LMFDB - Embedded newform 5077.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$0$
Dimension:	$216$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49199 q^{2} +1.36067 q^{3} +4.21003 q^{4} -1.81458 q^{5} -3.39077 q^{6} +0.512290 q^{7} -5.50738 q^{8} -1.14858 q^{9} +O(q^{10})$	\(q-2.49199 q^{2} +1.36067 q^{3} +4.21003 q^{4} -1.81458 q^{5} -3.39077 q^{6} +0.512290 q^{7} -5.50738 q^{8} -1.14858 q^{9} +4.52191 q^{10} -3.00840 q^{11} +5.72845 q^{12} -2.35946 q^{13} -1.27662 q^{14} -2.46903 q^{15} +5.30430 q^{16} +3.40058 q^{17} +2.86227 q^{18} -3.31296 q^{19} -7.63942 q^{20} +0.697056 q^{21} +7.49692 q^{22} -4.63075 q^{23} -7.49372 q^{24} -1.70732 q^{25} +5.87976 q^{26} -5.64484 q^{27} +2.15676 q^{28} +4.84984 q^{29} +6.15281 q^{30} -7.08465 q^{31} -2.20351 q^{32} -4.09343 q^{33} -8.47423 q^{34} -0.929588 q^{35} -4.83558 q^{36} -3.49372 q^{37} +8.25588 q^{38} -3.21044 q^{39} +9.99356 q^{40} +9.86767 q^{41} -1.73706 q^{42} +2.36986 q^{43} -12.6655 q^{44} +2.08419 q^{45} +11.5398 q^{46} +10.7109 q^{47} +7.21739 q^{48} -6.73756 q^{49} +4.25462 q^{50} +4.62706 q^{51} -9.93341 q^{52} -6.73596 q^{53} +14.0669 q^{54} +5.45897 q^{55} -2.82138 q^{56} -4.50784 q^{57} -12.0858 q^{58} -3.76947 q^{59} -10.3947 q^{60} -5.85227 q^{61} +17.6549 q^{62} -0.588408 q^{63} -5.11746 q^{64} +4.28142 q^{65} +10.2008 q^{66} -7.69235 q^{67} +14.3166 q^{68} -6.30091 q^{69} +2.31653 q^{70} +0.317430 q^{71} +6.32570 q^{72} +1.09624 q^{73} +8.70633 q^{74} -2.32309 q^{75} -13.9477 q^{76} -1.54117 q^{77} +8.00040 q^{78} +10.2566 q^{79} -9.62505 q^{80} -4.23500 q^{81} -24.5902 q^{82} -0.399742 q^{83} +2.93463 q^{84} -6.17062 q^{85} -5.90568 q^{86} +6.59902 q^{87} +16.5684 q^{88} +15.2571 q^{89} -5.19380 q^{90} -1.20873 q^{91} -19.4956 q^{92} -9.63985 q^{93} -26.6915 q^{94} +6.01162 q^{95} -2.99825 q^{96} +11.2814 q^{97} +16.7900 q^{98} +3.45541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) $ 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * 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 $

$2$	−2.49199	−1.76211	−0.881053	−	0.473018i	$-0.843165\pi$
$2$	−2.49199	−1.76211	−0.881053	+	0.473018i	$0.843165\pi$
$3$	1.36067	0.785582	0.392791	−	0.919628i	$-0.371510\pi$
$3$	1.36067	0.785582	0.392791	+	0.919628i	$0.371510\pi$
$4$	4.21003	2.10502
$5$	−1.81458	−0.811503	−0.405751	−	0.913983i	$-0.632990\pi$
$5$	−1.81458	−0.811503	−0.405751	+	0.913983i	$0.632990\pi$
$6$	−3.39077	−1.38428
$7$	0.512290	0.193627	0.0968136	−	0.995303i	$-0.469135\pi$
$7$	0.512290	0.193627	0.0968136	+	0.995303i	$0.469135\pi$
$8$	−5.50738	−1.94715
$9$	−1.14858	−0.382862
$10$	4.52191	1.42995
$11$	−3.00840	−0.907067	−0.453534	−	0.891239i	$-0.649837\pi$
$11$	−3.00840	−0.907067	−0.453534	+	0.891239i	$0.649837\pi$
$12$	5.72845	1.65366
$13$	−2.35946	−0.654397	−0.327198	−	0.944956i	$-0.606105\pi$
$13$	−2.35946	−0.654397	−0.327198	+	0.944956i	$0.606105\pi$
$14$	−1.27662	−0.341192
$15$	−2.46903	−0.637502
$16$	5.30430	1.32608
$17$	3.40058	0.824763	0.412381	−	0.911011i	$-0.364697\pi$
$17$	3.40058	0.824763	0.412381	+	0.911011i	$0.364697\pi$
$18$	2.86227	0.674643
$19$	−3.31296	−0.760046	−0.380023	−	0.924977i	$-0.624084\pi$
$19$	−3.31296	−0.760046	−0.380023	+	0.924977i	$0.624084\pi$
$20$	−7.63942	−1.70823
$21$	0.697056	0.152110
$22$	7.49692	1.59835
$23$	−4.63075	−0.965578	−0.482789	−	0.875737i	$-0.660376\pi$
$23$	−4.63075	−0.965578	−0.482789	+	0.875737i	$0.660376\pi$
$24$	−7.49372	−1.52965
$25$	−1.70732	−0.341463
$26$	5.87976	1.15312
$27$	−5.64484	−1.08635
$28$	2.15676	0.407588
$29$	4.84984	0.900593	0.450297	−	0.892879i	$-0.351318\pi$
$29$	4.84984	0.900593	0.450297	+	0.892879i	$0.351318\pi$
$30$	6.15281	1.12335
$31$	−7.08465	−1.27244	−0.636220	−	0.771508i	$-0.719503\pi$
$31$	−7.08465	−1.27244	−0.636220	+	0.771508i	$0.719503\pi$
$32$	−2.20351	−0.389530
$33$	−4.09343	−0.712575
$34$	−8.47423	−1.45332
$35$	−0.929588	−0.157129
$36$	−4.83558	−0.805930
$37$	−3.49372	−0.574364	−0.287182	−	0.957876i	$-0.592718\pi$
$37$	−3.49372	−0.574364	−0.287182	+	0.957876i	$0.592718\pi$
$38$	8.25588	1.33928
$39$	−3.21044	−0.514082
$40$	9.99356	1.58012
$41$	9.86767	1.54107	0.770535	−	0.637397i	$-0.219989\pi$
$41$	9.86767	1.54107	0.770535	+	0.637397i	$0.219989\pi$
$42$	−1.73706	−0.268034
$43$	2.36986	0.361401	0.180700	−	0.983538i	$-0.442164\pi$
$43$	2.36986	0.361401	0.180700	+	0.983538i	$0.442164\pi$
$44$	−12.6655	−1.90939
$45$	2.08419	0.310693
$46$	11.5398	1.70145
$47$	10.7109	1.56234	0.781172	−	0.624316i	$-0.214622\pi$
$47$	10.7109	1.56234	0.781172	+	0.624316i	$0.214622\pi$
$48$	7.21739	1.04174
$49$	−6.73756	−0.962508
$50$	4.25462	0.601694
$51$	4.62706	0.647918
$52$	−9.93341	−1.37752
$53$	−6.73596	−0.925256	−0.462628	−	0.886553i	$-0.653093\pi$
$53$	−6.73596	−0.925256	−0.462628	+	0.886553i	$0.653093\pi$
$54$	14.0669	1.91426
$55$	5.45897	0.736088
$56$	−2.82138	−0.377022
$57$	−4.50784	−0.597078
$58$	−12.0858	−1.58694
$59$	−3.76947	−0.490743	−0.245372	−	0.969429i	$-0.578910\pi$
$59$	−3.76947	−0.490743	−0.245372	+	0.969429i	$0.578910\pi$
$60$	−10.3947	−1.34195
$61$	−5.85227	−0.749307	−0.374653	−	0.927165i	$-0.622238\pi$
$61$	−5.85227	−0.749307	−0.374653	+	0.927165i	$0.622238\pi$
$62$	17.6549	2.24217
$63$	−0.588408	−0.0741325
$64$	−5.11746	−0.639682
$65$	4.28142	0.531045
$66$	10.2008	1.25563
$67$	−7.69235	−0.939770	−0.469885	−	0.882728i	$-0.655705\pi$
$67$	−7.69235	−0.939770	−0.469885	+	0.882728i	$0.655705\pi$
$68$	14.3166	1.73614
$69$	−6.30091	−0.758541
$70$	2.31653	0.276878
$71$	0.317430	0.0376720	0.0188360	−	0.999823i	$-0.494004\pi$
