LMFDB - Embedded newform 221.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [221,2,Mod(1,221)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(221, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("221.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 221 = 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	221.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:	$1.76469388467$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} -0.381966 q^{3} -1.61803 q^{4} -2.23607 q^{5} -0.236068 q^{6} -1.61803 q^{7} -2.23607 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} -0.381966 q^{3} -1.61803 q^{4} -2.23607 q^{5} -0.236068 q^{6} -1.61803 q^{7} -2.23607 q^{8} -2.85410 q^{9} -1.38197 q^{10} +1.85410 q^{11} +0.618034 q^{12} -1.00000 q^{13} -1.00000 q^{14} +0.854102 q^{15} +1.85410 q^{16} -1.00000 q^{17} -1.76393 q^{18} -0.145898 q^{19} +3.61803 q^{20} +0.618034 q^{21} +1.14590 q^{22} +0.763932 q^{23} +0.854102 q^{24} -0.618034 q^{26} +2.23607 q^{27} +2.61803 q^{28} -1.76393 q^{29} +0.527864 q^{30} -7.00000 q^{31} +5.61803 q^{32} -0.708204 q^{33} -0.618034 q^{34} +3.61803 q^{35} +4.61803 q^{36} +9.47214 q^{37} -0.0901699 q^{38} +0.381966 q^{39} +5.00000 q^{40} -2.47214 q^{41} +0.381966 q^{42} -11.0000 q^{43} -3.00000 q^{44} +6.38197 q^{45} +0.472136 q^{46} +3.23607 q^{47} -0.708204 q^{48} -4.38197 q^{49} +0.381966 q^{51} +1.61803 q^{52} -0.381966 q^{53} +1.38197 q^{54} -4.14590 q^{55} +3.61803 q^{56} +0.0557281 q^{57} -1.09017 q^{58} -6.23607 q^{59} -1.38197 q^{60} +4.85410 q^{61} -4.32624 q^{62} +4.61803 q^{63} -0.236068 q^{64} +2.23607 q^{65} -0.437694 q^{66} -12.1803 q^{67} +1.61803 q^{68} -0.291796 q^{69} +2.23607 q^{70} +12.4721 q^{71} +6.38197 q^{72} +3.94427 q^{73} +5.85410 q^{74} +0.236068 q^{76} -3.00000 q^{77} +0.236068 q^{78} -5.47214 q^{79} -4.14590 q^{80} +7.70820 q^{81} -1.52786 q^{82} -6.23607 q^{83} -1.00000 q^{84} +2.23607 q^{85} -6.79837 q^{86} +0.673762 q^{87} -4.14590 q^{88} +4.14590 q^{89} +3.94427 q^{90} +1.61803 q^{91} -1.23607 q^{92} +2.67376 q^{93} +2.00000 q^{94} +0.326238 q^{95} -2.14590 q^{96} -6.56231 q^{97} -2.70820 q^{98} -5.29180 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} + 4 q^{6} - q^{7} + q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 - q^4 + 4 * q^6 - q^7 + q^9	$ 2 q - q^{2} - 3 q^{3} - q^{4} + 4 q^{6} - q^{7} + q^{9} - 5 q^{10} - 3 q^{11} - q^{12} - 2 q^{13} - 2 q^{14} - 5 q^{15} - 3 q^{16} - 2 q^{17} - 8 q^{18} - 7 q^{19} + 5 q^{20} - q^{21} + 9 q^{22} + 6 q^{23} - 5 q^{24} + q^{26} + 3 q^{28} - 8 q^{29} + 10 q^{30} - 14 q^{31} + 9 q^{32} + 12 q^{33} + q^{34} + 5 q^{35} + 7 q^{36} + 10 q^{37} + 11 q^{38} + 3 q^{39} + 10 q^{40} + 4 q^{41} + 3 q^{42} - 22 q^{43} - 6 q^{44} + 15 q^{45} - 8 q^{46} + 2 q^{47} + 12 q^{48} - 11 q^{49} + 3 q^{51} + q^{52} - 3 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} + 18 q^{57} + 9 q^{58} - 8 q^{59} - 5 q^{60} + 3 q^{61} + 7 q^{62} + 7 q^{63} + 4 q^{64} - 21 q^{66} - 2 q^{67} + q^{68} - 14 q^{69} + 16 q^{71} + 15 q^{72} - 10 q^{73} + 5 q^{74} - 4 q^{76} - 6 q^{77} - 4 q^{78} - 2 q^{79} - 15 q^{80} + 2 q^{81} - 12 q^{82} - 8 q^{83} - 2 q^{84} + 11 q^{86} + 17 q^{87} - 15 q^{88} + 15 q^{89} - 10 q^{90} + q^{91} + 2 q^{92} + 21 q^{93} + 4 q^{94} - 15 q^{95} - 11 q^{96} + 7 q^{97} + 8 q^{98} - 24 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 - q^4 + 4 * q^6 - q^7 + q^9 - 5 * q^10 - 3 * q^11 - q^12 - 2 * q^13 - 2 * q^14 - 5 * q^15 - 3 * q^16 - 2 * q^17 - 8 * q^18 - 7 * q^19 + 5 * q^20 - q^21 + 9 * q^22 + 6 * q^23 - 5 * q^24 + q^26 + 3 * q^28 - 8 * q^29 + 10 * q^30 - 14 * q^31 + 9 * q^32 + 12 * q^33 + q^34 + 5 * q^35 + 7 * q^36 + 10 * q^37 + 11 * q^38 + 3 * q^39 + 10 * q^40 + 4 * q^41 + 3 * q^42 - 22 * q^43 - 6 * q^44 + 15 * q^45 - 8 * q^46 + 2 * q^47 + 12 * q^48 - 11 * q^49 + 3 * q^51 + q^52 - 3 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 + 18 * q^57 + 9 * q^58 - 8 * q^59 - 5 * q^60 + 3 * q^61 + 7 * q^62 + 7 * q^63 + 4 * q^64 - 21 * q^66 - 2 * q^67 + q^68 - 14 * q^69 + 16 * q^71 + 15 * q^72 - 10 * q^73 + 5 * q^74 - 4 * q^76 - 6 * q^77 - 4 * q^78 - 2 * q^79 - 15 * q^80 + 2 * q^81 - 12 * q^82 - 8 * q^83 - 2 * q^84 + 11 * q^86 + 17 * q^87 - 15 * q^88 + 15 * q^89 - 10 * q^90 + q^91 + 2 * q^92 + 21 * q^93 + 4 * q^94 - 15 * q^95 - 11 * q^96 + 7 * q^97 + 8 * q^98 - 24 * 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 $

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	−0.381966	−0.220528	−0.110264	−	0.993902i	$-0.535170\pi$
$3$	−0.381966	−0.220528	−0.110264	+	0.993902i	$0.535170\pi$
$4$	−1.61803	−0.809017
$5$	−2.23607	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$5$	−2.23607	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$6$	−0.236068	−0.0963743
$7$	−1.61803	−0.611559	−0.305780	−	0.952102i	$-0.598917\pi$
$7$	−1.61803	−0.611559	−0.305780	+	0.952102i	$0.598917\pi$
$8$	−2.23607	−0.790569
$9$	−2.85410	−0.951367
$10$	−1.38197	−0.437016
$11$	1.85410	0.559033	0.279516	−	0.960141i	$-0.409826\pi$
$11$	1.85410	0.559033	0.279516	+	0.960141i	$0.409826\pi$
$12$	0.618034	0.178411
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.00000	−0.267261
$15$	0.854102	0.220528
$16$	1.85410	0.463525
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.76393	−0.415763
$19$	−0.145898	−0.0334713	−0.0167357	−	0.999860i	$-0.505327\pi$
$19$	−0.145898	−0.0334713	−0.0167357	+	0.999860i	$0.505327\pi$
$20$	3.61803	0.809017
$21$	0.618034	0.134866
$22$	1.14590	0.244306
$23$	0.763932	0.159291	0.0796454	−	0.996823i	$-0.474621\pi$
$23$	0.763932	0.159291	0.0796454	+	0.996823i	$0.474621\pi$
$24$	0.854102	0.174343
$25$	0	0
$26$	−0.618034	−0.121206
$27$	2.23607	0.430331
$28$	2.61803	0.494762
$29$	−1.76393	−0.327554	−0.163777	−	0.986497i	$-0.552368\pi$
$29$	−1.76393	−0.327554	−0.163777	+	0.986497i	$0.552368\pi$
$30$	0.527864	0.0963743
$31$	−7.00000	−1.25724	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000	−1.25724	−0.628619	+	0.777714i	$0.716379\pi$
$32$	5.61803	0.993137
$33$	−0.708204	−0.123282
$34$	−0.618034	−0.105992
$35$	3.61803	0.611559
$36$	4.61803	0.769672
$37$	9.47214	1.55721	0.778605	−	0.627515i	$-0.215928\pi$
