973i	$0.520269\pi$
$558$	−0.0245366	−0.00103872
$559$	0	0
$560$	−19.5492	−0.826105
$561$	0.141676	0.00598157
$562$	−1.53538	−0.0647663
$563$	−7.11559	−0.299886	−0.149943	−	0.988695i	$-0.547909\pi$
$563$	−7.11559	−0.299886	−0.149943	+	0.988695i	$0.547909\pi$
$564$	1.55451	0.0654567
$565$	−13.9624	−0.587401
$566$	−1.37313	−0.0577170
$567$	27.3551	1.14881
$568$	−3.21459	−0.134881
$569$	31.6390	1.32637	0.663187	−	0.748453i	$-0.269203\pi$
$569$	31.6390	1.32637	0.663187	+	0.748453i	$0.269203\pi$
$570$	10.7406	0.449876
$571$	−2.30954	−0.0966512	−0.0483256	−	0.998832i	$-0.515389\pi$
$571$	−2.30954	−0.0966512	−0.0483256	+	0.998832i	$0.515389\pi$
$572$	0	0
$573$	21.1973	0.885531
$574$	46.6400	1.94671
$575$	20.9759	0.874754
$576$	0.114451	0.00476881
$577$	−17.9966	−0.749208	−0.374604	−	0.927185i	$-0.622221\pi$
$577$	−17.9966	−0.749208	−0.374604	+	0.927185i	$0.622221\pi$
$578$	19.5571	0.813469
$579$	32.1598	1.33652
$580$	2.95022	0.122501
$581$	−34.8288	−1.44494
$582$	29.0331	1.20346
$583$	0.106129	0.00439541
$584$	−16.6599	−0.689393
$585$	0	0
$586$	−17.7614	−0.733717
$587$	−28.3927	−1.17189	−0.585947	−	0.810350i	$-0.699277\pi$
$587$	−28.3927	−1.17189	−0.585947	+	0.810350i	$0.699277\pi$
$588$	−0.810311	−0.0334167
$589$	−2.81790	−0.116110
$590$	23.6506	0.973680
$591$	−34.1895	−1.40637
$592$	−2.84639	−0.116986
$593$	−45.7660	−1.87938	−0.939692	−	0.342023i	$-0.888888\pi$
$593$	−45.7660	−1.87938	−0.939692	+	0.342023i	$0.888888\pi$
$594$	0.114688	0.00470571
$595$	−24.4508	−1.00238
$596$	1.21661	0.0498342
$597$	35.0173	1.43316
$598$	0	0
$599$	−32.1404	−1.31322	−0.656610	−	0.754230i	$-0.728010\pi$
$599$	−32.1404	−1.31322	−0.656610	+	0.754230i	$0.728010\pi$
$600$	−13.0378	−0.532267
$601$	11.6357	0.474629	0.237314	−	0.971433i	$-0.423733\pi$
$601$	11.6357	0.474629	0.237314	+	0.971433i	$0.423733\pi$
$602$	52.7844	2.15133
$603$	−0.0757040	−0.00308290
$604$	−1.94181	−0.0790110
$605$	16.2083	0.658962
$606$	−14.3318	−0.582191
$607$	−41.8176	−1.69732	−0.848662	−	0.528936i	$-0.822591\pi$
$607$	−41.8176	−1.69732	−0.848662	+	0.528936i	$0.822591\pi$
$608$	−3.46318	−0.140451
$609$	−48.1759	−1.95219
$610$	−16.5465	−0.669950
$611$	0	0
$612$	−0.0197321	−0.000797622 0
$613$	10.9775	0.443376	0.221688	−	0.975118i	$-0.428843\pi$
$613$	10.9775	0.443376	0.221688	+	0.975118i	$0.428843\pi$
$614$	−29.6215	−1.19543
$615$	−26.5113	−1.06904
$616$	0.119214	0.00480329
$617$	12.6111	0.507705	0.253852	−	0.967243i	$-0.418302\pi$
$617$	12.6111	0.507705	0.253852	+	0.967243i	$0.418302\pi$
$618$	−20.4618	−0.823095
$619$	3.52492	0.141679	0.0708393	−	0.997488i	$-0.477432\pi$
$619$	3.52492	0.141679	0.0708393	+	0.997488i	$0.477432\pi$
