LMFDB - Embedded newform 5077.2.a.c.1.18

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			1.18
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)

$f(q)$	$=$	$q-2.43502 q^{2} +2.39261 q^{3} +3.92934 q^{4} +2.97521 q^{5} -5.82606 q^{6} +3.62580 q^{7} -4.69798 q^{8} +2.72458 q^{9} +O(q^{10})$	\(q-2.43502 q^{2} +2.39261 q^{3} +3.92934 q^{4} +2.97521 q^{5} -5.82606 q^{6} +3.62580 q^{7} -4.69798 q^{8} +2.72458 q^{9} -7.24469 q^{10} +3.86590 q^{11} +9.40137 q^{12} -2.18560 q^{13} -8.82890 q^{14} +7.11850 q^{15} +3.58101 q^{16} -5.33733 q^{17} -6.63441 q^{18} +6.97449 q^{19} +11.6906 q^{20} +8.67511 q^{21} -9.41356 q^{22} +4.02613 q^{23} -11.2404 q^{24} +3.85185 q^{25} +5.32199 q^{26} -0.658974 q^{27} +14.2470 q^{28} +1.27555 q^{29} -17.3337 q^{30} -1.05636 q^{31} +0.676118 q^{32} +9.24959 q^{33} +12.9965 q^{34} +10.7875 q^{35} +10.7058 q^{36} -8.51792 q^{37} -16.9831 q^{38} -5.22929 q^{39} -13.9774 q^{40} +1.23232 q^{41} -21.1241 q^{42} +4.20610 q^{43} +15.1904 q^{44} +8.10618 q^{45} -9.80372 q^{46} -8.87292 q^{47} +8.56795 q^{48} +6.14640 q^{49} -9.37933 q^{50} -12.7702 q^{51} -8.58796 q^{52} +5.84170 q^{53} +1.60462 q^{54} +11.5019 q^{55} -17.0339 q^{56} +16.6872 q^{57} -3.10600 q^{58} +9.50615 q^{59} +27.9710 q^{60} -7.33471 q^{61} +2.57225 q^{62} +9.87877 q^{63} -8.80838 q^{64} -6.50262 q^{65} -22.5230 q^{66} +1.24804 q^{67} -20.9722 q^{68} +9.63295 q^{69} -26.2678 q^{70} -5.76301 q^{71} -12.8000 q^{72} +4.80385 q^{73} +20.7413 q^{74} +9.21596 q^{75} +27.4051 q^{76} +14.0170 q^{77} +12.7334 q^{78} -13.2199 q^{79} +10.6542 q^{80} -9.75041 q^{81} -3.00072 q^{82} -2.38199 q^{83} +34.0874 q^{84} -15.8797 q^{85} -10.2419 q^{86} +3.05190 q^{87} -18.1619 q^{88} +5.81748 q^{89} -19.7387 q^{90} -7.92455 q^{91} +15.8200 q^{92} -2.52745 q^{93} +21.6058 q^{94} +20.7506 q^{95} +1.61769 q^{96} +19.1223 q^{97} -14.9666 q^{98} +10.5330 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.43502	−1.72182	−0.860911	−	0.508756i	$-0.830105\pi$
$2$	−2.43502	−1.72182	−0.860911	+	0.508756i	$0.830105\pi$
$3$	2.39261	1.38137	0.690687	−	0.723154i	$-0.257308\pi$
$3$	2.39261	1.38137	0.690687	+	0.723154i	$0.257308\pi$
$4$	3.92934	1.96467
$5$	2.97521	1.33055	0.665276	−	0.746597i	$-0.268314\pi$
$5$	2.97521	1.33055	0.665276	+	0.746597i	$0.268314\pi$
$6$	−5.82606	−2.37848
$7$	3.62580	1.37042	0.685211	−	0.728345i	$-0.259710\pi$
$7$	3.62580	1.37042	0.685211	+	0.728345i	$0.259710\pi$
$8$	−4.69798	−1.66099
$9$	2.72458	0.908193
$10$	−7.24469	−2.29097
$11$	3.86590	1.16561	0.582807	−	0.812611i	$-0.301955\pi$
$11$	3.86590	1.16561	0.582807	+	0.812611i	$0.301955\pi$
$12$	9.40137	2.71394
$13$	−2.18560	−0.606177	−0.303088	−	0.952962i	$-0.598018\pi$
$13$	−2.18560	−0.606177	−0.303088	+	0.952962i	$0.598018\pi$
$14$	−8.82890	−2.35962
$15$	7.11850	1.83799
$16$	3.58101	0.895252
$17$	−5.33733	−1.29449	−0.647247	−	0.762280i	$-0.724080\pi$
$17$	−5.33733	−1.29449	−0.647247	+	0.762280i	$0.724080\pi$
$18$	−6.63441	−1.56375
$19$	6.97449	1.60006	0.800029	−	0.599961i	$-0.204817\pi$
$19$	6.97449	1.60006	0.800029	+	0.599961i	$0.204817\pi$
$20$	11.6906	2.61409
$21$	8.67511	1.89306
$22$	−9.41356	−2.00698
$23$	4.02613	0.839506	0.419753	−	0.907638i	$-0.362117\pi$
$23$	4.02613	0.839506	0.419753	+	0.907638i	$0.362117\pi$
$24$	−11.2404	−2.29444
$25$	3.85185	0.770369
$26$	5.32199	1.04373
$27$	−0.658974	−0.126820
$28$	14.2470	2.69242
$29$	1.27555	0.236864	0.118432	−	0.992962i	$-0.462213\pi$
$29$	1.27555	0.236864	0.118432	+	0.992962i	$0.462213\pi$
$30$	−17.3337	−3.16469
$31$	−1.05636	−0.189727	−0.0948636	−	0.995490i	$-0.530241\pi$
$31$	−1.05636	−0.189727	−0.0948636	+	0.995490i	$0.530241\pi$
$32$	0.676118	0.119522
$33$	9.24959	1.61015
$34$	12.9965	2.22889
$35$	10.7875	1.82342
$36$	10.7058	1.78430
$37$	−8.51792	−1.40034	−0.700169	−	0.713978i	$-0.746892\pi$
$37$	−8.51792	−1.40034	−0.700169	+	0.713978i	$0.746892\pi$
$38$	−16.9831	−2.75501
$39$	−5.22929	−0.837357
$40$	−13.9774	−2.21003
$41$	1.23232	0.192455	0.0962277	−	0.995359i	$-0.469322\pi$
$41$	1.23232	0.192455	0.0962277	+	0.995359i	$0.469322\pi$
$42$	−21.1241	−3.25952
$43$	4.20610	0.641424	0.320712	−	0.947177i	$-0.396078\pi$
$43$	4.20610	0.641424	0.320712	+	0.947177i	$0.396078\pi$
$44$	15.1904	2.29004
$45$	8.10618	1.20840
$46$	−9.80372	−1.44548
$47$	−8.87292	−1.29425	−0.647124	−	0.762385i	$-0.724029\pi$
$47$	−8.87292	−1.29425	−0.647124	+	0.762385i	$0.724029\pi$
$48$	8.56795	1.23668
$49$	6.14640	0.878057
$50$	−9.37933	−1.32644
$51$	−12.7702	−1.78818
$52$	−8.58796	−1.19094
$53$	5.84170	0.802419	0.401209	−	0.915986i	$-0.368590\pi$
$53$	5.84170	0.802419	0.401209	+	0.915986i	$0.368590\pi$
$54$	1.60462	0.218361
$55$	11.5019	1.55091
$56$	−17.0339	−2.27625
$57$	16.6872	2.21028
$58$	−3.10600	−0.407838
$59$	9.50615	1.23760	0.618798	−	0.785550i	$-0.287620\pi$
$59$	9.50615	1.23760	0.618798	+	0.785550i	$0.287620\pi$
$60$	27.9710	3.61104
$61$	−7.33471	−0.939113	−0.469557	−	0.882902i	$-0.655586\pi$
$61$	−7.33471	−0.939113	−0.469557	+	0.882902i	$0.655586\pi$
$62$	2.57225	0.326676
$63$	9.87877	1.24461
$64$	−8.80838	−1.10105
$65$	−6.50262	−0.806550
$66$	−22.5230	−2.77239
$67$	1.24804	0.152472	0.0762362	−	0.997090i	$-0.475710\pi$
$67$	1.24804	0.152472	0.0762362	+	0.997090i	$0.475710\pi$
$68$	−20.9722	−2.54325
$69$	9.63295	1.15967
$70$	−26.2678	−3.13960
$71$	−5.76301	−0.683943	−0.341972	−	0.939710i	$-0.611095\pi$
$71$	−5.76301	−0.683943	−0.341972	+	0.939710i	$0.611095\pi$
$72$	−12.8000	−1.50850
$73$	4.80385	0.562249	0.281124	−	0.959671i	$-0.409293\pi$