$37$	9.47214	1.55721	0.778605	+	0.627515i	$0.215928\pi$
$38$	−0.0901699	−0.0146275
$39$	0.381966	0.0611635
$40$	5.00000	0.790569
$41$	−2.47214	−0.386083	−0.193041	−	0.981191i	$-0.561835\pi$
$41$	−2.47214	−0.386083	−0.193041	+	0.981191i	$0.561835\pi$
$42$	0.381966	0.0589386
$43$	−11.0000	−1.67748	−0.838742	−	0.544529i	$-0.816708\pi$
$43$	−11.0000	−1.67748	−0.838742	+	0.544529i	$0.816708\pi$
$44$	−3.00000	−0.452267
$45$	6.38197	0.951367
$46$	0.472136	0.0696126
$47$	3.23607	0.472029	0.236015	−	0.971750i	$-0.424159\pi$
$47$	3.23607	0.472029	0.236015	+	0.971750i	$0.424159\pi$
$48$	−0.708204	−0.102220
$49$	−4.38197	−0.625995
$50$	0	0
$51$	0.381966	0.0534859
$52$	1.61803	0.224381
$53$	−0.381966	−0.0524671	−0.0262335	−	0.999656i	$-0.508351\pi$
$53$	−0.381966	−0.0524671	−0.0262335	+	0.999656i	$0.508351\pi$
$54$	1.38197	0.188062
$55$	−4.14590	−0.559033
$56$	3.61803	0.483480
$57$	0.0557281	0.00738137
$58$	−1.09017	−0.143146
$59$	−6.23607	−0.811867	−0.405933	−	0.913903i	$-0.633054\pi$
$59$	−6.23607	−0.811867	−0.405933	+	0.913903i	$0.633054\pi$
$60$	−1.38197	−0.178411
$61$	4.85410	0.621504	0.310752	−	0.950491i	$-0.399419\pi$
$61$	4.85410	0.621504	0.310752	+	0.950491i	$0.399419\pi$
$62$	−4.32624	−0.549433
$63$	4.61803	0.581818
$64$	−0.236068	−0.0295085
$65$	2.23607	0.277350
$66$	−0.437694	−0.0538764
$67$	−12.1803	−1.48807	−0.744033	−	0.668143i	$-0.767089\pi$
$67$	−12.1803	−1.48807	−0.744033	+	0.668143i	$0.767089\pi$
$68$	1.61803	0.196215
$69$	−0.291796	−0.0351281
$70$	2.23607	0.267261
$71$	12.4721	1.48017	0.740085	−	0.672513i	$-0.234785\pi$
$71$	12.4721	1.48017	0.740085	+	0.672513i	$0.234785\pi$
$72$	6.38197	0.752122
$73$	3.94427	0.461642	0.230821	−	0.972996i	$-0.425859\pi$
$73$	3.94427	0.461642	0.230821	+	0.972996i	$0.425859\pi$
$74$	5.85410	0.680526
$75$	0	0
$76$	0.236068	0.0270789
$77$	−3.00000	−0.341882
$78$	0.236068	0.0267294
$79$	−5.47214	−0.615663	−0.307832	−	0.951441i	$-0.599603\pi$
$79$	−5.47214	−0.615663	−0.307832	+	0.951441i	$0.599603\pi$
$80$	−4.14590	−0.463525
$81$	7.70820	0.856467
$82$	−1.52786	−0.168724
$83$	−6.23607	−0.684497	−0.342249	−	0.939609i	$-0.611189\pi$
$83$	−6.23607	−0.684497	−0.342249	+	0.939609i	$0.611189\pi$
$84$	−1.00000	−0.109109
$85$	2.23607	0.242536
$86$	−6.79837	−0.733088
$87$	0.673762	0.0722349
$88$	−4.14590	−0.441954
$89$	4.14590	0.439464	0.219732	−	0.975560i	$-0.429482\pi$
$89$	4.14590	0.439464	0.219732	+	0.975560i	$0.429482\pi$
$90$	3.94427	0.415763
$91$	1.61803	0.169616
$92$	−1.23607	−0.128869
$93$	2.67376	0.277256
$94$	2.00000	0.206284
$95$	0.326238	0.0334713
$96$	−2.14590	−0.219015
$97$	−6.56231	−0.666301	−0.333151	−	0.942874i	$-0.608112\pi$
$97$	−6.56231	−0.666301	−0.333151	+	0.942874i	$0.608112\pi$
$98$	−2.70820	−0.273570
$99$	−5.29180	−0.531846
$100$	0	0
$101$	−7.47214	−0.743505	−0.371753	−	0.928332i	$-0.621243\pi$
$101$	−7.47214	−0.743505	−0.371753	+	0.928332i	$0.621243\pi$
$102$	0.236068	0.0233742
$103$	−6.52786	−0.643210	−0.321605	−	0.946874i	$-0.604222\pi$
$103$	−6.52786	−0.643210	−0.321605	+	0.946874i	$0.604222\pi$
$104$	2.23607	0.219265
$105$	−1.38197	−0.134866
$106$	−0.236068	−0.0229289
$107$	−5.56231	−0.537728	−0.268864	−	0.963178i	$-0.586648\pi$
$107$	−5.56231	−0.537728	−0.268864	+	0.963178i	$0.586648\pi$
$108$	−3.61803	−0.348145
$109$	−10.8541	−1.03963	−0.519817	−	0.854278i	$-0.674000\pi$
$109$	−10.8541	−1.03963	−0.519817	+	0.854278i	$0.674000\pi$
$110$	−2.56231	−0.244306
$111$	−3.61803	−0.343409
$112$	−3.00000	−0.283473
$113$	12.0902	1.13735	0.568674	−	0.822563i	$-0.307457\pi$
$113$	12.0902	1.13735	0.568674	+	0.822563i	$0.307457\pi$
$114$	0.0344419	0.00322578
$115$	−1.70820	−0.159291
$116$	2.85410	0.264997
$117$	2.85410	0.263862
$118$	−3.85410	−0.354799
$119$	1.61803	0.148325
$120$	−1.90983	−0.174343
$121$	−7.56231	−0.687482
$122$	3.00000	0.271607
$123$	0.944272	0.0851421
$124$	11.3262	1.01713
$125$	11.1803	1.00000
$126$	2.85410	0.254264
$127$	5.56231	0.493575	0.246787	−	0.969070i	$-0.420625\pi$
$127$	5.56231	0.493575	0.246787	+	0.969070i	$0.420625\pi$
$128$	−11.3820	−1.00603
$129$	4.20163	0.369933
$130$	1.38197	0.121206
$131$	−9.47214	−0.827584	−0.413792	−	0.910371i	$-0.635796\pi$
$131$	−9.47214	−0.827584	−0.413792	+	0.910371i	$0.635796\pi$
$132$	1.14590	0.0997376
$133$	0.236068	0.0204697
$134$	−7.52786	−0.650308
$135$	−5.00000	−0.430331
$136$	2.23607	0.191741
$137$	11.5623	0.987834	0.493917	−	0.869509i	$-0.335565\pi$
$137$	11.5623	0.987834	0.493917	+	0.869509i	$0.335565\pi$
$138$	−0.180340	−0.0153516
$139$	−16.1803	−1.37240	−0.686199	−	0.727414i	$-0.740722\pi$
$139$	−16.1803	−1.37240	−0.686199	+	0.727414i	$0.740722\pi$
$140$	−5.85410	−0.494762
$141$	−1.23607	−0.104096
$142$	7.70820	0.646858
$143$	−1.85410	−0.155048
$144$	−5.29180	−0.440983
$145$	3.94427	0.327554
$146$	2.43769	0.201745
$147$	1.67376	0.138050
$148$	−15.3262	−1.25981
$149$	7.85410	0.643433	0.321717	−	0.946836i	$-0.395740\pi$
$149$	7.85410	0.643433	0.321717	+	0.946836i	$0.395740\pi$
$150$	0	0
$151$	−4.18034	−0.340191	−0.170096	−	0.985428i	$-0.554408\pi$
$151$	−4.18034	−0.340191	−0.170096	+	0.985428i	$0.554408\pi$
$152$	0.326238	0.0264614
$153$	2.85410	0.230740
$154$	−1.85410	−0.149408
$155$	15.6525	1.25724
$156$	−0.618034	−0.0494823
$157$	−22.1246	−1.76574	−0.882868	−	0.469621i	$-0.844391\pi$
$157$	−22.1246	−1.76574	−0.882868	+	0.469621i	$0.844391\pi$
$158$	−3.38197	−0.269055
$159$	0.145898	0.0115705
$160$	−12.5623	−0.993137
$161$	−1.23607	−0.0974158
$162$	4.76393	0.374290
$163$	10.3820	0.813178	0.406589	−	0.913611i	$-0.366718\pi$
$163$	10.3820	0.813178	0.406589	+	0.913611i	$0.366718\pi$
$164$	4.00000	0.312348
$165$	1.58359	0.123282
$166$	−3.85410	−0.299136
$167$	8.23607	0.637326	0.318663	−	0.947868i	$-0.396766\pi$
$167$	8.23607	0.637326	0.318663	+	0.947868i	$0.396766\pi$
$168$	−1.38197	−0.106621
$169$	1.00000	0.0769231
$170$	1.38197	0.105992
$171$	0.416408	0.0318435
$172$	17.7984	1.35711
$173$	21.6525	1.64621	0.823104	−	0.567891i	$-0.192241\pi$
$173$	21.6525	1.64621	0.823104	+	0.567891i	$0.192241\pi$
$174$	0.416408	0.0315678
$175$	0	0
$176$	3.43769	0.259126
$177$	2.38197	0.179040
$178$	2.56231	0.192053