$620$	0.321517	0.0129125
$621$	−38.4241	−1.54190
$622$	32.1903	1.29071
$623$	−34.0789	−1.36534
$624$	0	0
$625$	−2.85432	−0.114173
$626$	−13.4114	−0.536029
$627$	−0.0727301	−0.00290456
$628$	−0.712439	−0.0284294
$629$	−3.56006	−0.141949
$630$	0.109295	0.00435440
$631$	17.0654	0.679362	0.339681	−	0.940541i	$-0.389681\pi$
$631$	17.0654	0.679362	0.339681	+	0.940541i	$0.389681\pi$
$632$	29.3432	1.16721
$633$	−20.3808	−0.810066
$634$	35.2685	1.40069
$635$	−3.89387	−0.154524
$636$	−2.70642	−0.107317
$637$	0	0
$638$	−0.203090	−0.00804040
$639$	0.0199563	0.000789458 0
$640$	−18.8681	−0.745826
$641$	22.3997	0.884734	0.442367	−	0.896834i	$-0.354139\pi$
$641$	22.3997	0.884734	0.442367	+	0.896834i	$0.354139\pi$
$642$	−39.5521	−1.56100
$643$	11.2847	0.445024	0.222512	−	0.974930i	$-0.428574\pi$
$643$	11.2847	0.445024	0.222512	+	0.974930i	$0.428574\pi$
$644$	4.89108	0.192736
$645$	−30.0040	−1.18140
$646$	−23.0374	−0.906396
$647$	−26.8541	−1.05574	−0.527871	−	0.849325i	$-0.677009\pi$
$647$	−26.8541	−1.05574	−0.527871	+	0.849325i	$0.677009\pi$
$648$	24.0142	0.943366
$649$	−0.160150	−0.00628644
$650$	0	0
$651$	−5.25026	−0.205774
$652$	−0.296903	−0.0116276
$653$	−7.22476	−0.282727	−0.141363	−	0.989958i	$-0.545149\pi$
$653$	−7.22476	−0.282727	−0.141363	+	0.989958i	$0.545149\pi$
$654$	17.3147	0.677060
$655$	−14.3066	−0.559005
$656$	45.4644	1.77509
$657$	0.103426	0.00403501
$658$	18.4682	0.719964
$659$	−39.5960	−1.54244	−0.771221	−	0.636567i	$-0.780354\pi$
$659$	−39.5960	−1.54244	−0.771221	+	0.636567i	$0.780354\pi$
$660$	0.00829838	0.000323014 0
$661$	−17.9704	−0.698968	−0.349484	−	0.936942i	$-0.613643\pi$
$661$	−17.9704	−0.698968	−0.349484	+	0.936942i	$0.613643\pi$
$662$	23.8896	0.928497
$663$	0	0
$664$	−30.5750	−1.18654
$665$	12.5519	0.486743
$666$	0.0159134	0.000616633 0
$667$	68.0414	2.63457
$668$	−4.09739	−0.158533
$669$	12.6299	0.488299
$670$	10.0846	0.389602
$671$	0.112045	0.00432544
$672$	−6.45253	−0.248912
$673$	40.1383	1.54722	0.773610	−	0.633663i	$-0.218449\pi$
$673$	40.1383	1.54722	0.773610	+	0.633663i	$0.218449\pi$
$674$	−13.6002	−0.523862
$675$	−14.6580	−0.564188
$676$	0	0
$677$	7.86849	0.302411	0.151205	−	0.988502i	$-0.451685\pi$
$677$	7.86849	0.302411	0.151205	+	0.988502i	$0.451685\pi$
$678$	−24.5106	−0.941326
$679$	33.9292	1.30208
$680$	−21.4646	−0.823128
$681$	32.8828	1.26007
$682$	−0.0221329	−0.000847514 0
$683$	35.3164	1.35135	0.675673	−	0.737201i	$-0.263853\pi$
$683$	35.3164	1.35135	0.675673	+	0.737201i	$0.263853\pi$
$684$	0.0101296	0.000387313 0
$685$	33.6643	1.28625
$686$	21.8890	0.835727
$687$	42.7739	1.63193
$688$	51.4540	1.96166
$689$	0	0
$690$	−28.2636	−1.07598