$73$	4.80385	0.562249	0.281124	+	0.959671i	$0.409293\pi$
$74$	20.7413	2.41113
$75$	9.21596	1.06417
$76$	27.4051	3.14358
$77$	14.0170	1.59738
$78$	12.7334	1.44178
$79$	−13.2199	−1.48735	−0.743677	−	0.668540i	$-0.766920\pi$
$79$	−13.2199	−1.48735	−0.743677	+	0.668540i	$0.766920\pi$
$80$	10.6542	1.19118
$81$	−9.75041	−1.08338
$82$	−3.00072	−0.331374
$83$	−2.38199	−0.261457	−0.130729	−	0.991418i	$-0.541732\pi$
$83$	−2.38199	−0.261457	−0.130729	+	0.991418i	$0.541732\pi$
$84$	34.0874	3.71924
$85$	−15.8797	−1.72239
$86$	−10.2419	−1.10442
$87$	3.05190	0.327198
$88$	−18.1619	−1.93607
$89$	5.81748	0.616651	0.308326	−	0.951281i	$-0.400231\pi$
$89$	5.81748	0.616651	0.308326	+	0.951281i	$0.400231\pi$
$90$	−19.7387	−2.08065
$91$	−7.92455	−0.830718
$92$	15.8200	1.64935
$93$	−2.52745	−0.262084
$94$	21.6058	2.22846
$95$	20.7506	2.12896
$96$	1.61769	0.165104
$97$	19.1223	1.94158	0.970789	−	0.239933i	$-0.0771256\pi$
$97$	19.1223	1.94158	0.970789	+	0.239933i	$0.0771256\pi$
$98$	−14.9666	−1.51186
$99$	10.5330	1.05860
$100$	15.1352	1.51352
$101$	1.57578	0.156796	0.0783981	−	0.996922i	$-0.475019\pi$
$101$	1.57578	0.156796	0.0783981	+	0.996922i	$0.475019\pi$
$102$	31.0956	3.07893
$103$	11.2834	1.11179	0.555894	−	0.831253i	$-0.312376\pi$
$103$	11.2834	1.11179	0.555894	+	0.831253i	$0.312376\pi$
$104$	10.2679	1.00685
$105$	25.8102	2.51882
$106$	−14.2247	−1.38162
$107$	19.0096	1.83772	0.918862	−	0.394579i	$-0.129109\pi$
$107$	19.0096	1.83772	0.918862	+	0.394579i	$0.129109\pi$
$108$	−2.58933	−0.249158
$109$	−13.3728	−1.28088	−0.640441	−	0.768007i	$-0.721248\pi$
$109$	−13.3728	−1.28088	−0.640441	+	0.768007i	$0.721248\pi$
$110$	−28.0073	−2.67039
$111$	−20.3800	−1.93439
$112$	12.9840	1.22687
$113$	8.41050	0.791194	0.395597	−	0.918424i	$-0.370538\pi$
$113$	8.41050	0.791194	0.395597	+	0.918424i	$0.370538\pi$
$114$	−40.6338	−3.80570
$115$	11.9786	1.11701
$116$	5.01208	0.465360
$117$	−5.95485	−0.550526
$118$	−23.1477	−2.13092
$119$	−19.3521	−1.77400
$120$	−33.4426	−3.05287
$121$	3.94520	0.358654
$122$	17.8602	1.61699
$123$	2.94845	0.265853
$124$	−4.15078	−0.372751
$125$	−3.41599	−0.305536
$126$	−24.0550	−2.14299
$127$	−19.1208	−1.69669	−0.848347	−	0.529440i	$-0.822402\pi$
$127$	−19.1208	−1.69669	−0.848347	+	0.529440i	$0.822402\pi$
$128$	20.0964	1.77628
$129$	10.0635	0.886046
$130$	15.8340	1.38874
$131$	−9.56606	−0.835791	−0.417895	−	0.908495i	$-0.637232\pi$
$131$	−9.56606	−0.835791	−0.417895	+	0.908495i	$0.637232\pi$
$132$	36.3448	3.16340
$133$	25.2881	2.19276
$134$	−3.03901	−0.262530
$135$	−1.96058	−0.168740
$136$	25.0747	2.15014
$137$	13.6226	1.16386	0.581928	−	0.813240i	$-0.302298\pi$
$137$	13.6226	1.16386	0.581928	+	0.813240i	$0.302298\pi$
$138$	−23.4565	−1.99675
$139$	13.6917	1.16131	0.580656	−	0.814149i	$-0.302796\pi$
$139$	13.6917	1.16131	0.580656	+	0.814149i	$0.302796\pi$
$140$	42.3877	3.58241
$141$	−21.2294	−1.78784
$142$	14.0331	1.17763
$143$	−8.44932	−0.706568
$144$	9.75674	0.813062
$145$	3.79503	0.315160
$146$	−11.6975	−0.968091
$147$	14.7059	1.21292
$148$	−33.4698	−2.75120
$149$	−14.6338	−1.19885	−0.599424	−	0.800431i	$-0.704604\pi$
$149$	−14.6338	−1.19885	−0.599424	+	0.800431i	$0.704604\pi$
$150$	−22.4411	−1.83231
$151$	5.44621	0.443206	0.221603	−	0.975137i	$-0.428871\pi$
$151$	5.44621	0.443206	0.221603	+	0.975137i	$0.428871\pi$
$152$	−32.7660	−2.65767
$153$	−14.5420	−1.17565
$154$	−34.1316	−2.75041
$155$	−3.14288	−0.252442
$156$	−20.5476	−1.64513
$157$	0.631467	0.0503966	0.0251983	−	0.999682i	$-0.491978\pi$
$157$	0.631467	0.0503966	0.0251983	+	0.999682i	$0.491978\pi$
$158$	32.1907	2.56096
$159$	13.9769	1.10844
$160$	2.01159	0.159030
$161$	14.5979	1.15048
$162$	23.7425	1.86538
$163$	14.5819	1.14214	0.571070	−	0.820902i	$-0.306529\pi$
$163$	14.5819	1.14214	0.571070	+	0.820902i	$0.306529\pi$
$164$	4.84218	0.378111
$165$	27.5194	2.14239
$166$	5.80020	0.450183
$167$	−12.9680	−1.00350	−0.501748	−	0.865014i	$-0.667309\pi$
$167$	−12.9680	−1.00350	−0.501748	+	0.865014i	$0.667309\pi$
$168$	−40.7555	−3.14435
$169$	−8.22314	−0.632549
$170$	38.6673	2.96565
$171$	19.0026	1.45316
$172$	16.5272	1.26018
$173$	22.7625	1.73060	0.865302	−	0.501251i	$-0.167127\pi$
$173$	22.7625	1.73060	0.865302	+	0.501251i	$0.167127\pi$
$174$	−7.43145	−0.563377
$175$	13.9660	1.05573
$176$	13.8438	1.04352
$177$	22.7445	1.70958
$178$	−14.1657	−1.06176
$179$	8.04535	0.601338	0.300669	−	0.953729i	$-0.402790\pi$
$179$	8.04535	0.601338	0.300669	+	0.953729i	$0.402790\pi$
$180$	31.8519	2.37410
$181$	9.67121	0.718855	0.359428	−	0.933173i	$-0.382972\pi$
$181$	9.67121	0.718855	0.359428	+	0.933173i	$0.382972\pi$
$182$	19.2965	1.43035
$183$	−17.5491	−1.29727
$184$	−18.9147	−1.39441
$185$	−25.3426	−1.86322
$186$	6.15439	0.451262
$187$	−20.6336	−1.50888
$188$	−34.8647	−2.54277
$189$	−2.38931	−0.173796
$190$	−50.5281	−3.66569
$191$	7.50880	0.543318	0.271659	−	0.962394i	$-0.412428\pi$
$191$	7.50880	0.543318	0.271659	+	0.962394i	$0.412428\pi$
$192$	−21.0750	−1.52096
$193$	−14.5882	−1.05008	−0.525041	−	0.851077i	$-0.675950\pi$
$193$	−14.5882	−1.05008	−0.525041	+	0.851077i	$0.675950\pi$
$194$	−46.5633	−3.34305
$195$	−15.5582	−1.11415
$196$	24.1513	1.72509
$197$	−5.58894	−0.398196	−0.199098	−	0.979980i	$-0.563801\pi$
$197$	−5.58894	−0.398196	−0.199098	+	0.979980i	$0.563801\pi$
$198$	−25.6480	−1.82272
$199$	−1.62205	−0.114984	−0.0574922	−	0.998346i	$-0.518310\pi$
$199$	−1.62205	−0.114984	−0.0574922	+	0.998346i	$0.518310\pi$
$200$	−18.0959	−1.27957
$201$	2.98607	0.210621