$179$	−15.0000	−1.12115	−0.560576	−	0.828103i	$-0.689420\pi$
$179$	−15.0000	−1.12115	−0.560576	+	0.828103i	$0.689420\pi$
$180$	−10.3262	−0.769672
$181$	2.56231	0.190455	0.0952273	−	0.995456i	$-0.469642\pi$
$181$	2.56231	0.190455	0.0952273	+	0.995456i	$0.469642\pi$
$182$	1.00000	0.0741249
$183$	−1.85410	−0.137059
$184$	−1.70820	−0.125930
$185$	−21.1803	−1.55721
$186$	1.65248	0.121165
$187$	−1.85410	−0.135585
$188$	−5.23607	−0.381880
$189$	−3.61803	−0.263173
$190$	0.201626	0.0146275
$191$	21.6525	1.56672	0.783359	−	0.621569i	$-0.213505\pi$
$191$	21.6525	1.56672	0.783359	+	0.621569i	$0.213505\pi$
$192$	0.0901699	0.00650746
$193$	20.7639	1.49462	0.747310	−	0.664475i	$-0.231345\pi$
$193$	20.7639	1.49462	0.747310	+	0.664475i	$0.231345\pi$
$194$	−4.05573	−0.291184
$195$	−0.854102	−0.0611635
$196$	7.09017	0.506441
$197$	19.2361	1.37051	0.685257	−	0.728302i	$-0.259690\pi$
$197$	19.2361	1.37051	0.685257	+	0.728302i	$0.259690\pi$
$198$	−3.27051	−0.232425
$199$	−22.5967	−1.60184	−0.800920	−	0.598771i	$-0.795656\pi$
$199$	−22.5967	−1.60184	−0.800920	+	0.598771i	$0.795656\pi$
$200$	0	0
$201$	4.65248	0.328160
$202$	−4.61803	−0.324924
$203$	2.85410	0.200319
$204$	−0.618034	−0.0432710
$205$	5.52786	0.386083
$206$	−4.03444	−0.281093
$207$	−2.18034	−0.151544
$208$	−1.85410	−0.128559
$209$	−0.270510	−0.0187116
$210$	−0.854102	−0.0589386
$211$	13.9443	0.959963	0.479982	−	0.877279i	$-0.340643\pi$
$211$	13.9443	0.959963	0.479982	+	0.877279i	$0.340643\pi$
$212$	0.618034	0.0424467
$213$	−4.76393	−0.326419
$214$	−3.43769	−0.234996
$215$	24.5967	1.67748
$216$	−5.00000	−0.340207
$217$	11.3262	0.768875
$218$	−6.70820	−0.454337
$219$	−1.50658	−0.101805
$220$	6.70820	0.452267
$221$	1.00000	0.0672673
$222$	−2.23607	−0.150075
$223$	9.14590	0.612455	0.306227	−	0.951958i	$-0.400933\pi$
$223$	9.14590	0.612455	0.306227	+	0.951958i	$0.400933\pi$
$224$	−9.09017	−0.607363
$225$	0	0
$226$	7.47214	0.497039
$227$	12.7639	0.847172	0.423586	−	0.905856i	$-0.360771\pi$
$227$	12.7639	0.847172	0.423586	+	0.905856i	$0.360771\pi$
$228$	−0.0901699	−0.00597165
$229$	20.1246	1.32987	0.664936	−	0.746900i	$-0.268459\pi$
$229$	20.1246	1.32987	0.664936	+	0.746900i	$0.268459\pi$
$230$	−1.05573	−0.0696126
$231$	1.14590	0.0753946
$232$	3.94427	0.258954
$233$	−7.47214	−0.489516	−0.244758	−	0.969584i	$-0.578708\pi$
$233$	−7.47214	−0.489516	−0.244758	+	0.969584i	$0.578708\pi$
$234$	1.76393	0.115312
$235$	−7.23607	−0.472029
$236$	10.0902	0.656814
$237$	2.09017	0.135771
$238$	1.00000	0.0648204
$239$	23.6525	1.52995	0.764976	−	0.644059i	$-0.222751\pi$
$239$	23.6525	1.52995	0.764976	+	0.644059i	$0.222751\pi$
$240$	1.58359	0.102220
$241$	−15.0000	−0.966235	−0.483117	−	0.875556i	$-0.660496\pi$
$241$	−15.0000	−0.966235	−0.483117	+	0.875556i	$0.660496\pi$
$242$	−4.67376	−0.300441
$243$	−9.65248	−0.619207
$244$	−7.85410	−0.502807
$245$	9.79837	0.625995
$246$	0.583592	0.0372085
$247$	0.145898	0.00928327
$248$	15.6525	0.993933
$249$	2.38197	0.150951
$250$	6.90983	0.437016
$251$	−24.3820	−1.53898	−0.769488	−	0.638661i	$-0.779489\pi$
$251$	−24.3820	−1.53898	−0.769488	+	0.638661i	$0.779489\pi$
$252$	−7.47214	−0.470700
$253$	1.41641	0.0890488
$254$	3.43769	0.215700
$255$	−0.854102	−0.0534859
$256$	−6.56231	−0.410144
$257$	16.4164	1.02403	0.512014	−	0.858977i	$-0.328900\pi$
$257$	16.4164	1.02403	0.512014	+	0.858977i	$0.328900\pi$
$258$	2.59675	0.161666
$259$	−15.3262	−0.952326
$260$	−3.61803	−0.224381
$261$	5.03444	0.311624
$262$	−5.85410	−0.361668
$263$	−20.4721	−1.26237	−0.631183	−	0.775634i	$-0.717430\pi$
$263$	−20.4721	−1.26237	−0.631183	+	0.775634i	$0.717430\pi$
$264$	1.58359	0.0974634
$265$	0.854102	0.0524671
$266$	0.145898	0.00894558
$267$	−1.58359	−0.0969143
$268$	19.7082	1.20387
$269$	−22.3262	−1.36125	−0.680627	−	0.732630i	$-0.738293\pi$
$269$	−22.3262	−1.36125	−0.680627	+	0.732630i	$0.738293\pi$
$270$	−3.09017	−0.188062
$271$	3.79837	0.230735	0.115367	−	0.993323i	$-0.463195\pi$
$271$	3.79837	0.230735	0.115367	+	0.993323i	$0.463195\pi$
$272$	−1.85410	−0.112421
$273$	−0.618034	−0.0374051
$274$	7.14590	0.431699
$275$	0	0
$276$	0.472136	0.0284192
$277$	15.8885	0.954650	0.477325	−	0.878727i	$-0.341606\pi$
$277$	15.8885	0.954650	0.477325	+	0.878727i	$0.341606\pi$
$278$	−10.0000	−0.599760
$279$	19.9787	1.19609
$280$	−8.09017	−0.483480
$281$	7.90983	0.471861	0.235930	−	0.971770i	$-0.424186\pi$
$281$	7.90983	0.471861	0.235930	+	0.971770i	$0.424186\pi$
$282$	−0.763932	−0.0454915
$283$	−13.1459	−0.781443	−0.390721	−	0.920509i	$-0.627774\pi$
$283$	−13.1459	−0.781443	−0.390721	+	0.920509i	$0.627774\pi$
$284$	−20.1803	−1.19748
$285$	−0.124612	−0.00738137
$286$	−1.14590	−0.0677584
$287$	4.00000	0.236113
$288$	−16.0344	−0.944839
$289$	1.00000	0.0588235
$290$	2.43769	0.143146
$291$	2.50658	0.146938
$292$	−6.38197	−0.373476
$293$	−24.3820	−1.42441	−0.712205	−	0.701972i	$-0.752303\pi$
$293$	−24.3820	−1.42441	−0.712205	+	0.701972i	$0.752303\pi$
$294$	1.03444	0.0603299
$295$	13.9443	0.811867
$296$	−21.1803	−1.23108
$297$	4.14590	0.240569
$298$	4.85410	0.281191
$299$	−0.763932	−0.0441793
$300$	0	0
$301$	17.7984	1.02588
$302$	−2.58359	−0.148669
$303$	2.85410	0.163964
$304$	−0.270510	−0.0155148
$305$	−10.8541	−0.621504
$306$	1.76393	0.100837
$307$	−15.2705	−0.871534	−0.435767	−	0.900060i	$-0.643523\pi$
$307$	−15.2705	−0.871534	−0.435767	+	0.900060i	$0.643523\pi$
$308$	4.85410	0.276588
$309$	2.49342	0.141846
$310$	9.67376	0.549433
$311$	−30.8885	−1.75153	−0.875764	−	0.482739i	$-0.839642\pi$
$311$	−30.8885	−1.75153	−0.875764	+	0.482739i	$0.839642\pi$
$312$	−0.854102	−0.0483540
$313$	14.7082	0.831357	0.415678	−	0.909512i	$-0.363544\pi$
$313$	14.7082	0.831357	0.415678	+	0.909512i	$0.363544\pi$
$314$	−13.6738	−0.771655
$315$	−10.3262	−0.581818
$316$	8.85410	0.498082
$317$	−17.1803	−0.964944	−0.482472	−	0.875911i	$-0.660261\pi$
$317$	−17.1803	−0.964944	−0.482472	+	0.875911i	$0.660261\pi$
$318$	0.0901699	0.00505648
$319$	−3.27051	−0.183113
$320$	0.527864	0.0295085
$321$	2.12461	0.118584
$322$	−0.763932	−0.0425723
$323$	0.145898	0.00811798
$324$	−12.4721	−0.692896
$325$	0	0
$326$	6.41641	0.355372
$327$	4.14590	0.229269
