LMFDB - Embedded newform 6015.2.a.d.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.64211 q^{2} -1.00000 q^{3} +0.696514 q^{4} +1.00000 q^{5} +1.64211 q^{6} -2.05425 q^{7} +2.14046 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.64211 q^{2} -1.00000 q^{3} +0.696514 q^{4} +1.00000 q^{5} +1.64211 q^{6} -2.05425 q^{7} +2.14046 q^{8} +1.00000 q^{9} -1.64211 q^{10} +4.93387 q^{11} -0.696514 q^{12} +3.82066 q^{13} +3.37331 q^{14} -1.00000 q^{15} -4.90790 q^{16} -1.93147 q^{17} -1.64211 q^{18} -1.25020 q^{19} +0.696514 q^{20} +2.05425 q^{21} -8.10194 q^{22} +6.51958 q^{23} -2.14046 q^{24} +1.00000 q^{25} -6.27393 q^{26} -1.00000 q^{27} -1.43082 q^{28} -2.18390 q^{29} +1.64211 q^{30} -10.9064 q^{31} +3.77836 q^{32} -4.93387 q^{33} +3.17168 q^{34} -2.05425 q^{35} +0.696514 q^{36} -6.17825 q^{37} +2.05297 q^{38} -3.82066 q^{39} +2.14046 q^{40} +10.1764 q^{41} -3.37331 q^{42} +7.99289 q^{43} +3.43651 q^{44} +1.00000 q^{45} -10.7058 q^{46} -12.0112 q^{47} +4.90790 q^{48} -2.78004 q^{49} -1.64211 q^{50} +1.93147 q^{51} +2.66114 q^{52} -1.04907 q^{53} +1.64211 q^{54} +4.93387 q^{55} -4.39706 q^{56} +1.25020 q^{57} +3.58619 q^{58} -12.7641 q^{59} -0.696514 q^{60} -13.5520 q^{61} +17.9095 q^{62} -2.05425 q^{63} +3.61131 q^{64} +3.82066 q^{65} +8.10194 q^{66} -1.41869 q^{67} -1.34530 q^{68} -6.51958 q^{69} +3.37331 q^{70} +1.67250 q^{71} +2.14046 q^{72} -11.2027 q^{73} +10.1453 q^{74} -1.00000 q^{75} -0.870785 q^{76} -10.1354 q^{77} +6.27393 q^{78} -6.90323 q^{79} -4.90790 q^{80} +1.00000 q^{81} -16.7107 q^{82} +9.69548 q^{83} +1.43082 q^{84} -1.93147 q^{85} -13.1252 q^{86} +2.18390 q^{87} +10.5608 q^{88} -2.34975 q^{89} -1.64211 q^{90} -7.84860 q^{91} +4.54098 q^{92} +10.9064 q^{93} +19.7236 q^{94} -1.25020 q^{95} -3.77836 q^{96} +9.09266 q^{97} +4.56512 q^{98} +4.93387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.64211	−1.16114	−0.580572	−	0.814209i	$-0.697171\pi$
$2$	−1.64211	−1.16114	−0.580572	+	0.814209i	$0.697171\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.696514	0.348257
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.64211	0.670387
$7$	−2.05425	−0.776435	−0.388218	−	0.921568i	$-0.626909\pi$
$7$	−2.05425	−0.776435	−0.388218	+	0.921568i	$0.626909\pi$
$8$	2.14046	0.756768
$9$	1.00000	0.333333
$10$	−1.64211	−0.519280
$11$	4.93387	1.48762	0.743809	−	0.668393i	$-0.233017\pi$
$11$	4.93387	1.48762	0.743809	+	0.668393i	$0.233017\pi$
$12$	−0.696514	−0.201066
$13$	3.82066	1.05966	0.529830	−	0.848104i	$-0.322256\pi$
$13$	3.82066	1.05966	0.529830	+	0.848104i	$0.322256\pi$
$14$	3.37331	0.901554
$15$	−1.00000	−0.258199
$16$	−4.90790	−1.22697
$17$	−1.93147	−0.468451	−0.234225	−	0.972182i	$-0.575255\pi$
$17$	−1.93147	−0.468451	−0.234225	+	0.972182i	$0.575255\pi$
$18$	−1.64211	−0.387048
$19$	−1.25020	−0.286817	−0.143408	−	0.989664i	$-0.545806\pi$
$19$	−1.25020	−0.286817	−0.143408	+	0.989664i	$0.545806\pi$
$20$	0.696514	0.155745
$21$	2.05425	0.448275
$22$	−8.10194	−1.72734
$23$	6.51958	1.35943	0.679713	−	0.733478i	$-0.262104\pi$
$23$	6.51958	1.35943	0.679713	+	0.733478i	$0.262104\pi$
$24$	−2.14046	−0.436920
$25$	1.00000	0.200000
$26$	−6.27393	−1.23042
$27$	−1.00000	−0.192450
$28$	−1.43082	−0.270399
$29$	−2.18390	−0.405540	−0.202770	−	0.979226i	$-0.564994\pi$
$29$	−2.18390	−0.405540	−0.202770	+	0.979226i	$0.564994\pi$
$30$	1.64211	0.299806
$31$	−10.9064	−1.95885	−0.979425	−	0.201811i	$-0.935317\pi$
$31$	−10.9064	−1.95885	−0.979425	+	0.201811i	$0.935317\pi$
$32$	3.77836	0.667927
$33$	−4.93387	−0.858876
$34$	3.17168	0.543939
$35$	−2.05425	−0.347232
$36$	0.696514	0.116086
$37$	−6.17825	−1.01570	−0.507849	−	0.861446i	$-0.669559\pi$
$37$	−6.17825	−1.01570	−0.507849	+	0.861446i	$0.669559\pi$
$38$	2.05297	0.333036
$39$	−3.82066	−0.611795
$40$	2.14046	0.338437
$41$	10.1764	1.58929	0.794643	−	0.607077i	$-0.207658\pi$
$41$	10.1764	1.58929	0.794643	+	0.607077i	$0.207658\pi$
$42$	−3.37331	−0.520512
$43$	7.99289	1.21890	0.609452	−	0.792823i	$-0.291390\pi$
$43$	7.99289	1.21890	0.609452	+	0.792823i	$0.291390\pi$
$44$	3.43651	0.518073
$45$	1.00000	0.149071
$46$	−10.7058	−1.57849
$47$	−12.0112	−1.75201	−0.876004	−	0.482304i	$-0.839800\pi$
$47$	−12.0112	−1.75201	−0.876004	+	0.482304i	$0.839800\pi$
$48$	4.90790	0.708394
$49$	−2.78004	−0.397148
$50$	−1.64211	−0.232229
$51$	1.93147	0.270460
$52$	2.66114	0.369034
$53$	−1.04907	−0.144101	−0.0720503	−	0.997401i	$-0.522954\pi$
$53$	−1.04907	−0.144101	−0.0720503	+	0.997401i	$0.522954\pi$
$54$	1.64211	0.223462
$55$	4.93387	0.665283
$56$	−4.39706	−0.587581
$57$	1.25020	0.165594
$58$	3.58619	0.470890
$59$	−12.7641	−1.66174	−0.830872	−	0.556464i	$-0.812158\pi$
$59$	−12.7641	−1.66174	−0.830872	+	0.556464i	$0.812158\pi$
$60$	−0.696514	−0.0899196
$61$	−13.5520	−1.73516	−0.867579	−	0.497299i	$-0.834325\pi$
$61$	−13.5520	−1.73516	−0.867579	+	0.497299i	$0.834325\pi$
$62$	17.9095	2.27451
$63$	−2.05425	−0.258812
$64$	3.61131	0.451414
$65$	3.82066	0.473894
$66$	8.10194	0.997280
$67$	−1.41869	−0.173320	−0.0866601	−	0.996238i	$-0.527619\pi$
$67$	−1.41869	−0.173320	−0.0866601	+	0.996238i	$0.527619\pi$
$68$	−1.34530	−0.163141
$69$	−6.51958	−0.784865
$70$	3.37331	0.403187
$71$	1.67250	0.198489	0.0992446	−	0.995063i	$-0.468357\pi$
$71$	1.67250	0.198489	0.0992446	+	0.995063i	$0.468357\pi$
$72$	2.14046	0.252256
$73$	−11.2027	−1.31117	−0.655587	−	0.755119i	$-0.727579\pi$
$73$	−11.2027	−1.31117	−0.655587	+	0.755119i	$0.727579\pi$
$74$	10.1453	1.17937
$75$	−1.00000	−0.115470
$76$	−0.870785	−0.0998859
$77$	−10.1354	−1.15504
