LMFDB - Embedded newform 4022.2.a.f.1.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.28
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.761659 q^{3} +1.00000 q^{4} +0.666338 q^{5} +0.761659 q^{6} -1.04704 q^{7} +1.00000 q^{8} -2.41987 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.761659 q^{3} +1.00000 q^{4} +0.666338 q^{5} +0.761659 q^{6} -1.04704 q^{7} +1.00000 q^{8} -2.41987 q^{9} +0.666338 q^{10} +5.59142 q^{11} +0.761659 q^{12} +5.65052 q^{13} -1.04704 q^{14} +0.507523 q^{15} +1.00000 q^{16} +2.95743 q^{17} -2.41987 q^{18} -7.03919 q^{19} +0.666338 q^{20} -0.797490 q^{21} +5.59142 q^{22} +7.83967 q^{23} +0.761659 q^{24} -4.55599 q^{25} +5.65052 q^{26} -4.12810 q^{27} -1.04704 q^{28} -6.27325 q^{29} +0.507523 q^{30} +5.53392 q^{31} +1.00000 q^{32} +4.25876 q^{33} +2.95743 q^{34} -0.697684 q^{35} -2.41987 q^{36} +10.8183 q^{37} -7.03919 q^{38} +4.30377 q^{39} +0.666338 q^{40} +2.70991 q^{41} -0.797490 q^{42} -9.38170 q^{43} +5.59142 q^{44} -1.61245 q^{45} +7.83967 q^{46} +4.88764 q^{47} +0.761659 q^{48} -5.90370 q^{49} -4.55599 q^{50} +2.25255 q^{51} +5.65052 q^{52} +3.98589 q^{53} -4.12810 q^{54} +3.72578 q^{55} -1.04704 q^{56} -5.36147 q^{57} -6.27325 q^{58} +1.28571 q^{59} +0.507523 q^{60} -2.84008 q^{61} +5.53392 q^{62} +2.53371 q^{63} +1.00000 q^{64} +3.76515 q^{65} +4.25876 q^{66} -14.0926 q^{67} +2.95743 q^{68} +5.97116 q^{69} -0.697684 q^{70} +14.7891 q^{71} -2.41987 q^{72} -3.54962 q^{73} +10.8183 q^{74} -3.47012 q^{75} -7.03919 q^{76} -5.85446 q^{77} +4.30377 q^{78} +8.00316 q^{79} +0.666338 q^{80} +4.11542 q^{81} +2.70991 q^{82} -0.521301 q^{83} -0.797490 q^{84} +1.97065 q^{85} -9.38170 q^{86} -4.77808 q^{87} +5.59142 q^{88} +10.7638 q^{89} -1.61245 q^{90} -5.91633 q^{91} +7.83967 q^{92} +4.21497 q^{93} +4.88764 q^{94} -4.69048 q^{95} +0.761659 q^{96} +2.41476 q^{97} -5.90370 q^{98} -13.5305 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.761659	0.439744	0.219872	−	0.975529i	$-0.429436\pi$
$3$	0.761659	0.439744	0.219872	+	0.975529i	$0.429436\pi$
$4$	1.00000	0.500000
$5$	0.666338	0.297995	0.148998	−	0.988838i	$-0.452395\pi$
$5$	0.666338	0.297995	0.148998	+	0.988838i	$0.452395\pi$
$6$	0.761659	0.310946
$7$	−1.04704	−0.395745	−0.197872	−	0.980228i	$-0.563403\pi$
$7$	−1.04704	−0.395745	−0.197872	+	0.980228i	$0.563403\pi$
$8$	1.00000	0.353553
$9$	−2.41987	−0.806625
$10$	0.666338	0.210715
$11$	5.59142	1.68588	0.842939	−	0.538009i	$-0.180823\pi$
$11$	5.59142	1.68588	0.842939	+	0.538009i	$0.180823\pi$
$12$	0.761659	0.219872