$71$	0.317430	0.0376720	0.0188360	+	0.999823i	$0.494004\pi$
$72$	6.32570	0.745491
$73$	1.09624	0.128305	0.0641526	−	0.997940i	$-0.479566\pi$
$73$	1.09624	0.128305	0.0641526	+	0.997940i	$0.479566\pi$
$74$	8.70633	1.01209
$75$	−2.32309	−0.268247
$76$	−13.9477	−1.59991
$77$	−1.54117	−0.175633
$78$	8.00040	0.905867
$79$	10.2566	1.15396	0.576978	−	0.816759i	$-0.304232\pi$
$79$	10.2566	1.15396	0.576978	+	0.816759i	$0.304232\pi$
$80$	−9.62505	−1.07611
$81$	−4.23500	−0.470555
$82$	−24.5902	−2.71553
$83$	−0.399742	−0.0438774	−0.0219387	−	0.999759i	$-0.506984\pi$
$83$	−0.399742	−0.0438774	−0.0219387	+	0.999759i	$0.506984\pi$
$84$	2.93463	0.320194
$85$	−6.17062	−0.669297
$86$	−5.90568	−0.636826
$87$	6.59902	0.707489
$88$	16.5684	1.76620
$89$	15.2571	1.61725	0.808625	−	0.588324i	$-0.200212\pi$
$89$	15.2571	1.61725	0.808625	+	0.588324i	$0.200212\pi$
$90$	−5.19380	−0.547474
$91$	−1.20873	−0.126709
$92$	−19.4956	−2.03256
$93$	−9.63985	−0.999606
$94$	−26.6915	−2.75302
$95$	6.01162	0.616779
$96$	−2.99825	−0.306008
$97$	11.2814	1.14545	0.572724	−	0.819748i	$-0.305887\pi$
$97$	11.2814	1.14545	0.572724	+	0.819748i	$0.305887\pi$
$98$	16.7900	1.69604
$99$	3.45541	0.347281
$100$	−7.18785	−0.718785
$101$	6.46082	0.642876	0.321438	−	0.946931i	$-0.395834\pi$
$101$	6.46082	0.642876	0.321438	+	0.946931i	$0.395834\pi$
$102$	−11.5306	−1.14170
$103$	−8.13531	−0.801596	−0.400798	−	0.916166i	$-0.631267\pi$
$103$	−8.13531	−0.801596	−0.400798	+	0.916166i	$0.631267\pi$
$104$	12.9945	1.27421
$105$	−1.26486	−0.123438
$106$	16.7860	1.63040
$107$	10.4304	1.00834	0.504171	−	0.863604i	$-0.331798\pi$
$107$	10.4304	1.00834	0.504171	+	0.863604i	$0.331798\pi$
$108$	−23.7650	−2.28678
$109$	−3.74534	−0.358739	−0.179369	−	0.983782i	$-0.557406\pi$
$109$	−3.74534	−0.358739	−0.179369	+	0.983782i	$0.557406\pi$
$110$	−13.6037	−1.29706
$111$	−4.75379	−0.451210
$112$	2.71734	0.256764
$113$	−15.2430	−1.43394	−0.716969	−	0.697105i	$-0.754471\pi$
$113$	−15.2430	−1.43394	−0.716969	+	0.697105i	$0.754471\pi$
$114$	11.2335	1.05211
$115$	8.40285	0.783569
$116$	20.4180	1.89576
$117$	2.71004	0.250543
$118$	9.39349	0.864741
$119$	1.74208	0.159697
$120$	13.5979	1.24131
$121$	−1.94952	−0.177229
$122$	14.5838	1.32036
$123$	13.4266	1.21064
$124$	−29.8266	−2.67851
$125$	12.1709	1.08860
$126$	1.46631	0.130629
$127$	−22.0317	−1.95500	−0.977501	−	0.210932i	$-0.932350\pi$
$127$	−22.0317	−1.95500	−0.977501	+	0.210932i	$0.932350\pi$
$128$	17.1597	1.51672
$129$	3.22459	0.283910
$130$	−10.6693	−0.935757
$131$	8.36085	0.730491	0.365246	−	0.930911i	$-0.380985\pi$
$131$	8.36085	0.730491	0.365246	+	0.930911i	$0.380985\pi$
$132$	−17.2335	−1.49998
$133$	−1.69720	−0.147166
$134$	19.1693	1.65597
$135$	10.2430	0.881577
$136$	−18.7283	−1.60594
$137$	−5.51957	−0.471568	−0.235784	−	0.971805i	$-0.575766\pi$
$137$	−5.51957	−0.471568	−0.235784	+	0.971805i	$0.575766\pi$
$138$	15.7018	1.33663
$139$	13.7119	1.16303	0.581514	−	0.813537i	$-0.302461\pi$
$139$	13.7119	1.16303	0.581514	+	0.813537i	$0.302461\pi$
$140$	−3.91359	−0.330759
$141$	14.5740	1.22735
$142$	−0.791033	−0.0663820
$143$	7.09821	0.593582
$144$	−6.09244	−0.507703
$145$	−8.80040	−0.730834
$146$	−2.73182	−0.226087
$147$	−9.16758	−0.756129
$148$	−14.7087	−1.20905
$149$	−3.14875	−0.257956	−0.128978	−	0.991647i	$-0.541170\pi$
$149$	−3.14875	−0.257956	−0.128978	+	0.991647i	$0.541170\pi$
$150$	5.78912	0.472680
$151$	20.9607	1.70575	0.852877	−	0.522112i	$-0.174856\pi$
$151$	20.9607	1.70575	0.852877	+	0.522112i	$0.174856\pi$
$152$	18.2458	1.47993
$153$	−3.90586	−0.315770
$154$	3.84059	0.309484
$155$	12.8556	1.03259
$156$	−13.5161	−1.08215
$157$	6.51309	0.519801	0.259901	−	0.965635i	$-0.416310\pi$
$157$	6.51309	0.519801	0.259901	+	0.965635i	$0.416310\pi$
$158$	−25.5594	−2.03339
$159$	−9.16541	−0.726864
$160$	3.99844	0.316105
$161$	−2.37229	−0.186962
$162$	10.5536	0.829168
$163$	11.4678	0.898224	0.449112	−	0.893475i	$-0.351740\pi$
$163$	11.4678	0.898224	0.449112	+	0.893475i	$0.351740\pi$
$164$	41.5432	3.24398
$165$	7.42784	0.578257
$166$	0.996154	0.0773165
$167$	−7.28721	−0.563901	−0.281951	−	0.959429i	$-0.590981\pi$
$167$	−7.28721	−0.563901	−0.281951	+	0.959429i	$0.590981\pi$
$168$	−3.83895	−0.296182
$169$	−7.43294	−0.571765
$170$	15.3771	1.17937
$171$	3.80522	0.290992
$172$	9.97719	0.760754
$173$	3.74482	0.284714	0.142357	−	0.989815i	$-0.454532\pi$
$173$	3.74482	0.284714	0.142357	+	0.989815i	$0.454532\pi$
$174$	−16.4447	−1.24667
$175$	−0.874640	−0.0661166
$176$	−15.9575	−1.20284
$177$	−5.12899	−0.385519
$178$	−38.0206	−2.84977
$179$	−7.78663	−0.582000	−0.291000	−	0.956723i	$-0.593988\pi$
$179$	−7.78663	−0.582000	−0.291000	+	0.956723i	$0.593988\pi$
$180$	8.77452	0.654014
$181$	21.5800	1.60403	0.802014	−	0.597306i	$-0.203762\pi$
$181$	21.5800	1.60403	0.802014	+	0.597306i	$0.203762\pi$
$182$	3.01214	0.223275
$183$	−7.96299	−0.588641
$184$	25.5033	1.88013
$185$	6.33962	0.466098
$186$	24.0224	1.76141
$187$	−10.2303	−0.748115
$188$	45.0932	3.28876
$189$	−2.89179	−0.210347
$190$	−14.9809	−1.08683
$191$	26.0340	1.88375	0.941876	−	0.335960i	$-0.109061\pi$
$191$	26.0340	1.88375	0.941876	+	0.335960i	$0.109061\pi$
$192$	−6.96315	−0.502522
$193$	11.0302	0.793971	0.396985	−	0.917825i	$-0.370056\pi$
$193$	11.0302	0.793971	0.396985	+	0.917825i	$0.370056\pi$
$194$	−28.1131	−2.01840
$195$	5.82559	0.417179
$196$	−28.3653	−2.02610
$197$	9.89003	0.704635	0.352318	−	0.935880i	$-0.385394\pi$
$197$	9.89003	0.704635	0.352318	+	0.935880i	$0.385394\pi$
$198$	−8.61085	−0.611946
$199$	−10.2461	−0.726325	−0.363163	−	0.931726i	$-0.618303\pi$