$328$	5.52786	0.305225
$329$	−5.23607	−0.288674
$330$	0.978714	0.0538764
$331$	−19.9443	−1.09624	−0.548118	−	0.836401i	$-0.684656\pi$
$331$	−19.9443	−1.09624	−0.548118	+	0.836401i	$0.684656\pi$
$332$	10.0902	0.553770
$333$	−27.0344	−1.48148
$334$	5.09017	0.278522
$335$	27.2361	1.48807
$336$	1.14590	0.0625139
$337$	−11.5623	−0.629839	−0.314919	−	0.949118i	$-0.601978\pi$
$337$	−11.5623	−0.629839	−0.314919	+	0.949118i	$0.601978\pi$
$338$	0.618034	0.0336166
$339$	−4.61803	−0.250817
$340$	−3.61803	−0.196215
$341$	−12.9787	−0.702837
$342$	0.257354	0.0139161
$343$	18.4164	0.994393
$344$	24.5967	1.32617
$345$	0.652476	0.0351281
$346$	13.3820	0.719419
$347$	1.58359	0.0850117	0.0425058	−	0.999096i	$-0.486466\pi$
$347$	1.58359	0.0850117	0.0425058	+	0.999096i	$0.486466\pi$
$348$	−1.09017	−0.0584392
$349$	−20.9098	−1.11928	−0.559639	−	0.828737i	$-0.689060\pi$
$349$	−20.9098	−1.11928	−0.559639	+	0.828737i	$0.689060\pi$
$350$	0	0
$351$	−2.23607	−0.119352
$352$	10.4164	0.555196
$353$	7.41641	0.394736	0.197368	−	0.980330i	$-0.436761\pi$
$353$	7.41641	0.394736	0.197368	+	0.980330i	$0.436761\pi$
$354$	1.47214	0.0782431
$355$	−27.8885	−1.48017
$356$	−6.70820	−0.355534
$357$	−0.618034	−0.0327098
$358$	−9.27051	−0.489962
$359$	−26.0902	−1.37699	−0.688493	−	0.725243i	$-0.741728\pi$
$359$	−26.0902	−1.37699	−0.688493	+	0.725243i	$0.741728\pi$
$360$	−14.2705	−0.752122
$361$	−18.9787	−0.998880
$362$	1.58359	0.0832318
$363$	2.88854	0.151609
$364$	−2.61803	−0.137222
$365$	−8.81966	−0.461642
$366$	−1.14590	−0.0598970
$367$	15.0344	0.784791	0.392396	−	0.919796i	$-0.371646\pi$
$367$	15.0344	0.784791	0.392396	+	0.919796i	$0.371646\pi$
$368$	1.41641	0.0738354
$369$	7.05573	0.367307
$370$	−13.0902	−0.680526
$371$	0.618034	0.0320867
$372$	−4.32624	−0.224305
$373$	8.56231	0.443339	0.221670	−	0.975122i	$-0.428849\pi$
$373$	8.56231	0.443339	0.221670	+	0.975122i	$0.428849\pi$
$374$	−1.14590	−0.0592530
$375$	−4.27051	−0.220528
$376$	−7.23607	−0.373172
$377$	1.76393	0.0908471
$378$	−2.23607	−0.115011
$379$	−4.29180	−0.220455	−0.110227	−	0.993906i	$-0.535158\pi$
$379$	−4.29180	−0.220455	−0.110227	+	0.993906i	$0.535158\pi$
$380$	−0.527864	−0.0270789
$381$	−2.12461	−0.108847
$382$	13.3820	0.684681
$383$	−14.5967	−0.745859	−0.372929	−	0.927860i	$-0.621647\pi$
$383$	−14.5967	−0.745859	−0.372929	+	0.927860i	$0.621647\pi$
$384$	4.34752	0.221859
$385$	6.70820	0.341882
$386$	12.8328	0.653173
$387$	31.3951	1.59590
$388$	10.6180	0.539049
$389$	4.14590	0.210205	0.105103	−	0.994461i	$-0.466483\pi$
$389$	4.14590	0.210205	0.105103	+	0.994461i	$0.466483\pi$
$390$	−0.527864	−0.0267294
$391$	−0.763932	−0.0386337
$392$	9.79837	0.494893
$393$	3.61803	0.182506
$394$	11.8885	0.598936
$395$	12.2361	0.615663
$396$	8.56231	0.430272
$397$	−25.4164	−1.27561	−0.637806	−	0.770197i	$-0.720158\pi$
$397$	−25.4164	−1.27561	−0.637806	+	0.770197i	$0.720158\pi$
$398$	−13.9656	−0.700030
$399$	−0.0901699	−0.00451414
$400$	0	0
$401$	−31.1591	−1.55601	−0.778004	−	0.628259i	$-0.783768\pi$
$401$	−31.1591	−1.55601	−0.778004	+	0.628259i	$0.783768\pi$
$402$	2.87539	0.143411
$403$	7.00000	0.348695
$404$	12.0902	0.601508
$405$	−17.2361	−0.856467
$406$	1.76393	0.0875425
$407$	17.5623	0.870531
$408$	−0.854102	−0.0422843
$409$	−10.9443	−0.541159	−0.270580	−	0.962698i	$-0.587215\pi$
$409$	−10.9443	−0.541159	−0.270580	+	0.962698i	$0.587215\pi$
$410$	3.41641	0.168724
$411$	−4.41641	−0.217845
$412$	10.5623	0.520367
$413$	10.0902	0.496505
$414$	−1.34752	−0.0662272
$415$	13.9443	0.684497
$416$	−5.61803	−0.275447
$417$	6.18034	0.302653
$418$	−0.167184	−0.00817725
$419$	−16.2148	−0.792144	−0.396072	−	0.918219i	$-0.629627\pi$
$419$	−16.2148	−0.792144	−0.396072	+	0.918219i	$0.629627\pi$
$420$	2.23607	0.109109
$421$	15.6738	0.763892	0.381946	−	0.924185i	$-0.375254\pi$
$421$	15.6738	0.763892	0.381946	+	0.924185i	$0.375254\pi$
$422$	8.61803	0.419519
$423$	−9.23607	−0.449073
$424$	0.854102	0.0414789
$425$	0	0
$426$	−2.94427	−0.142650
$427$	−7.85410	−0.380087
$428$	9.00000	0.435031
$429$	0.708204	0.0341924
$430$	15.2016	0.733088
$431$	2.47214	0.119079	0.0595393	−	0.998226i	$-0.481037\pi$
$431$	2.47214	0.119079	0.0595393	+	0.998226i	$0.481037\pi$
$432$	4.14590	0.199470
$433$	32.8328	1.57784	0.788922	−	0.614493i	$-0.210639\pi$
$433$	32.8328	1.57784	0.788922	+	0.614493i	$0.210639\pi$
$434$	7.00000	0.336011
$435$	−1.50658	−0.0722349
$436$	17.5623	0.841082
$437$	−0.111456	−0.00533167
$438$	−0.931116	−0.0444905
$439$	−2.96556	−0.141538	−0.0707692	−	0.997493i	$-0.522545\pi$
$439$	−2.96556	−0.141538	−0.0707692	+	0.997493i	$0.522545\pi$
$440$	9.27051	0.441954
$441$	12.5066	0.595551
$442$	0.618034	0.0293969
$443$	6.81966	0.324012	0.162006	−	0.986790i	$-0.448204\pi$
$443$	6.81966	0.324012	0.162006	+	0.986790i	$0.448204\pi$
$444$	5.85410	0.277823
$445$	−9.27051	−0.439464
$446$	5.65248	0.267652
$447$	−3.00000	−0.141895
$448$	0.381966	0.0180462
$449$	−0.673762	−0.0317968	−0.0158984	−	0.999874i	$-0.505061\pi$
$449$	−0.673762	−0.0317968	−0.0158984	+	0.999874i	$0.505061\pi$
$450$	0	0
$451$	−4.58359	−0.215833
$452$	−19.5623	−0.920133
$453$	1.59675	0.0750218
$454$	7.88854	0.370228
$455$	−3.61803	−0.169616
$456$	−0.124612	−0.00583548
$457$	27.7984	1.30035	0.650177	−	0.759783i	$-0.274695\pi$
$457$	27.7984	1.30035	0.650177	+	0.759783i	$0.274695\pi$
$458$	12.4377	0.581175
$459$	−2.23607	−0.104371
$460$	2.76393	0.128869
$461$	−33.5410	−1.56216	−0.781081	−	0.624430i	$-0.785331\pi$
$461$	−33.5410	−1.56216	−0.781081	+	0.624430i	$0.785331\pi$
$462$	0.708204	0.0329486
$463$	10.8197	0.502832	0.251416	−	0.967879i	$-0.419104\pi$
$463$	10.8197	0.502832	0.251416	+	0.967879i	$0.419104\pi$
$464$	−3.27051	−0.151830
$465$	−5.97871	−0.277256
$466$	−4.61803	−0.213926
$467$	−0.381966	−0.0176753	−0.00883764	−	0.999961i	$-0.502813\pi$
$467$	−0.381966	−0.0176753	−0.00883764	+	0.999961i	$0.502813\pi$
$468$	−4.61803	−0.213469
$469$	19.7082	0.910040
$470$	−4.47214	−0.206284
$471$	8.45085	0.389395
$472$	13.9443	0.641837
$473$	−20.3951	−0.937769
$474$	1.29180	0.0593342
$475$	0	0
$476$	−2.61803	−0.119997
$477$	1.09017	0.0499155
$478$	14.6180	0.668613
$479$	14.5623	0.665369	0.332684	−	0.943038i	$-0.392046\pi$