$202$	−3.83707	−0.269975
$203$	4.62490	0.324604
$204$	−50.1782	−3.51318
$205$	3.66639	0.256072
$206$	−27.4754	−1.91430
$207$	10.9695	0.762434
$208$	−7.82666	−0.542681
$209$	26.9627	1.86505
$210$	−62.8485	−4.33696
$211$	−12.4747	−0.858794	−0.429397	−	0.903116i	$-0.641274\pi$
$211$	−12.4747	−0.858794	−0.429397	+	0.903116i	$0.641274\pi$
$212$	22.9540	1.57649
$213$	−13.7886	−0.944781
$214$	−46.2887	−3.16423
$215$	12.5140	0.853448
$216$	3.09584	0.210646
$217$	−3.83013	−0.260006
$218$	32.5631	2.20545
$219$	11.4937	0.776675
$220$	45.1946	3.04702
$221$	11.6653	0.784692
$222$	49.6259	3.33067
$223$	10.5911	0.709235	0.354617	−	0.935012i	$-0.384611\pi$
$223$	10.5911	0.709235	0.354617	+	0.935012i	$0.384611\pi$
$224$	2.45147	0.163795
$225$	10.4947	0.699644
$226$	−20.4798	−1.36229
$227$	1.52010	0.100892	0.0504461	−	0.998727i	$-0.483936\pi$
$227$	1.52010	0.100892	0.0504461	+	0.998727i	$0.483936\pi$
$228$	65.5698	4.34246
$229$	3.51289	0.232138	0.116069	−	0.993241i	$-0.462971\pi$
$229$	3.51289	0.232138	0.116069	+	0.993241i	$0.462971\pi$
$230$	−29.1681	−1.92329
$231$	33.5371	2.20658
$232$	−5.99252	−0.393428
$233$	25.5923	1.67661	0.838304	−	0.545204i	$-0.183548\pi$
$233$	25.5923	1.67661	0.838304	+	0.545204i	$0.183548\pi$
$234$	14.5002	0.947907
$235$	−26.3988	−1.72207
$236$	37.3529	2.43146
$237$	−31.6300	−2.05459
$238$	47.1228	3.05452
$239$	−23.1730	−1.49893	−0.749467	−	0.662042i	$-0.769690\pi$
$239$	−23.1730	−1.49893	−0.749467	+	0.662042i	$0.769690\pi$
$240$	25.4914	1.64546
$241$	−7.22448	−0.465370	−0.232685	−	0.972552i	$-0.574751\pi$
$241$	−7.22448	−0.465370	−0.232685	+	0.972552i	$0.574751\pi$
$242$	−9.60664	−0.617538
$243$	−21.3520	−1.36973
$244$	−28.8205	−1.84505
$245$	18.2868	1.16830
$246$	−7.17955	−0.457751
$247$	−15.2435	−0.969919
$248$	4.96273	0.315134
$249$	−5.69917	−0.361170
$250$	8.31802	0.526078
$251$	−15.3812	−0.970852	−0.485426	−	0.874278i	$-0.661336\pi$
$251$	−15.3812	−0.970852	−0.485426	+	0.874278i	$0.661336\pi$
$252$	38.8170	2.44524
$253$	15.5646	0.978539
$254$	46.5595	2.92140
$255$	−37.9938	−2.37927
$256$	−31.3183	−1.95740
$257$	−6.35474	−0.396398	−0.198199	−	0.980162i	$-0.563509\pi$
$257$	−6.35474	−0.396398	−0.198199	+	0.980162i	$0.563509\pi$
$258$	−24.5050	−1.52561
$259$	−30.8842	−1.91905
$260$	−25.5510	−1.58460
$261$	3.47535	0.215118
$262$	23.2936	1.43908
$263$	10.8471	0.668860	0.334430	−	0.942421i	$-0.391456\pi$
$263$	10.8471	0.668860	0.334430	+	0.942421i	$0.391456\pi$
$264$	−43.4544	−2.67443
$265$	17.3802	1.06766
$266$	−61.5771	−3.77553
$267$	13.9189	0.851826
$268$	4.90397	0.299558
$269$	13.8113	0.842088	0.421044	−	0.907040i	$-0.361664\pi$
$269$	13.8113	0.842088	0.421044	+	0.907040i	$0.361664\pi$
$270$	4.77406	0.290540
$271$	−0.140142	−0.00851304	−0.00425652	−	0.999991i	$-0.501355\pi$
$271$	−0.140142	−0.00851304	−0.00425652	+	0.999991i	$0.501355\pi$
$272$	−19.1130	−1.15890
$273$	−18.9603	−1.14753
$274$	−33.1713	−2.00395
$275$	14.8909	0.897953
$276$	37.8511	2.27837
$277$	−20.1103	−1.20831	−0.604157	−	0.796866i	$-0.706490\pi$
$277$	−20.1103	−1.20831	−0.604157	+	0.796866i	$0.706490\pi$
$278$	−33.3395	−1.99957
$279$	−2.87813	−0.172309
$280$	−50.6794	−3.02867
$281$	−14.1427	−0.843682	−0.421841	−	0.906670i	$-0.638616\pi$
$281$	−14.1427	−0.843682	−0.421841	+	0.906670i	$0.638616\pi$
$282$	51.6942	3.07834
$283$	−16.9198	−1.00578	−0.502889	−	0.864351i	$-0.667729\pi$
$283$	−16.9198	−1.00578	−0.502889	+	0.864351i	$0.667729\pi$
$284$	−22.6448	−1.34372
$285$	49.6480	2.94089
$286$	20.5743	1.21658
$287$	4.46813	0.263745
$288$	1.84214	0.108549
$289$	11.4871	0.675714
$290$	−9.24099	−0.542650
$291$	45.7523	2.68205
$292$	18.8760	1.10463
$293$	17.8455	1.04255	0.521273	−	0.853390i	$-0.325457\pi$
$293$	17.8455	1.04255	0.521273	+	0.853390i	$0.325457\pi$
$294$	−35.8093	−2.08844
$295$	28.2828	1.64669
$296$	40.0170	2.32594
$297$	−2.54753	−0.147823
$298$	35.6337	2.06420
$299$	−8.79952	−0.508889
$300$	36.2126	2.09074
$301$	15.2505	0.879021
$302$	−13.2616	−0.763122
$303$	3.77023	0.216594
$304$	24.9757	1.43246
$305$	−21.8223	−1.24954
$306$	35.4101	2.02426
$307$	−30.8644	−1.76153	−0.880763	−	0.473557i	$-0.842970\pi$
$307$	−30.8644	−1.76153	−0.880763	+	0.473557i	$0.842970\pi$
$308$	55.0774	3.13833
$309$	26.9968	1.53579
$310$	7.65297	0.434660
$311$	−27.9464	−1.58469	−0.792347	−	0.610070i	$-0.791141\pi$
$311$	−27.9464	−1.58469	−0.792347	+	0.610070i	$0.791141\pi$
$312$	24.5671	1.39084
$313$	−15.5951	−0.881486	−0.440743	−	0.897633i	$-0.645285\pi$
$313$	−15.5951	−0.881486	−0.440743	+	0.897633i	$0.645285\pi$
$314$	−1.53764	−0.0867739
$315$	29.3914	1.65602
$316$	−51.9454	−2.92216
$317$	−4.57734	−0.257089	−0.128545	−	0.991704i	$-0.541031\pi$
$317$	−4.57734	−0.257089	−0.128545	+	0.991704i	$0.541031\pi$
$318$	−34.0341	−1.90854
$319$	4.93116	0.276092
$320$	−26.2067	−1.46500
$321$	45.4825	2.53858
$322$	−35.5463	−1.98092
$323$	−37.2252	−2.07127
$324$	−38.3126	−2.12848
$325$	−8.41860	−0.466980
$326$	−35.5071	−1.96656
$327$	−31.9959	−1.76938
$328$	−5.78939	−0.319666
$329$	−32.1714	−1.77367
$330$	−67.0105	−3.68880
$331$	9.24139	0.507953	0.253976	−	0.967210i	$-0.418261\pi$
$331$	9.24139	0.507953	0.253976	+	0.967210i	$0.418261\pi$
$332$	−9.35964	−0.513677
$333$	−23.2077	−1.27178
$334$	31.5774	1.72784
$335$	3.71318	0.202873
$336$	31.0656	1.69477
$337$	27.6687	1.50721	0.753606	−	0.657326i	$-0.228313\pi$
$337$	27.6687	1.50721	0.753606	+	0.657326i	$0.228313\pi$
$338$	20.0235	1.08914
$339$	20.1231	1.09293
$340$	−62.3965	−3.38393
$341$	−4.08377	−0.221148
$342$	−46.2717	−2.50209