$78$	6.27393	0.710382
$79$	−6.90323	−0.776674	−0.388337	−	0.921517i	$-0.626950\pi$
$79$	−6.90323	−0.776674	−0.388337	+	0.921517i	$0.626950\pi$
$80$	−4.90790	−0.548720
$81$	1.00000	0.111111
$82$	−16.7107	−1.84539
$83$	9.69548	1.06422	0.532108	−	0.846676i	$-0.321400\pi$
$83$	9.69548	1.06422	0.532108	+	0.846676i	$0.321400\pi$
$84$	1.43082	0.156115
$85$	−1.93147	−0.209498
$86$	−13.1252	−1.41532
$87$	2.18390	0.234138
$88$	10.5608	1.12578
$89$	−2.34975	−0.249073	−0.124536	−	0.992215i	$-0.539744\pi$
$89$	−2.34975	−0.249073	−0.124536	+	0.992215i	$0.539744\pi$
$90$	−1.64211	−0.173093
$91$	−7.84860	−0.822757
$92$	4.54098	0.473430
$93$	10.9064	1.13094
$94$	19.7236	2.03433
$95$	−1.25020	−0.128268
$96$	−3.77836	−0.385628
$97$	9.09266	0.923220	0.461610	−	0.887083i	$-0.347272\pi$
$97$	9.09266	0.923220	0.461610	+	0.887083i	$0.347272\pi$
$98$	4.56512	0.461146
$99$	4.93387	0.495872
$100$	0.696514	0.0696514
$101$	2.47674	0.246445	0.123222	−	0.992379i	$-0.460677\pi$
$101$	2.47674	0.246445	0.123222	+	0.992379i	$0.460677\pi$
$102$	−3.17168	−0.314043
$103$	17.7625	1.75019	0.875096	−	0.483949i	$-0.160798\pi$
$103$	17.7625	1.75019	0.875096	+	0.483949i	$0.160798\pi$
$104$	8.17797	0.801916
$105$	2.05425	0.200475
$106$	1.72268	0.167322
$107$	1.43328	0.138560	0.0692802	−	0.997597i	$-0.477930\pi$
$107$	1.43328	0.138560	0.0692802	+	0.997597i	$0.477930\pi$
$108$	−0.696514	−0.0670221
$109$	−13.1496	−1.25951	−0.629754	−	0.776795i	$-0.716844\pi$
$109$	−13.1496	−1.25951	−0.629754	+	0.776795i	$0.716844\pi$
$110$	−8.10194	−0.772489
$111$	6.17825	0.586413
$112$	10.0821	0.952666
$113$	−15.3166	−1.44087	−0.720433	−	0.693525i	$-0.756057\pi$
$113$	−15.3166	−1.44087	−0.720433	+	0.693525i	$0.756057\pi$
$114$	−2.05297	−0.192278
$115$	6.51958	0.607954
$116$	−1.52112	−0.141232
$117$	3.82066	0.353220
$118$	20.9600	1.92952
$119$	3.96774	0.363722
$120$	−2.14046	−0.195397
$121$	13.3431	1.21300
$122$	22.2539	2.01477
$123$	−10.1764	−0.917575
$124$	−7.59647	−0.682183
$125$	1.00000	0.0894427
$126$	3.37331	0.300518
$127$	0.354471	0.0314542	0.0157271	−	0.999876i	$-0.494994\pi$
$127$	0.354471	0.0314542	0.0157271	+	0.999876i	$0.494994\pi$
$128$	−13.4869	−1.19208
$129$	−7.99289	−0.703734
$130$	−6.27393	−0.550260
$131$	1.84185	0.160923	0.0804615	−	0.996758i	$-0.474361\pi$
$131$	1.84185	0.160923	0.0804615	+	0.996758i	$0.474361\pi$
$132$	−3.43651	−0.299110
$133$	2.56824	0.222695
$134$	2.32963	0.201250
$135$	−1.00000	−0.0860663
$136$	−4.13424	−0.354508
$137$	−8.81991	−0.753536	−0.376768	−	0.926308i	$-0.622965\pi$
$137$	−8.81991	−0.753536	−0.376768	+	0.926308i	$0.622965\pi$
$138$	10.7058	0.911342
$139$	5.95763	0.505319	0.252660	−	0.967555i	$-0.418695\pi$
$139$	5.95763	0.505319	0.252660	+	0.967555i	$0.418695\pi$
$140$	−1.43082	−0.120926
$141$	12.0112	1.01152
$142$	−2.74642	−0.230475
$143$	18.8506	1.57637
$144$	−4.90790	−0.408991
$145$	−2.18390	−0.181363
$146$	18.3960	1.52246
$147$	2.78004	0.229294
$148$	−4.30324	−0.353724
$149$	5.82379	0.477104	0.238552	−	0.971130i	$-0.423327\pi$
$149$	5.82379	0.477104	0.238552	+	0.971130i	$0.423327\pi$
$150$	1.64211	0.134077
$151$	−19.6395	−1.59824	−0.799118	−	0.601174i	$-0.794700\pi$
$151$	−19.6395	−1.59824	−0.799118	+	0.601174i	$0.794700\pi$
$152$	−2.67602	−0.217054
$153$	−1.93147	−0.156150
$154$	16.6434	1.34117
$155$	−10.9064	−0.876024
$156$	−2.66114	−0.213062
$157$	13.9723	1.11511	0.557557	−	0.830139i	$-0.311739\pi$
$157$	13.9723	1.11511	0.557557	+	0.830139i	$0.311739\pi$
$158$	11.3358	0.901831
$159$	1.04907	0.0831966
$160$	3.77836	0.298706
$161$	−13.3929	−1.05551
$162$	−1.64211	−0.129016
$163$	14.4563	1.13230	0.566151	−	0.824302i	$-0.308432\pi$
$163$	14.4563	1.13230	0.566151	+	0.824302i	$0.308432\pi$
$164$	7.08801	0.553480
$165$	−4.93387	−0.384101
$166$	−15.9210	−1.23571
$167$	−7.04796	−0.545387	−0.272694	−	0.962101i	$-0.587915\pi$
$167$	−7.04796	−0.545387	−0.272694	+	0.962101i	$0.587915\pi$
$168$	4.39706	0.339240
$169$	1.59742	0.122879
$170$	3.17168	0.243257
$171$	−1.25020	−0.0956055
$172$	5.56716	0.424492
$173$	−0.468300	−0.0356042	−0.0178021	−	0.999842i	$-0.505667\pi$
$173$	−0.468300	−0.0356042	−0.0178021	+	0.999842i	$0.505667\pi$
$174$	−3.58619	−0.271869
$175$	−2.05425	−0.155287
$176$	−24.2149	−1.82527
$177$	12.7641	0.959408
$178$	3.85854	0.289209
$179$	−14.6533	−1.09524	−0.547619	−	0.836728i	$-0.684466\pi$
$179$	−14.6533	−1.09524	−0.547619	+	0.836728i	$0.684466\pi$
$180$	0.696514	0.0519151
$181$	−24.7649	−1.84076	−0.920380	−	0.391025i	$-0.872121\pi$
$181$	−24.7649	−1.84076	−0.920380	+	0.391025i	$0.872121\pi$
$182$	12.8882	0.955340
$183$	13.5520	1.00179
$184$	13.9549	1.02877
$185$	−6.17825	−0.454234
$186$	−17.9095	−1.31319
$187$	−9.52963	−0.696875
$188$	−8.36595	−0.610149
$189$	2.05425	0.149425
$190$	2.05297	0.148938
$191$	−2.30148	−0.166529	−0.0832645	−	0.996527i	$-0.526535\pi$
$191$	−2.30148	−0.166529	−0.0832645	+	0.996527i	$0.526535\pi$
$192$	−3.61131	−0.260624
$193$	−9.81360	−0.706398	−0.353199	−	0.935548i	$-0.614906\pi$
$193$	−9.81360	−0.706398	−0.353199	+	0.935548i	$0.614906\pi$
$194$	−14.9311	−1.07199
$195$	−3.82066	−0.273603
$196$	−1.93634	−0.138310
$197$	23.4250	1.66896	0.834480	−	0.551038i	$-0.185768\pi$
$197$	23.4250	1.66896	0.834480	+	0.551038i	$0.185768\pi$
$198$	−8.10194	−0.575780
$199$	13.8997	0.985322	0.492661	−	0.870221i	$-0.336024\pi$
$199$	13.8997	0.985322	0.492661	+	0.870221i	$0.336024\pi$
$200$	2.14046	0.151354
$201$	1.41869	0.100066
$202$	−4.06707	−0.286158
$203$	4.48628	0.314875
$204$	1.34530	0.0941897
$205$	10.1764	0.710750
$206$	−29.1679	−2.03223