$479$	14.5623	0.665369	0.332684	+	0.943038i	$0.392046\pi$
$480$	4.79837	0.219015
$481$	−9.47214	−0.431892
$482$	−9.27051	−0.422260
$483$	0.472136	0.0214829
$484$	12.2361	0.556185
$485$	14.6738	0.666301
$486$	−5.96556	−0.270603
$487$	9.29180	0.421051	0.210526	−	0.977588i	$-0.432482\pi$
$487$	9.29180	0.421051	0.210526	+	0.977588i	$0.432482\pi$
$488$	−10.8541	−0.491342
$489$	−3.96556	−0.179329
$490$	6.05573	0.273570
$491$	36.3262	1.63938	0.819690	−	0.572807i	$-0.194146\pi$
$491$	36.3262	1.63938	0.819690	+	0.572807i	$0.194146\pi$
$492$	−1.52786	−0.0688814
$493$	1.76393	0.0794435
$494$	0.0901699	0.00405694
$495$	11.8328	0.531846
$496$	−12.9787	−0.582761
$497$	−20.1803	−0.905212
$498$	1.47214	0.0659680
$499$	13.4164	0.600601	0.300300	−	0.953845i	$-0.402913\pi$
$499$	13.4164	0.600601	0.300300	+	0.953845i	$0.402913\pi$
$500$	−18.0902	−0.809017
$501$	−3.14590	−0.140548
$502$	−15.0689	−0.672557
$503$	−8.90983	−0.397270	−0.198635	−	0.980074i	$-0.563651\pi$
$503$	−8.90983	−0.397270	−0.198635	+	0.980074i	$0.563651\pi$
$504$	−10.3262	−0.459967
$505$	16.7082	0.743505
$506$	0.875388	0.0389158
$507$	−0.381966	−0.0169637
$508$	−9.00000	−0.399310
$509$	−23.7639	−1.05332	−0.526659	−	0.850077i	$-0.676555\pi$
$509$	−23.7639	−1.05332	−0.526659	+	0.850077i	$0.676555\pi$
$510$	−0.527864	−0.0233742
$511$	−6.38197	−0.282322
$512$	18.7082	0.826794
$513$	−0.326238	−0.0144038
$514$	10.1459	0.447516
$515$	14.5967	0.643210
$516$	−6.79837	−0.299282
$517$	6.00000	0.263880
$518$	−9.47214	−0.416182
$519$	−8.27051	−0.363035
$520$	−5.00000	−0.219265
$521$	−39.9443	−1.74999	−0.874995	−	0.484132i	$-0.839136\pi$
$521$	−39.9443	−1.74999	−0.874995	+	0.484132i	$0.839136\pi$
$522$	3.11146	0.136185
$523$	6.97871	0.305158	0.152579	−	0.988291i	$-0.451242\pi$
$523$	6.97871	0.305158	0.152579	+	0.988291i	$0.451242\pi$
$524$	15.3262	0.669530
$525$	0	0
$526$	−12.6525	−0.551674
$527$	7.00000	0.304925
$528$	−1.31308	−0.0571446
$529$	−22.4164	−0.974626
$530$	0.527864	0.0229289
$531$	17.7984	0.772384
$532$	−0.381966	−0.0165603
$533$	2.47214	0.107080
$534$	−0.978714	−0.0423531
$535$	12.4377	0.537728
$536$	27.2361	1.17642
$537$	5.72949	0.247246
$538$	−13.7984	−0.594890
$539$	−8.12461	−0.349952
$540$	8.09017	0.348145
$541$	5.38197	0.231389	0.115694	−	0.993285i	$-0.463091\pi$
$541$	5.38197	0.231389	0.115694	+	0.993285i	$0.463091\pi$
$542$	2.34752	0.100835
$543$	−0.978714	−0.0420006
$544$	−5.61803	−0.240871
$545$	24.2705	1.03963
$546$	−0.381966	−0.0163466
$547$	−42.7426	−1.82754	−0.913772	−	0.406228i	$-0.866844\pi$
$547$	−42.7426	−1.82754	−0.913772	+	0.406228i	$0.866844\pi$
$548$	−18.7082	−0.799175
$549$	−13.8541	−0.591279
$550$	0	0
$551$	0.257354	0.0109637
$552$	0.652476	0.0277712
$553$	8.85410	0.376515
$554$	9.81966	0.417197
$555$	8.09017	0.343409
$556$	26.1803	1.11029
$557$	−24.1803	−1.02455	−0.512277	−	0.858820i	$-0.671198\pi$
$557$	−24.1803	−1.02455	−0.512277	+	0.858820i	$0.671198\pi$
$558$	12.3475	0.522712
$559$	11.0000	0.465250
$560$	6.70820	0.283473
$561$	0.708204	0.0299004
$562$	4.88854	0.206211
$563$	−8.38197	−0.353258	−0.176629	−	0.984278i	$-0.556519\pi$
$563$	−8.38197	−0.353258	−0.176629	+	0.984278i	$0.556519\pi$
$564$	2.00000	0.0842152
$565$	−27.0344	−1.13735
$566$	−8.12461	−0.341503
$567$	−12.4721	−0.523780
$568$	−27.8885	−1.17018
$569$	47.4508	1.98924	0.994622	−	0.103576i	$-0.0330285\pi$
$569$	47.4508	1.98924	0.994622	+	0.103576i	$0.0330285\pi$
$570$	−0.0770143	−0.00322578
$571$	−8.58359	−0.359212	−0.179606	−	0.983739i	$-0.557482\pi$
$571$	−8.58359	−0.359212	−0.179606	+	0.983739i	$0.557482\pi$
$572$	3.00000	0.125436
$573$	−8.27051	−0.345506
$574$	2.47214	0.103185
$575$	0	0
$576$	0.673762	0.0280734
$577$	35.9787	1.49781	0.748907	−	0.662675i	$-0.230579\pi$
$577$	35.9787	1.49781	0.748907	+	0.662675i	$0.230579\pi$
$578$	0.618034	0.0257068
$579$	−7.93112	−0.329606
$580$	−6.38197	−0.264997
$581$	10.0902	0.418611
$582$	1.54915	0.0642143
$583$	−0.708204	−0.0293308
$584$	−8.81966	−0.364960
$585$	−6.38197	−0.263862
$586$	−15.0689	−0.622490
$587$	−20.0902	−0.829210	−0.414605	−	0.910001i	$-0.636080\pi$
$587$	−20.0902	−0.829210	−0.414605	+	0.910001i	$0.636080\pi$
$588$	−2.70820	−0.111684
$589$	1.02129	0.0420814
$590$	8.61803	0.354799
$591$	−7.34752	−0.302237
$592$	17.5623	0.721806
$593$	−7.14590	−0.293447	−0.146723	−	0.989178i	$-0.546873\pi$
$593$	−7.14590	−0.293447	−0.146723	+	0.989178i	$0.546873\pi$
$594$	2.56231	0.105133
$595$	−3.61803	−0.148325
$596$	−12.7082	−0.520548
$597$	8.63119	0.353251
$598$	−0.472136	−0.0193071
$599$	25.9443	1.06005	0.530027	−	0.847981i	$-0.322182\pi$
$599$	25.9443	1.06005	0.530027	+	0.847981i	$0.322182\pi$
$600$	0	0
$601$	−12.5623	−0.512427	−0.256214	−	0.966620i	$-0.582475\pi$
$601$	−12.5623	−0.512427	−0.256214	+	0.966620i	$0.582475\pi$
$602$	11.0000	0.448327
$603$	34.7639	1.41570
$604$	6.76393	0.275220
$605$	16.9098	0.687482
$606$	1.76393	0.0716548
$607$	−25.8328	−1.04852	−0.524261	−	0.851558i	$-0.675658\pi$
$607$	−25.8328	−1.04852	−0.524261	+	0.851558i	$0.675658\pi$
$608$	−0.819660	−0.0332416
$609$	−1.09017	−0.0441759
$610$	−6.70820	−0.271607
$611$	−3.23607	−0.130917
$612$	−4.61803	−0.186673
$613$	10.3475	0.417933	0.208966	−	0.977923i	$-0.432990\pi$
$613$	10.3475	0.417933	0.208966	+	0.977923i	$0.432990\pi$
$614$	−9.43769	−0.380874
$615$	−2.11146	−0.0851421
$616$	6.70820	0.270281
$617$	−27.0000	−1.08698	−0.543490	−	0.839416i	$-0.682897\pi$
$617$	−27.0000	−1.08698	−0.543490	+	0.839416i	$0.682897\pi$
$618$	1.54102	0.0619889
$619$	47.5410	1.91083	0.955417	−	0.295258i	$-0.0954057\pi$
$619$	47.5410	1.91083	0.955417	+	0.295258i	$0.0954057\pi$
$620$	−25.3262	−1.01713
$621$	1.70820	0.0685479
$622$	−19.0902	−0.765446
$623$	−6.70820	−0.268759
$624$	0.708204	0.0283508
$625$	−25.0000	−1.00000
$626$	9.09017	0.363316
$627$	0.103326	0.00412643
$628$	35.7984	1.42851
$629$	−9.47214	−0.377679
$630$	−6.38197	−0.254264
$631$	−41.8328	−1.66534	−0.832669	−	0.553771i	$-0.813188\pi$
$631$	−41.8328	−1.66534	−0.832669	+	0.553771i	$0.813188\pi$
$632$	12.2361	0.486725
$633$	−5.32624	−0.211699
$634$	−10.6180	−0.421696
$635$	−12.4377	−0.493575
$636$	−0.236068	−0.00936070