$199$	−10.2461	−0.726325	−0.363163	+	0.931726i	$0.618303\pi$
$200$	9.40284	0.664882
$201$	−10.4667	−0.738266
$202$	−16.1003	−1.13281
$203$	2.48452	0.174379
$204$	19.4801	1.36388
$205$	−17.9056	−1.25058
$206$	20.2731	1.41250
$207$	5.31881	0.369683
$208$	−12.5153	−0.867779
$209$	9.96673	0.689413
$210$	3.15202	0.217510
$211$	22.8926	1.57599	0.787995	−	0.615682i	$-0.211119\pi$
$211$	22.8926	1.57599	0.787995	+	0.615682i	$0.211119\pi$
$212$	−28.3586	−1.94768
$213$	0.431916	0.0295944
$214$	−25.9924	−1.77680
$215$	−4.30029	−0.293278
$216$	31.0883	2.11529
$217$	−3.62939	−0.246379
$218$	9.33337	0.632135
$219$	1.49162	0.100794
$220$	22.9824	1.54948
$221$	−8.02355	−0.539722
$222$	11.8464	0.795079
$223$	25.1335	1.68306	0.841531	−	0.540209i	$-0.181655\pi$
$223$	25.1335	1.68306	0.841531	+	0.540209i	$0.181655\pi$
$224$	−1.12884	−0.0754236
$225$	1.96100	0.130733
$226$	37.9854	2.52675
$227$	−5.65346	−0.375233	−0.187617	−	0.982242i	$-0.560076\pi$
$227$	−5.65346	−0.375233	−0.187617	+	0.982242i	$0.560076\pi$
$228$	−18.9782	−1.25686
$229$	−6.61196	−0.436930	−0.218465	−	0.975845i	$-0.570105\pi$
$229$	−6.61196	−0.436930	−0.218465	+	0.975845i	$0.570105\pi$
$230$	−20.9398	−1.38073
$231$	−2.09702	−0.137974
$232$	−26.7099	−1.75359
$233$	8.63136	0.565459	0.282729	−	0.959200i	$-0.408760\pi$
$233$	8.63136	0.565459	0.282729	+	0.959200i	$0.408760\pi$
$234$	−6.75341	−0.441484
$235$	−19.4357	−1.26785
$236$	−15.8696	−1.03302
$237$	13.9558	0.906527
$238$	−4.34126	−0.281402
$239$	18.0615	1.16830	0.584151	−	0.811645i	$-0.301428\pi$
$239$	18.0615	1.16830	0.584151	+	0.811645i	$0.301428\pi$
$240$	−13.0965	−0.845375
$241$	−18.8189	−1.21223	−0.606115	−	0.795377i	$-0.707273\pi$
$241$	−18.8189	−1.21223	−0.606115	+	0.795377i	$0.707273\pi$
$242$	4.85818	0.312296
$243$	11.1721	0.716691
$244$	−24.6382	−1.57730
$245$	12.2258	0.781078
$246$	−33.4590	−2.13327
$247$	7.81681	0.497372
$248$	39.0179	2.47764
$249$	−0.543916	−0.0344693
$250$	−30.3299	−1.91823
$251$	−20.7115	−1.30730	−0.653650	−	0.756797i	$-0.726763\pi$
$251$	−20.7115	−1.30730	−0.653650	+	0.756797i	$0.726763\pi$
$252$	−2.47722	−0.156050
$253$	13.9312	0.875845
$254$	54.9030	3.44492
$255$	−8.39615	−0.525788
$256$	−32.5269	−2.03293
$257$	−6.51829	−0.406600	−0.203300	−	0.979116i	$-0.565167\pi$
$257$	−6.51829	−0.406600	−0.203300	+	0.979116i	$0.565167\pi$
$258$	−8.03567	−0.500279
$259$	−1.78980	−0.111213
$260$	18.0249	1.11786
$261$	−5.57046	−0.344803
$262$	−20.8352	−1.28720
$263$	−1.37161	−0.0845770	−0.0422885	−	0.999105i	$-0.513465\pi$
$263$	−1.37161	−0.0845770	−0.0422885	+	0.999105i	$0.513465\pi$
$264$	22.5441	1.38749
$265$	12.2229	0.750848
$266$	4.22940	0.259321
$267$	20.7598	1.27048
$268$	−32.3850	−1.97823
$269$	−25.6805	−1.56577	−0.782883	−	0.622170i	$-0.786251\pi$
$269$	−25.6805	−1.56577	−0.782883	+	0.622170i	$0.786251\pi$
$270$	−25.5255	−1.55343
$271$	−30.7191	−1.86605	−0.933026	−	0.359810i	$-0.882842\pi$
$271$	−30.7191	−1.86605	−0.933026	+	0.359810i	$0.882842\pi$
$272$	18.0377	1.09370
$273$	−1.64468	−0.0995403
$274$	13.7547	0.830953
$275$	5.13629	0.309730
$276$	−26.5270	−1.59674
$277$	−15.9672	−0.959375	−0.479687	−	0.877439i	$-0.659250\pi$
$277$	−15.9672	−0.959375	−0.479687	+	0.877439i	$0.659250\pi$
$278$	−34.1699	−2.04938
$279$	8.13732	0.487169
$280$	5.11960	0.305954
$281$	−29.8097	−1.77830	−0.889149	−	0.457618i	$-0.848703\pi$
$281$	−29.8097	−1.77830	−0.889149	+	0.457618i	$0.848703\pi$
$282$	−36.3182	−2.16272
$283$	22.5367	1.33967	0.669834	−	0.742511i	$-0.266365\pi$
$283$	22.5367	1.33967	0.669834	+	0.742511i	$0.266365\pi$
$284$	1.33639	0.0793001
$285$	8.17982	0.484531
$286$	−17.6887	−1.04595
$287$	5.05510	0.298393
$288$	2.53092	0.149136
$289$	−5.43603	−0.319766
$290$	21.9305	1.28781
$291$	15.3502	0.899843
$292$	4.61521	0.270085
$293$	−7.60079	−0.444043	−0.222021	−	0.975042i	$-0.571265\pi$
$293$	−7.60079	−0.444043	−0.222021	+	0.975042i	$0.571265\pi$
$294$	22.8455	1.33238
$295$	6.83999	0.398239
$296$	19.2413	1.11838
$297$	16.9820	0.985393
$298$	7.84667	0.454545
$299$	10.9261	0.631871
$300$	−9.78028	−0.564665
$301$	1.21406	0.0699770
$302$	−52.2338	−3.00572
$303$	8.79103	0.505031
$304$	−17.5730	−1.00788
$305$	10.6194	0.608064
$306$	9.73338	0.556420
$307$	25.1769	1.43692	0.718460	−	0.695568i	$-0.244847\pi$
$307$	25.1769	1.43692	0.718460	+	0.695568i	$0.244847\pi$
$308$	−6.48839	−0.369710
$309$	−11.0694	−0.629719
$310$	−32.0361	−1.81953
$311$	−11.5492	−0.654892	−0.327446	−	0.944870i	$-0.606188\pi$
$311$	−11.5492	−0.654892	−0.327446	+	0.944870i	$0.606188\pi$
$312$	17.6811	1.00100
$313$	−0.629683	−0.0355918	−0.0177959	−	0.999842i	$-0.505665\pi$
$313$	−0.629683	−0.0355918	−0.0177959	+	0.999842i	$0.505665\pi$
$314$	−16.2306	−0.915945
$315$	1.06771	0.0601587
$316$	43.1806	2.42910
$317$	9.76090	0.548227	0.274113	−	0.961697i	$-0.411616\pi$
$317$	9.76090	0.548227	0.274113	+	0.961697i	$0.411616\pi$
$318$	22.8401	1.28081
$319$	−14.5903	−0.816899
$320$	9.28601	0.519104
$321$	14.1923	0.792134
$322$	5.91172	0.329447
$323$	−11.2660	−0.626858
$324$	−17.8295	−0.990526
$325$	4.02835	0.223453
$326$	−28.5776	−1.58277
$327$	−5.09616	−0.281819
$328$	−54.3450	−3.00070
$329$	5.48708	0.302512
$330$	−18.5101	−1.01895
$331$	35.6830	1.96132	0.980659	−	0.195725i	$-0.0627060\pi$
$331$	35.6830	1.96132	0.980659	+	0.195725i	$0.0627060\pi$
$332$	−1.68293	−0.0923625
$333$	4.01283	0.219902
$334$	18.1597	0.993654
$335$	13.9583	0.762626
$336$	3.69739	0.201709
$337$	−13.6237	−0.742131	−0.371066	−	0.928607i	$-0.621008\pi$
$337$	−13.6237	−0.742131	−0.371066	+	0.928607i	$0.621008\pi$