$13$	5.65052	1.56717	0.783586	−	0.621283i	$-0.213388\pi$
$13$	5.65052	1.56717	0.783586	+	0.621283i	$0.213388\pi$
$14$	−1.04704	−0.279834
$15$	0.507523	0.131042
$16$	1.00000	0.250000
$17$	2.95743	0.717281	0.358641	−	0.933476i	$-0.383240\pi$
$17$	2.95743	0.717281	0.358641	+	0.933476i	$0.383240\pi$
$18$	−2.41987	−0.570370
$19$	−7.03919	−1.61490	−0.807451	−	0.589935i	$-0.799153\pi$
$19$	−7.03919	−1.61490	−0.807451	+	0.589935i	$0.799153\pi$
$20$	0.666338	0.148998
$21$	−0.797490	−0.174027
$22$	5.59142	1.19210
$23$	7.83967	1.63468	0.817342	−	0.576153i	$-0.195447\pi$
$23$	7.83967	1.63468	0.817342	+	0.576153i	$0.195447\pi$
$24$	0.761659	0.155473
$25$	−4.55599	−0.911199
$26$	5.65052	1.10816
$27$	−4.12810	−0.794453
$28$	−1.04704	−0.197872
$29$	−6.27325	−1.16491	−0.582457	−	0.812862i	$-0.697909\pi$
$29$	−6.27325	−1.16491	−0.582457	+	0.812862i	$0.697909\pi$
$30$	0.507523	0.0926605
$31$	5.53392	0.993922	0.496961	−	0.867773i	$-0.334449\pi$
$31$	5.53392	0.993922	0.496961	+	0.867773i	$0.334449\pi$
$32$	1.00000	0.176777
$33$	4.25876	0.741355
$34$	2.95743	0.507194
$35$	−0.697684	−0.117930
$36$	−2.41987	−0.403312
$37$	10.8183	1.77852	0.889261	−	0.457400i	$-0.151219\pi$
$37$	10.8183	1.77852	0.889261	+	0.457400i	$0.151219\pi$
$38$	−7.03919	−1.14191
$39$	4.30377	0.689155
$40$	0.666338	0.105357
$41$	2.70991	0.423217	0.211608	−	0.977355i	$-0.432130\pi$
$41$	2.70991	0.423217	0.211608	+	0.977355i	$0.432130\pi$
$42$	−0.797490	−0.123055
$43$	−9.38170	−1.43070	−0.715348	−	0.698769i	$-0.753732\pi$
$43$	−9.38170	−1.43070	−0.715348	+	0.698769i	$0.753732\pi$
$44$	5.59142	0.842939
$45$	−1.61245	−0.240370
$46$	7.83967	1.15590
$47$	4.88764	0.712935	0.356468	−	0.934308i	$-0.383981\pi$
$47$	4.88764	0.712935	0.356468	+	0.934308i	$0.383981\pi$
$48$	0.761659	0.109936
$49$	−5.90370	−0.843386
$50$	−4.55599	−0.644315
$51$	2.25255	0.315420
$52$	5.65052	0.783586
$53$	3.98589	0.547504	0.273752	−	0.961800i	$-0.411735\pi$
$53$	3.98589	0.547504	0.273752	+	0.961800i	$0.411735\pi$
$54$	−4.12810	−0.561763
$55$	3.72578	0.502384
$56$	−1.04704	−0.139917
$57$	−5.36147	−0.710144
$58$	−6.27325	−0.823719
$59$	1.28571	0.167385	0.0836923	−	0.996492i	$-0.473329\pi$
$59$	1.28571	0.167385	0.0836923	+	0.996492i	$0.473329\pi$
$60$	0.507523	0.0655209
$61$	−2.84008	−0.363635	−0.181818	−	0.983332i	$-0.558198\pi$
$61$	−2.84008	−0.363635	−0.181818	+	0.983332i	$0.558198\pi$
$62$	5.53392	0.702809
$63$	2.53371	0.319218
$64$	1.00000	0.125000
$65$	3.76515	0.467010
$66$	4.25876	0.524217
$67$	−14.0926	−1.72169	−0.860844	−	0.508869i	$-0.830064\pi$
$67$	−14.0926	−1.72169	−0.860844	+	0.508869i	$0.830064\pi$