$637$	4.38197	0.173620
$638$	−2.02129	−0.0800235
$639$	−35.5967	−1.40819
$640$	25.4508	1.00603
$641$	−18.8885	−0.746053	−0.373026	−	0.927821i	$-0.621680\pi$
$641$	−18.8885	−0.746053	−0.373026	+	0.927821i	$0.621680\pi$
$642$	1.31308	0.0518232
$643$	0.270510	0.0106679	0.00533393	−	0.999986i	$-0.498302\pi$
$643$	0.270510	0.0106679	0.00533393	+	0.999986i	$0.498302\pi$
$644$	2.00000	0.0788110
$645$	−9.39512	−0.369933
$646$	0.0901699	0.00354769
$647$	41.3951	1.62741	0.813705	−	0.581278i	$-0.197447\pi$
$647$	41.3951	1.62741	0.813705	+	0.581278i	$0.197447\pi$
$648$	−17.2361	−0.677097
$649$	−11.5623	−0.453860
$650$	0	0
$651$	−4.32624	−0.169559
$652$	−16.7984	−0.657875
$653$	−2.05573	−0.0804469	−0.0402234	−	0.999191i	$-0.512807\pi$
$653$	−2.05573	−0.0804469	−0.0402234	+	0.999191i	$0.512807\pi$
$654$	2.56231	0.100194
$655$	21.1803	0.827584
$656$	−4.58359	−0.178959
$657$	−11.2574	−0.439191
$658$	−3.23607	−0.126155
$659$	−36.5967	−1.42561	−0.712803	−	0.701364i	$-0.752575\pi$
$659$	−36.5967	−1.42561	−0.712803	+	0.701364i	$0.752575\pi$
$660$	−2.56231	−0.0997376
$661$	15.1246	0.588279	0.294140	−	0.955762i	$-0.404967\pi$
$661$	15.1246	0.588279	0.294140	+	0.955762i	$0.404967\pi$
$662$	−12.3262	−0.479073
$663$	−0.381966	−0.0148343
$664$	13.9443	0.541143
$665$	−0.527864	−0.0204697
$666$	−16.7082	−0.647430
$667$	−1.34752	−0.0521763
$668$	−13.3262	−0.515608
$669$	−3.49342	−0.135064
$670$	16.8328	0.650308
$671$	9.00000	0.347441
$672$	3.47214	0.133941
$673$	−23.8197	−0.918180	−0.459090	−	0.888390i	$-0.651825\pi$
$673$	−23.8197	−0.918180	−0.459090	+	0.888390i	$0.651825\pi$
$674$	−7.14590	−0.275250
$675$	0	0
$676$	−1.61803	−0.0622321
$677$	39.0344	1.50022	0.750108	−	0.661316i	$-0.230002\pi$
$677$	39.0344	1.50022	0.750108	+	0.661316i	$0.230002\pi$
$678$	−2.85410	−0.109611
$679$	10.6180	0.407483
$680$	−5.00000	−0.191741
$681$	−4.87539	−0.186825
$682$	−8.02129	−0.307151
$683$	−33.5967	−1.28554	−0.642772	−	0.766058i	$-0.722216\pi$
$683$	−33.5967	−1.28554	−0.642772	+	0.766058i	$0.722216\pi$
$684$	−0.673762	−0.0257619
$685$	−25.8541	−0.987834
$686$	11.3820	0.434565
$687$	−7.68692	−0.293274
$688$	−20.3951	−0.777557
$689$	0.381966	0.0145517
$690$	0.403252	0.0153516
$691$	−25.7082	−0.977986	−0.488993	−	0.872288i	$-0.662636\pi$
$691$	−25.7082	−0.977986	−0.488993	+	0.872288i	$0.662636\pi$
$692$	−35.0344	−1.33181
$693$	8.56231	0.325255
$694$	0.978714	0.0371515
$695$	36.1803	1.37240
$696$	−1.50658	−0.0571067
$697$	2.47214	0.0936388
$698$	−12.9230	−0.489142
$699$	2.85410	0.107952
$700$	0	0
$701$	34.6869	1.31011	0.655053	−	0.755583i	$-0.272646\pi$
$701$	34.6869	1.31011	0.655053	+	0.755583i	$0.272646\pi$
$702$	−1.38197	−0.0521589
$703$	−1.38197	−0.0521218
$704$	−0.437694	−0.0164962
$705$	2.76393	0.104096
$706$	4.58359	0.172506
$707$	12.0902	0.454698
$708$	−3.85410	−0.144846
$709$	−5.56231	−0.208897	−0.104448	−	0.994530i	$-0.533308\pi$
$709$	−5.56231	−0.208897	−0.104448	+	0.994530i	$0.533308\pi$
$710$	−17.2361	−0.646858
$711$	15.6180	0.585722
$712$	−9.27051	−0.347427
$713$	−5.34752	−0.200266
$714$	−0.381966	−0.0142947
$715$	4.14590	0.155048
$716$	24.2705	0.907032
$717$	−9.03444	−0.337397
$718$	−16.1246	−0.601765
$719$	29.0557	1.08360	0.541798	−	0.840509i	$-0.317744\pi$
$719$	29.0557	1.08360	0.541798	+	0.840509i	$0.317744\pi$
$720$	11.8328	0.440983
$721$	10.5623	0.393361
$722$	−11.7295	−0.436526
$723$	5.72949	0.213082
$724$	−4.14590	−0.154081
$725$	0	0
$726$	1.78522	0.0662557
$727$	−27.3050	−1.01268	−0.506342	−	0.862333i	$-0.669003\pi$
$727$	−27.3050	−1.01268	−0.506342	+	0.862333i	$0.669003\pi$
$728$	−3.61803	−0.134093
$729$	−19.4377	−0.719915
$730$	−5.45085	−0.201745
$731$	11.0000	0.406850
$732$	3.00000	0.110883
$733$	0.527864	0.0194971	0.00974855	−	0.999952i	$-0.496897\pi$
$733$	0.527864	0.0194971	0.00974855	+	0.999952i	$0.496897\pi$
$734$	9.29180	0.342966
$735$	−3.74265	−0.138050
$736$	4.29180	0.158198
$737$	−22.5836	−0.831877
$738$	4.36068	0.160519
$739$	−13.1459	−0.483580	−0.241790	−	0.970329i	$-0.577734\pi$
$739$	−13.1459	−0.483580	−0.241790	+	0.970329i	$0.577734\pi$
$740$	34.2705	1.25981
$741$	−0.0557281	−0.00204722
$742$	0.381966	0.0140224
$743$	20.6525	0.757666	0.378833	−	0.925465i	$-0.376325\pi$
$743$	20.6525	0.757666	0.378833	+	0.925465i	$0.376325\pi$
$744$	−5.97871	−0.219190
$745$	−17.5623	−0.643433
$746$	5.29180	0.193746
$747$	17.7984	0.651208
$748$	3.00000	0.109691
$749$	9.00000	0.328853
$750$	−2.63932	−0.0963743
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	6.00000	0.218797
$753$	9.31308	0.339388
$754$	1.09017	0.0397016
$755$	9.34752	0.340191
$756$	5.85410	0.212912
$757$	51.7426	1.88062	0.940309	−	0.340321i	$-0.110536\pi$
$757$	51.7426	1.88062	0.940309	+	0.340321i	$0.110536\pi$
$758$	−2.65248	−0.0963423
$759$	−0.541020	−0.0196378
$760$	−0.729490	−0.0264614
$761$	−31.7639	−1.15144	−0.575721	−	0.817646i	$-0.695278\pi$
$761$	−31.7639	−1.15144	−0.575721	+	0.817646i	$0.695278\pi$
$762$	−1.31308	−0.0475680
$763$	17.5623	0.635798
$764$	−35.0344	−1.26750
$765$	−6.38197	−0.230740
$766$	−9.02129	−0.325952
$767$	6.23607	0.225171
$768$	2.50658	0.0904483
$769$	22.8541	0.824140	0.412070	−	0.911152i	$-0.364806\pi$
$769$	22.8541	0.824140	0.412070	+	0.911152i	$0.364806\pi$
$770$	4.14590	0.149408
$771$	−6.27051	−0.225827
$772$	−33.5967	−1.20917
$773$	7.67376	0.276006	0.138003	−	0.990432i	$-0.455932\pi$
$773$	7.67376	0.276006	0.138003	+	0.990432i	$0.455932\pi$
$774$	19.4033	0.697435
$775$	0	0
$776$	14.6738	0.526757
$777$	5.85410	0.210015
$778$	2.56231	0.0918631
$779$	0.360680	0.0129227
$780$	1.38197	0.0494823
$781$	23.1246	0.827464
$782$	−0.472136	−0.0168835
$783$	−3.94427	−0.140957
$784$	−8.12461	−0.290165
$785$	49.4721	1.76574
$786$	2.23607	0.0797579
$787$	10.4164	0.371305	0.185652	−	0.982615i	$-0.440560\pi$
$787$	10.4164	0.371305	0.185652	+	0.982615i	$0.440560\pi$
$788$	−31.1246	−1.10877
$789$	7.81966	0.278387
$790$	7.56231	0.269055
$791$	−19.5623	−0.695556
$792$	11.8328	0.420461
$793$	−4.85410	−0.172374
$794$	−15.7082	−0.557463
$795$	−0.326238	−0.0115705
$796$	36.5623	1.29592
$797$	−15.2016	−0.538469	−0.269235	−	0.963075i	$-0.586771\pi$