$338$	18.5228	1.00751
$339$	−20.7406	−1.12648
$340$	−25.9785	−1.40888
$341$	21.3135	1.15419
$342$	−9.48258	−0.512759
$343$	−7.03761	−0.379995
$344$	−13.0517	−0.703703
$345$	11.4335	0.615558
$346$	−9.33207	−0.501695
$347$	28.1710	1.51230	0.756151	−	0.654398i	$-0.227078\pi$
$347$	28.1710	1.51230	0.756151	+	0.654398i	$0.227078\pi$
$348$	27.7821	1.48928
$349$	9.89154	0.529482	0.264741	−	0.964320i	$-0.414714\pi$
$349$	9.89154	0.529482	0.264741	+	0.964320i	$0.414714\pi$
$350$	2.17960	0.116504
$351$	13.3188	0.710904
$352$	6.62906	0.353330
$353$	9.05771	0.482093	0.241047	−	0.970514i	$-0.422509\pi$
$353$	9.05771	0.482093	0.241047	+	0.970514i	$0.422509\pi$
$354$	12.7814	0.679325
$355$	−0.576001	−0.0305709
$356$	64.2329	3.40434
$357$	2.37040	0.125455
$358$	19.4042	1.02555
$359$	−0.380069	−0.0200593	−0.0100296	−	0.999950i	$-0.503193\pi$
$359$	−0.380069	−0.0200593	−0.0100296	+	0.999950i	$0.503193\pi$
$360$	−11.4785	−0.604968
$361$	−8.02427	−0.422330
$362$	−53.7772	−2.82646
$363$	−2.65264	−0.139228
$364$	−5.08878	−0.266725
$365$	−1.98921	−0.104120
$366$	19.8437	1.03725
$367$	−20.5074	−1.07048	−0.535238	−	0.844701i	$-0.679778\pi$
$367$	−20.5074	−1.07048	−0.535238	+	0.844701i	$0.679778\pi$
$368$	−24.5629	−1.28043
$369$	−11.3339	−0.590017
$370$	−15.7983	−0.821314
$371$	−3.45076	−0.179155
$372$	−40.5841	−2.10419
$373$	28.9303	1.49796	0.748978	−	0.662595i	$-0.230545\pi$
$373$	28.9303	1.49796	0.748978	+	0.662595i	$0.230545\pi$
$374$	25.4939	1.31826
$375$	16.5606	0.855185
$376$	−58.9890	−3.04212
$377$	−11.4430	−0.589345
$378$	7.20633	0.370654
$379$	−1.87085	−0.0960993	−0.0480497	−	0.998845i	$-0.515301\pi$
$379$	−1.87085	−0.0960993	−0.0480497	+	0.998845i	$0.515301\pi$
$380$	25.3091	1.29833
$381$	−29.9779	−1.53581
$382$	−64.8765	−3.31937
$383$	−12.8186	−0.655002	−0.327501	−	0.944851i	$-0.606206\pi$
$383$	−12.8186	−0.655002	−0.327501	+	0.944851i	$0.606206\pi$
$384$	23.3486	1.19151
$385$	2.79658	0.142527
$386$	−27.4872	−1.39906
$387$	−2.72199	−0.138366
$388$	47.4949	2.41119
$389$	−11.9404	−0.605405	−0.302702	−	0.953085i	$-0.597889\pi$
$389$	−11.9404	−0.605405	−0.302702	+	0.953085i	$0.597889\pi$
$390$	−14.5173	−0.735114
$391$	−15.7473	−0.796373
$392$	37.1063	1.87415
$393$	11.3763	0.573860
$394$	−24.6459	−1.24164
$395$	−18.6114	−0.936439
$396$	14.5474	0.731033
$397$	−5.56832	−0.279466	−0.139733	−	0.990189i	$-0.544624\pi$
$397$	−5.56832	−0.279466	−0.139733	+	0.990189i	$0.544624\pi$
$398$	25.5332	1.27986
$399$	−2.30932	−0.115611
$400$	−9.05612	−0.452806
$401$	20.2629	1.01188	0.505941	−	0.862568i	$-0.331145\pi$
$401$	20.2629	1.01188	0.505941	+	0.862568i	$0.331145\pi$
$402$	26.0830	1.30090
$403$	16.7160	0.832681
$404$	27.2003	1.35326
$405$	7.68472	0.381857
$406$	−6.19142	−0.307275
$407$	10.5105	0.520987
$408$	−25.4830	−1.26160
$409$	−24.1456	−1.19392	−0.596962	−	0.802269i	$-0.703626\pi$
$409$	−24.1456	−1.19392	−0.596962	+	0.802269i	$0.703626\pi$
$410$	44.6207	2.20366
$411$	−7.51029	−0.370455
$412$	−34.2499	−1.68737
$413$	−1.93106	−0.0950213
$414$	−13.2544	−0.651420
$415$	0.725362	0.0356066
$416$	5.19911	0.254907
$417$	18.6573	0.913653
$418$	−24.8370	−1.21482
$419$	8.70428	0.425232	0.212616	−	0.977136i	$-0.431802\pi$
$419$	8.70428	0.425232	0.212616	+	0.977136i	$0.431802\pi$
$420$	−5.32510	−0.259838
$421$	22.1647	1.08024	0.540122	−	0.841587i	$-0.318378\pi$
$421$	22.1647	1.08024	0.540122	+	0.841587i	$0.318378\pi$
$422$	−57.0482	−2.77706
$423$	−12.3024	−0.598162
$424$	37.0975	1.80162
$425$	−5.80587	−0.281626
$426$	−1.07633	−0.0521485
$427$	−2.99806	−0.145086
$428$	43.9122	2.12257
$429$	9.65830	0.466307
$430$	10.7163	0.516786
$431$	−33.2190	−1.60010	−0.800052	−	0.599931i	$-0.795195\pi$
$431$	−33.2190	−1.60010	−0.800052	+	0.599931i	$0.795195\pi$
$432$	−29.9419	−1.44058
$433$	−23.0968	−1.10996	−0.554980	−	0.831864i	$-0.687274\pi$
$433$	−23.0968	−1.10996	−0.554980	+	0.831864i	$0.687274\pi$
$434$	9.04442	0.434146
$435$	−11.9744	−0.574130
$436$	−15.7680	−0.755151
$437$	15.3415	0.733884
$438$	−3.71710	−0.177610
$439$	−28.0195	−1.33730	−0.668650	−	0.743578i	$-0.733127\pi$
$439$	−28.0195	−1.33730	−0.668650	+	0.743578i	$0.733127\pi$
$440$	−30.0647	−1.43328
$441$	7.73866	0.368508
$442$	19.9946	0.951047
$443$	−7.63730	−0.362859	−0.181430	−	0.983404i	$-0.558072\pi$
$443$	−7.63730	−0.362859	−0.181430	+	0.983404i	$0.558072\pi$
$444$	−20.0136	−0.949804
$445$	−27.6852	−1.31240
$446$	−62.6325	−2.96573
$447$	−4.28440	−0.202645
$448$	−2.62162	−0.123860
$449$	21.8958	1.03333	0.516664	−	0.856188i	$-0.327174\pi$
$449$	21.8958	1.03333	0.516664	+	0.856188i	$0.327174\pi$
$450$	−4.88679	−0.230366
$451$	−29.6859	−1.39786
$452$	−64.1734	−3.01846
$453$	28.5205	1.34001
$454$	14.0884	0.661201
$455$	2.19333	0.102825
$456$	24.8264	1.16260
$457$	22.8014	1.06661	0.533303	−	0.845924i	$-0.320950\pi$
$457$	22.8014	1.06661	0.533303	+	0.845924i	$0.320950\pi$
$458$	16.4770	0.769917
$459$	−19.1958	−0.895981
$460$	35.3762	1.64943
$461$	12.6269	0.588095	0.294048	−	0.955791i	$-0.404998\pi$
$461$	12.6269	0.588095	0.294048	+	0.955791i	$0.404998\pi$
$462$	5.22577	0.243125
$463$	32.7446	1.52177	0.760886	−	0.648885i	$-0.224764\pi$
$463$	32.7446	1.52177	0.760886	+	0.648885i	$0.224764\pi$
$464$	25.7250	1.19425
$465$	17.4922	0.811183
$466$	−21.5093	−0.996398
$467$	−21.1605	−0.979189	−0.489595	−	0.871950i	$-0.662855\pi$
$467$	−21.1605	−0.979189	−0.489595	+	0.871950i	$0.662855\pi$
$468$	11.4094	0.527398
$469$	−3.94071	−0.181965
$470$	48.4337	2.23408
$471$	8.86215	0.408346
$472$	20.7599	0.955552
$473$	−7.12950	−0.327815