$207$	6.51958	0.453142
$208$	−18.7514	−1.30018
$209$	−6.16834	−0.426673
$210$	−3.37331	−0.232780
$211$	22.6065	1.55630	0.778149	−	0.628080i	$-0.216159\pi$
$211$	22.6065	1.55630	0.778149	+	0.628080i	$0.216159\pi$
$212$	−0.730691	−0.0501841
$213$	−1.67250	−0.114598
$214$	−2.35360	−0.160889
$215$	7.99289	0.545110
$216$	−2.14046	−0.145640
$217$	22.4045	1.52092
$218$	21.5931	1.46247
$219$	11.2027	0.757007
$220$	3.43651	0.231689
$221$	−7.37949	−0.496398
$222$	−10.1453	−0.680911
$223$	11.9713	0.801656	0.400828	−	0.916153i	$-0.368722\pi$
$223$	11.9713	0.801656	0.400828	+	0.916153i	$0.368722\pi$
$224$	−7.76172	−0.518602
$225$	1.00000	0.0666667
$226$	25.1515	1.67305
$227$	−12.2368	−0.812187	−0.406093	−	0.913832i	$-0.633109\pi$
$227$	−12.2368	−0.812187	−0.406093	+	0.913832i	$0.633109\pi$
$228$	0.870785	0.0576692
$229$	−15.0243	−0.992834	−0.496417	−	0.868084i	$-0.665351\pi$
$229$	−15.0243	−0.992834	−0.496417	+	0.868084i	$0.665351\pi$
$230$	−10.7058	−0.705923
$231$	10.1354	0.666862
$232$	−4.67455	−0.306899
$233$	−20.9894	−1.37506	−0.687531	−	0.726155i	$-0.741305\pi$
$233$	−20.9894	−1.37506	−0.687531	+	0.726155i	$0.741305\pi$
$234$	−6.27393	−0.410139
$235$	−12.0112	−0.783522
$236$	−8.89038	−0.578714
$237$	6.90323	0.448413
$238$	−6.51544	−0.422334
$239$	8.04109	0.520135	0.260067	−	0.965590i	$-0.416255\pi$
$239$	8.04109	0.520135	0.260067	+	0.965590i	$0.416255\pi$
$240$	4.90790	0.316803
$241$	14.0300	0.903754	0.451877	−	0.892080i	$-0.350755\pi$
$241$	14.0300	0.903754	0.451877	+	0.892080i	$0.350755\pi$
$242$	−21.9107	−1.40847
$243$	−1.00000	−0.0641500
$244$	−9.43918	−0.604282
$245$	−2.78004	−0.177610
$246$	16.7107	1.06544
$247$	−4.77660	−0.303928
$248$	−23.3448	−1.48239
$249$	−9.69548	−0.614426
$250$	−1.64211	−0.103856
$251$	2.73387	0.172560	0.0862802	−	0.996271i	$-0.472502\pi$
$251$	2.73387	0.172560	0.0862802	+	0.996271i	$0.472502\pi$
$252$	−1.43082	−0.0901331
$253$	32.1668	2.02231
$254$	−0.582079	−0.0365229
$255$	1.93147	0.120953
$256$	14.9243	0.932768
$257$	−6.20040	−0.386771	−0.193385	−	0.981123i	$-0.561947\pi$
$257$	−6.20040	−0.386771	−0.193385	+	0.981123i	$0.561947\pi$
$258$	13.1252	0.817137
$259$	12.6917	0.788623
$260$	2.66114	0.165037
$261$	−2.18390	−0.135180
$262$	−3.02451	−0.186855
$263$	−6.24615	−0.385154	−0.192577	−	0.981282i	$-0.561685\pi$
$263$	−6.24615	−0.385154	−0.192577	+	0.981282i	$0.561685\pi$
$264$	−10.5608	−0.649970
$265$	−1.04907	−0.0644438
$266$	−4.21732	−0.258581
$267$	2.34975	0.143802
$268$	−0.988136	−0.0603600
$269$	−28.9924	−1.76770	−0.883849	−	0.467772i	$-0.845057\pi$
$269$	−28.9924	−1.76770	−0.883849	+	0.467772i	$0.845057\pi$
$270$	1.64211	0.0999354
$271$	12.8444	0.780239	0.390120	−	0.920764i	$-0.372434\pi$
$271$	12.8444	0.780239	0.390120	+	0.920764i	$0.372434\pi$
$272$	9.47946	0.574777
$273$	7.84860	0.475019
$274$	14.4832	0.874964
$275$	4.93387	0.297523
$276$	−4.54098	−0.273335
$277$	14.6199	0.878425	0.439213	−	0.898383i	$-0.355257\pi$
$277$	14.6199	0.878425	0.439213	+	0.898383i	$0.355257\pi$
$278$	−9.78306	−0.586749
$279$	−10.9064	−0.652950
$280$	−4.39706	−0.262774
$281$	−13.5210	−0.806597	−0.403299	−	0.915068i	$-0.632136\pi$
$281$	−13.5210	−0.806597	−0.403299	+	0.915068i	$0.632136\pi$
$282$	−19.7236	−1.17452
$283$	−11.3566	−0.675079	−0.337540	−	0.941311i	$-0.609595\pi$
$283$	−11.3566	−0.675079	−0.337540	+	0.941311i	$0.609595\pi$
$284$	1.16492	0.0691253
$285$	1.25020	0.0740557
$286$	−30.9547	−1.83039
$287$	−20.9049	−1.23398
$288$	3.77836	0.222642
$289$	−13.2694	−0.780554
$290$	3.58619	0.210588
$291$	−9.09266	−0.533021
$292$	−7.80283	−0.456626
$293$	−4.36317	−0.254899	−0.127450	−	0.991845i	$-0.540679\pi$
$293$	−4.36317	−0.254899	−0.127450	+	0.991845i	$0.540679\pi$
$294$	−4.56512	−0.266243
$295$	−12.7641	−0.743154
$296$	−13.2243	−0.768647
$297$	−4.93387	−0.286292
$298$	−9.56329	−0.553987
$299$	24.9091	1.44053
$300$	−0.696514	−0.0402133
$301$	−16.4194	−0.946400
$302$	32.2501	1.85578
$303$	−2.47674	−0.142285
$304$	6.13587	0.351916
$305$	−13.5520	−0.775987
$306$	3.17168	0.181313
$307$	−9.14688	−0.522040	−0.261020	−	0.965333i	$-0.584059\pi$
$307$	−9.14688	−0.522040	−0.261020	+	0.965333i	$0.584059\pi$
$308$	−7.05947	−0.402250
$309$	−17.7625	−1.01047
$310$	17.9095	1.01719
$311$	21.0091	1.19132	0.595659	−	0.803238i	$-0.296891\pi$
$311$	21.0091	1.19132	0.595659	+	0.803238i	$0.296891\pi$
$312$	−8.17797	−0.462987
$313$	−16.8512	−0.952488	−0.476244	−	0.879313i	$-0.658002\pi$
$313$	−16.8512	−0.952488	−0.476244	+	0.879313i	$0.658002\pi$
$314$	−22.9441	−1.29481
$315$	−2.05425	−0.115744
$316$	−4.80820	−0.270482
$317$	33.7740	1.89694	0.948469	−	0.316870i	$-0.102632\pi$
$317$	33.7740	1.89694	0.948469	+	0.316870i	$0.102632\pi$
$318$	−1.72268	−0.0966032
$319$	−10.7751	−0.603288
$320$	3.61131	0.201879
$321$	−1.43328	−0.0799978
$322$	21.9925	1.22560
$323$	2.41473	0.134359
$324$	0.696514	0.0386952
$325$	3.82066	0.211932
$326$	−23.7387	−1.31477
$327$	13.1496	0.727177
$328$	21.7822	1.20272
$329$	24.6740	1.36032
$330$	8.10194	0.445997
$331$	−18.8570	−1.03647	−0.518236	−	0.855237i	$-0.673411\pi$
$331$	−18.8570	−1.03647	−0.518236	+	0.855237i	$0.673411\pi$
$332$	6.75304	0.370621
$333$	−6.17825	−0.338566
$334$	11.5735	0.633273
$335$	−1.41869	−0.0775111
$336$	−10.0821	−0.550022
$337$	−6.01612	−0.327719	−0.163860	−	0.986484i	$-0.552394\pi$
$337$	−6.01612	−0.327719	−0.163860	+	0.986484i	$0.552394\pi$
$338$	−2.62314	−0.142680
$339$	15.3166	0.831884
$340$	−1.34530	−0.0729590
$341$	−53.8108	−2.91402
$342$	2.05297	0.111012
$343$	20.0907	1.08480