$343$	−3.09499	−0.167114
$344$	−19.7601	−1.06540
$345$	28.6600	1.54300
$346$	−55.4273	−2.97979
$347$	5.50791	0.295680	0.147840	−	0.989011i	$-0.452768\pi$
$347$	5.50791	0.295680	0.147840	+	0.989011i	$0.452768\pi$
$348$	11.9919	0.642836
$349$	−28.3536	−1.51773	−0.758866	−	0.651247i	$-0.774246\pi$
$349$	−28.3536	−1.51773	−0.758866	+	0.651247i	$0.774246\pi$
$350$	−34.0076	−1.81778
$351$	1.44026	0.0768751
$352$	2.61380	0.139316
$353$	−25.0867	−1.33523	−0.667615	−	0.744506i	$-0.732685\pi$
$353$	−25.0867	−1.33523	−0.667615	+	0.744506i	$0.732685\pi$
$354$	−55.3834	−2.94359
$355$	−17.1461	−0.910022
$356$	22.8588	1.21152
$357$	−46.3020	−2.45056
$358$	−19.5906	−1.03540
$359$	−16.2633	−0.858343	−0.429171	−	0.903223i	$-0.641194\pi$
$359$	−16.2633	−0.858343	−0.429171	+	0.903223i	$0.641194\pi$
$360$	−38.0827	−2.00713
$361$	29.6436	1.56019
$362$	−23.5496	−1.23774
$363$	9.43931	0.495436
$364$	−31.1382	−1.63209
$365$	14.2925	0.748101
$366$	42.7324	2.23366
$367$	−31.9483	−1.66769	−0.833843	−	0.552001i	$-0.813864\pi$
$367$	−31.9483	−1.66769	−0.833843	+	0.552001i	$0.813864\pi$
$368$	14.4176	0.751569
$369$	3.35754	0.174787
$370$	61.7097	3.20813
$371$	21.1808	1.09965
$372$	−9.93119	−0.514908
$373$	−25.7708	−1.33436	−0.667181	−	0.744896i	$-0.732499\pi$
$373$	−25.7708	−1.33436	−0.667181	+	0.744896i	$0.732499\pi$
$374$	50.2433	2.59802
$375$	−8.17313	−0.422059
$376$	41.6848	2.14973
$377$	−2.78785	−0.143582
$378$	5.81801	0.299246
$379$	−31.8836	−1.63775	−0.818875	−	0.573972i	$-0.805402\pi$
$379$	−31.8836	−1.63775	−0.818875	+	0.573972i	$0.805402\pi$
$380$	81.5359	4.18270
$381$	−45.7485	−2.34377
$382$	−18.2841	−0.935496
$383$	−2.43471	−0.124408	−0.0622039	−	0.998063i	$-0.519813\pi$
$383$	−2.43471	−0.124408	−0.0622039	+	0.998063i	$0.519813\pi$
$384$	48.0827	2.45371
$385$	41.7034	2.12540
$386$	35.5226	1.80805
$387$	11.4598	0.582537
$388$	75.1381	3.81456
$389$	−7.09833	−0.359900	−0.179950	−	0.983676i	$-0.557594\pi$
$389$	−7.09833	−0.359900	−0.179950	+	0.983676i	$0.557594\pi$
$390$	37.8846	1.91836
$391$	−21.4888	−1.08674
$392$	−28.8756	−1.45844
$393$	−22.8879	−1.15454
$394$	13.6092	0.685622
$395$	−39.3319	−1.97900
$396$	41.3875	2.07980
$397$	−17.1690	−0.861689	−0.430844	−	0.902426i	$-0.641784\pi$
$397$	−17.1690	−0.861689	−0.430844	+	0.902426i	$0.641784\pi$
$398$	3.94974	0.197983
$399$	60.5045	3.02901
$400$	13.7935	0.689675
$401$	−19.1715	−0.957379	−0.478690	−	0.877984i	$-0.658888\pi$
$401$	−19.1715	−0.957379	−0.478690	+	0.877984i	$0.658888\pi$
$402$	−7.27116	−0.362652
$403$	2.30877	0.115008
$404$	6.19178	0.308053
$405$	−29.0095	−1.44149
$406$	−11.2617	−0.558910
$407$	−32.9294	−1.63225
$408$	59.9939	2.97014
$409$	3.90390	0.193035	0.0965177	−	0.995331i	$-0.469230\pi$
$409$	3.90390	0.193035	0.0965177	+	0.995331i	$0.469230\pi$
$410$	−8.92775	−0.440910
$411$	32.5935	1.60772
$412$	44.3363	2.18429
$413$	34.4674	1.69603
$414$	−26.7110	−1.31277
$415$	−7.08691	−0.347883
$416$	−1.47772	−0.0724514
$417$	32.7588	1.60420
$418$	−65.6548	−3.21128
$419$	−2.01086	−0.0982369	−0.0491185	−	0.998793i	$-0.515641\pi$
$419$	−2.01086	−0.0982369	−0.0491185	+	0.998793i	$0.515641\pi$
$420$	101.417	4.94865
$421$	1.54727	0.0754094	0.0377047	−	0.999289i	$-0.487995\pi$
$421$	1.54727	0.0754094	0.0377047	+	0.999289i	$0.487995\pi$
$422$	30.3762	1.47869
$423$	−24.1750	−1.17543
$424$	−27.4442	−1.33281
$425$	−20.5586	−0.997238
$426$	33.5756	1.62674
$427$	−26.5942	−1.28698
$428$	74.6950	3.61052
$429$	−20.2159	−0.976034
$430$	−30.4719	−1.46948
$431$	−7.10285	−0.342132	−0.171066	−	0.985260i	$-0.554721\pi$
$431$	−7.10285	−0.342132	−0.171066	+	0.985260i	$0.554721\pi$
$432$	−2.35979	−0.113536
$433$	27.9140	1.34146	0.670729	−	0.741702i	$-0.265981\pi$
$433$	27.9140	1.34146	0.670729	+	0.741702i	$0.265981\pi$
$434$	9.32646	0.447684
$435$	9.08003	0.435354
$436$	−52.5462	−2.51651
$437$	28.0802	1.34326
$438$	−27.9875	−1.33730
$439$	−8.94710	−0.427022	−0.213511	−	0.976941i	$-0.568490\pi$
$439$	−8.94710	−0.427022	−0.213511	+	0.976941i	$0.568490\pi$
$440$	−54.0354	−2.57604
$441$	16.7463	0.797445
$442$	−28.4052	−1.35110
$443$	−8.85279	−0.420609	−0.210304	−	0.977636i	$-0.567445\pi$
$443$	−8.85279	−0.420609	−0.210304	+	0.977636i	$0.567445\pi$
$444$	−80.0801	−3.80043
$445$	17.3082	0.820487
$446$	−25.7896	−1.22118
$447$	−35.0130	−1.65606
$448$	−31.9374	−1.50890
$449$	20.1869	0.952678	0.476339	−	0.879262i	$-0.341964\pi$
$449$	20.1869	0.952678	0.476339	+	0.879262i	$0.341964\pi$
$450$	−25.5547	−1.20466
$451$	4.76401	0.224329
$452$	33.0477	1.55443
$453$	13.0306	0.612233
$454$	−3.70147	−0.173718
$455$	−23.5772	−1.10531
$456$	−78.3963	−3.67124
$457$	−18.2974	−0.855917	−0.427959	−	0.903798i	$-0.640767\pi$
$457$	−18.2974	−0.855917	−0.427959	+	0.903798i	$0.640767\pi$
$458$	−8.55396	−0.399700
$459$	3.51717	0.164167
$460$	47.0678	2.19455
$461$	39.7046	1.84923	0.924614	−	0.380904i	$-0.124387\pi$
$461$	39.7046	1.84923	0.924614	+	0.380904i	$0.124387\pi$
$462$	−81.6637	−3.79934
$463$	39.1184	1.81798	0.908992	−	0.416813i	$-0.136853\pi$
$463$	39.1184	1.81798	0.908992	+	0.416813i	$0.136853\pi$
$464$	4.56777	0.212053
$465$	−7.51967	−0.348717
$466$	−62.3178	−2.88682
$467$	18.1117	0.838109	0.419055	−	0.907961i	$-0.362362\pi$
$467$	18.1117	0.838109	0.419055	+	0.907961i	$0.362362\pi$
$468$	−23.3986	−1.08160
$469$	4.52514	0.208952
$470$	64.2816	2.96509
$471$	1.51085	0.0696165
$472$	−44.6597	−2.05563
$473$	16.2604	0.747652
$474$	77.0198	3.53764
$475$	26.8647	1.23264
$476$	−76.0408	−3.48533
$477$	15.9162	0.728751
$478$	56.4267	2.58090