$474$	−34.7778	−1.59740
$475$	5.65628	0.259528
$476$	7.33423	0.336164
$477$	7.73683	0.354245
$478$	−45.0092	−2.05867
$479$	−25.1452	−1.14891	−0.574457	−	0.818534i	$-0.694787\pi$
$479$	−25.1452	−1.14891	−0.574457	+	0.818534i	$0.694787\pi$
$480$	5.44055	0.248326
$481$	8.24330	0.375862
$482$	46.8965	2.13608
$483$	−3.22789	−0.146874
$484$	−8.20752	−0.373069
$485$	−20.4709	−0.929535
$486$	−27.8408	−1.26289
$487$	40.5311	1.83664	0.918321	−	0.395838i	$-0.129546\pi$
$487$	40.5311	1.83664	0.918321	+	0.395838i	$0.129546\pi$
$488$	32.2307	1.45902
$489$	15.6038	0.705628
$490$	−30.4666	−1.37634
$491$	4.51990	0.203980	0.101990	−	0.994785i	$-0.467479\pi$
$491$	4.51990	0.203980	0.101990	+	0.994785i	$0.467479\pi$
$492$	56.5265	2.54841
$493$	16.4923	0.742776
$494$	−19.4794	−0.876421
$495$	−6.27009	−0.281820
$496$	−37.5791	−1.68735
$497$	0.162616	0.00729433
$498$	1.35543	0.0607385
$499$	36.1623	1.61885	0.809423	−	0.587226i	$-0.199780\pi$
$499$	36.1623	1.61885	0.809423	+	0.587226i	$0.199780\pi$
$500$	51.2400	2.29152
$501$	−9.91547	−0.442991
$502$	51.6130	2.30360
$503$	−26.9054	−1.19965	−0.599826	−	0.800131i	$-0.704763\pi$
$503$	−26.9054	−1.19965	−0.599826	+	0.800131i	$0.704763\pi$
$504$	3.24059	0.144347
$505$	−11.7236	−0.521695
$506$	−34.7164	−1.54333
$507$	−10.1138	−0.449168
$508$	−92.7543	−4.11531
$509$	3.48536	0.154486	0.0772429	−	0.997012i	$-0.475388\pi$
$509$	3.48536	0.154486	0.0772429	+	0.997012i	$0.475388\pi$
$510$	20.9232	0.926493
$511$	0.561593	0.0248434
$512$	46.7375	2.06553
$513$	18.7012	0.825676
$514$	16.2435	0.716472
$515$	14.7621	0.650497
$516$	13.5756	0.597634
$517$	−32.2227	−1.41715
$518$	4.46016	0.195968
$519$	5.09546	0.223666
$520$	−23.5794	−1.03403
$521$	−11.8954	−0.521145	−0.260573	−	0.965454i	$-0.583911\pi$
$521$	−11.8954	−0.521145	−0.260573	+	0.965454i	$0.583911\pi$
$522$	13.8815	0.607578
$523$	21.5635	0.942907	0.471453	−	0.881891i	$-0.343730\pi$
$523$	21.5635	0.942907	0.471453	+	0.881891i	$0.343730\pi$
$524$	35.1995	1.53770
$525$	−1.19009	−0.0519400
$526$	3.41804	0.149034
$527$	−24.0919	−1.04946
$528$	−21.7128	−0.944929
$529$	−1.55615	−0.0676585
$530$	−30.4594	−1.32307
$531$	4.32956	0.187887
$532$	−7.14525	−0.309786
$533$	−23.2824	−1.00847
$534$	−51.7334	−2.23872
$535$	−18.9267	−0.818272
$536$	42.3647	1.82988
$537$	−10.5950	−0.457208
$538$	63.9955	2.75904
$539$	20.2693	0.873060
$540$	43.1233	1.85573
$541$	36.8686	1.58510	0.792552	−	0.609804i	$-0.208752\pi$
$541$	36.8686	1.58510	0.792552	+	0.609804i	$0.208752\pi$
$542$	76.5517	3.28818
$543$	29.3632	1.26009
$544$	−7.49324	−0.321270
$545$	6.79621	0.291117
$546$	4.09852	0.175401
$547$	6.52774	0.279106	0.139553	−	0.990215i	$-0.455433\pi$
$547$	6.52774	0.279106	0.139553	+	0.990215i	$0.455433\pi$
$548$	−23.2376	−0.992659
$549$	6.72183	0.286881
$550$	−12.7996	−0.545777
$551$	−16.0674	−0.684492
$552$	34.7015	1.47700
$553$	5.25435	0.223437
$554$	39.7901	1.69052
$555$	8.62611	0.366158
$556$	57.7275	2.44819
$557$	35.5163	1.50487	0.752437	−	0.658664i	$-0.228878\pi$
$557$	35.5163	1.50487	0.752437	+	0.658664i	$0.228878\pi$
$558$	−20.2781	−0.858442
$559$	−5.59160	−0.236499
$560$	−4.93081	−0.208365
$561$	−13.9201	−0.587706
$562$	74.2856	3.13355
$563$	36.6482	1.54454	0.772269	−	0.635296i	$-0.219122\pi$
$563$	36.6482	1.54454	0.772269	+	0.635296i	$0.219122\pi$
$564$	61.3568	2.58359
$565$	27.6595	1.16364
$566$	−56.1613	−2.36064
$567$	−2.16955	−0.0911124
$568$	−1.74821	−0.0733532
$569$	−7.17768	−0.300904	−0.150452	−	0.988617i	$-0.548073\pi$
$569$	−7.17768	−0.300904	−0.150452	+	0.988617i	$0.548073\pi$
$570$	−20.3840	−0.853794
$571$	2.26544	0.0948058	0.0474029	−	0.998876i	$-0.484906\pi$
$571$	2.26544	0.0948058	0.0474029	+	0.998876i	$0.484906\pi$
$572$	29.8837	1.24950
$573$	35.4236	1.47984
$574$	−12.5973	−0.525801
$575$	7.90616	0.329710
$576$	5.87783	0.244910
$577$	−13.4283	−0.559029	−0.279515	−	0.960141i	$-0.590174\pi$
$577$	−13.4283	−0.559029	−0.279515	+	0.960141i	$0.590174\pi$
$578$	13.5465	0.563462
$579$	15.0084	0.623729
$580$	−37.0500	−1.53842
$581$	−0.204784	−0.00849586
$582$	−38.2525	−1.58562
$583$	20.2645	0.839270
$584$	−6.03742	−0.249830
$585$	−4.91758	−0.203317
$586$	18.9411	0.782450
$587$	27.4001	1.13092	0.565462	−	0.824774i	$-0.308698\pi$
$587$	27.4001	1.13092	0.565462	+	0.824774i	$0.308698\pi$
$588$	−38.5958	−1.59166
$589$	23.4712	0.967113
$590$	−17.0452	−0.701740
$591$	13.4570	0.553549
$592$	−18.5317	−0.761650
$593$	−13.0818	−0.537206	−0.268603	−	0.963251i	$-0.586562\pi$
$593$	−13.0818	−0.537206	−0.268603	+	0.963251i	$0.586562\pi$
$594$	−42.3189	−1.73637
$595$	−3.16114	−0.129594
$596$	−13.2563	−0.543001
$597$	−13.9415	−0.570588
$598$	−27.2277	−1.11342
$599$	23.5557	0.962459	0.481230	−	0.876595i	$-0.340190\pi$
$599$	23.5557	0.962459	0.481230	+	0.876595i	$0.340190\pi$
$600$	12.7941	0.522319
$601$	14.3441	0.585108	0.292554	−	0.956249i	$-0.405495\pi$
$601$	14.3441	0.585108	0.292554	+	0.956249i	$0.405495\pi$
$602$	−3.02542	−0.123307
$603$	8.83531	0.359802
$604$	88.2450	3.59064
$605$	3.53754	0.143822
$606$	−21.9072	−0.889918
$607$	−13.9269	−0.565274	−0.282637	−	0.959227i	$-0.591209\pi$
$607$	−13.9269	−0.565274	−0.282637	+	0.959227i	$0.591209\pi$
$608$	7.30016	0.296061
$609$	3.38061	0.136989
$610$	−26.4634	−1.07147
$611$	−25.2719	−1.02239
$612$	−16.4438	−0.664701
$613$	18.6322	0.752549	0.376275	−	0.926508i	$-0.377205\pi$
$613$	18.6322	0.752549	0.376275	+	0.926508i	$0.377205\pi$
$614$	−62.7406	−2.53200
$615$	−24.3636	−0.982435
$616$	8.48783	0.341984
$617$	42.3108	1.70337	0.851685	−	0.524054i	$-0.175581\pi$