$344$	17.1085	0.922427
$345$	−6.51958	−0.351002
$346$	0.768999	0.0413417
$347$	−33.2912	−1.78717	−0.893584	−	0.448896i	$-0.851817\pi$
$347$	−33.2912	−1.78717	−0.893584	+	0.448896i	$0.851817\pi$
$348$	1.52112	0.0815404
$349$	18.1001	0.968876	0.484438	−	0.874826i	$-0.339024\pi$
$349$	18.1001	0.968876	0.484438	+	0.874826i	$0.339024\pi$
$350$	3.37331	0.180311
$351$	−3.82066	−0.203932
$352$	18.6420	0.993619
$353$	−1.51805	−0.0807975	−0.0403987	−	0.999184i	$-0.512863\pi$
$353$	−1.51805	−0.0807975	−0.0403987	+	0.999184i	$0.512863\pi$
$354$	−20.9600	−1.11401
$355$	1.67250	0.0887671
$356$	−1.63663	−0.0867414
$357$	−3.96774	−0.209995
$358$	24.0622	1.27173
$359$	14.6429	0.772824	0.386412	−	0.922326i	$-0.373714\pi$
$359$	14.6429	0.772824	0.386412	+	0.922326i	$0.373714\pi$
$360$	2.14046	0.112812
$361$	−17.4370	−0.917736
$362$	40.6666	2.13739
$363$	−13.3431	−0.700329
$364$	−5.46667	−0.286531
$365$	−11.2027	−0.586375
$366$	−22.2539	−1.16323
$367$	32.7804	1.71112	0.855561	−	0.517702i	$-0.173212\pi$
$367$	32.7804	1.71112	0.855561	+	0.517702i	$0.173212\pi$
$368$	−31.9974	−1.66798
$369$	10.1764	0.529762
$370$	10.1453	0.527431
$371$	2.15505	0.111885
$372$	7.59647	0.393859
$373$	21.7385	1.12558	0.562788	−	0.826601i	$-0.309729\pi$
$373$	21.7385	1.12558	0.562788	+	0.826601i	$0.309729\pi$
$374$	15.6487	0.809173
$375$	−1.00000	−0.0516398
$376$	−25.7094	−1.32586
$377$	−8.34392	−0.429734
$378$	−3.37331	−0.173504
$379$	2.50858	0.128857	0.0644285	−	0.997922i	$-0.479478\pi$
$379$	2.50858	0.128857	0.0644285	+	0.997922i	$0.479478\pi$
$380$	−0.870785	−0.0446703
$381$	−0.354471	−0.0181601
$382$	3.77927	0.193364
$383$	25.3232	1.29395	0.646977	−	0.762509i	$-0.276033\pi$
$383$	25.3232	1.29395	0.646977	+	0.762509i	$0.276033\pi$
$384$	13.4869	0.688250
$385$	−10.1354	−0.516549
$386$	16.1150	0.820231
$387$	7.99289	0.406301
$388$	6.33317	0.321518
$389$	1.80265	0.0913978	0.0456989	−	0.998955i	$-0.485449\pi$
$389$	1.80265	0.0913978	0.0456989	+	0.998955i	$0.485449\pi$
$390$	6.27393	0.317693
$391$	−12.5924	−0.636824
$392$	−5.95056	−0.300549
$393$	−1.84185	−0.0929089
$394$	−38.4663	−1.93790
$395$	−6.90323	−0.347339
$396$	3.43651	0.172691
$397$	6.56298	0.329386	0.164693	−	0.986345i	$-0.447337\pi$
$397$	6.56298	0.329386	0.164693	+	0.986345i	$0.447337\pi$
$398$	−22.8248	−1.14410
$399$	−2.56824	−0.128573
$400$	−4.90790	−0.245395
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−2.32963	−0.116192
$403$	−41.6697	−2.07571
$404$	1.72508	0.0858261
$405$	1.00000	0.0496904
$406$	−7.36695	−0.365616
$407$	−30.4827	−1.51097
$408$	4.13424	0.204676
$409$	7.12340	0.352230	0.176115	−	0.984370i	$-0.443647\pi$
$409$	7.12340	0.352230	0.176115	+	0.984370i	$0.443647\pi$
$410$	−16.7107	−0.825284
$411$	8.81991	0.435054
$412$	12.3718	0.609517
$413$	26.2207	1.29024
$414$	−10.7058	−0.526164
$415$	9.69548	0.475932
$416$	14.4358	0.707775
$417$	−5.95763	−0.291746
$418$	10.1291	0.495429
$419$	−27.8220	−1.35919	−0.679596	−	0.733587i	$-0.737845\pi$
$419$	−27.8220	−1.35919	−0.679596	+	0.733587i	$0.737845\pi$
$420$	1.43082	0.0698168
$421$	−34.6819	−1.69029	−0.845146	−	0.534536i	$-0.820486\pi$
$421$	−34.6819	−1.69029	−0.845146	+	0.534536i	$0.820486\pi$
$422$	−37.1223	−1.80709
$423$	−12.0112	−0.584003
$424$	−2.24549	−0.109051
$425$	−1.93147	−0.0936901
$426$	2.74642	0.133065
$427$	27.8393	1.34724
$428$	0.998300	0.0482546
$429$	−18.8506	−0.910116
$430$	−13.1252	−0.632952
$431$	19.5063	0.939583	0.469792	−	0.882777i	$-0.344329\pi$
$431$	19.5063	0.939583	0.469792	+	0.882777i	$0.344329\pi$
$432$	4.90790	0.236131
$433$	−8.23416	−0.395709	−0.197854	−	0.980231i	$-0.563397\pi$
$433$	−8.23416	−0.395709	−0.197854	+	0.980231i	$0.563397\pi$
$434$	−36.7907	−1.76601
$435$	2.18390	0.104710
$436$	−9.15892	−0.438633
$437$	−8.15081	−0.389906
$438$	−18.3960	−0.878995
$439$	−14.4690	−0.690568	−0.345284	−	0.938498i	$-0.612217\pi$
$439$	−14.4690	−0.690568	−0.345284	+	0.938498i	$0.612217\pi$
$440$	10.5608	0.503464
$441$	−2.78004	−0.132383
$442$	12.1179	0.576390
$443$	−9.64057	−0.458037	−0.229019	−	0.973422i	$-0.573552\pi$
$443$	−9.64057	−0.458037	−0.229019	+	0.973422i	$0.573552\pi$
$444$	4.30324	0.204223
$445$	−2.34975	−0.111389
$446$	−19.6581	−0.930839
$447$	−5.82379	−0.275456
$448$	−7.41856	−0.350494
$449$	−17.9668	−0.847906	−0.423953	−	0.905684i	$-0.639358\pi$
$449$	−17.9668	−0.847906	−0.423953	+	0.905684i	$0.639358\pi$
$450$	−1.64211	−0.0774097
$451$	50.2090	2.36425
$452$	−10.6682	−0.501792
$453$	19.6395	0.922742
$454$	20.0942	0.943066
$455$	−7.84860	−0.367948
$456$	2.67602	0.125316
$457$	19.9376	0.932643	0.466322	−	0.884615i	$-0.345579\pi$
$457$	19.9376	0.932643	0.466322	+	0.884615i	$0.345579\pi$
$458$	24.6715	1.15282
$459$	1.93147	0.0901534
$460$	4.54098	0.211724
$461$	29.5494	1.37625	0.688125	−	0.725592i	$-0.258434\pi$
$461$	29.5494	1.37625	0.688125	+	0.725592i	$0.258434\pi$
$462$	−16.6434	−0.774323
$463$	−25.0229	−1.16291	−0.581455	−	0.813578i	$-0.697517\pi$
$463$	−25.0229	−1.16291	−0.581455	+	0.813578i	$0.697517\pi$
$464$	10.7183	0.497587
$465$	10.9064	0.505773
$466$	34.4668	1.59665
$467$	−40.2869	−1.86425	−0.932127	−	0.362131i	$-0.882049\pi$
$467$	−40.2869	−1.86425	−0.932127	+	0.362131i	$0.882049\pi$
$468$	2.66114	0.123011
$469$	2.91434	0.134572
$470$	19.7236	0.909782
$471$	−13.9723	−0.643811
$472$	−27.3211	−1.25755
$473$	39.4358	1.81326
$474$	−11.3358	−0.520673
$475$	−1.25020	−0.0573633
$476$	2.76358	0.126669
$477$	−1.04907	−0.0480336
$478$	−13.2043	−0.603952
$479$	−11.7357	−0.536216	−0.268108	−	0.963389i	$-0.586398\pi$