$68$	2.95743	0.358641
$69$	5.97116	0.718843
$70$	−0.697684	−0.0833892
$71$	14.7891	1.75514	0.877570	−	0.479448i	$-0.159163\pi$
$71$	14.7891	1.75514	0.877570	+	0.479448i	$0.159163\pi$
$72$	−2.41987	−0.285185
$73$	−3.54962	−0.415451	−0.207726	−	0.978187i	$-0.566606\pi$
$73$	−3.54962	−0.415451	−0.207726	+	0.978187i	$0.566606\pi$
$74$	10.8183	1.25761
$75$	−3.47012	−0.400694
$76$	−7.03919	−0.807451
$77$	−5.85446	−0.667177
$78$	4.30377	0.487306
$79$	8.00316	0.900426	0.450213	−	0.892921i	$-0.351348\pi$
$79$	8.00316	0.900426	0.450213	+	0.892921i	$0.351348\pi$
$80$	0.666338	0.0744988
$81$	4.11542	0.457269
$82$	2.70991	0.299260
$83$	−0.521301	−0.0572202	−0.0286101	−	0.999591i	$-0.509108\pi$
$83$	−0.521301	−0.0572202	−0.0286101	+	0.999591i	$0.509108\pi$
$84$	−0.797490	−0.0870133
$85$	1.97065	0.213746
$86$	−9.38170	−1.01165
$87$	−4.77808	−0.512264
$88$	5.59142	0.596048
$89$	10.7638	1.14096	0.570480	−	0.821312i	$-0.306757\pi$
$89$	10.7638	1.14096	0.570480	+	0.821312i	$0.306757\pi$
$90$	−1.61245	−0.169968
$91$	−5.91633	−0.620200
$92$	7.83967	0.817342
$93$	4.21497	0.437072
$94$	4.88764	0.504121
$95$	−4.69048	−0.481233
$96$	0.761659	0.0777365
$97$	2.41476	0.245182	0.122591	−	0.992457i	$-0.460880\pi$
$97$	2.41476	0.245182	0.122591	+	0.992457i	$0.460880\pi$
$98$	−5.90370	−0.596364
$99$	−13.5305	−1.35987
$100$	−4.55599	−0.455599
$101$	−7.11368	−0.707838	−0.353919	−	0.935276i	$-0.615151\pi$
$101$	−7.11368	−0.707838	−0.353919	+	0.935276i	$0.615151\pi$
$102$	2.25255	0.223036
$103$	11.9810	1.18052	0.590260	−	0.807213i	$-0.299025\pi$
$103$	11.9810	1.18052	0.590260	+	0.807213i	$0.299025\pi$
$104$	5.65052	0.554079
$105$	−0.531398	−0.0518591
$106$	3.98589	0.387144
$107$	−10.7637	−1.04057	−0.520283	−	0.853994i	$-0.674174\pi$
$107$	−10.7637	−1.04057	−0.520283	+	0.853994i	$0.674174\pi$
$108$	−4.12810	−0.397227
$109$	−1.80414	−0.172805	−0.0864026	−	0.996260i	$-0.527537\pi$
$109$	−1.80414	−0.172805	−0.0864026	+	0.996260i	$0.527537\pi$
$110$	3.72578	0.355239
$111$	8.23988	0.782095
$112$	−1.04704	−0.0989362
$113$	18.0034	1.69362	0.846808	−	0.531899i	$-0.178521\pi$
$113$	18.0034	1.69362	0.846808	+	0.531899i	$0.178521\pi$
$114$	−5.36147	−0.502147
$115$	5.22387	0.487128
$116$	−6.27325	−0.582457
$117$	−13.6735	−1.26412
$118$	1.28571	0.118359
$119$	−3.09655	−0.283860
$120$	0.507523	0.0463303
$121$	20.2640	1.84218
$122$	−2.84008	−0.257129
$123$	2.06403	0.186107
$124$	5.53392	0.496961
$125$	−6.36752	−0.569528
$126$	2.53371	0.225721
$127$	2.94717	0.261519	0.130760	−	0.991414i	$-0.458258\pi$