$479$	2.27339	0.103874	0.0519369	−	0.998650i	$-0.483461\pi$
$479$	2.27339	0.103874	0.0519369	+	0.998650i	$0.483461\pi$
$480$	4.81295	0.219680
$481$	18.6168	0.848852
$482$	17.5918	0.801284
$483$	34.9271	1.58924
$484$	15.5020	0.704636
$485$	56.8929	2.58337
$486$	51.9926	2.35843
$487$	−6.85428	−0.310597	−0.155299	−	0.987868i	$-0.549634\pi$
$487$	−6.85428	−0.310597	−0.155299	+	0.987868i	$0.549634\pi$
$488$	34.4583	1.55985
$489$	34.8887	1.57772
$490$	−44.5288	−2.01160
$491$	−17.5114	−0.790280	−0.395140	−	0.918621i	$-0.629304\pi$
$491$	−17.5114	−0.790280	−0.395140	+	0.918621i	$0.629304\pi$
$492$	11.5855	0.522313
$493$	−6.80805	−0.306619
$494$	37.1182	1.67003
$495$	31.3377	1.40853
$496$	−3.78282	−0.169854
$497$	−20.8955	−0.937291
$498$	13.8776	0.621871
$499$	0.947905	0.0424341	0.0212170	−	0.999775i	$-0.493246\pi$
$499$	0.947905	0.0424341	0.0212170	+	0.999775i	$0.493246\pi$
$500$	−13.4226	−0.600276
$501$	−31.0274	−1.38620
$502$	37.4536	1.67163
$503$	−7.22953	−0.322349	−0.161174	−	0.986926i	$-0.551528\pi$
$503$	−7.22953	−0.322349	−0.161174	+	0.986926i	$0.551528\pi$
$504$	−46.4102	−2.06728
$505$	4.68828	0.208626
$506$	−37.9002	−1.68487
$507$	−19.6748	−0.873787
$508$	−75.1319	−3.33344
$509$	−0.278015	−0.0123228	−0.00616141	−	0.999981i	$-0.501961\pi$
$509$	−0.278015	−0.0123228	−0.00616141	+	0.999981i	$0.501961\pi$
$510$	92.5159	4.09667
$511$	17.4178	0.770518
$512$	36.0682	1.59400
$513$	−4.59601	−0.202919
$514$	15.4739	0.682526
$515$	33.5705	1.47929
$516$	39.5431	1.74079
$517$	−34.3018	−1.50859
$518$	75.2038	3.30427
$519$	54.4619	2.39061
$520$	30.5491	1.33967
$521$	31.9828	1.40119	0.700596	−	0.713558i	$-0.252918\pi$
$521$	31.9828	1.40119	0.700596	+	0.713558i	$0.252918\pi$
$522$	−8.46255	−0.370396
$523$	25.1888	1.10143	0.550714	−	0.834694i	$-0.314356\pi$
$523$	25.1888	1.10143	0.550714	+	0.834694i	$0.314356\pi$
$524$	−37.5883	−1.64205
$525$	33.4152	1.45836
$526$	−26.4129	−1.15166
$527$	5.63812	0.245601
$528$	33.1229	1.44149
$529$	−6.79028	−0.295230
$530$	−42.3213	−1.83832
$531$	25.9003	1.12398
$532$	99.3654	4.30804
$533$	−2.69335	−0.116662
$534$	−33.8930	−1.46669
$535$	56.5574	2.44519
$536$	−5.86327	−0.253255
$537$	19.2494	0.830672
$538$	−33.6307	−1.44992
$539$	23.7614	1.02347
$540$	−7.70379	−0.331518
$541$	32.6938	1.40561	0.702807	−	0.711380i	$-0.251930\pi$
$541$	32.6938	1.40561	0.702807	+	0.711380i	$0.251930\pi$
$542$	0.341250	0.0146579
$543$	23.1394	0.993007
$544$	−3.60867	−0.154720
$545$	−39.7868	−1.70428
$546$	46.1689	1.97585
$547$	−18.7171	−0.800287	−0.400144	−	0.916452i	$-0.631040\pi$
$547$	−18.7171	−0.800287	−0.400144	+	0.916452i	$0.631040\pi$
$548$	53.5277	2.28659
$549$	−19.9840	−0.852896
$550$	−36.2596	−1.54611
$551$	8.89634	0.378997
$552$	−45.2554	−1.92620
$553$	−47.9326	−2.03830
$554$	48.9691	2.08050
$555$	−60.6348	−2.57381
$556$	53.7991	2.28159
$557$	13.1985	0.559239	0.279619	−	0.960111i	$-0.409792\pi$
$557$	13.1985	0.559239	0.279619	+	0.960111i	$0.409792\pi$
$558$	7.00830	0.296685
$559$	−9.19286	−0.388816
$560$	38.6301	1.63242
$561$	−49.3682	−2.08433
$562$	34.4377	1.45267
$563$	−11.5093	−0.485059	−0.242530	−	0.970144i	$-0.577977\pi$
$563$	−11.5093	−0.485059	−0.242530	+	0.970144i	$0.577977\pi$
$564$	−83.4176	−3.51251
$565$	25.0230	1.05272
$566$	41.2001	1.73177
$567$	−35.3530	−1.48469
$568$	27.0745	1.13602
$569$	28.6722	1.20200	0.601000	−	0.799249i	$-0.294769\pi$
$569$	28.6722	1.20200	0.601000	+	0.799249i	$0.294769\pi$
$570$	−120.894	−5.06369
$571$	−23.0367	−0.964058	−0.482029	−	0.876155i	$-0.660100\pi$
$571$	−23.0367	−0.964058	−0.482029	+	0.876155i	$0.660100\pi$
$572$	−33.2002	−1.38817
$573$	17.9656	0.750525
$574$	−10.8800	−0.454122
$575$	15.5080	0.646730
$576$	−23.9991	−0.999963
$577$	−17.8774	−0.744245	−0.372123	−	0.928184i	$-0.621370\pi$
$577$	−17.8774	−0.744245	−0.372123	+	0.928184i	$0.621370\pi$
$578$	−27.9714	−1.16346
$579$	−34.9039	−1.45055
$580$	14.9120	0.619185
$581$	−8.63661	−0.358307
$582$	−111.408	−4.61800
$583$	22.5834	0.935310
$584$	−22.5684	−0.933887
$585$	−17.7169	−0.732503
$586$	−43.4543	−1.79508
$587$	36.3205	1.49911	0.749555	−	0.661942i	$-0.230268\pi$
$587$	36.3205	1.49911	0.749555	+	0.661942i	$0.230268\pi$
$588$	57.7845	2.38299
$589$	−7.36755	−0.303575
$590$	−68.8691	−2.83530
$591$	−13.3722	−0.550057
$592$	−30.5027	−1.25365
$593$	16.9232	0.694952	0.347476	−	0.937689i	$-0.387039\pi$
$593$	16.9232	0.694952	0.347476	+	0.937689i	$0.387039\pi$
$594$	6.20329	0.254524
$595$	−57.5764	−2.36040
$596$	−57.5012	−2.35534
$597$	−3.88094	−0.158836
$598$	21.4270	0.876216
$599$	30.5568	1.24852	0.624258	−	0.781218i	$-0.285401\pi$
$599$	30.5568	1.24852	0.624258	+	0.781218i	$0.285401\pi$
$600$	−43.2964	−1.76757
$601$	−36.4012	−1.48484	−0.742419	−	0.669936i	$-0.766322\pi$
$601$	−36.4012	−1.48484	−0.742419	+	0.669936i	$0.766322\pi$
$602$	−37.1352	−1.51352
$603$	3.40039	0.138474
$604$	21.4000	0.870753
$605$	11.7378	0.477208
$606$	−9.18060	−0.372937
$607$	8.22180	0.333713	0.166856	−	0.985981i	$-0.446638\pi$
$607$	8.22180	0.333713	0.166856	+	0.985981i	$0.446638\pi$
$608$	4.71558	0.191242
$609$	11.0656	0.448399
$610$	53.1377	2.15148
$611$	19.3927	0.784544
$612$	−57.1404	−2.30976
$613$	−15.2003	−0.613934	−0.306967	−	0.951720i	$-0.599314\pi$
$613$	−15.2003	−0.613934	−0.306967	+	0.951720i	$0.599314\pi$
$614$	75.1556	3.03303
$615$	8.77225	0.353731
$616$	−65.8514	−2.65323
$617$	6.11397	0.246139	0.123070	−	0.992398i	$-0.460726\pi$
$617$	6.11397	0.246139	0.123070	+	0.992398i	$0.460726\pi$
$618$	−65.7378	−2.64436