$797$	−15.2016	−0.538469	−0.269235	+	0.963075i	$0.586771\pi$
$798$	−0.0557281	−0.00197275
$799$	−3.23607	−0.114484
$800$	0	0
$801$	−11.8328	−0.418092
$802$	−19.2574	−0.680001
$803$	7.31308	0.258073
$804$	−7.52786	−0.265487
$805$	2.76393	0.0974158
$806$	4.32624	0.152385
$807$	8.52786	0.300195
$808$	16.7082	0.587793
$809$	55.1935	1.94050	0.970250	−	0.242105i	$-0.0778379\pi$
$809$	55.1935	1.94050	0.970250	+	0.242105i	$0.0778379\pi$
$810$	−10.6525	−0.374290
$811$	19.0689	0.669599	0.334800	−	0.942289i	$-0.391331\pi$
$811$	19.0689	0.669599	0.334800	+	0.942289i	$0.391331\pi$
$812$	−4.61803	−0.162061
$813$	−1.45085	−0.0508835
$814$	10.8541	0.380436
$815$	−23.2148	−0.813178
$816$	0.708204	0.0247921
$817$	1.60488	0.0561476
$818$	−6.76393	−0.236495
$819$	−4.61803	−0.161367
$820$	−8.94427	−0.312348
$821$	1.47214	0.0513779	0.0256889	−	0.999670i	$-0.491822\pi$
$821$	1.47214	0.0513779	0.0256889	+	0.999670i	$0.491822\pi$
$822$	−2.72949	−0.0952019
$823$	36.3050	1.26551	0.632756	−	0.774352i	$-0.281924\pi$
$823$	36.3050	1.26551	0.632756	+	0.774352i	$0.281924\pi$
$824$	14.5967	0.508502
$825$	0	0
$826$	6.23607	0.216981
$827$	−3.90983	−0.135958	−0.0679791	−	0.997687i	$-0.521655\pi$
$827$	−3.90983	−0.135958	−0.0679791	+	0.997687i	$0.521655\pi$
$828$	3.52786	0.122602
$829$	14.6525	0.508902	0.254451	−	0.967086i	$-0.418105\pi$
$829$	14.6525	0.508902	0.254451	+	0.967086i	$0.418105\pi$
$830$	8.61803	0.299136
$831$	−6.06888	−0.210527
$832$	0.236068	0.00818418
$833$	4.38197	0.151826
$834$	3.81966	0.132264
$835$	−18.4164	−0.637326
$836$	0.437694	0.0151380
$837$	−15.6525	−0.541029
$838$	−10.0213	−0.346180
$839$	−12.9787	−0.448075	−0.224037	−	0.974581i	$-0.571924\pi$
$839$	−12.9787	−0.448075	−0.224037	+	0.974581i	$0.571924\pi$
$840$	3.09017	0.106621
$841$	−25.8885	−0.892708
$842$	9.68692	0.333833
$843$	−3.02129	−0.104059
$844$	−22.5623	−0.776627
$845$	−2.23607	−0.0769231
$846$	−5.70820	−0.196252
$847$	12.2361	0.420436
$848$	−0.708204	−0.0243198
$849$	5.02129	0.172330
$850$	0	0
$851$	7.23607	0.248049
$852$	7.70820	0.264079
$853$	22.7082	0.777514	0.388757	−	0.921340i	$-0.372905\pi$
$853$	22.7082	0.777514	0.388757	+	0.921340i	$0.372905\pi$
$854$	−4.85410	−0.166104
$855$	−0.931116	−0.0318435
$856$	12.4377	0.425112
$857$	−17.4721	−0.596837	−0.298418	−	0.954435i	$-0.596459\pi$
$857$	−17.4721	−0.596837	−0.298418	+	0.954435i	$0.596459\pi$
$858$	0.437694	0.0149426
$859$	38.6869	1.31998	0.659990	−	0.751274i	$-0.270560\pi$
$859$	38.6869	1.31998	0.659990	+	0.751274i	$0.270560\pi$
$860$	−39.7984	−1.35711
$861$	−1.52786	−0.0520695
$862$	1.52786	0.0520393
$863$	−38.7771	−1.31999	−0.659994	−	0.751271i	$-0.729441\pi$
$863$	−38.7771	−1.31999	−0.659994	+	0.751271i	$0.729441\pi$
$864$	12.5623	0.427378
$865$	−48.4164	−1.64621
$866$	20.2918	0.689543
$867$	−0.381966	−0.0129722
$868$	−18.3262	−0.622033
$869$	−10.1459	−0.344176
$870$	−0.931116	−0.0315678
$871$	12.1803	0.412715
$872$	24.2705	0.821903
$873$	18.7295	0.633897
$874$	−0.0688837	−0.00233003
$875$	−18.0902	−0.611559
$876$	2.43769	0.0823621
$877$	−14.4377	−0.487526	−0.243763	−	0.969835i	$-0.578382\pi$
$877$	−14.4377	−0.487526	−0.243763	+	0.969835i	$0.578382\pi$
$878$	−1.83282	−0.0618545
$879$	9.31308	0.314122
$880$	−7.68692	−0.259126
$881$	20.6180	0.694639	0.347320	−	0.937747i	$-0.387092\pi$
$881$	20.6180	0.694639	0.347320	+	0.937747i	$0.387092\pi$
$882$	7.72949	0.260265
$883$	21.9443	0.738484	0.369242	−	0.929333i	$-0.379617\pi$
$883$	21.9443	0.738484	0.369242	+	0.929333i	$0.379617\pi$
$884$	−1.61803	−0.0544204
$885$	−5.32624	−0.179040
$886$	4.21478	0.141598
$887$	−7.96556	−0.267457	−0.133729	−	0.991018i	$-0.542695\pi$
$887$	−7.96556	−0.267457	−0.133729	+	0.991018i	$0.542695\pi$
$888$	8.09017	0.271488
$889$	−9.00000	−0.301850
$890$	−5.72949	−0.192053
$891$	14.2918	0.478793
$892$	−14.7984	−0.495486
$893$	−0.472136	−0.0157994
$894$	−1.85410	−0.0620104
$895$	33.5410	1.12115
$896$	18.4164	0.615249
$897$	0.291796	0.00974279
$898$	−0.416408	−0.0138957
$899$	12.3475	0.411813
$900$	0	0
$901$	0.381966	0.0127251
$902$	−2.83282	−0.0943224
$903$	−6.79837	−0.226236
$904$	−27.0344	−0.899152
$905$	−5.72949	−0.190455
$906$	0.986844	0.0327857
$907$	−49.8115	−1.65396	−0.826982	−	0.562228i	$-0.809944\pi$
$907$	−49.8115	−1.65396	−0.826982	+	0.562228i	$0.809944\pi$
$908$	−20.6525	−0.685376
$909$	21.3262	0.707347
$910$	−2.23607	−0.0741249
$911$	33.6525	1.11496	0.557478	−	0.830192i	$-0.311769\pi$
$911$	33.6525	1.11496	0.557478	+	0.830192i	$0.311769\pi$
$912$	0.103326	0.00342145
$913$	−11.5623	−0.382656
$914$	17.1803	0.568275
$915$	4.14590	0.137059
$916$	−32.5623	−1.07589
$917$	15.3262	0.506117
$918$	−1.38197	−0.0456117
$919$	19.5967	0.646437	0.323219	−	0.946324i	$-0.395235\pi$
$919$	19.5967	0.646437	0.323219	+	0.946324i	$0.395235\pi$
$920$	3.81966	0.125930
$921$	5.83282	0.192198
$922$	−20.7295	−0.682689
$923$	−12.4721	−0.410525
$924$	−1.85410	−0.0609955
$925$	0	0
$926$	6.68692	0.219746
$927$	18.6312	0.611929
$928$	−9.90983	−0.325306
$929$	26.8673	0.881486	0.440743	−	0.897633i	$-0.354715\pi$
$929$	26.8673	0.881486	0.440743	+	0.897633i	$0.354715\pi$
$930$	−3.69505	−0.121165
$931$	0.639320	0.0209529
$932$	12.0902	0.396027
$933$	11.7984	0.386261
$934$	−0.236068	−0.00772438
$935$	4.14590	0.135585
$936$	−6.38197	−0.208601
$937$	−15.8754	−0.518626	−0.259313	−	0.965793i	$-0.583496\pi$
$937$	−15.8754	−0.518626	−0.259313	+	0.965793i	$0.583496\pi$
$938$	12.1803	0.397702
$939$	−5.61803	−0.183338
$940$	11.7082	0.381880
$941$	−28.7984	−0.938800	−0.469400	−	0.882986i	$-0.655530\pi$
$941$	−28.7984	−0.938800	−0.469400	+	0.882986i	$0.655530\pi$
$942$	5.22291	0.170172
$943$	−1.88854	−0.0614994
$944$	−11.5623	−0.376321
$945$	8.09017	0.263173
$946$	−12.6049	−0.409820
$947$	44.9443	1.46049	0.730246	−	0.683184i	$-0.239405\pi$
$947$	44.9443	1.46049	0.730246	+	0.683184i	$0.239405\pi$
$948$	−3.38197	−0.109841
$949$	−3.94427	−0.128036
$950$	0	0
$951$	6.56231	0.212797
$952$	−3.61803	−0.117261
$953$	32.2918	1.04603	0.523017	−	0.852322i	$-0.324806\pi$
$953$	32.2918	1.04603	0.523017	+	0.852322i	$0.324806\pi$
$954$	0.673762	0.0218139
$955$	−48.4164	−1.56672
$956$	−38.2705	−1.23776