$127$	2.94717	0.261519	0.130760	+	0.991414i	$0.458258\pi$
$128$	1.00000	0.0883883
$129$	−7.14566	−0.629140
$130$	3.76515	0.330226
$131$	7.32746	0.640203	0.320102	−	0.947383i	$-0.396283\pi$
$131$	7.32746	0.640203	0.320102	+	0.947383i	$0.396283\pi$
$132$	4.25876	0.370678
$133$	7.37033	0.639089
$134$	−14.0926	−1.21742
$135$	−2.75071	−0.236743
$136$	2.95743	0.253597
$137$	−3.30748	−0.282577	−0.141288	−	0.989968i	$-0.545124\pi$
$137$	−3.30748	−0.282577	−0.141288	+	0.989968i	$0.545124\pi$
$138$	5.97116	0.508299
$139$	−14.0592	−1.19249	−0.596244	−	0.802803i	$-0.703341\pi$
$139$	−14.0592	−1.19249	−0.596244	+	0.802803i	$0.703341\pi$
$140$	−0.697684	−0.0589650
$141$	3.72272	0.313509
$142$	14.7891	1.24107
$143$	31.5944	2.64206
$144$	−2.41987	−0.201656
$145$	−4.18011	−0.347139
$146$	−3.54962	−0.293768
$147$	−4.49661	−0.370874
$148$	10.8183	0.889261
$149$	5.91750	0.484780	0.242390	−	0.970179i	$-0.422069\pi$
$149$	5.91750	0.484780	0.242390	+	0.970179i	$0.422069\pi$
$150$	−3.47012	−0.283334
$151$	3.67450	0.299026	0.149513	−	0.988760i	$-0.452229\pi$
$151$	3.67450	0.299026	0.149513	+	0.988760i	$0.452229\pi$
$152$	−7.03919	−0.570954
$153$	−7.15660	−0.578577
$154$	−5.85446	−0.471766
$155$	3.68746	0.296184
$156$	4.30377	0.344577
$157$	1.32258	0.105553	0.0527767	−	0.998606i	$-0.483193\pi$
$157$	1.32258	0.105553	0.0527767	+	0.998606i	$0.483193\pi$
$158$	8.00316	0.636697
$159$	3.03589	0.240762
$160$	0.666338	0.0526786
$161$	−8.20847	−0.646918
$162$	4.11542	0.323338
$163$	−9.20222	−0.720774	−0.360387	−	0.932803i	$-0.617355\pi$
$163$	−9.20222	−0.720774	−0.360387	+	0.932803i	$0.617355\pi$
$164$	2.70991	0.211608
$165$	2.83777	0.220920
$166$	−0.521301	−0.0404608
$167$	5.95338	0.460686	0.230343	−	0.973109i	$-0.426015\pi$
$167$	5.95338	0.460686	0.230343	+	0.973109i	$0.426015\pi$
$168$	−0.797490	−0.0615277
$169$	18.9284	1.45603
$170$	1.97065	0.151142
$171$	17.0340	1.30262
$172$	−9.38170	−0.715348
$173$	11.6552	0.886128	0.443064	−	0.896490i	$-0.353892\pi$
$173$	11.6552	0.886128	0.443064	+	0.896490i	$0.353892\pi$
$174$	−4.77808	−0.362226
$175$	4.77032	0.360602
$176$	5.59142	0.421469
$177$	0.979270	0.0736064
$178$	10.7638	0.806780
$179$	2.79125	0.208628	0.104314	−	0.994544i	$-0.466735\pi$
$179$	2.79125	0.208628	0.104314	+	0.994544i	$0.466735\pi$
$180$	−1.61245	−0.120185
$181$	−17.7142	−1.31669	−0.658345	−	0.752717i	$-0.728743\pi$
$181$	−17.7142	−1.31669	−0.658345	+	0.752717i	$0.728743\pi$
$182$	−5.91633	−0.438548
$183$	−2.16318	−0.159907
$184$	7.83967	0.577948
$185$	7.20866	0.529991
$186$	4.21497	0.309056