$691$	23.9725	0.911958	0.455979	−	0.889990i	$-0.349289\pi$
$691$	23.9725	0.911958	0.455979	+	0.889990i	$0.349289\pi$
$692$	2.45969	0.0935032
$693$	−0.000740088 0	−2.81136e−5 0
$694$	−20.3056	−0.770789
$695$	−11.8476	−0.449405
$696$	−42.2921	−1.60308
$697$	56.8638	2.15387
$698$	−4.36248	−0.165122
$699$	−11.5052	−0.435167
$700$	1.86585	0.0705226
$701$	29.0364	1.09669	0.548345	−	0.836252i	$-0.315258\pi$
$701$	29.0364	1.09669	0.548345	+	0.836252i	$0.315258\pi$
$702$	0	0
$703$	1.82758	0.0689283
$704$	0.103239	0.00389098
$705$	−10.4978	−0.395369
$706$	−15.2745	−0.574864
$707$	−16.7487	−0.629901
$708$	4.08403	0.153487
$709$	28.4199	1.06733	0.533665	−	0.845696i	$-0.320814\pi$
$709$	28.4199	1.06733	0.533665	+	0.845696i	$0.320814\pi$
$710$	−2.65840	−0.0997678
$711$	−0.182164	−0.00683168
$712$	−29.9167	−1.12118
$713$	7.41521	0.277702
$714$	−42.9229	−1.60635
$715$	0	0
$716$	3.25807	0.121760
$717$	3.46686	0.129472
$718$	42.6767	1.59268
$719$	1.16613	0.0434892	0.0217446	−	0.999764i	$-0.493078\pi$
$719$	1.16613	0.0434892	0.0217446	+	0.999764i	$0.493078\pi$
$720$	0.106540	0.00397051
$721$	−23.9125	−0.890548
$722$	−16.4715	−0.613005
$723$	0.303613	0.0112915
$724$	−3.17994	−0.118181
$725$	25.9565	0.963998
$726$	28.4534	1.05600
$727$	−39.7938	−1.47587	−0.737935	−	0.674872i	$-0.764199\pi$
$727$	−39.7938	−1.47587	−0.737935	+	0.674872i	$0.764199\pi$
$728$	0	0
$729$	26.8501	0.994448
$730$	−13.7774	−0.509925
$731$	64.3551	2.38026
$732$	−2.85729	−0.105608
$733$	35.3965	1.30740	0.653699	−	0.756754i	$-0.273216\pi$
$733$	35.3965	1.30740	0.653699	+	0.756754i	$0.273216\pi$
$734$	1.62236	0.0598826
$735$	5.47211	0.201842
$736$	9.11325	0.335919
$737$	−0.0682878	−0.00251542
$738$	−0.254180	−0.00935650
$739$	4.76812	0.175398	0.0876990	−	0.996147i	$-0.472049\pi$
$739$	4.76812	0.175398	0.0876990	+	0.996147i	$0.472049\pi$
$740$	−0.208523	−0.00766546
$741$	0	0
$742$	−32.1533	−1.18039
$743$	−47.4743	−1.74166	−0.870831	−	0.491582i	$-0.836419\pi$
$743$	−47.4743	−1.74166	−0.870831	+	0.491582i	$0.836419\pi$
$744$	−4.60903	−0.168975
$745$	−8.21587	−0.301006
$746$	−46.1694	−1.69038
$747$	0.189811	0.00694482
$748$	−0.0177991	−0.000650799 0
$749$	−46.2222	−1.68892
$750$	−29.8399	−1.08960
$751$	−46.7776	−1.70694	−0.853470	−	0.521142i	$-0.825506\pi$
$751$	−46.7776	−1.70694	−0.853470	+	0.521142i	$0.825506\pi$
$752$	18.0027	0.656490
$753$	−8.48274	−0.309128
$754$	0	0
$755$	13.1132	0.477239
$756$	−3.41791	−0.124308
$757$	−18.4221	−0.669563	−0.334782	−	0.942296i	$-0.608663\pi$
$757$	−18.4221	−0.669563	−0.334782	+	0.942296i	$0.608663\pi$
$758$	−3.23820	−0.117617
$759$	0.191387	0.00694691
$760$	11.0189	0.399699
$761$	50.4930	1.83037	0.915184	−	0.403036i	$-0.132045\pi$