$957$	1.24922	0.0403817
$958$	9.00000	0.290777
$959$	−18.7082	−0.604119
$960$	−0.201626	−0.00650746
$961$	18.0000	0.580645
$962$	−5.85410	−0.188744
$963$	15.8754	0.511577
$964$	24.2705	0.781700
$965$	−46.4296	−1.49462
$966$	0.291796	0.00938838
$967$	47.6525	1.53240	0.766200	−	0.642602i	$-0.222145\pi$
$967$	47.6525	1.53240	0.766200	+	0.642602i	$0.222145\pi$
$968$	16.9098	0.543503
$969$	−0.0557281	−0.00179024
$970$	9.06888	0.291184
$971$	11.9098	0.382205	0.191102	−	0.981570i	$-0.438794\pi$
$971$	11.9098	0.382205	0.191102	+	0.981570i	$0.438794\pi$
$972$	15.6180	0.500949
$973$	26.1803	0.839303
$974$	5.74265	0.184006
$975$	0	0
$976$	9.00000	0.288083
$977$	8.67376	0.277498	0.138749	−	0.990328i	$-0.455692\pi$
$977$	8.67376	0.277498	0.138749	+	0.990328i	$0.455692\pi$
$978$	−2.45085	−0.0783695
$979$	7.68692	0.245675
$980$	−15.8541	−0.506441
$981$	30.9787	0.989074
$982$	22.4508	0.716435
$983$	34.3050	1.09416	0.547079	−	0.837081i	$-0.315740\pi$
$983$	34.3050	1.09416	0.547079	+	0.837081i	$0.315740\pi$
$984$	−2.11146	−0.0673108
$985$	−43.0132	−1.37051
$986$	1.09017	0.0347181
$987$	2.00000	0.0636607
$988$	−0.236068	−0.00751032
$989$	−8.40325	−0.267208
$990$	7.31308	0.232425
$991$	59.8115	1.89998	0.949988	−	0.312287i	$-0.101095\pi$
$991$	59.8115	1.89998	0.949988	+	0.312287i	$0.101095\pi$
$992$	−39.3262	−1.24861
$993$	7.61803	0.241751
$994$	−12.4721	−0.395592
$995$	50.5279	1.60184
$996$	−3.85410	−0.122122
$997$	−57.0000	−1.80521	−0.902604	−	0.430472i	$-0.858347\pi$
$997$	−57.0000	−1.80521	−0.902604	+	0.430472i	$0.858347\pi$
$998$	8.29180	0.262472
$999$	21.1803	0.670116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	221.2.a.c.1.2	✓	2
3.2	odd	2		1989.2.a.g.1.1		2
4.3	odd	2		3536.2.a.y.1.1		2
5.4	even	2		5525.2.a.q.1.1		2
13.12	even	2		2873.2.a.h.1.1		2
17.16	even	2		3757.2.a.h.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.a.c.1.2	✓	2	1.1	even	1	trivial
1989.2.a.g.1.1		2	3.2	odd	2
2873.2.a.h.1.1		2	13.12	even	2
3536.2.a.y.1.1		2	4.3	odd	2
3757.2.a.h.1.2		2	17.16	even	2
5525.2.a.q.1.1		2	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 221 = 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	221.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} -0.381966 q^{3} -1.61803 q^{4} -2.23607 q^{5} -0.236068 q^{6} -1.61803 q^{7} -2.23607 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} -0.381966 q^{3} -1.61803 q^{4} -2.23607 q^{5} -0.236068 q^{6} -1.61803 q^{7} -2.23607 q^{8} -2.85410 q^{9} -1.38197 q^{10} +1.85410 q^{11} +0.618034 q^{12} -1.00000 q^{13} -1.00000 q^{14} +0.854102 q^{15} +1.85410 q^{16} -1.00000 q^{17} -1.76393 q^{18} -0.145898 q^{19} +3.61803 q^{20} +0.618034 q^{21} +1.14590 q^{22} +0.763932 q^{23} +0.854102 q^{24} -0.618034 q^{26} +2.23607 q^{27} +2.61803 q^{28} -1.76393 q^{29} +0.527864 q^{30} -7.00000 q^{31} +5.61803 q^{32} -0.708204 q^{33} -0.618034 q^{34} +3.61803 q^{35} +4.61803 q^{36} +9.47214 q^{37} -0.0901699 q^{38} +0.381966 q^{39} +5.00000 q^{40} -2.47214 q^{41} +0.381966 q^{42} -11.0000 q^{43} -3.00000 q^{44} +6.38197 q^{45} +0.472136 q^{46} +3.23607 q^{47} -0.708204 q^{48} -4.38197 q^{49} +0.381966 q^{51} +1.61803 q^{52} -0.381966 q^{53} +1.38197 q^{54} -4.14590 q^{55} +3.61803 q^{56} +0.0557281 q^{57} -1.09017 q^{58} -6.23607 q^{59} -1.38197 q^{60} +4.85410 q^{61} -4.32624 q^{62} +4.61803 q^{63} -0.236068 q^{64} +2.23607 q^{65} -0.437694 q^{66} -12.1803 q^{67} +1.61803 q^{68} -0.291796 q^{69} +2.23607 q^{70} +12.4721 q^{71} +6.38197 q^{72} +3.94427 q^{73} +5.85410 q^{74} +0.236068 q^{76} -3.00000 q^{77} +0.236068 q^{78} -5.47214 q^{79} -4.14590 q^{80} +7.70820 q^{81} -1.52786 q^{82} -6.23607 q^{83} -1.00000 q^{84} +2.23607 q^{85} -6.79837 q^{86} +0.673762 q^{87} -4.14590 q^{88} +4.14590 q^{89} +3.94427 q^{90} +1.61803 q^{91} -1.23607 q^{92} +2.67376 q^{93} +2.00000 q^{94} +0.326238 q^{95} -2.14590 q^{96} -6.56231 q^{97} -2.70820 q^{98} -5.29180 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} + 4 q^{6} - q^{7} + q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 - q^4 + 4 * q^6 - q^7 + q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} + 4 q^{6} - q^{7} + q^{9} - 5 q^{10} - 3 q^{11} - q^{12} - 2 q^{13} - 2 q^{14} - 5 q^{15} - 3 q^{16} - 2 q^{17} - 8 q^{18} - 7 q^{19} + 5 q^{20} - q^{21} + 9 q^{22} + 6 q^{23} - 5 q^{24} + q^{26} + 3 q^{28} - 8 q^{29} + 10 q^{30} - 14 q^{31} + 9 q^{32} + 12 q^{33} + q^{34} + 5 q^{35} + 7 q^{36} + 10 q^{37} + 11 q^{38} + 3 q^{39} + 10 q^{40} + 4 q^{41} + 3 q^{42} - 22 q^{43} - 6 q^{44} + 15 q^{45} - 8 q^{46} + 2 q^{47} + 12 q^{48} - 11 q^{49} + 3 q^{51} + q^{52} - 3 q^{53} + 5 q^{54} - 15 q^{55} + 5 q^{56} + 18 q^{57} + 9 q^{58} - 8 q^{59} - 5 q^{60} + 3 q^{61} + 7 q^{62} + 7 q^{63} + 4 q^{64} - 21 q^{66} - 2 q^{67} + q^{68} - 14 q^{69} + 16 q^{71} + 15 q^{72} - 10 q^{73} + 5 q^{74} - 4 q^{76} - 6 q^{77} - 4 q^{78} - 2 q^{79} - 15 q^{80} + 2 q^{81} - 12 q^{82} - 8 q^{83} - 2 q^{84} + 11 q^{86} + 17 q^{87} - 15 q^{88} + 15 q^{89} - 10 q^{90} + q^{91} + 2 q^{92} + 21 q^{93} + 4 q^{94} - 15 q^{95} - 11 q^{96} + 7 q^{97} + 8 q^{98} - 24 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 + 4 * q^6 - q^7 + q^9 - 5 * q^10 - 3 * q^11 - q^12 - 2 * q^13 - 2 * q^14 - 5 * q^15 - 3 * q^16 - 2 * q^17 - 8 * q^18 - 7 * q^19 + 5 * q^20 - q^21 + 9 * q^22 + 6 * q^23 - 5 * q^24 + q^26 + 3 * q^28 - 8 * q^29 + 10 * q^30 - 14 * q^31 + 9 * q^32 + 12 * q^33 + q^34 + 5 * q^35 + 7 * q^36 + 10 * q^37 + 11 * q^38 + 3 * q^39 + 10 * q^40 + 4 * q^41 + 3 * q^42 - 22 * q^43 - 6 * q^44 + 15 * q^45 - 8 * q^46 + 2 * q^47 + 12 * q^48 - 11 * q^49 + 3 * q^51 + q^52 - 3 * q^53 + 5 * q^54 - 15 * q^55 + 5 * q^56 + 18 * q^57 + 9 * q^58 - 8 * q^59 - 5 * q^60 + 3 * q^61 + 7 * q^62 + 7 * q^63 + 4 * q^64 - 21 * q^66 - 2 * q^67 + q^68 - 14 * q^69 + 16 * q^71 + 15 * q^72 - 10 * q^73 + 5 * q^74 - 4 * q^76 - 6 * q^77 - 4 * q^78 - 2 * q^79 - 15 * q^80 + 2 * q^81 - 12 * q^82 - 8 * q^83 - 2 * q^84 + 11 * q^86 + 17 * q^87 - 15 * q^88 + 15 * q^89 - 10 * q^90 + q^91 + 2 * q^92 + 21 * q^93 + 4 * q^94 - 15 * q^95 - 11 * q^96 + 7 * q^97 + 8 * q^98 - 24 * q^99

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