$617$	42.3108	1.70337	0.851685	+	0.524054i	$0.175581\pi$
$618$	27.5850	1.10963
$619$	−17.1210	−0.688150	−0.344075	−	0.938942i	$-0.611808\pi$
$619$	−17.1210	−0.688150	−0.344075	+	0.938942i	$0.611808\pi$
$620$	54.1226	2.17362
$621$	26.1399	1.04896
$622$	28.7804	1.15399
$623$	7.81606	0.313144
$624$	−17.0291	−0.681712
$625$	−13.5485	−0.541940
$626$	1.56917	0.0627165
$627$	13.5614	0.541590
$628$	27.4203	1.09419
$629$	−11.8807	−0.473714
$630$	−2.66073	−0.106006
$631$	−16.8010	−0.668839	−0.334420	−	0.942424i	$-0.608540\pi$
$631$	−16.8010	−0.668839	−0.334420	+	0.942424i	$0.608540\pi$
$632$	−56.4870	−2.24693
$633$	31.1492	1.23807
$634$	−24.3241	−0.966033
$635$	39.9783	1.58649
$636$	−38.5866	−1.53006
$637$	15.8970	0.629863
$638$	36.3589	1.43946
$639$	−0.364595	−0.0144232
$640$	−31.1376	−1.23082
$641$	38.1190	1.50561	0.752805	−	0.658244i	$-0.228700\pi$
$641$	38.1190	1.50561	0.752805	+	0.658244i	$0.228700\pi$
$642$	−35.3670	−1.39582
$643$	24.9236	0.982891	0.491445	−	0.870908i	$-0.336469\pi$
$643$	24.9236	0.982891	0.491445	+	0.870908i	$0.336469\pi$
$644$	−9.98740	−0.393559
$645$	−5.85127	−0.230393
$646$	28.0748	1.10459
$647$	30.6660	1.20561	0.602803	−	0.797890i	$-0.294050\pi$
$647$	30.6660	1.20561	0.602803	+	0.797890i	$0.294050\pi$
$648$	23.3238	0.916244
$649$	11.3401	0.445137
$650$	−10.0386	−0.393747
$651$	−4.93839	−0.193551
$652$	48.2796	1.89078
$653$	−41.6499	−1.62988	−0.814942	−	0.579542i	$-0.803231\pi$
$653$	−41.6499	−1.62988	−0.814942	+	0.579542i	$0.803231\pi$
$654$	12.6996	0.496594
$655$	−15.1714	−0.592796
$656$	52.3411	2.04358
$657$	−1.25913	−0.0491232
$658$	−13.6738	−0.533059
$659$	−3.44756	−0.134298	−0.0671488	−	0.997743i	$-0.521390\pi$
$659$	−3.44756	−0.134298	−0.0671488	+	0.997743i	$0.521390\pi$
$660$	31.2715	1.21724
$661$	−5.20211	−0.202339	−0.101169	−	0.994869i	$-0.532258\pi$
$661$	−5.20211	−0.202339	−0.101169	+	0.994869i	$0.532258\pi$
$662$	−88.9219	−3.45605
$663$	−10.9174	−0.423996
$664$	2.20153	0.0854360
$665$	3.07969	0.119425
$666$	−9.99996	−0.387490
$667$	−22.4584	−0.869593
$668$	−30.6794	−1.18702
$669$	34.1983	1.32218
$670$	−34.7841	−1.34383
$671$	17.6060	0.679672
$672$	−1.53597	−0.0592514
$673$	2.62727	0.101274	0.0506369	−	0.998717i	$-0.483875\pi$
$673$	2.62727	0.101274	0.0506369	+	0.998717i	$0.483875\pi$
$674$	33.9502	1.30771
$675$	9.63753	0.370949
$676$	−31.2929	−1.20357
$677$	25.1463	0.966452	0.483226	−	0.875496i	$-0.339465\pi$
$677$	25.1463	0.966452	0.483226	+	0.875496i	$0.339465\pi$
$678$	51.6855	1.98497
$679$	5.77932	0.221790
$680$	33.9839	1.30322
$681$	−7.69248	−0.294777
$682$	−53.1130	−2.03380
$683$	−29.8515	−1.14224	−0.571119	−	0.820867i	$-0.693490\pi$
$683$	−29.8515	−1.14224	−0.571119	+	0.820867i	$0.693490\pi$
$684$	16.0201	0.612544
$685$	10.0157	0.382679
$686$	17.5377	0.669592
$687$	−8.99667	−0.343244
$688$	12.5705	0.479244
$689$	15.8933	0.605485
$690$	−28.4922	−1.08468
$691$	−33.7003	−1.28202	−0.641010	−	0.767532i	$-0.721484\pi$
$691$	−33.7003	−1.28202	−0.641010	+	0.767532i	$0.721484\pi$
$692$	15.7658	0.599327
$693$	1.77017	0.0672431
$694$	−70.2021	−2.66483
$695$	−24.8813	−0.943800
$696$	−36.3433	−1.37759
$697$	33.5558	1.27102
$698$	−24.6496	−0.933003
$699$	11.7444	0.444214
$700$	−3.68226	−0.139176
$701$	4.91523	0.185646	0.0928228	−	0.995683i	$-0.470411\pi$
$701$	4.91523	0.185646	0.0928228	+	0.995683i	$0.470411\pi$
$702$	−33.1903	−1.25269
$703$	11.5746	0.436543
$704$	15.3954	0.580235
$705$	−26.4455	−0.995997
$706$	−22.5718	−0.849499
$707$	3.30981	0.124478
$708$	−21.5932	−0.811523
$709$	37.5864	1.41159	0.705793	−	0.708418i	$-0.250591\pi$
$709$	37.5864	1.41159	0.705793	+	0.708418i	$0.250591\pi$
$710$	1.43539	0.0538692
$711$	−11.7806	−0.441806
$712$	−84.0267	−3.14904
$713$	32.8072	1.22864
$714$	−5.90701	−0.221064
$715$	−12.8802	−0.481694
$716$	−32.7819	−1.22512
$717$	24.5757	0.917797
$718$	0.947130	0.0353466
$719$	29.5220	1.10098	0.550492	−	0.834841i	$-0.314440\pi$
$719$	29.5220	1.10098	0.550492	+	0.834841i	$0.314440\pi$
$720$	11.0552	0.412003
$721$	−4.16763	−0.155211
$722$	19.9964	0.744190
$723$	−25.6062	−0.952306
$724$	90.8524	3.37650
$725$	−8.28021	−0.307519
$726$	6.61037	0.245334
$727$	14.0981	0.522868	0.261434	−	0.965221i	$-0.415805\pi$
$727$	14.0981	0.522868	0.261434	+	0.965221i	$0.415805\pi$
$728$	6.65693	0.246722
$729$	27.9065	1.03357
$730$	4.95710	0.183471
$731$	8.05891	0.298070
$732$	−33.5244	−1.23910
$733$	−45.4599	−1.67910	−0.839551	−	0.543282i	$-0.817182\pi$
$733$	−45.4599	−1.67910	−0.839551	+	0.543282i	$0.817182\pi$
$734$	51.1042	1.88629
$735$	16.6353	0.613601
$736$	10.2039	0.376122
$737$	23.1417	0.852435
$738$	28.2439	1.03967
$739$	−8.32747	−0.306331	−0.153166	−	0.988201i	$-0.548947\pi$
$739$	−8.32747	−0.306331	−0.153166	+	0.988201i	$0.548947\pi$
$740$	26.6900	0.981144
$741$	10.6361	0.390726
$742$	8.59928	0.315690
$743$	22.1916	0.814130	0.407065	−	0.913399i	$-0.366552\pi$
$743$	22.1916	0.814130	0.407065	+	0.913399i	$0.366552\pi$
$744$	53.0903	1.94639
$745$	5.71365	0.209332
$746$	−72.0942	−2.63956
$747$	0.459137	0.0167990
$748$	−43.0700	−1.57479
$749$	5.34337	0.195242
$750$	−41.2689	−1.50693
$751$	3.98537	0.145428	0.0727141	−	0.997353i	$-0.476834\pi$
$751$	3.98537	0.145428	0.0727141	+	0.997353i	$0.476834\pi$
$752$	56.8138	2.07179
$753$	−28.1815	−1.02699
$754$	28.5159	1.03849
$755$	−38.0347	−1.38422
$756$	−12.1745	−0.442784
$757$	16.1230	0.586002	0.293001	−	0.956112i	$-0.405346\pi$
$757$	16.1230	0.586002	0.293001	+	0.956112i	$0.405346\pi$
$758$	4.66216	0.169337
$759$	18.9557	0.688047
$760$	−33.1083	−1.20096