$761$	50.4930	1.83037	0.915184	+	0.403036i	$0.132045\pi$
$762$	−6.83562	−0.247628
$763$	20.2347	0.732545
$764$	−2.66306	−0.0963463
$765$	0.133253	0.00481776
$766$	−28.6839	−1.03639
$767$	0	0
$768$	−8.99087	−0.324430
$769$	34.4840	1.24353	0.621763	−	0.783205i	$-0.286417\pi$
$769$	34.4840	1.24353	0.621763	+	0.783205i	$0.286417\pi$
$770$	0.0985879	0.00355286
$771$	12.7936	0.460751
$772$	−4.04031	−0.145414
$773$	33.8539	1.21764	0.608820	−	0.793308i	$-0.291643\pi$
$773$	33.8539	1.21764	0.608820	+	0.793308i	$0.291643\pi$
$774$	−0.287666	−0.0103399
$775$	2.82876	0.101612
$776$	29.7854	1.06923
$777$	3.40510	0.122157
$778$	51.7722	1.85612
$779$	−29.1913	−1.04589
$780$	0	0
$781$	0.0180013	0.000644138 0
$782$	60.6223	2.16785
$783$	−47.5476	−1.69921
$784$	−9.38416	−0.335149
$785$	4.81117	0.171718
$786$	−25.1150	−0.895821
$787$	−24.9536	−0.889500	−0.444750	−	0.895655i	$-0.646707\pi$
$787$	−24.9536	−0.889500	−0.444750	+	0.895655i	$0.646707\pi$
$788$	4.29530	0.153014
$789$	41.7656	1.48689
$790$	24.2662	0.863354
$791$	−28.6441	−1.01847
$792$	−0.000649699 0	−2.30861e−5 0
$793$	0	0
$794$	−16.6522	−0.590965
$795$	18.2768	0.648210
$796$	−4.39930	−0.155929
$797$	18.0451	0.639189	0.319594	−	0.947554i	$-0.396453\pi$
$797$	18.0451	0.639189	0.319594	+	0.947554i	$0.396453\pi$
$798$	22.0347	0.780019
$799$	22.5165	0.796577
$800$	3.47653	0.122914
$801$	0.185724	0.00656224
$802$	−19.1840	−0.677411
$803$	0.0932937	0.00329226
$804$	1.74143	0.0614154
$805$	−33.0300	−1.16415
$806$	0	0
$807$	−0.610583	−0.0214935
$808$	−14.7032	−0.517256
$809$	38.2784	1.34580	0.672899	−	0.739735i	$-0.265049\pi$
$809$	38.2784	1.34580	0.672899	+	0.739735i	$0.265049\pi$
$810$	19.8592	0.697782
$811$	−28.8116	−1.01171	−0.505856	−	0.862618i	$-0.668823\pi$
$811$	−28.8116	−1.01171	−0.505856	+	0.862618i	$0.668823\pi$
$812$	6.05244	0.212399
$813$	32.0876	1.12536
$814$	0.0143545	0.000503125 0
$815$	2.00502	0.0702327
$816$	−41.8410	−1.46473
$817$	−33.0370	−1.15582
$818$	−38.0507	−1.33041
$819$	0	0
$820$	3.33067	0.116312
$821$	43.9360	1.53338	0.766688	−	0.642019i	$-0.221903\pi$
$821$	43.9360	1.53338	0.766688	+	0.642019i	$0.221903\pi$
$822$	59.0970	2.06125
$823$	−47.7186	−1.66337	−0.831683	−	0.555250i	$-0.812623\pi$
$823$	−47.7186	−1.66337	−0.831683	+	0.555250i	$0.812623\pi$
$824$	−20.9920	−0.731291
$825$	0.0730104	0.00254189
$826$	48.5198	1.68822
$827$	−25.6950	−0.893504	−0.446752	−	0.894658i	$-0.647419\pi$
$827$	−25.6950	−0.893504	−0.446752	+	0.894658i	$0.647419\pi$
$828$	−0.0266556	−0.000926346 0
$829$	46.1554	1.60304	0.801521	−	0.597967i	$-0.204024\pi$
$829$	46.1554	1.60304	0.801521	+	0.597967i	$0.204024\pi$
$830$	−25.2849	−0.877652