$619$	−30.0068	−1.20607	−0.603037	−	0.797713i	$-0.706043\pi$
$619$	−30.0068	−1.20607	−0.603037	+	0.797713i	$0.706043\pi$
$620$	−12.3494	−0.495964
$621$	−2.65311	−0.106466
$622$	68.0501	2.72856
$623$	21.0930	0.845073
$624$	−18.7261	−0.749645
$625$	−29.4225	−1.17690
$626$	37.9744	1.51776
$627$	64.5112	2.57633
$628$	2.48125	0.0990125
$629$	45.4630	1.81273
$630$	−71.5686	−2.85136
$631$	−5.92911	−0.236034	−0.118017	−	0.993012i	$-0.537654\pi$
$631$	−5.92911	−0.236034	−0.118017	+	0.993012i	$0.537654\pi$
$632$	62.1067	2.47047
$633$	−29.8471	−1.18631
$634$	11.1459	0.442661
$635$	−56.8882	−2.25754
$636$	54.9199	2.17772
$637$	−13.4336	−0.532258
$638$	−12.0075	−0.475381
$639$	−15.7018	−0.621153
$640$	59.7908	2.36344
$641$	35.7446	1.41183	0.705914	−	0.708297i	$-0.250536\pi$
$641$	35.7446	1.41183	0.705914	+	0.708297i	$0.250536\pi$
$642$	−110.751	−4.37099
$643$	22.6249	0.892238	0.446119	−	0.894974i	$-0.352806\pi$
$643$	22.6249	0.892238	0.446119	+	0.894974i	$0.352806\pi$
$644$	57.3601	2.26031
$645$	29.9411	1.17893
$646$	90.6442	3.56635
$647$	−10.5516	−0.414826	−0.207413	−	0.978253i	$-0.566504\pi$
$647$	−10.5516	−0.414826	−0.207413	+	0.978253i	$0.566504\pi$
$648$	45.8072	1.79948
$649$	36.7498	1.44256
$650$	20.4995	0.804056
$651$	−9.16401	−0.359166
$652$	57.2970	2.24392
$653$	50.6682	1.98280	0.991399	−	0.130874i	$-0.0417784\pi$
$653$	50.6682	1.98280	0.991399	+	0.130874i	$0.0417784\pi$
$654$	77.9107	3.04655
$655$	−28.4610	−1.11206
$656$	4.41293	0.172296
$657$	13.0885	0.510630
$658$	78.3381	3.05394
$659$	35.1648	1.36982	0.684912	−	0.728625i	$-0.259840\pi$
$659$	35.1648	1.36982	0.684912	+	0.728625i	$0.259840\pi$
$660$	108.133	4.20908
$661$	3.39076	0.131885	0.0659427	−	0.997823i	$-0.478995\pi$
$661$	3.39076	0.131885	0.0659427	+	0.997823i	$0.478995\pi$
$662$	−22.5030	−0.874604
$663$	27.9105	1.08395
$664$	11.1905	0.434277
$665$	75.2373	2.91758
$666$	56.5114	2.18977
$667$	5.13554	0.198849
$668$	−50.9557	−1.97154
$669$	25.3404	0.979718
$670$	−9.04167	−0.349310
$671$	−28.3553	−1.09464
$672$	5.86540	0.226263
$673$	−32.2711	−1.24396	−0.621980	−	0.783033i	$-0.713672\pi$
$673$	−32.2711	−1.24396	−0.621980	+	0.783033i	$0.713672\pi$
$674$	−67.3740	−2.59515
$675$	−2.53827	−0.0976979
$676$	−32.3115	−1.24275
$677$	2.07821	0.0798722	0.0399361	−	0.999202i	$-0.487285\pi$
$677$	2.07821	0.0798722	0.0399361	+	0.999202i	$0.487285\pi$
$678$	−49.0001	−1.88184
$679$	69.3337	2.66078
$680$	74.6023	2.86087
$681$	3.63699	0.139370
$682$	9.94407	0.380778
$683$	−31.7398	−1.21449	−0.607244	−	0.794515i	$-0.707725\pi$
$683$	−31.7398	−1.21449	−0.607244	+	0.794515i	$0.707725\pi$
$684$	74.6674	2.85498
$685$	40.5300	1.54857
$686$	7.53637	0.287740
$687$	8.40497	0.320670
$688$	15.0621	0.574236
$689$	−12.7676	−0.486408
$690$	−69.7878	−2.65678
$691$	−36.2489	−1.37897	−0.689487	−	0.724298i	$-0.742164\pi$
$691$	−36.2489	−1.37897	−0.689487	+	0.724298i	$0.742164\pi$
$692$	89.4416	3.40006
$693$	38.1904	1.45073
$694$	−13.4119	−0.509108
$695$	40.7355	1.54519
$696$	−14.3378	−0.543471
$697$	−6.57728	−0.249132
$698$	69.0416	2.61326
$699$	61.2324	2.31602
$700$	54.8771	2.07416
$701$	−6.37857	−0.240915	−0.120458	−	0.992718i	$-0.538436\pi$
$701$	−6.37857	−0.240915	−0.120458	+	0.992718i	$0.538436\pi$
$702$	−3.50705	−0.132365
$703$	−59.4082	−2.24062
$704$	−34.0523	−1.28340
$705$	−63.1619	−2.37882
$706$	61.0867	2.29903
$707$	5.71347	0.214877
$708$	89.3708	3.35876
$709$	−8.49080	−0.318879	−0.159439	−	0.987208i	$-0.550969\pi$
$709$	−8.49080	−0.318879	−0.159439	+	0.987208i	$0.550969\pi$
$710$	41.7512	1.56690
$711$	−36.0186	−1.35080
$712$	−27.3304	−1.02425
$713$	−4.25303	−0.159277
$714$	112.746	4.21943
$715$	−25.1385	−0.940126
$716$	31.6129	1.18143
$717$	−55.4438	−2.07059
$718$	39.6015	1.47791
$719$	−47.3743	−1.76676	−0.883382	−	0.468653i	$-0.844739\pi$
$719$	−47.3743	−1.76676	−0.883382	+	0.468653i	$0.844739\pi$
$720$	29.0283	1.08182
$721$	40.9114	1.52362
$722$	−72.1827	−2.68636
$723$	−17.2854	−0.642850
$724$	38.0014	1.41231
$725$	4.91324	0.182473
$726$	−22.9849	−0.853051
$727$	34.2286	1.26947	0.634734	−	0.772730i	$-0.281110\pi$
$727$	34.2286	1.26947	0.634734	+	0.772730i	$0.281110\pi$
$728$	37.2293	1.37981
$729$	−21.8358	−0.808732
$730$	−34.8024	−1.28810
$731$	−22.4494	−0.830319
$732$	−68.9563	−2.54870
$733$	−6.53757	−0.241471	−0.120735	−	0.992685i	$-0.538525\pi$
$733$	−6.53757	−0.241471	−0.120735	+	0.992685i	$0.538525\pi$
$734$	77.7948	2.87146
$735$	43.7532	1.61386
$736$	2.72214	0.100339
$737$	4.82480	0.177724
$738$	−8.17569	−0.300951
$739$	1.73943	0.0639858	0.0319929	−	0.999488i	$-0.489815\pi$
$739$	1.73943	0.0639858	0.0319929	+	0.999488i	$0.489815\pi$
$740$	−99.5794	−3.66061
$741$	−36.4717	−1.33982
$742$	−51.5757	−1.89340
$743$	−34.2926	−1.25807	−0.629036	−	0.777376i	$-0.716550\pi$
$743$	−34.2926	−1.25807	−0.629036	+	0.777376i	$0.716550\pi$
$744$	11.8739	0.435318
$745$	−43.5386	−1.59513
$746$	62.7525	2.29753
$747$	−6.48992	−0.237454
$748$	−81.0764	−2.96445
$749$	68.9248	2.51846
$750$	19.9018	0.726710
$751$	29.6568	1.08219	0.541096	−	0.840961i	$-0.318010\pi$
$751$	29.6568	1.08219	0.541096	+	0.840961i	$0.318010\pi$
$752$	−31.7740	−1.15868
$753$	−36.8012	−1.34111
$754$	6.78848	0.247222
$755$	16.2036	0.589709
$756$	−9.38838	−0.341452
$757$	25.2425	0.917455	0.458727	−	0.888577i	$-0.348305\pi$
$757$	25.2425	0.917455	0.458727	+	0.888577i	$0.348305\pi$
$758$	77.6373	2.81991
$759$	37.2401	1.35173
$760$	−97.4856	−3.53617
$761$	−9.70283	−0.351727	−0.175864	−	0.984415i	$-0.556272\pi$