$761$	52.0191	1.88569	0.942845	−	0.333231i	$-0.108139\pi$
$761$	52.0191	1.88569	0.942845	+	0.333231i	$0.108139\pi$
$762$	74.7047	2.70626
$763$	−1.91870	−0.0694616
$764$	109.604	3.96533
$765$	7.08748	0.256248
$766$	31.9440	1.15418
$767$	8.89392	0.321141
$768$	−44.2583	−1.59704
$769$	3.18271	0.114771	0.0573857	−	0.998352i	$-0.481724\pi$
$769$	3.18271	0.114771	0.0573857	+	0.998352i	$0.481724\pi$
$770$	−6.96905	−0.251147
$771$	−8.86923	−0.319417
$772$	46.4375	1.67132
$773$	43.2851	1.55686	0.778428	−	0.627734i	$-0.216017\pi$
$773$	43.2851	1.55686	0.778428	+	0.627734i	$0.216017\pi$
$774$	6.78318	0.243816
$775$	12.0957	0.434492
$776$	−62.1308	−2.23036
$777$	−2.43532	−0.0873665
$778$	29.7555	1.06679
$779$	−32.6912	−1.17128
$780$	24.5259	0.878168
$781$	−0.954957	−0.0341710
$782$	39.2421	1.40329
$783$	−27.3766	−0.978360
$784$	−35.7380	−1.27636
$785$	−11.8185	−0.421820
$786$	−28.3498	−1.01120
$787$	42.2240	1.50512	0.752562	−	0.658522i	$-0.228818\pi$
$787$	42.2240	1.50512	0.752562	+	0.658522i	$0.228818\pi$
$788$	41.6373	1.48327
$789$	−1.86630	−0.0664421
$790$	46.3794	1.65010
$791$	−7.80882	−0.277650
$792$	−19.0302	−0.676210
$793$	13.8082	0.490344
$794$	13.8762	0.492448
$795$	16.6313	0.589852
$796$	−43.1363	−1.52893
$797$	22.7388	0.805449	0.402725	−	0.915321i	$-0.368063\pi$
$797$	22.7388	0.805449	0.402725	+	0.915321i	$0.368063\pi$
$798$	5.75481	0.203718
$799$	36.4233	1.28856
$800$	3.76210	0.133010
$801$	−17.5241	−0.619183
$802$	−50.4951	−1.78304
$803$	−3.29793	−0.116382
$804$	−44.0652	−1.55406
$805$	4.30469	0.151720
$806$	−41.6561	−1.46727
$807$	−34.9426	−1.23004
$808$	−35.5822	−1.25178
$809$	−0.0868030	−0.00305183	−0.00152591	−	0.999999i	$-0.500486\pi$
$809$	−0.0868030	−0.00305183	−0.00152591	+	0.999999i	$0.500486\pi$
$810$	−19.1503	−0.672872
$811$	−31.4066	−1.10283	−0.551417	−	0.834230i	$-0.685913\pi$
$811$	−31.4066	−1.10283	−0.551417	+	0.834230i	$0.685913\pi$
$812$	10.4599	0.367071
$813$	−41.7984	−1.46594
$814$	−26.1921	−0.918034
$815$	−20.8091	−0.728911
$816$	24.5433	0.859188
$817$	−7.85127	−0.274681
$818$	60.1708	2.10382
$819$	1.38833	0.0485120
$820$	−75.3833	−2.63250
$821$	−6.67996	−0.233132	−0.116566	−	0.993183i	$-0.537189\pi$
$821$	−6.67996	−0.233132	−0.116566	+	0.993183i	$0.537189\pi$
$822$	18.7156	0.652782
$823$	29.6088	1.03210	0.516050	−	0.856559i	$-0.327402\pi$
$823$	29.6088	1.03210	0.516050	+	0.856559i	$0.327402\pi$
$824$	44.8043	1.56083
$825$	6.98879	0.243318
$826$	4.81219	0.167437
$827$	−43.5090	−1.51296	−0.756479	−	0.654018i	$-0.773082\pi$
$827$	−43.5090	−1.51296	−0.756479	+	0.654018i	$0.773082\pi$
$828$	22.3924	0.778188
$829$	27.0151	0.938272	0.469136	−	0.883126i	$-0.344565\pi$
$829$	27.0151	0.938272	0.469136	+	0.883126i	$0.344565\pi$
$830$	−1.80760	−0.0627426
$831$	−21.7260	−0.753667
$832$	12.0744	0.418606
$833$	−22.9116	−0.793841
$834$	−46.4939	−1.60995
$835$	13.2232	0.457608
$836$	41.9602	1.45122
$837$	39.9917	1.38232
$838$	−21.6910	−0.749303
$839$	−17.6099	−0.607960	−0.303980	−	0.952678i	$-0.598316\pi$
$839$	−17.6099	−0.607960	−0.303980	+	0.952678i	$0.598316\pi$
$840$	6.96607	0.240352
$841$	−5.47903	−0.188932
$842$	−55.2344	−1.90350
$843$	−40.5611	−1.39700
$844$	96.3785	3.31748
$845$	13.4876	0.463989
$846$	30.6574	1.05402
$847$	−0.998717	−0.0343163
$848$	−35.7296	−1.22696
$849$	30.6650	1.05242
$850$	14.4682	0.496255
$851$	16.1785	0.554594
$852$	1.81838	0.0622967
$853$	−11.5200	−0.394438	−0.197219	−	0.980359i	$-0.563191\pi$
$853$	−11.5200	−0.394438	−0.197219	+	0.980359i	$0.563191\pi$
$854$	7.47114	0.255657
$855$	−6.90486	−0.236141
$856$	−57.4440	−1.96340
$857$	42.6810	1.45795	0.728977	−	0.684538i	$-0.239996\pi$
$857$	42.6810	1.45795	0.728977	+	0.684538i	$0.239996\pi$
$858$	−24.0684	−0.821682
$859$	5.37251	0.183308	0.0916539	−	0.995791i	$-0.470785\pi$
$859$	5.37251	0.183308	0.0916539	+	0.995791i	$0.470785\pi$
$860$	−18.1044	−0.617354
$861$	6.87831	0.234412
$862$	82.7816	2.81955
$863$	−39.3149	−1.33830	−0.669148	−	0.743129i	$-0.733341\pi$
$863$	−39.3149	−1.33830	−0.669148	+	0.743129i	$0.733341\pi$
$864$	12.4385	0.423166
$865$	−6.79526	−0.231046
$866$	57.5570	1.95587
$867$	−7.39663	−0.251203
$868$	−15.2799	−0.518632
$869$	−30.8560	−1.04672
$870$	29.8402	1.01168
$871$	18.1498	0.614982
$872$	20.6270	0.698519
$873$	−12.9576	−0.438548
$874$	−38.2309	−1.29318
$875$	6.23504	0.210783
$876$	6.27976	0.212173
$877$	11.6510	0.393426	0.196713	−	0.980461i	$-0.436973\pi$
$877$	11.6510	0.393426	0.196713	+	0.980461i	$0.436973\pi$
$878$	69.8245	2.35646
$879$	−10.3421	−0.348832
$880$	28.9560	0.976108
$881$	−46.9121	−1.58051	−0.790255	−	0.612778i	$-0.790052\pi$
$881$	−46.9121	−1.58051	−0.790255	+	0.612778i	$0.790052\pi$
$882$	−19.2847	−0.649349
$883$	−37.5313	−1.26303	−0.631514	−	0.775364i	$-0.717566\pi$
$883$	−37.5313	−1.26303	−0.631514	+	0.775364i	$0.717566\pi$
$884$	−33.7794	−1.13612
$885$	9.30695	0.312850
$886$	19.0321	0.639396
$887$	−51.6675	−1.73482	−0.867412	−	0.497590i	$-0.834218\pi$
$887$	−51.6675	−1.73482	−0.867412	+	0.497590i	$0.834218\pi$
$888$	26.1809	0.878575
$889$	−11.2866	−0.378542
$890$	68.9913	2.31259
$891$	12.7406	0.426825
$892$	105.813	3.54287
$893$	−35.4848	−1.18745
$894$	10.6767	0.357083
$895$	14.1294	0.472295
$896$	8.79073	0.293678
$897$	14.8668	0.496387
$898$	−54.5643	−1.82083
$899$	−34.3594	−1.14595
$900$	8.25586	0.275195
$901$	−22.9062	−0.763117
$902$	73.9771	2.46317
$903$	1.65193	0.0549726
$904$	83.9489	2.79210
$905$	−39.1585	−1.30167
$906$	−71.0728	−2.36124
$907$	21.0701	0.699620	0.349810	−	0.936821i	$-0.386246\pi$