$187$	16.5362	1.20925
$188$	4.88764	0.356468
$189$	4.32229	0.314401
$190$	−4.69048	−0.340283
$191$	19.3018	1.39663	0.698313	−	0.715792i	$-0.253934\pi$
$191$	19.3018	1.39663	0.698313	+	0.715792i	$0.253934\pi$
$192$	0.761659	0.0549680
$193$	−25.1722	−1.81193	−0.905967	−	0.423348i	$-0.860855\pi$
$193$	−25.1722	−1.81193	−0.905967	+	0.423348i	$0.860855\pi$
$194$	2.41476	0.173370
$195$	2.86777	0.205365
$196$	−5.90370	−0.421693
$197$	−9.92864	−0.707386	−0.353693	−	0.935361i	$-0.615074\pi$
$197$	−9.92864	−0.707386	−0.353693	+	0.935361i	$0.615074\pi$
$198$	−13.5305	−0.961574
$199$	3.69638	0.262030	0.131015	−	0.991380i	$-0.458176\pi$
$199$	3.69638	0.262030	0.131015	+	0.991380i	$0.458176\pi$
$200$	−4.55599	−0.322157
$201$	−10.7338	−0.757102
$202$	−7.11368	−0.500517
$203$	6.56836	0.461009
$204$	2.25255	0.157710
$205$	1.80572	0.126117
$206$	11.9810	0.834753
$207$	−18.9710	−1.31858
$208$	5.65052	0.391793
$209$	−39.3591	−2.72253
$210$	−0.531398	−0.0366699
$211$	3.09119	0.212806	0.106403	−	0.994323i	$-0.466067\pi$
$211$	3.09119	0.212806	0.106403	+	0.994323i	$0.466067\pi$
$212$	3.98589	0.273752
$213$	11.2642	0.771813
$214$	−10.7637	−0.735792
$215$	−6.25138	−0.426341
$216$	−4.12810	−0.280882
$217$	−5.79425	−0.393339
$218$	−1.80414	−0.122192
$219$	−2.70360	−0.182692
$220$	3.72578	0.251192
$221$	16.7110	1.12410
$222$	8.23988	0.553025
$223$	−4.04328	−0.270758	−0.135379	−	0.990794i	$-0.543225\pi$
$223$	−4.04328	−0.270758	−0.135379	+	0.990794i	$0.543225\pi$
$224$	−1.04704	−0.0699585
$225$	11.0249	0.734996
$226$	18.0034	1.19757
$227$	6.90052	0.458004	0.229002	−	0.973426i	$-0.426454\pi$
$227$	6.90052	0.458004	0.229002	+	0.973426i	$0.426454\pi$
$228$	−5.36147	−0.355072
$229$	14.9265	0.986369	0.493184	−	0.869925i	$-0.335833\pi$
$229$	14.9265	0.986369	0.493184	+	0.869925i	$0.335833\pi$
$230$	5.22387	0.344452
$231$	−4.45910	−0.293387
$232$	−6.27325	−0.411859
$233$	−9.07074	−0.594244	−0.297122	−	0.954840i	$-0.596027\pi$
$233$	−9.07074	−0.594244	−0.297122	+	0.954840i	$0.596027\pi$
$234$	−13.6735	−0.893868
$235$	3.25682	0.212451
$236$	1.28571	0.0836923
$237$	6.09568	0.395957
$238$	−3.09655	−0.200720
$239$	−5.66975	−0.366746	−0.183373	−	0.983043i	$-0.558702\pi$
$239$	−5.66975	−0.366746	−0.183373	+	0.983043i	$0.558702\pi$
$240$	0.507523	0.0327604
$241$	3.75268	0.241731	0.120866	−	0.992669i	$-0.461433\pi$
$241$	3.75268	0.241731	0.120866	+	0.992669i	$0.461433\pi$
$242$	20.2640	1.30262
$243$	15.5188	0.995534
$244$	−2.84008	−0.181818
$245$	−3.93386	−0.251325
$246$	2.06403	0.131598
$247$	−39.7751	−2.53083
$248$	5.53392	0.351405