$479$	−11.7357	−0.536216	−0.268108	+	0.963389i	$0.586398\pi$
$480$	−3.77836	−0.172458
$481$	−23.6050	−1.07629
$482$	−23.0388	−1.04939
$483$	13.3929	0.609397
$484$	9.29363	0.422438
$485$	9.09266	0.412876
$486$	1.64211	0.0744875
$487$	24.9049	1.12855	0.564274	−	0.825587i	$-0.309156\pi$
$487$	24.9049	1.12855	0.564274	+	0.825587i	$0.309156\pi$
$488$	−29.0076	−1.31311
$489$	−14.4563	−0.653734
$490$	4.56512	0.206231
$491$	−37.2022	−1.67891	−0.839456	−	0.543428i	$-0.817126\pi$
$491$	−37.2022	−1.67891	−0.839456	+	0.543428i	$0.817126\pi$
$492$	−7.08801	−0.319552
$493$	4.21814	0.189975
$494$	7.84369	0.352904
$495$	4.93387	0.221761
$496$	53.5275	2.40346
$497$	−3.43574	−0.154114
$498$	15.9210	0.713437
$499$	−13.4325	−0.601320	−0.300660	−	0.953731i	$-0.597207\pi$
$499$	−13.4325	−0.601320	−0.300660	+	0.953731i	$0.597207\pi$
$500$	0.696514	0.0311491
$501$	7.04796	0.314879
$502$	−4.48931	−0.200368
$503$	−31.8170	−1.41865	−0.709326	−	0.704881i	$-0.751000\pi$
$503$	−31.8170	−1.41865	−0.709326	+	0.704881i	$0.751000\pi$
$504$	−4.39706	−0.195860
$505$	2.47674	0.110213
$506$	−52.8212	−2.34819
$507$	−1.59742	−0.0709441
$508$	0.246894	0.0109541
$509$	−27.5599	−1.22157	−0.610785	−	0.791796i	$-0.709146\pi$
$509$	−27.5599	−1.22157	−0.610785	+	0.791796i	$0.709146\pi$
$510$	−3.17168	−0.140444
$511$	23.0132	1.01804
$512$	2.46651	0.109005
$513$	1.25020	0.0551979
$514$	10.1817	0.449097
$515$	17.7625	0.782710
$516$	−5.56716	−0.245081
$517$	−59.2615	−2.60632
$518$	−20.8411	−0.915706
$519$	0.468300	0.0205561
$520$	8.17797	0.358628
$521$	−34.1708	−1.49705	−0.748526	−	0.663105i	$-0.769238\pi$
$521$	−34.1708	−1.49705	−0.748526	+	0.663105i	$0.769238\pi$
$522$	3.58619	0.156963
$523$	−20.2074	−0.883609	−0.441805	−	0.897111i	$-0.645662\pi$
$523$	−20.2074	−0.883609	−0.441805	+	0.897111i	$0.645662\pi$
$524$	1.28287	0.0560426
$525$	2.05425	0.0896550
$526$	10.2568	0.447220
$527$	21.0654	0.917624
$528$	24.2149	1.05382
$529$	19.5049	0.848041
$530$	1.72268	0.0748286
$531$	−12.7641	−0.553915
$532$	1.78882	0.0775550
$533$	38.8805	1.68410
$534$	−3.85854	−0.166975
$535$	1.43328	0.0619661
$536$	−3.03665	−0.131163
$537$	14.6533	0.632335
$538$	47.6086	2.05255
$539$	−13.7163	−0.590804
$540$	−0.696514	−0.0299732
$541$	28.7343	1.23538	0.617692	−	0.786420i	$-0.288068\pi$
$541$	28.7343	1.23538	0.617692	+	0.786420i	$0.288068\pi$
$542$	−21.0918	−0.905971
$543$	24.7649	1.06276
$544$	−7.29780	−0.312891
$545$	−13.1496	−0.563269
$546$	−12.8882	−0.551566
$547$	38.3022	1.63768	0.818841	−	0.574020i	$-0.194617\pi$
$547$	38.3022	1.63768	0.818841	+	0.574020i	$0.194617\pi$
$548$	−6.14320	−0.262424
$549$	−13.5520	−0.578386
$550$	−8.10194	−0.345468
$551$	2.73032	0.116315
$552$	−13.9549	−0.593961
$553$	14.1810	0.603037
$554$	−24.0075	−1.01998
$555$	6.17825	0.262252
$556$	4.14957	0.175981
$557$	0.109804	0.00465254	0.00232627	−	0.999997i	$-0.499260\pi$
$557$	0.109804	0.00465254	0.00232627	+	0.999997i	$0.499260\pi$
$558$	17.9095	0.758169
$559$	30.5381	1.29162
$560$	10.0821	0.426045
$561$	9.52963	0.402341
$562$	22.2030	0.936576
$563$	−21.7574	−0.916967	−0.458483	−	0.888703i	$-0.651607\pi$
$563$	−21.7574	−0.916967	−0.458483	+	0.888703i	$0.651607\pi$
$564$	8.36595	0.352270
$565$	−15.3166	−0.644375
$566$	18.6487	0.783865
$567$	−2.05425	−0.0862706
$568$	3.57992	0.150210
$569$	1.59227	0.0667513	0.0333757	−	0.999443i	$-0.489374\pi$
$569$	1.59227	0.0667513	0.0333757	+	0.999443i	$0.489374\pi$
$570$	−2.05297	−0.0859894
$571$	12.6316	0.528618	0.264309	−	0.964438i	$-0.414856\pi$
$571$	12.6316	0.528618	0.264309	+	0.964438i	$0.414856\pi$
$572$	13.1297	0.548981
$573$	2.30148	0.0961455
$574$	34.3281	1.43283
$575$	6.51958	0.271885
$576$	3.61131	0.150471
$577$	−10.6229	−0.442239	−0.221119	−	0.975247i	$-0.570971\pi$
$577$	−10.6229	−0.442239	−0.221119	+	0.975247i	$0.570971\pi$
$578$	21.7898	0.906336
$579$	9.81360	0.407839
$580$	−1.52112	−0.0631609
$581$	−19.9170	−0.826296
$582$	14.9311	0.618915
$583$	−5.17597	−0.214367
$584$	−23.9789	−0.992255
$585$	3.82066	0.157965
$586$	7.16480	0.295975
$587$	−19.8621	−0.819797	−0.409898	−	0.912131i	$-0.634436\pi$
$587$	−19.8621	−0.819797	−0.409898	+	0.912131i	$0.634436\pi$
$588$	1.93634	0.0798531
$589$	13.6352	0.561830
$590$	20.9600	0.862910
$591$	−23.4250	−0.963574
$592$	30.3222	1.24623
$593$	−41.8448	−1.71836	−0.859181	−	0.511672i	$-0.829026\pi$
$593$	−41.8448	−1.71836	−0.859181	+	0.511672i	$0.829026\pi$
$594$	8.10194	0.332427
$595$	3.96774	0.162661
$596$	4.05636	0.166155
$597$	−13.8997	−0.568876
$598$	−40.9034	−1.67266
$599$	8.03554	0.328323	0.164162	−	0.986433i	$-0.447508\pi$
$599$	8.03554	0.328323	0.164162	+	0.986433i	$0.447508\pi$
$600$	−2.14046	−0.0873840
$601$	−20.7518	−0.846482	−0.423241	−	0.906017i	$-0.639108\pi$
$601$	−20.7518	−0.846482	−0.423241	+	0.906017i	$0.639108\pi$
$602$	26.9624	1.09891
$603$	−1.41869	−0.0577734
$604$	−13.6792	−0.556597
$605$	13.3431	0.542472
$606$	4.06707	0.165213
$607$	−26.2554	−1.06567	−0.532837	−	0.846218i	$-0.678874\pi$
$607$	−26.2554	−1.06567	−0.532837	+	0.846218i	$0.678874\pi$
$608$	−4.72373	−0.191572
$609$	−4.48628	−0.181793
$610$	22.2539	0.901033
$611$	−45.8905	−1.85653
$612$	−1.34530	−0.0543804
$613$	16.7572	0.676817	0.338408	−	0.940999i	$-0.390111\pi$
$613$	16.7572	0.676817	0.338408	+	0.940999i	$0.390111\pi$
$614$	15.0201	0.606164
$615$	−10.1764	−0.410352
$616$	−21.6945	−0.874096
$617$	−20.6219	−0.830207	−0.415103	−	0.909774i	$-0.636255\pi$
$617$	−20.6219	−0.830207	−0.415103	+	0.909774i	$0.636255\pi$
$618$	29.1679	1.17331
$619$	−42.8374	−1.72178	−0.860890	−	0.508792i	$-0.830092\pi$