$831$	−3.75301	−0.130191
$832$	0	0
$833$	−11.7371	−0.406665
$834$	−20.7982	−0.720183
$835$	27.6701	0.957562
$836$	0.00913724	0.000316018 0
$837$	−5.18179	−0.179109
$838$	15.0080	0.518441
$839$	−42.7228	−1.47496	−0.737478	−	0.675371i	$-0.763983\pi$
$839$	−42.7228	−1.47496	−0.737478	+	0.675371i	$0.763983\pi$
$840$	20.5302	0.708361
$841$	55.1974	1.90336
$842$	11.3107	0.389794
$843$	1.79047	0.0616670
$844$	2.56049	0.0881357
$845$	0	0
$846$	−0.100648	−0.00346037
$847$	33.2518	1.14254
$848$	−31.3429	−1.07632
$849$	1.60126	0.0549551
$850$	23.1262	0.793222
$851$	−4.80920	−0.164857
$852$	−0.459056	−0.0157270
$853$	−21.6680	−0.741897	−0.370949	−	0.928653i	$-0.620967\pi$
$853$	−21.6680	−0.741897	−0.370949	+	0.928653i	$0.620967\pi$
$854$	−33.9456	−1.16160
$855$	−0.0684060	−0.00233943
$856$	−40.5769	−1.38689
$857$	36.7134	1.25411	0.627053	−	0.778977i	$-0.284261\pi$
$857$	36.7134	1.25411	0.627053	+	0.778977i	$0.284261\pi$
$858$	0	0
$859$	37.8180	1.29034	0.645168	−	0.764041i	$-0.276788\pi$
$859$	37.8180	1.29034	0.645168	+	0.764041i	$0.276788\pi$
$860$	3.76946	0.128538
$861$	−54.3886	−1.85356
$862$	−17.1185	−0.583057
$863$	−18.4354	−0.627547	−0.313774	−	0.949498i	$-0.601593\pi$
$863$	−18.4354	−0.627547	−0.313774	+	0.949498i	$0.601593\pi$
$864$	−6.36838	−0.216657
$865$	−16.6105	−0.564774
$866$	−7.25656	−0.246588
$867$	−22.8063	−0.774542
$868$	0.659601	0.0223883
$869$	−0.164319	−0.00557413
$870$	−34.9746	−1.18575
$871$	0	0
$872$	17.7634	0.601544
$873$	−0.184909	−0.00625821
$874$	−31.1207	−1.05267
$875$	−34.8721	−1.17889
$876$	−2.37911	−0.0803826
$877$	−27.8022	−0.938813	−0.469406	−	0.882982i	$-0.655532\pi$
$877$	−27.8022	−0.938813	−0.469406	+	0.882982i	$0.655532\pi$
$878$	9.29046	0.313538
$879$	20.7122	0.698607
$880$	0.0961030	0.00323963
$881$	33.7456	1.13692	0.568459	−	0.822712i	$-0.307540\pi$
$881$	33.7456	1.13692	0.568459	+	0.822712i	$0.307540\pi$
$882$	0.0524645	0.00176657
$883$	−49.4867	−1.66536	−0.832680	−	0.553755i	$-0.813194\pi$
$883$	−49.4867	−1.66536	−0.832680	+	0.553755i	$0.813194\pi$
$884$	0	0
$885$	−27.5799	−0.927087
$886$	−25.3447	−0.851473
$887$	−41.9781	−1.40949	−0.704744	−	0.709462i	$-0.748938\pi$
$887$	−41.9781	−1.40949	−0.704744	+	0.709462i	$0.748938\pi$
$888$	2.98923	0.100312
$889$	−7.98838	−0.267922
$890$	−24.7405	−0.829303
$891$	−0.134477	−0.00450513
$892$	−1.58672	−0.0531272
$893$	−11.5590	−0.386806
$894$	−14.4228	−0.482371
$895$	−22.0021	−0.735449
$896$	−38.7083	−1.29315
$897$	0	0
$898$	0.110310	0.00368108
$899$	9.17591	0.306034
$900$	−0.0101686	−0.000338953 0
$901$	−39.2016	−1.30599
$902$	−0.229280	−0.00763419
$903$	−61.5538	−2.04838
$904$	−25.1457	−0.836335