$249$	−0.397054	−0.0251623
$250$	−6.36752	−0.402717
$251$	−14.7879	−0.933401	−0.466701	−	0.884415i	$-0.654557\pi$
$251$	−14.7879	−0.933401	−0.466701	+	0.884415i	$0.654557\pi$
$252$	2.53371	0.159609
$253$	43.8349	2.75588
$254$	2.94717	0.184922
$255$	1.50096	0.0939938
$256$	1.00000	0.0625000
$257$	−27.9458	−1.74321	−0.871605	−	0.490208i	$-0.836921\pi$
$257$	−27.9458	−1.74321	−0.871605	+	0.490208i	$0.836921\pi$
$258$	−7.14566	−0.444869
$259$	−11.3272	−0.703841
$260$	3.76515	0.233505
$261$	15.1805	0.939649
$262$	7.32746	0.452692
$263$	−4.30098	−0.265210	−0.132605	−	0.991169i	$-0.542334\pi$
$263$	−4.30098	−0.265210	−0.132605	+	0.991169i	$0.542334\pi$
$264$	4.25876	0.262109
$265$	2.65595	0.163154
$266$	7.37033	0.451904
$267$	8.19834	0.501730
$268$	−14.0926	−0.860844
$269$	−1.00842	−0.0614845	−0.0307423	−	0.999527i	$-0.509787\pi$
$269$	−1.00842	−0.0614845	−0.0307423	+	0.999527i	$0.509787\pi$
$270$	−2.75071	−0.167403
$271$	−19.7572	−1.20016	−0.600082	−	0.799939i	$-0.704865\pi$
$271$	−19.7572	−1.20016	−0.600082	+	0.799939i	$0.704865\pi$
$272$	2.95743	0.179320
$273$	−4.50623	−0.272729
$274$	−3.30748	−0.199812
$275$	−25.4745	−1.53617
$276$	5.97116	0.359422
$277$	−28.6740	−1.72286	−0.861428	−	0.507880i	$-0.830429\pi$
$277$	−28.6740	−1.72286	−0.861428	+	0.507880i	$0.830429\pi$
$278$	−14.0592	−0.843217
$279$	−13.3914	−0.801722
$280$	−0.697684	−0.0416946
$281$	16.1533	0.963623	0.481812	−	0.876275i	$-0.339979\pi$
$281$	16.1533	0.963623	0.481812	+	0.876275i	$0.339979\pi$
$282$	3.72272	0.221684
$283$	−29.4514	−1.75071	−0.875353	−	0.483484i	$-0.839371\pi$
$283$	−29.4514	−1.75071	−0.875353	+	0.483484i	$0.839371\pi$
$284$	14.7891	0.877570
$285$	−3.57255	−0.211620
$286$	31.5944	1.86822
$287$	−2.83739	−0.167486
$288$	−2.41987	−0.142592
$289$	−8.25363	−0.485508
$290$	−4.18011	−0.245464
$291$	1.83923	0.107817
$292$	−3.54962	−0.207726
$293$	1.74817	0.102129	0.0510647	−	0.998695i	$-0.483739\pi$
$293$	1.74817	0.102129	0.0510647	+	0.998695i	$0.483739\pi$
$294$	−4.49661	−0.262248
$295$	0.856714	0.0498798
$296$	10.8183	0.628803
$297$	−23.0820	−1.33935
$298$	5.91750	0.342792
$299$	44.2982	2.56183
$300$	−3.47012	−0.200347
$301$	9.82303	0.566190
$302$	3.67450	0.211443
$303$	−5.41820	−0.311268
$304$	−7.03919	−0.403725
$305$	−1.89245	−0.108362
$306$	−7.15660	−0.409116
$307$	−0.989292	−0.0564619	−0.0282309	−	0.999601i	$-0.508987\pi$
$307$	−0.989292	−0.0564619	−0.0282309	+	0.999601i	$0.508987\pi$
$308$	−5.85446	−0.333589
$309$	9.12541	0.519127
$310$	3.68746	0.209434
$311$	33.9195	1.92340	0.961699	−	0.274109i	$-0.0883828\pi$