$761$	−9.70283	−0.351727	−0.175864	+	0.984415i	$0.556272\pi$
$762$	111.399	4.03555
$763$	−48.4870	−1.75535
$764$	29.5046	1.06744
$765$	−43.2654	−1.56426
$766$	5.92857	0.214208
$767$	−20.7767	−0.750202
$768$	−74.9326	−2.70390
$769$	23.9716	0.864436	0.432218	−	0.901769i	$-0.357731\pi$
$769$	23.9716	0.864436	0.432218	+	0.901769i	$0.357731\pi$
$770$	−101.549	−3.65956
$771$	−15.2044	−0.547573
$772$	−57.3219	−2.06306
$773$	−12.1885	−0.438389	−0.219194	−	0.975681i	$-0.570343\pi$
$773$	−12.1885	−0.438389	−0.219194	+	0.975681i	$0.570343\pi$
$774$	−27.9050	−1.00302
$775$	−4.06892	−0.146160
$776$	−89.8363	−3.22493
$777$	−73.8939	−2.65093
$778$	17.2846	0.619683
$779$	8.59478	0.307940
$780$	−61.1335	−2.18893
$781$	−22.2792	−0.797213
$782$	52.3257	1.87116
$783$	−0.840556	−0.0300390
$784$	22.0103	0.786082
$785$	1.87874	0.0670553
$786$	55.7324	1.98791
$787$	−34.7676	−1.23933	−0.619666	−	0.784866i	$-0.712732\pi$
$787$	−34.7676	−1.23933	−0.619666	+	0.784866i	$0.712732\pi$
$788$	−21.9608	−0.782322
$789$	25.9528	0.923946
$790$	95.7740	3.40749
$791$	30.4948	1.08427
$792$	−49.4836	−1.75832
$793$	16.0308	0.569269
$794$	41.8070	1.48367
$795$	41.5841	1.47484
$796$	−6.37360	−0.225906
$797$	−16.3193	−0.578061	−0.289030	−	0.957320i	$-0.593333\pi$
$797$	−16.3193	−0.578061	−0.289030	+	0.957320i	$0.593333\pi$
$798$	−147.330	−5.21542
$799$	47.3577	1.67540
$800$	2.60430	0.0920760
$801$	15.8502	0.560038
$802$	46.6830	1.64844
$803$	18.5712	0.655364
$804$	11.7333	0.413801
$805$	43.4318	1.53077
$806$	−5.62192	−0.198024
$807$	33.0450	1.16324
$808$	−7.40299	−0.260436
$809$	13.0347	0.458274	0.229137	−	0.973394i	$-0.426410\pi$
$809$	13.0347	0.458274	0.229137	+	0.973394i	$0.426410\pi$
$810$	70.6387	2.48199
$811$	−17.6821	−0.620904	−0.310452	−	0.950589i	$-0.600480\pi$
$811$	−17.6821	−0.620904	−0.310452	+	0.950589i	$0.600480\pi$
$812$	18.1728	0.637739
$813$	−0.335306	−0.0117597
$814$	80.1839	2.81044
$815$	43.3840	1.51968
$816$	−45.7300	−1.60087
$817$	29.3354	1.02632
$818$	−9.50609	−0.332373
$819$	−21.5911	−0.754453
$820$	14.4065	0.503097
$821$	−35.1270	−1.22594	−0.612970	−	0.790106i	$-0.710025\pi$
$821$	−35.1270	−1.22594	−0.612970	+	0.790106i	$0.710025\pi$
$822$	−79.3660	−2.76821
$823$	56.5437	1.97099	0.985495	−	0.169703i	$-0.0542807\pi$
$823$	56.5437	1.97099	0.985495	+	0.169703i	$0.0542807\pi$
$824$	−53.0092	−1.84666
$825$	35.6280	1.24041
$826$	−83.9288	−2.92026
$827$	31.3054	1.08860	0.544298	−	0.838892i	$-0.316796\pi$
$827$	31.3054	1.08860	0.544298	+	0.838892i	$0.316796\pi$
$828$	43.1029	1.49793
$829$	17.4882	0.607389	0.303695	−	0.952769i	$-0.401780\pi$
$829$	17.4882	0.607389	0.303695	+	0.952769i	$0.401780\pi$
$830$	17.2568	0.598992
$831$	−48.1162	−1.66913
$832$	19.2516	0.667429
$833$	−32.8054	−1.13664
$834$	−79.7684	−2.76215
$835$	−38.5825	−1.33520
$836$	105.946	3.66420
$837$	0.696111	0.0240611
$838$	4.89649	0.169146
$839$	−49.4807	−1.70826	−0.854132	−	0.520056i	$-0.825911\pi$
$839$	−49.4807	−1.70826	−0.854132	+	0.520056i	$0.825911\pi$
$840$	−121.256	−4.18373
$841$	−27.3730	−0.943895
$842$	−3.76764	−0.129842
$843$	−33.8379	−1.16544
$844$	−49.0173	−1.68724
$845$	−24.4655	−0.841640
$846$	58.8666	2.02388
$847$	14.3045	0.491508
$848$	20.9192	0.718367
$849$	−40.4824	−1.38935
$850$	50.0606	1.71707
$851$	−34.2942	−1.17559
$852$	−54.1801	−1.85618
$853$	−33.0821	−1.13271	−0.566354	−	0.824162i	$-0.691647\pi$
$853$	−33.0821	−1.13271	−0.566354	+	0.824162i	$0.691647\pi$
$854$	64.7574	2.21595
$855$	56.5365	1.93351
$856$	−89.3065	−3.05243
$857$	45.2819	1.54680	0.773400	−	0.633919i	$-0.218555\pi$
$857$	45.2819	1.54680	0.773400	+	0.633919i	$0.218555\pi$
$858$	49.2262	1.68056
$859$	21.1811	0.722689	0.361345	−	0.932432i	$-0.382318\pi$
$859$	21.1811	0.722689	0.361345	+	0.932432i	$0.382318\pi$
$860$	49.1717	1.67674
$861$	10.6905	0.364331
$862$	17.2956	0.589091
$863$	30.3164	1.03198	0.515991	−	0.856594i	$-0.327424\pi$
$863$	30.3164	1.03198	0.515991	+	0.856594i	$0.327424\pi$
$864$	−0.445544	−0.0151577
$865$	67.7232	2.30266
$866$	−67.9711	−2.30975
$867$	27.4842	0.933414
$868$	−15.0499	−0.510826
$869$	−51.1068	−1.73368
$870$	−22.1101	−0.749602
$871$	−2.72772	−0.0924253
$872$	62.8251	2.12753
$873$	52.1003	1.76333
$874$	−68.3760	−2.31285
$875$	−12.3857	−0.418713
$876$	45.1628	1.52591
$877$	42.5199	1.43579	0.717897	−	0.696149i	$-0.245105\pi$
$877$	42.5199	1.43579	0.717897	+	0.696149i	$0.245105\pi$
$878$	21.7864	0.735256
$879$	42.6974	1.44015
$880$	41.1882	1.38845
$881$	−43.1458	−1.45362	−0.726810	−	0.686839i	$-0.758998\pi$
$881$	−43.1458	−1.45362	−0.726810	+	0.686839i	$0.758998\pi$
$882$	−40.7777	−1.37306
$883$	17.9940	0.605547	0.302773	−	0.953063i	$-0.402087\pi$
$883$	17.9940	0.605547	0.302773	+	0.953063i	$0.402087\pi$
$884$	45.8368	1.54166
$885$	67.6696	2.27469
$886$	21.5567	0.724213
$887$	−33.8644	−1.13706	−0.568528	−	0.822664i	$-0.692487\pi$
$887$	−33.8644	−1.13706	−0.568528	+	0.822664i	$0.692487\pi$
$888$	95.7450	3.21299
$889$	−69.3280	−2.32519
$890$	−42.1458	−1.41273
$891$	−37.6941	−1.26280
$892$	41.6161	1.39341
$893$	−61.8841	−2.07087
$894$	85.2574	2.85144
$895$	23.9366	0.800112
$896$	72.8653	2.43426
$897$	−21.0538	−0.702966
$898$	−49.1555	−1.64034
$899$	−1.34744	−0.0449396
$900$	41.2370	1.37457
$901$	−31.1791	−1.03873
$902$	−11.6005	−0.386254
$903$	36.4884	1.21426
$904$	−39.5124	−1.31416
$905$	28.7738	0.956474
$906$	−31.7299	−1.05416
$907$	28.5992	0.949619	0.474810	−	0.880089i	$-0.342517\pi$
$907$	28.5992	0.949619	0.474810	+	0.880089i	$0.342517\pi$
$908$	5.97297	0.198220
$909$	4.29335	0.142401