$905$	21.4745	0.713835
$906$	23.0200	0.764789
$907$	−57.2085	−1.89958	−0.949788	−	0.312893i	$-0.898702\pi$
$907$	−57.2085	−1.89958	−0.949788	+	0.312893i	$0.898702\pi$
$908$	−4.13113	−0.137096
$909$	0.0912779	0.00302750
$910$	0	0
$911$	42.3680	1.40371	0.701857	−	0.712318i	$-0.252355\pi$
$911$	42.3680	1.40371	0.701857	+	0.712318i	$0.252355\pi$
$912$	21.4793	0.711251
$913$	0.171217	0.00566645
$914$	−39.8813	−1.31916
$915$	19.2955	0.637891
$916$	−5.37378	−0.177555
$917$	−29.3504	−0.969234
$918$	−42.3631	−1.39819
$919$	−5.36562	−0.176995	−0.0884977	−	0.996076i	$-0.528207\pi$
$919$	−5.36562	−0.176995	−0.0884977	+	0.996076i	$0.528207\pi$
$920$	−28.9959	−0.955968
$921$	34.5427	1.13822
$922$	−47.3134	−1.55818
$923$	0	0
$924$	0.0170243	0.000560059 0
$925$	−1.83462	−0.0603218
$926$	−5.19301	−0.170653
$927$	0.130319	0.00428024
$928$	11.2771	0.370190
$929$	−0.793573	−0.0260363	−0.0130181	−	0.999915i	$-0.504144\pi$
$929$	−0.793573	−0.0260363	−0.0130181	+	0.999915i	$0.504144\pi$
$930$	−3.81157	−0.124986
$931$	6.02528	0.197470
$932$	1.44543	0.0473465
$933$	−37.5384	−1.22895
$934$	−57.5329	−1.88254
$935$	0.120199	0.00393093
$936$	0	0
$937$	−31.8747	−1.04130	−0.520651	−	0.853769i	$-0.674311\pi$
$937$	−31.8747	−1.04130	−0.520651	+	0.853769i	$0.674311\pi$
$938$	20.6888	0.675514
$939$	15.6396	0.510378
$940$	1.31886	0.0430164
$941$	5.18519	0.169032	0.0845162	−	0.996422i	$-0.473066\pi$
$941$	5.18519	0.169032	0.0845162	+	0.996422i	$0.473066\pi$
$942$	8.44592	0.275183
$943$	76.8159	2.50147
$944$	47.2969	1.53938
$945$	23.0815	0.750842
$946$	−0.259486	−0.00843661
$947$	8.87820	0.288503	0.144251	−	0.989541i	$-0.453923\pi$
$947$	8.87820	0.288503	0.144251	+	0.989541i	$0.453923\pi$
$948$	4.19034	0.136096
$949$	0	0
$950$	−11.8719	−0.385177
$951$	−41.1279	−1.33366
$952$	−44.0351	−1.42718
$953$	9.44379	0.305914	0.152957	−	0.988233i	$-0.451120\pi$
$953$	9.44379	0.305914	0.152957	+	0.988233i	$0.451120\pi$
$954$	0.175230	0.00567329
$955$	17.9839	0.581947
$956$	−0.435549	−0.0140866
$957$	0.236831	0.00765565
$958$	−10.9163	−0.352689
$959$	69.0632	2.23017
$960$	17.7791	0.573819
$961$	1.00000	0.0322581
$962$	0	0
$963$	0.251903	0.00811747
$964$	−0.0381435	−0.00122852
$965$	27.2846	0.878323
$966$	−57.9835	−1.86559
$967$	17.3044	0.556473	0.278236	−	0.960513i	$-0.410250\pi$
$967$	17.3044	0.556473	0.278236	+	0.960513i	$0.410250\pi$
$968$	29.1906	0.938223
$969$	26.8648	0.863022
$970$	24.6319	0.790882
$971$	15.0360	0.482529	0.241265	−	0.970459i	$-0.422438\pi$
$971$	15.0360	0.482529	0.241265	+	0.970459i	$0.422438\pi$
$972$	0.0373570	0.00119823
$973$	−24.3056	−0.779202
$974$	46.9017	1.50283
$975$	0	0
$976$	−33.0901	−1.05919