$619$	−42.8374	−1.72178	−0.860890	+	0.508792i	$0.830092\pi$
$620$	−7.59647	−0.305082
$621$	−6.51958	−0.261622
$622$	−34.4992	−1.38329
$623$	4.82698	0.193389
$624$	18.7514	0.750656
$625$	1.00000	0.0400000
$626$	27.6715	1.10598
$627$	6.16834	0.246340
$628$	9.73193	0.388346
$629$	11.9331	0.475804
$630$	3.37331	0.134396
$631$	4.25552	0.169409	0.0847047	−	0.996406i	$-0.473005\pi$
$631$	4.25552	0.169409	0.0847047	+	0.996406i	$0.473005\pi$
$632$	−14.7761	−0.587762
$633$	−22.6065	−0.898529
$634$	−55.4605	−2.20262
$635$	0.354471	0.0140667
$636$	0.730691	0.0289738
$637$	−10.6216	−0.420842
$638$	17.6938	0.700504
$639$	1.67250	0.0661631
$640$	−13.4869	−0.533116
$641$	34.5301	1.36386	0.681928	−	0.731419i	$-0.261142\pi$
$641$	34.5301	1.36386	0.681928	+	0.731419i	$0.261142\pi$
$642$	2.35360	0.0928891
$643$	8.37034	0.330094	0.165047	−	0.986286i	$-0.447222\pi$
$643$	8.37034	0.330094	0.165047	+	0.986286i	$0.447222\pi$
$644$	−9.32834	−0.367588
$645$	−7.99289	−0.314720
$646$	−3.96525	−0.156011
$647$	26.8777	1.05667	0.528335	−	0.849036i	$-0.322817\pi$
$647$	26.8777	1.05667	0.528335	+	0.849036i	$0.322817\pi$
$648$	2.14046	0.0840853
$649$	−62.9764	−2.47204
$650$	−6.27393	−0.246084
$651$	−22.4045	−0.878103
$652$	10.0690	0.394332
$653$	8.14750	0.318836	0.159418	−	0.987211i	$-0.449038\pi$
$653$	8.14750	0.318836	0.159418	+	0.987211i	$0.449038\pi$
$654$	−21.5931	−0.844358
$655$	1.84185	0.0719669
$656$	−49.9447	−1.95001
$657$	−11.2027	−0.437058
$658$	−40.5173	−1.57953
$659$	34.6480	1.34969	0.674847	−	0.737958i	$-0.264210\pi$
$659$	34.6480	1.34969	0.674847	+	0.737958i	$0.264210\pi$
$660$	−3.43651	−0.133766
$661$	−8.26055	−0.321298	−0.160649	−	0.987012i	$-0.551359\pi$
$661$	−8.26055	−0.321298	−0.160649	+	0.987012i	$0.551359\pi$
$662$	30.9652	1.20350
$663$	7.37949	0.286596
$664$	20.7528	0.805365
$665$	2.56824	0.0995920
$666$	10.1453	0.393124
$667$	−14.2381	−0.551301
$668$	−4.90900	−0.189935
$669$	−11.9713	−0.462837
$670$	2.32963	0.0900016
$671$	−66.8639	−2.58125
$672$	7.76172	0.299415
$673$	5.15274	0.198624	0.0993118	−	0.995056i	$-0.468336\pi$
$673$	5.15274	0.198624	0.0993118	+	0.995056i	$0.468336\pi$
$674$	9.87911	0.380529
$675$	−1.00000	−0.0384900
$676$	1.11263	0.0427934
$677$	7.31923	0.281301	0.140651	−	0.990059i	$-0.455081\pi$
$677$	7.31923	0.281301	0.140651	+	0.990059i	$0.455081\pi$
$678$	−25.1515	−0.965938
$679$	−18.6786	−0.716820
$680$	−4.13424	−0.158541
$681$	12.2368	0.468916
$682$	88.3631	3.38360
$683$	2.55878	0.0979090	0.0489545	−	0.998801i	$-0.484411\pi$
$683$	2.55878	0.0979090	0.0489545	+	0.998801i	$0.484411\pi$
$684$	−0.870785	−0.0332953
$685$	−8.81991	−0.336992
$686$	−32.9911	−1.25960
$687$	15.0243	0.573213
$688$	−39.2283	−1.49556
$689$	−4.00813	−0.152698
$690$	10.7058	0.407565
$691$	−9.23132	−0.351176	−0.175588	−	0.984464i	$-0.556183\pi$
$691$	−9.23132	−0.351176	−0.175588	+	0.984464i	$0.556183\pi$
$692$	−0.326178	−0.0123994
$693$	−10.1354	−0.385013
$694$	54.6678	2.07516
$695$	5.95763	0.225986
$696$	4.67455	0.177188
$697$	−19.6554	−0.744502
$698$	−29.7223	−1.12501
$699$	20.9894	0.793892
$700$	−1.43082	−0.0540798
$701$	−13.4419	−0.507692	−0.253846	−	0.967245i	$-0.581696\pi$
$701$	−13.4419	−0.507692	−0.253846	+	0.967245i	$0.581696\pi$
$702$	6.27393	0.236794
$703$	7.72407	0.291319
$704$	17.8177	0.671532
$705$	12.0112	0.452366
$706$	2.49279	0.0938176
$707$	−5.08785	−0.191348
$708$	8.89038	0.334121
$709$	−16.5344	−0.620964	−0.310482	−	0.950579i	$-0.600490\pi$
$709$	−16.5344	−0.620964	−0.310482	+	0.950579i	$0.600490\pi$
$710$	−2.74642	−0.103071
$711$	−6.90323	−0.258891
$712$	−5.02954	−0.188490
$713$	−71.1052	−2.66291
$714$	6.51544	0.243834
$715$	18.8506	0.704973
$716$	−10.2062	−0.381424
$717$	−8.04109	−0.300300
$718$	−24.0452	−0.897360
$719$	−1.27637	−0.0476007	−0.0238004	−	0.999717i	$-0.507577\pi$
$719$	−1.27637	−0.0476007	−0.0238004	+	0.999717i	$0.507577\pi$
$720$	−4.90790	−0.182907
$721$	−36.4887	−1.35891
$722$	28.6334	1.06562
$723$	−14.0300	−0.521782
$724$	−17.2491	−0.641058
$725$	−2.18390	−0.0811079
$726$	21.9107	0.813183
$727$	−2.07880	−0.0770984	−0.0385492	−	0.999257i	$-0.512274\pi$
$727$	−2.07880	−0.0770984	−0.0385492	+	0.999257i	$0.512274\pi$
$728$	−16.7996	−0.622636
$729$	1.00000	0.0370370
$730$	18.3960	0.680866
$731$	−15.4380	−0.570996
$732$	9.43918	0.348882
$733$	9.00137	0.332473	0.166237	−	0.986086i	$-0.446838\pi$
$733$	9.00137	0.332473	0.166237	+	0.986086i	$0.446838\pi$
$734$	−53.8289	−1.98686
$735$	2.78004	0.102543
$736$	24.6334	0.907998
$737$	−6.99961	−0.257834
$738$	−16.7107	−0.615130
$739$	−48.0646	−1.76809	−0.884043	−	0.467405i	$-0.845189\pi$
$739$	−48.0646	−1.76809	−0.884043	+	0.467405i	$0.845189\pi$
$740$	−4.30324	−0.158190
$741$	4.77660	0.175473
$742$	−3.53883	−0.129915
$743$	−17.6880	−0.648911	−0.324455	−	0.945901i	$-0.605181\pi$
$743$	−17.6880	−0.648911	−0.324455	+	0.945901i	$0.605181\pi$
$744$	23.3448	0.855860
$745$	5.82379	0.213367
$746$	−35.6969	−1.30696
$747$	9.69548	0.354739
$748$	−6.63752	−0.242692
$749$	−2.94432	−0.107583
$750$	1.64211	0.0599613
$751$	11.6103	0.423666	0.211833	−	0.977306i	$-0.432057\pi$
$751$	11.6103	0.423666	0.211833	+	0.977306i	$0.432057\pi$
$752$	58.9495	2.14967
$753$	−2.73387	−0.0996277
$754$	13.7016	0.498983
$755$	−19.6395	−0.714753
$756$	1.43082	0.0520384
$757$	−29.6810	−1.07877	−0.539387	−	0.842058i	$-0.681344\pi$
$757$	−29.6810	−1.07877	−0.539387	+	0.842058i	$0.681344\pi$
$758$	−4.11935	−0.149622
$759$	−32.1668	−1.16758
$760$	−2.67602	−0.0970693
$761$	46.5672	1.68806	0.844029	−	0.536298i	$-0.180178\pi$