$311$	33.9195	1.92340	0.961699	+	0.274109i	$0.0883828\pi$
$312$	4.30377	0.243653
$313$	−6.28253	−0.355110	−0.177555	−	0.984111i	$-0.556819\pi$
$313$	−6.28253	−0.355110	−0.177555	+	0.984111i	$0.556819\pi$
$314$	1.32258	0.0746376
$315$	1.68831	0.0951254
$316$	8.00316	0.450213
$317$	−1.01507	−0.0570118	−0.0285059	−	0.999594i	$-0.509075\pi$
$317$	−1.01507	−0.0570118	−0.0285059	+	0.999594i	$0.509075\pi$
$318$	3.03589	0.170244
$319$	−35.0764	−1.96390
$320$	0.666338	0.0372494
$321$	−8.19828	−0.457583
$322$	−8.20847	−0.457440
$323$	−20.8179	−1.15834
$324$	4.11542	0.228634
$325$	−25.7437	−1.42801
$326$	−9.20222	−0.509664
$327$	−1.37414	−0.0759901
$328$	2.70991	0.149630
$329$	−5.11756	−0.282140
$330$	2.83777	0.156214
$331$	−21.0786	−1.15859	−0.579293	−	0.815119i	$-0.696671\pi$
$331$	−21.0786	−1.15859	−0.579293	+	0.815119i	$0.696671\pi$
$332$	−0.521301	−0.0286101
$333$	−26.1790	−1.43460
$334$	5.95338	0.325754
$335$	−9.39045	−0.513055
$336$	−0.797490	−0.0435066
$337$	−17.8275	−0.971125	−0.485562	−	0.874202i	$-0.661385\pi$
$337$	−17.8275	−0.971125	−0.485562	+	0.874202i	$0.661385\pi$
$338$	18.9284	1.02957
$339$	13.7124	0.744758
$340$	1.97065	0.106873
$341$	30.9425	1.67563
$342$	17.0340	0.921091
$343$	13.5107	0.729510
$344$	−9.38170	−0.505827
$345$	3.97881	0.214212
$346$	11.6552	0.626587
$347$	−20.3991	−1.09508	−0.547540	−	0.836780i	$-0.684435\pi$
$347$	−20.3991	−1.09508	−0.547540	+	0.836780i	$0.684435\pi$
$348$	−4.77808	−0.256132
$349$	−30.5134	−1.63335	−0.816673	−	0.577100i	$-0.804184\pi$
$349$	−30.5134	−1.63335	−0.816673	+	0.577100i	$0.804184\pi$
$350$	4.77032	0.254984
$351$	−23.3259	−1.24504
$352$	5.59142	0.298024
$353$	−9.66357	−0.514340	−0.257170	−	0.966366i	$-0.582790\pi$
$353$	−9.66357	−0.514340	−0.257170	+	0.966366i	$0.582790\pi$
$354$	0.979270	0.0520476
$355$	9.85452	0.523024
$356$	10.7638	0.570480
$357$	−2.35852	−0.124826
$358$	2.79125	0.147522
$359$	−33.1792	−1.75113	−0.875567	−	0.483097i	$-0.839512\pi$
$359$	−33.1792	−1.75113	−0.875567	+	0.483097i	$0.839512\pi$
$360$	−1.61245	−0.0849838
$361$	30.5502	1.60791
$362$	−17.7142	−0.931040
$363$	15.4343	0.810090
$364$	−5.91633	−0.310100
$365$	−2.36524	−0.123802
$366$	−2.16318	−0.113071
$367$	8.02979	0.419152	0.209576	−	0.977792i	$-0.432792\pi$
$367$	8.02979	0.419152	0.209576	+	0.977792i	$0.432792\pi$
$368$	7.83967	0.408671
$369$	−6.55764	−0.341377
$370$	7.20866	0.374761
$371$	−4.17340	−0.216672
$372$	4.21497	0.218536
$373$	−33.3927	−1.72901	−0.864505	−	0.502624i	$-0.832368\pi$
$373$	−33.3927	−1.72901	−0.864505	+	0.502624i	$0.832368\pi$