$907$	21.0701	0.699620	0.349810	+	0.936821i	$0.386246\pi$
$908$	−23.8013	−0.789872
$909$	−7.42080	−0.246132
$910$	−5.46576	−0.181188
$911$	−11.3971	−0.377602	−0.188801	−	0.982015i	$-0.560460\pi$
$911$	−11.3971	−0.377602	−0.188801	+	0.982015i	$0.560460\pi$
$912$	−23.9109	−0.791770
$913$	1.20258	0.0397997
$914$	−56.8210	−1.87947
$915$	14.4495	0.477684
$916$	−27.8365	−0.919745
$917$	4.28318	0.141443
$918$	47.8357	1.57881
$919$	19.0341	0.627878	0.313939	−	0.949443i	$-0.398351\pi$
$919$	19.0341	0.627878	0.313939	+	0.949443i	$0.398351\pi$
$920$	−46.2777	−1.52573
$921$	34.2573	1.12882
$922$	−31.4663	−1.03629
$923$	−0.748964	−0.0246524
$924$	−8.82854	−0.290438
$925$	5.96489	0.196124
$926$	−81.5994	−2.68152
$927$	9.34409	0.306900
$928$	−10.6867	−0.350808
$929$	11.1706	0.366495	0.183248	−	0.983067i	$-0.441339\pi$
$929$	11.1706	0.366495	0.183248	+	0.983067i	$0.441339\pi$
$930$	−43.5905	−1.42939
$931$	22.3213	0.731551
$932$	36.3383	1.19030
$933$	−15.7145	−0.514471
$934$	52.7317	1.72543
$935$	18.5637	0.607098
$936$	−14.9252	−0.487847
$937$	11.5626	0.377734	0.188867	−	0.982003i	$-0.439518\pi$
$937$	11.5626	0.377734	0.188867	+	0.982003i	$0.439518\pi$
$938$	9.82022	0.320642
$939$	−0.856789	−0.0279603
$940$	−81.8250	−2.66884
$941$	−27.9240	−0.910296	−0.455148	−	0.890416i	$-0.650414\pi$
$941$	−27.9240	−0.910296	−0.455148	+	0.890416i	$0.650414\pi$
$942$	−22.0844	−0.719549
$943$	−45.6947	−1.48802
$944$	−19.9944	−0.650762
$945$	5.24738	0.170697
$946$	17.7667	0.577644
$947$	−17.2983	−0.562120	−0.281060	−	0.959690i	$-0.590686\pi$
$947$	−17.2983	−0.562120	−0.281060	+	0.959690i	$0.590686\pi$
$948$	58.7544	1.90825
$949$	−2.58654	−0.0839626
$950$	−14.0954	−0.457315
$951$	13.2813	0.430677
$952$	−9.59432	−0.310954
$953$	35.6175	1.15376	0.576882	−	0.816827i	$-0.304269\pi$
$953$	35.6175	1.15376	0.576882	+	0.816827i	$0.304269\pi$
$954$	−19.2801	−0.624217
$955$	−47.2406	−1.52867
$956$	76.0395	2.45929
$957$	−19.8525	−0.641741
$958$	62.6617	2.02451
$959$	−2.82762	−0.0913085
$960$	12.6352	0.407798
$961$	19.1922	0.619104
$962$	−20.5422	−0.662309
$963$	−11.9802	−0.386055
$964$	−79.2281	−2.55176
$965$	−20.0151	−0.644309
$966$	8.04388	0.258808
$967$	47.5952	1.53056	0.765279	−	0.643699i	$-0.222601\pi$
$967$	47.5952	1.53056	0.765279	+	0.643699i	$0.222601\pi$
$968$	10.7367	0.345092
$969$	−15.3293	−0.492448
$970$	51.0133	1.63794
$971$	25.0675	0.804454	0.402227	−	0.915540i	$-0.368236\pi$
$971$	25.0675	0.804454	0.402227	+	0.915540i	$0.368236\pi$
$972$	47.0349	1.50865
$973$	7.02446	0.225194
$974$	−101.003	−3.23636
$975$	5.48124	0.175540
$976$	−31.0422	−0.993637
$977$	−19.4337	−0.621738	−0.310869	−	0.950453i	$-0.600620\pi$
$977$	−19.4337	−0.621738	−0.310869	+	0.950453i	$0.600620\pi$
$978$	−38.8846	−1.24339
$979$	−45.8995	−1.46695
$980$	51.4710	1.64418
$981$	4.30184	0.137347
$982$	−11.2635	−0.359434
$983$	−42.7531	−1.36361	−0.681805	−	0.731534i	$-0.738805\pi$
$983$	−42.7531	−1.36361	−0.681805	+	0.731534i	$0.738805\pi$
$984$	−73.9455	−2.35730
$985$	−17.9462	−0.571814
$986$	−41.0987	−1.30885
$987$	7.46609	0.237648
$988$	32.9090	1.04698
$989$	−10.9742	−0.348961
$990$	15.6250	0.496596
$991$	−37.6302	−1.19536	−0.597681	−	0.801734i	$-0.703911\pi$
$991$	−37.6302	−1.19536	−0.597681	+	0.801734i	$0.703911\pi$
$992$	15.6111	0.495654
$993$	48.5528	1.54077
$994$	−0.405238	−0.0128534
$995$	18.5923	0.589415
$996$	−2.28990	−0.0725583
$997$	−23.7150	−0.751060	−0.375530	−	0.926810i	$-0.622539\pi$
$997$	−23.7150	−0.751060	−0.375530	+	0.926810i	$0.622539\pi$
$998$	−90.1162	−2.85258
$999$	19.7215	0.623961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.12	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.12	✓	216	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49199 q^{2} +1.36067 q^{3} +4.21003 q^{4} -1.81458 q^{5} -3.39077 q^{6} +0.512290 q^{7} -5.50738 q^{8} -1.14858 q^{9} +O(q^{10})\)	\(q-2.49199 q^{2} +1.36067 q^{3} +4.21003 q^{4} -1.81458 q^{5} -3.39077 q^{6} +0.512290 q^{7} -5.50738 q^{8} -1.14858 q^{9} +4.52191 q^{10} -3.00840 q^{11} +5.72845 q^{12} -2.35946 q^{13} -1.27662 q^{14} -2.46903 q^{15} +5.30430 q^{16} +3.40058 q^{17} +2.86227 q^{18} -3.31296 q^{19} -7.63942 q^{20} +0.697056 q^{21} +7.49692 q^{22} -4.63075 q^{23} -7.49372 q^{24} -1.70732 q^{25} +5.87976 q^{26} -5.64484 q^{27} +2.15676 q^{28} +4.84984 q^{29} +6.15281 q^{30} -7.08465 q^{31} -2.20351 q^{32} -4.09343 q^{33} -8.47423 q^{34} -0.929588 q^{35} -4.83558 q^{36} -3.49372 q^{37} +8.25588 q^{38} -3.21044 q^{39} +9.99356 q^{40} +9.86767 q^{41} -1.73706 q^{42} +2.36986 q^{43} -12.6655 q^{44} +2.08419 q^{45} +11.5398 q^{46} +10.7109 q^{47} +7.21739 q^{48} -6.73756 q^{49} +4.25462 q^{50} +4.62706 q^{51} -9.93341 q^{52} -6.73596 q^{53} +14.0669 q^{54} +5.45897 q^{55} -2.82138 q^{56} -4.50784 q^{57} -12.0858 q^{58} -3.76947 q^{59} -10.3947 q^{60} -5.85227 q^{61} +17.6549 q^{62} -0.588408 q^{63} -5.11746 q^{64} +4.28142 q^{65} +10.2008 q^{66} -7.69235 q^{67} +14.3166 q^{68} -6.30091 q^{69} +2.31653 q^{70} +0.317430 q^{71} +6.32570 q^{72} +1.09624 q^{73} +8.70633 q^{74} -2.32309 q^{75} -13.9477 q^{76} -1.54117 q^{77} +8.00040 q^{78} +10.2566 q^{79} -9.62505 q^{80} -4.23500 q^{81} -24.5902 q^{82} -0.399742 q^{83} +2.93463 q^{84} -6.17062 q^{85} -5.90568 q^{86} +6.59902 q^{87} +16.5684 q^{88} +15.2571 q^{89} -5.19380 q^{90} -1.20873 q^{91} -19.4956 q^{92} -9.63985 q^{93} -26.6915 q^{94} +6.01162 q^{95} -2.99825 q^{96} +11.2814 q^{97} +16.7900 q^{98} +3.45541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

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