$910$	57.4109	1.90315
$911$	21.3574	0.707602	0.353801	−	0.935321i	$-0.384889\pi$
$911$	21.3574	0.707602	0.353801	+	0.935321i	$0.384889\pi$
$912$	59.7571	1.97876
$913$	−9.20854	−0.304758
$914$	44.5546	1.47374
$915$	−52.2122	−1.72608
$916$	13.8033	0.456074
$917$	−34.6846	−1.14539
$918$	−8.56438	−0.282667
$919$	−23.4921	−0.774933	−0.387466	−	0.921884i	$-0.626650\pi$
$919$	−23.4921	−0.774933	−0.387466	+	0.921884i	$0.626650\pi$
$920$	−56.2750	−1.85533
$921$	−73.8465	−2.43333
$922$	−96.6817	−3.18404
$923$	12.5956	0.414591
$924$	131.779	4.33520
$925$	−32.8097	−1.07878
$926$	−95.2541	−3.13024
$927$	30.7426	1.00972
$928$	0.862424	0.0283105
$929$	6.57180	0.215614	0.107807	−	0.994172i	$-0.465617\pi$
$929$	6.57180	0.215614	0.107807	+	0.994172i	$0.465617\pi$
$930$	18.3106	0.600427
$931$	42.8680	1.40494
$932$	100.561	3.29398
$933$	−66.8648	−2.18906
$934$	−44.1024	−1.44307
$935$	−61.3892	−2.00764
$936$	27.9757	0.914415
$937$	19.3674	0.632706	0.316353	−	0.948642i	$-0.397542\pi$
$937$	19.3674	0.632706	0.316353	+	0.948642i	$0.397542\pi$
$938$	−11.0188	−0.359777
$939$	−37.3129	−1.21766
$940$	−103.730	−3.38329
$941$	−28.7492	−0.937199	−0.468599	−	0.883411i	$-0.655241\pi$
$941$	−28.7492	−0.937199	−0.468599	+	0.883411i	$0.655241\pi$
$942$	−3.67896	−0.119867
$943$	4.96146	0.161567
$944$	34.0416	1.10796
$945$	−7.10867	−0.231245
$946$	−39.5943	−1.28732
$947$	−1.29786	−0.0421748	−0.0210874	−	0.999778i	$-0.506713\pi$
$947$	−1.29786	−0.0421748	−0.0210874	+	0.999778i	$0.506713\pi$
$948$	−124.285	−4.03659
$949$	−10.4993	−0.340822
$950$	−65.4161	−2.12238
$951$	−10.9518	−0.355136
$952$	90.9156	2.94659
$953$	4.47948	0.145104	0.0725522	−	0.997365i	$-0.476886\pi$
$953$	4.47948	0.145104	0.0725522	+	0.997365i	$0.476886\pi$
$954$	−38.7562	−1.25478
$955$	22.3402	0.722913
$956$	−91.0543	−2.94491
$957$	11.7983	0.381386
$958$	−5.53576	−0.178852
$959$	49.3927	1.59498
$960$	−62.7025	−2.02371
$961$	−29.8841	−0.964004
$962$	−45.3323	−1.46157
$963$	51.7931	1.66901
$964$	−28.3874	−0.914297
$965$	−43.4029	−1.39719
$966$	−85.0483	−2.73639
$967$	27.9357	0.898351	0.449176	−	0.893443i	$-0.351718\pi$
$967$	27.9357	0.898351	0.449176	+	0.893443i	$0.351718\pi$
$968$	−18.5344	−0.595719
$969$	−89.0654	−2.86119
$970$	−138.535	−4.44810
$971$	50.9471	1.63497	0.817485	−	0.575950i	$-0.195368\pi$
$971$	50.9471	1.63497	0.817485	+	0.575950i	$0.195368\pi$
$972$	−83.8991	−2.69107
$973$	49.6432	1.59149
$974$	16.6903	0.534793
$975$	−20.1424	−0.645074
$976$	−26.2657	−0.840743
$977$	−24.6332	−0.788086	−0.394043	−	0.919092i	$-0.628924\pi$
$977$	−24.6332	−0.788086	−0.394043	+	0.919092i	$0.628924\pi$
$978$	−84.9547	−2.71655
$979$	22.4898	0.718777
$980$	71.8549	2.29532
$981$	−36.4352	−1.16329
$982$	42.6407	1.36072
$983$	50.3525	1.60599	0.802997	−	0.595983i	$-0.203237\pi$
$983$	50.3525	1.60599	0.802997	+	0.595983i	$0.203237\pi$
$984$	−13.8518	−0.441578
$985$	−16.6283	−0.529820
$986$	16.5778	0.527944
$987$	−76.9736	−2.45010
$988$	−59.8967	−1.90557
$989$	16.9343	0.538479
$990$	−76.3080	−2.42523
$991$	33.7978	1.07362	0.536812	−	0.843702i	$-0.319629\pi$
$991$	33.7978	1.07362	0.536812	+	0.843702i	$0.319629\pi$
$992$	−0.714221	−0.0226765
$993$	22.1110	0.701672
$994$	50.8810	1.61385
$995$	−4.82595	−0.152993
$996$	−22.3940	−0.709580
$997$	−28.0884	−0.889567	−0.444784	−	0.895638i	$-0.646719\pi$
$997$	−28.0884	−0.889567	−0.444784	+	0.895638i	$0.646719\pi$
$998$	−2.30817	−0.0730638
$999$	5.61309	0.177590

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.18	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.18	✓	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)

\(f(q)\)	\(=\)	\(q-2.43502 q^{2} +2.39261 q^{3} +3.92934 q^{4} +2.97521 q^{5} -5.82606 q^{6} +3.62580 q^{7} -4.69798 q^{8} +2.72458 q^{9} +O(q^{10})\)	\(q-2.43502 q^{2} +2.39261 q^{3} +3.92934 q^{4} +2.97521 q^{5} -5.82606 q^{6} +3.62580 q^{7} -4.69798 q^{8} +2.72458 q^{9} -7.24469 q^{10} +3.86590 q^{11} +9.40137 q^{12} -2.18560 q^{13} -8.82890 q^{14} +7.11850 q^{15} +3.58101 q^{16} -5.33733 q^{17} -6.63441 q^{18} +6.97449 q^{19} +11.6906 q^{20} +8.67511 q^{21} -9.41356 q^{22} +4.02613 q^{23} -11.2404 q^{24} +3.85185 q^{25} +5.32199 q^{26} -0.658974 q^{27} +14.2470 q^{28} +1.27555 q^{29} -17.3337 q^{30} -1.05636 q^{31} +0.676118 q^{32} +9.24959 q^{33} +12.9965 q^{34} +10.7875 q^{35} +10.7058 q^{36} -8.51792 q^{37} -16.9831 q^{38} -5.22929 q^{39} -13.9774 q^{40} +1.23232 q^{41} -21.1241 q^{42} +4.20610 q^{43} +15.1904 q^{44} +8.10618 q^{45} -9.80372 q^{46} -8.87292 q^{47} +8.56795 q^{48} +6.14640 q^{49} -9.37933 q^{50} -12.7702 q^{51} -8.58796 q^{52} +5.84170 q^{53} +1.60462 q^{54} +11.5019 q^{55} -17.0339 q^{56} +16.6872 q^{57} -3.10600 q^{58} +9.50615 q^{59} +27.9710 q^{60} -7.33471 q^{61} +2.57225 q^{62} +9.87877 q^{63} -8.80838 q^{64} -6.50262 q^{65} -22.5230 q^{66} +1.24804 q^{67} -20.9722 q^{68} +9.63295 q^{69} -26.2678 q^{70} -5.76301 q^{71} -12.8000 q^{72} +4.80385 q^{73} +20.7413 q^{74} +9.21596 q^{75} +27.4051 q^{76} +14.0170 q^{77} +12.7334 q^{78} -13.2199 q^{79} +10.6542 q^{80} -9.75041 q^{81} -3.00072 q^{82} -2.38199 q^{83} +34.0874 q^{84} -15.8797 q^{85} -10.2419 q^{86} +3.05190 q^{87} -18.1619 q^{88} +5.81748 q^{89} -19.7387 q^{90} -7.92455 q^{91} +15.8200 q^{92} -2.52745 q^{93} +21.6058 q^{94} +20.7506 q^{95} +1.61769 q^{96} +19.1223 q^{97} -14.9666 q^{98} +10.5330 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 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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