$761$	46.5672	1.68806	0.844029	+	0.536298i	$0.180178\pi$
$762$	0.582079	0.0210865
$763$	27.0127	0.977926
$764$	−1.60301	−0.0579949
$765$	−1.93147	−0.0698325
$766$	−41.5834	−1.50247
$767$	−48.7672	−1.76088
$768$	−14.9243	−0.538534
$769$	25.8674	0.932802	0.466401	−	0.884573i	$-0.345550\pi$
$769$	25.8674	0.932802	0.466401	+	0.884573i	$0.345550\pi$
$770$	16.6434	0.599788
$771$	6.20040	0.223302
$772$	−6.83531	−0.246008
$773$	−8.36117	−0.300730	−0.150365	−	0.988631i	$-0.548045\pi$
$773$	−8.36117	−0.300730	−0.150365	+	0.988631i	$0.548045\pi$
$774$	−13.1252	−0.471775
$775$	−10.9064	−0.391770
$776$	19.4625	0.698663
$777$	−12.6917	−0.455312
$778$	−2.96014	−0.106126
$779$	−12.7226	−0.455834
$780$	−2.66114	−0.0952842
$781$	8.25189	0.295276
$782$	20.6780	0.739445
$783$	2.18390	0.0780461
$784$	13.6441	0.487290
$785$	13.9723	0.498694
$786$	3.02451	0.107881
$787$	−20.2929	−0.723364	−0.361682	−	0.932302i	$-0.617797\pi$
$787$	−20.2929	−0.723364	−0.361682	+	0.932302i	$0.617797\pi$
$788$	16.3158	0.581227
$789$	6.24615	0.222369
$790$	11.3358	0.403311
$791$	31.4642	1.11874
$792$	10.5608	0.375260
$793$	−51.7776	−1.83868
$794$	−10.7771	−0.382465
$795$	1.04907	0.0372066
$796$	9.68133	0.343146
$797$	−24.6889	−0.874525	−0.437262	−	0.899334i	$-0.644052\pi$
$797$	−24.6889	−0.874525	−0.437262	+	0.899334i	$0.644052\pi$
$798$	4.21732	0.149292
$799$	23.1992	0.820729
$800$	3.77836	0.133585
$801$	−2.34975	−0.0830242
$802$	−1.64211	−0.0579848
$803$	−55.2725	−1.95053
$804$	0.988136	0.0348489
$805$	−13.3929	−0.472037
$806$	68.4260	2.41020
$807$	28.9924	1.02058
$808$	5.30136	0.186501
$809$	15.4916	0.544655	0.272327	−	0.962205i	$-0.412207\pi$
$809$	15.4916	0.544655	0.272327	+	0.962205i	$0.412207\pi$
$810$	−1.64211	−0.0576977
$811$	40.8592	1.43476	0.717381	−	0.696681i	$-0.245341\pi$
$811$	40.8592	1.43476	0.717381	+	0.696681i	$0.245341\pi$
$812$	3.12476	0.109658
$813$	−12.8444	−0.450471
$814$	50.0558	1.75445
$815$	14.4563	0.506381
$816$	−9.47946	−0.331848
$817$	−9.99274	−0.349602
$818$	−11.6974	−0.408990
$819$	−7.84860	−0.274252
$820$	7.08801	0.247524
$821$	−14.4233	−0.503376	−0.251688	−	0.967808i	$-0.580986\pi$
$821$	−14.4233	−0.503376	−0.251688	+	0.967808i	$0.580986\pi$
$822$	−14.4832	−0.505161
$823$	25.9923	0.906034	0.453017	−	0.891502i	$-0.350348\pi$
$823$	25.9923	0.906034	0.453017	+	0.891502i	$0.350348\pi$
$824$	38.0200	1.32449
$825$	−4.93387	−0.171775
$826$	−43.0572	−1.49815
$827$	−25.6297	−0.891230	−0.445615	−	0.895225i	$-0.647015\pi$
$827$	−25.6297	−0.891230	−0.445615	+	0.895225i	$0.647015\pi$
$828$	4.54098	0.157810
$829$	−33.7099	−1.17079	−0.585396	−	0.810748i	$-0.699061\pi$
$829$	−33.7099	−1.17079	−0.585396	+	0.810748i	$0.699061\pi$
$830$	−15.9210	−0.552626
$831$	−14.6199	−0.507159
$832$	13.7976	0.478346
$833$	5.36956	0.186044
$834$	9.78306	0.338760
$835$	−7.04796	−0.243905
$836$	−4.29634	−0.148592
$837$	10.9064	0.376981
$838$	45.6866	1.57822
$839$	−6.70346	−0.231429	−0.115715	−	0.993282i	$-0.536916\pi$
$839$	−6.70346	−0.231429	−0.115715	+	0.993282i	$0.536916\pi$
$840$	4.39706	0.151713
$841$	−24.2306	−0.835538
$842$	56.9514	1.96267
$843$	13.5210	0.465689
$844$	15.7458	0.541992
$845$	1.59742	0.0549530
$846$	19.7236	0.678112
$847$	−27.4100	−0.941820
$848$	5.14872	0.176808
$849$	11.3566	0.389757
$850$	3.17168	0.108788
$851$	−40.2796	−1.38077
$852$	−1.16492	−0.0399095
$853$	−35.0213	−1.19911	−0.599553	−	0.800335i	$-0.704655\pi$
$853$	−35.0213	−1.19911	−0.599553	+	0.800335i	$0.704655\pi$
$854$	−45.7151	−1.56434
$855$	−1.25020	−0.0427561
$856$	3.06788	0.104858
$857$	3.13398	0.107055	0.0535273	−	0.998566i	$-0.482954\pi$
$857$	3.13398	0.107055	0.0535273	+	0.998566i	$0.482954\pi$
$858$	30.9547	1.05678
$859$	−25.4802	−0.869372	−0.434686	−	0.900582i	$-0.643141\pi$
$859$	−25.4802	−0.869372	−0.434686	+	0.900582i	$0.643141\pi$
$860$	5.56716	0.189839
$861$	20.9049	0.712437
$862$	−32.0313	−1.09099
$863$	−4.34873	−0.148033	−0.0740163	−	0.997257i	$-0.523582\pi$
$863$	−4.34873	−0.148033	−0.0740163	+	0.997257i	$0.523582\pi$
$864$	−3.77836	−0.128543
$865$	−0.468300	−0.0159227
$866$	13.5214	0.459475
$867$	13.2694	0.450653
$868$	15.6051	0.529671
$869$	−34.0596	−1.15539
$870$	−3.58619	−0.121583
$871$	−5.42032	−0.183660
$872$	−28.1463	−0.953155
$873$	9.09266	0.307740
$874$	13.3845	0.452737
$875$	−2.05425	−0.0694465
$876$	7.80283	0.263633
$877$	−33.3030	−1.12456	−0.562282	−	0.826946i	$-0.690076\pi$
$877$	−33.3030	−1.12456	−0.562282	+	0.826946i	$0.690076\pi$
$878$	23.7596	0.801849
$879$	4.36317	0.147166
$880$	−24.2149	−0.816285
$881$	−20.4908	−0.690352	−0.345176	−	0.938538i	$-0.612181\pi$
$881$	−20.4908	−0.690352	−0.345176	+	0.938538i	$0.612181\pi$
$882$	4.56512	0.153715
$883$	14.0667	0.473384	0.236692	−	0.971585i	$-0.423937\pi$
$883$	14.0667	0.473384	0.236692	+	0.971585i	$0.423937\pi$
$884$	−5.13992	−0.172874
$885$	12.7641	0.429060
$886$	15.8308	0.531848
$887$	−30.3995	−1.02072	−0.510358	−	0.859962i	$-0.670487\pi$
$887$	−30.3995	−1.02072	−0.510358	+	0.859962i	$0.670487\pi$
$888$	13.2243	0.443779
$889$	−0.728173	−0.0244221
$890$	3.85854	0.129338
$891$	4.93387	0.165291
$892$	8.33817	0.279183
$893$	15.0164	0.502505
$894$	9.56329	0.319844
$895$	−14.6533	−0.489805
$896$	27.7055	0.925576
$897$	−24.9091	−0.831690
$898$	29.5034	0.984542
$899$	23.8185	0.794391
$900$	0.696514	0.0232171
$901$	2.02625	0.0675041
$902$	−82.4485	−2.74524
$903$	16.4194	0.546404
$904$	−32.7846	−1.09040
$905$	−24.7649	−0.823213
$906$	−32.2501	−1.07144
$907$	16.0316	0.532320	0.266160	−	0.963929i	$-0.414245\pi$