$977$	−50.5878	−1.61845	−0.809224	−	0.587500i	$-0.800112\pi$
$977$	−50.5878	−1.61845	−0.809224	+	0.587500i	$0.800112\pi$
$978$	3.51977	0.112550
$979$	0.167530	0.00535429
$980$	−0.687473	−0.0219605
$981$	−0.110276	−0.00352083
$982$	−12.5495	−0.400472
$983$	−10.9477	−0.349179	−0.174589	−	0.984641i	$-0.555860\pi$
$983$	−10.9477	−0.349179	−0.174589	+	0.984641i	$0.555860\pi$
$984$	−47.7460	−1.52209
$985$	−29.0066	−0.924228
$986$	75.0167	2.38902
$987$	−21.5364	−0.685512
$988$	0	0
$989$	86.9357	2.76440
$990$	−0.000537288 0	−1.70761e−5 0
$991$	−30.8229	−0.979121	−0.489561	−	0.871969i	$-0.662843\pi$
$991$	−30.8229	−0.979121	−0.489561	+	0.871969i	$0.662843\pi$
$992$	1.22899	0.0390206
$993$	−27.8586	−0.884066
$994$	−5.45376	−0.172983
$995$	29.7089	0.941836
$996$	−4.36624	−0.138350
$997$	48.8986	1.54863	0.774317	−	0.632798i	$-0.218094\pi$
$997$	48.8986	1.54863	0.774317	+	0.632798i	$0.218094\pi$
$998$	−27.7319	−0.877837
$999$	3.36069	0.106328

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.u.1.41	✓	54
13.12	even	2		5239.2.a.v.1.14	yes	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.u.1.41	✓	54	1.1	even	1	trivial
5239.2.a.v.1.14	yes	54	13.12	even	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:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q+1.48936 q^{2} -1.73680 q^{3} +0.218198 q^{4} -1.47351 q^{5} -2.58672 q^{6} -3.02295 q^{7} -2.65375 q^{8} +0.0164746 q^{9} +O(q^{10})\)	\(q+1.48936 q^{2} -1.73680 q^{3} +0.218198 q^{4} -1.47351 q^{5} -2.58672 q^{6} -3.02295 q^{7} -2.65375 q^{8} +0.0164746 q^{9} -2.19459 q^{10} +0.0148607 q^{11} -0.378966 q^{12} -4.50226 q^{14} +2.55920 q^{15} -4.38879 q^{16} -5.48919 q^{17} +0.0245366 q^{18} +2.81790 q^{19} -0.321517 q^{20} +5.25026 q^{21} +0.0221329 q^{22} -7.41521 q^{23} +4.60903 q^{24} -2.82876 q^{25} +5.18179 q^{27} -0.659601 q^{28} -9.17591 q^{29} +3.81157 q^{30} -1.00000 q^{31} -1.22899 q^{32} -0.0258100 q^{33} -8.17539 q^{34} +4.45435 q^{35} +0.00359472 q^{36} +0.648559 q^{37} +4.19687 q^{38} +3.91033 q^{40} -10.3592 q^{41} +7.81953 q^{42} -11.7240 q^{43} +0.00324257 q^{44} -0.0242755 q^{45} -11.0439 q^{46} -4.10197 q^{47} +7.62244 q^{48} +2.13821 q^{49} -4.21305 q^{50} +9.53363 q^{51} +7.14159 q^{53} +7.71755 q^{54} -0.0218974 q^{55} +8.02214 q^{56} -4.89413 q^{57} -13.6663 q^{58} -10.7768 q^{59} +0.558412 q^{60} +7.53969 q^{61} -1.48936 q^{62} -0.0498018 q^{63} +6.94716 q^{64} -0.0384405 q^{66} -4.59520 q^{67} -1.19773 q^{68} +12.8787 q^{69} +6.63414 q^{70} +1.21134 q^{71} -0.0437193 q^{72} +6.27789 q^{73} +0.965939 q^{74} +4.91299 q^{75} +0.614860 q^{76} -0.0449231 q^{77} -11.0573 q^{79} +6.46693 q^{80} -9.04915 q^{81} -15.4286 q^{82} +11.5215 q^{83} +1.14560 q^{84} +8.08839 q^{85} -17.4612 q^{86} +15.9367 q^{87} -0.0394365 q^{88} +11.2734 q^{89} -0.0361550 q^{90} -1.61798 q^{92} +1.73680 q^{93} -6.10932 q^{94} -4.15222 q^{95} +2.13452 q^{96} -11.2239 q^{97} +3.18457 q^{98} +0.000244823 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9}+O(q^{10}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9	\( 54 q - 2 q^{2} + 7 q^{3} + 64 q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} - 6 q^{8} + 95 q^{9} - 6 q^{10} + 7 q^{11} + 5 q^{12} + 38 q^{14} - 4 q^{15} + 76 q^{16} + 62 q^{17} + 9 q^{18} - 8 q^{19} - 16 q^{20} + 6 q^{21} + 15 q^{22} + 38 q^{23} + 99 q^{24} + 87 q^{25} + 25 q^{27} - 19 q^{28} + 95 q^{29} + 41 q^{30} - 54 q^{31} - 9 q^{32} - 12 q^{33} - 7 q^{34} + 53 q^{35} + 97 q^{36} + 24 q^{37} - 16 q^{38} - 28 q^{40} - 22 q^{41} + 11 q^{42} + 11 q^{43} + 24 q^{44} - 8 q^{45} - 9 q^{46} - 45 q^{47} + 2 q^{48} + 105 q^{49} - 6 q^{50} + 58 q^{51} + 56 q^{53} - 50 q^{54} + q^{55} + 91 q^{56} + 51 q^{57} - 25 q^{58} - 36 q^{59} - 100 q^{60} + 48 q^{61} + 2 q^{62} + 56 q^{63} + 90 q^{64} - 24 q^{66} - 26 q^{67} + 140 q^{68} + 47 q^{69} + 24 q^{70} - 40 q^{71} - 7 q^{72} - 9 q^{73} + 114 q^{74} + 18 q^{75} + 67 q^{76} + 65 q^{77} + 33 q^{79} - 53 q^{80} + 210 q^{81} - 6 q^{82} + 41 q^{83} + 37 q^{84} - 37 q^{85} + 42 q^{86} - 16 q^{87} - 22 q^{88} + 24 q^{89} - 40 q^{90} + 87 q^{92} - 7 q^{93} - 4 q^{94} + 61 q^{95} + 200 q^{96} - 28 q^{97} - 68 q^{98} - 39 q^{99}+O(q^{100}) \) 54 * q - 2 * q^2 + 7 * q^3 + 64 * q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 - 6 * q^8 + 95 * q^9 - 6 * q^10 + 7 * q^11 + 5 * q^12 + 38 * q^14 - 4 * q^15 + 76 * q^16 + 62 * q^17 + 9 * q^18 - 8 * q^19 - 16 * q^20 + 6 * q^21 + 15 * q^22 + 38 * q^23 + 99 * q^24 + 87 * q^25 + 25 * q^27 - 19 * q^28 + 95 * q^29 + 41 * q^30 - 54 * q^31 - 9 * q^32 - 12 * q^33 - 7 * q^34 + 53 * q^35 + 97 * q^36 + 24 * q^37 - 16 * q^38 - 28 * q^40 - 22 * q^41 + 11 * q^42 + 11 * q^43 + 24 * q^44 - 8 * q^45 - 9 * q^46 - 45 * q^47 + 2 * q^48 + 105 * q^49 - 6 * q^50 + 58 * q^51 + 56 * q^53 - 50 * q^54 + q^55 + 91 * q^56 + 51 * q^57 - 25 * q^58 - 36 * q^59 - 100 * q^60 + 48 * q^61 + 2 * q^62 + 56 * q^63 + 90 * q^64 - 24 * q^66 - 26 * q^67 + 140 * q^68 + 47 * q^69 + 24 * q^70 - 40 * q^71 - 7 * q^72 - 9 * q^73 + 114 * q^74 + 18 * q^75 + 67 * q^76 + 65 * q^77 + 33 * q^79 - 53 * q^80 + 210 * q^81 - 6 * q^82 + 41 * q^83 + 37 * q^84 - 37 * q^85 + 42 * q^86 - 16 * q^87 - 22 * q^88 + 24 * q^89 - 40 * q^90 + 87 * q^92 - 7 * q^93 - 4 * q^94 + 61 * q^95 + 200 * q^96 - 28 * q^97 - 68 * q^98 - 39 * q^99

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