$907$	16.0316	0.532320	0.266160	+	0.963929i	$0.414245\pi$
$908$	−8.52313	−0.282850
$909$	2.47674	0.0821482
$910$	12.8882	0.427241
$911$	6.30926	0.209035	0.104517	−	0.994523i	$-0.466670\pi$
$911$	6.30926	0.209035	0.104517	+	0.994523i	$0.466670\pi$
$912$	−6.13587	−0.203179
$913$	47.8362	1.58315
$914$	−32.7397	−1.08293
$915$	13.5520	0.448016
$916$	−10.4646	−0.345762
$917$	−3.78362	−0.124946
$918$	−3.17168	−0.104681
$919$	30.9187	1.01991	0.509957	−	0.860200i	$-0.329661\pi$
$919$	30.9187	1.01991	0.509957	+	0.860200i	$0.329661\pi$
$920$	13.9549	0.460080
$921$	9.14688	0.301400
$922$	−48.5232	−1.59803
$923$	6.39005	0.210331
$924$	7.05947	0.232239
$925$	−6.17825	−0.203139
$926$	41.0902	1.35031
$927$	17.7625	0.583397
$928$	−8.25156	−0.270871
$929$	17.5825	0.576863	0.288431	−	0.957501i	$-0.406866\pi$
$929$	17.5825	0.576863	0.288431	+	0.957501i	$0.406866\pi$
$930$	−17.9095	−0.587275
$931$	3.47561	0.113909
$932$	−14.6194	−0.478875
$933$	−21.0091	−0.687807
$934$	66.1553	2.16467
$935$	−9.52963	−0.311652
$936$	8.17797	0.267305
$937$	3.65562	0.119424	0.0597119	−	0.998216i	$-0.480982\pi$
$937$	3.65562	0.119424	0.0597119	+	0.998216i	$0.480982\pi$
$938$	−4.78566	−0.156257
$939$	16.8512	0.549919
$940$	−8.36595	−0.272867
$941$	−58.6747	−1.91274	−0.956371	−	0.292156i	$-0.905627\pi$
$941$	−58.6747	−1.91274	−0.956371	+	0.292156i	$0.905627\pi$
$942$	22.9441	0.747558
$943$	66.3458	2.16052
$944$	62.6449	2.03892
$945$	2.05425	0.0668249
$946$	−64.7579	−2.10546
$947$	47.4158	1.54081	0.770403	−	0.637558i	$-0.220055\pi$
$947$	47.4158	1.54081	0.770403	+	0.637558i	$0.220055\pi$
$948$	4.80820	0.156163
$949$	−42.8016	−1.38940
$950$	2.05297	0.0666071
$951$	−33.7740	−1.09520
$952$	8.49279	0.275253
$953$	22.1880	0.718740	0.359370	−	0.933195i	$-0.382992\pi$
$953$	22.1880	0.718740	0.359370	+	0.933195i	$0.382992\pi$
$954$	1.72268	0.0557739
$955$	−2.30148	−0.0744740
$956$	5.60074	0.181141
$957$	10.7751	0.348308
$958$	19.2712	0.622624
$959$	18.1183	0.585072
$960$	−3.61131	−0.116555
$961$	87.9498	2.83709
$962$	38.7619	1.24973
$963$	1.43328	0.0461868
$964$	9.77212	0.314739
$965$	−9.81360	−0.315911
$966$	−21.9925	−0.707598
$967$	9.33356	0.300147	0.150073	−	0.988675i	$-0.452049\pi$
$967$	9.33356	0.300147	0.150073	+	0.988675i	$0.452049\pi$
$968$	28.5603	0.917963
$969$	−2.41473	−0.0775724
$970$	−14.9311	−0.479409
$971$	−45.0580	−1.44598	−0.722991	−	0.690858i	$-0.757233\pi$
$971$	−45.0580	−1.44598	−0.722991	+	0.690858i	$0.757233\pi$
$972$	−0.696514	−0.0223407
$973$	−12.2385	−0.392348
$974$	−40.8965	−1.31041
$975$	−3.82066	−0.122359
$976$	66.5119	2.12899
$977$	49.0433	1.56903	0.784516	−	0.620108i	$-0.212911\pi$
$977$	49.0433	1.56903	0.784516	+	0.620108i	$0.212911\pi$
$978$	23.7387	0.759080
$979$	−11.5933	−0.370525
$980$	−1.93634	−0.0618540
$981$	−13.1496	−0.419836
$982$	61.0900	1.94946
$983$	42.9602	1.37022	0.685109	−	0.728441i	$-0.259755\pi$
$983$	42.9602	1.37022	0.685109	+	0.728441i	$0.259755\pi$
$984$	−21.7822	−0.694391
$985$	23.4250	0.746382
$986$	−6.92663	−0.220589
$987$	−24.6740	−0.785382
$988$	−3.32697	−0.105845
$989$	52.1103	1.65701
$990$	−8.10194	−0.257496
$991$	8.00264	0.254212	0.127106	−	0.991889i	$-0.459431\pi$
$991$	8.00264	0.254212	0.127106	+	0.991889i	$0.459431\pi$
$992$	−41.2084	−1.30837
$993$	18.8570	0.598408
$994$	5.64185	0.178949
$995$	13.8997	0.440649
$996$	−6.75304	−0.213978
$997$	−5.07811	−0.160825	−0.0804126	−	0.996762i	$-0.525624\pi$
$997$	−5.07811	−0.160825	−0.0804126	+	0.996762i	$0.525624\pi$
$998$	22.0576	0.698220
$999$	6.17825	0.195471

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.8	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.8	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.64211 q^{2} -1.00000 q^{3} +0.696514 q^{4} +1.00000 q^{5} +1.64211 q^{6} -2.05425 q^{7} +2.14046 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.64211 q^{2} -1.00000 q^{3} +0.696514 q^{4} +1.00000 q^{5} +1.64211 q^{6} -2.05425 q^{7} +2.14046 q^{8} +1.00000 q^{9} -1.64211 q^{10} +4.93387 q^{11} -0.696514 q^{12} +3.82066 q^{13} +3.37331 q^{14} -1.00000 q^{15} -4.90790 q^{16} -1.93147 q^{17} -1.64211 q^{18} -1.25020 q^{19} +0.696514 q^{20} +2.05425 q^{21} -8.10194 q^{22} +6.51958 q^{23} -2.14046 q^{24} +1.00000 q^{25} -6.27393 q^{26} -1.00000 q^{27} -1.43082 q^{28} -2.18390 q^{29} +1.64211 q^{30} -10.9064 q^{31} +3.77836 q^{32} -4.93387 q^{33} +3.17168 q^{34} -2.05425 q^{35} +0.696514 q^{36} -6.17825 q^{37} +2.05297 q^{38} -3.82066 q^{39} +2.14046 q^{40} +10.1764 q^{41} -3.37331 q^{42} +7.99289 q^{43} +3.43651 q^{44} +1.00000 q^{45} -10.7058 q^{46} -12.0112 q^{47} +4.90790 q^{48} -2.78004 q^{49} -1.64211 q^{50} +1.93147 q^{51} +2.66114 q^{52} -1.04907 q^{53} +1.64211 q^{54} +4.93387 q^{55} -4.39706 q^{56} +1.25020 q^{57} +3.58619 q^{58} -12.7641 q^{59} -0.696514 q^{60} -13.5520 q^{61} +17.9095 q^{62} -2.05425 q^{63} +3.61131 q^{64} +3.82066 q^{65} +8.10194 q^{66} -1.41869 q^{67} -1.34530 q^{68} -6.51958 q^{69} +3.37331 q^{70} +1.67250 q^{71} +2.14046 q^{72} -11.2027 q^{73} +10.1453 q^{74} -1.00000 q^{75} -0.870785 q^{76} -10.1354 q^{77} +6.27393 q^{78} -6.90323 q^{79} -4.90790 q^{80} +1.00000 q^{81} -16.7107 q^{82} +9.69548 q^{83} +1.43082 q^{84} -1.93147 q^{85} -13.1252 q^{86} +2.18390 q^{87} +10.5608 q^{88} -2.34975 q^{89} -1.64211 q^{90} -7.84860 q^{91} +4.54098 q^{92} +10.9064 q^{93} +19.7236 q^{94} -1.25020 q^{95} -3.77836 q^{96} +9.09266 q^{97} +4.56512 q^{98} +4.93387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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