$374$	16.5362	0.855068
$375$	−4.84988	−0.250447
$376$	4.88764	0.252061
$377$	−35.4471	−1.82562
$378$	4.32229	0.222315
$379$	3.83439	0.196960	0.0984798	−	0.995139i	$-0.468602\pi$
$379$	3.83439	0.196960	0.0984798	+	0.995139i	$0.468602\pi$
$380$	−4.69048	−0.240617
$381$	2.24474	0.115002
$382$	19.3018	0.987564
$383$	−26.5822	−1.35829	−0.679143	−	0.734006i	$-0.737648\pi$
$383$	−26.5822	−1.35829	−0.679143	+	0.734006i	$0.737648\pi$
$384$	0.761659	0.0388683
$385$	−3.90105	−0.198816
$386$	−25.1722	−1.28123
$387$	22.7025	1.15403
$388$	2.41476	0.122591
$389$	33.3124	1.68901	0.844504	−	0.535550i	$-0.179896\pi$
$389$	33.3124	1.68901	0.844504	+	0.535550i	$0.179896\pi$
$390$	2.86777	0.145215
$391$	23.1852	1.17253
$392$	−5.90370	−0.298182
$393$	5.58103	0.281526
$394$	−9.92864	−0.500198
$395$	5.33281	0.268323
$396$	−13.5305	−0.679936
$397$	−6.20757	−0.311549	−0.155775	−	0.987793i	$-0.549787\pi$
$397$	−6.20757	−0.311549	−0.155775	+	0.987793i	$0.549787\pi$
$398$	3.69638	0.185283
$399$	5.61368	0.281036
$400$	−4.55599	−0.227800
$401$	7.34814	0.366949	0.183474	−	0.983024i	$-0.441266\pi$
$401$	7.34814	0.366949	0.183474	+	0.983024i	$0.441266\pi$
$402$	−10.7338	−0.535352
$403$	31.2695	1.55765
$404$	−7.11368	−0.353919
$405$	2.74226	0.136264
$406$	6.56836	0.325982
$407$	60.4899	2.99837
$408$	2.25255	0.111518
$409$	−34.0224	−1.68230	−0.841149	−	0.540804i	$-0.818120\pi$
$409$	−34.0224	−1.68230	−0.841149	+	0.540804i	$0.818120\pi$
$410$	1.80572	0.0891780
$411$	−2.51917	−0.124262
$412$	11.9810	0.590260
$413$	−1.34619	−0.0662416
$414$	−18.9710	−0.932375
$415$	−0.347363	−0.0170514
$416$	5.65052	0.277039
$417$	−10.7083	−0.524390
$418$	−39.3591	−1.92512
$419$	−29.8923	−1.46033	−0.730167	−	0.683269i	$-0.760558\pi$
$419$	−29.8923	−1.46033	−0.730167	+	0.683269i	$0.760558\pi$
$420$	−0.531398	−0.0259295
$421$	31.7449	1.54715	0.773575	−	0.633704i	$-0.218466\pi$
$421$	31.7449	1.54715	0.773575	+	0.633704i	$0.218466\pi$
$422$	3.09119	0.150477
$423$	−11.8275	−0.575071
$424$	3.98589	0.193572
$425$	−13.4740	−0.653586
$426$	11.2642	0.545754
$427$	2.97369	0.143907
$428$	−10.7637	−0.520283
$429$	24.0642	1.16183
$430$	−6.25138	−0.301468
$431$	−28.3601	−1.36606	−0.683030	−	0.730390i	$-0.739338\pi$
$431$	−28.3601	−1.36606	−0.683030	+	0.730390i	$0.739338\pi$
$432$	−4.12810	−0.198613
$433$	35.0024	1.68211	0.841054	−	0.540951i	$-0.181936\pi$
$433$	35.0024	1.68211	0.841054	+	0.540951i	$0.181936\pi$
$434$	−5.79425	−0.278133
$435$	−3.18382	−0.152652
$436$	−1.80414	−0.0864026
$437$	−55.1850	−2.63985
$438$	−2.70360	−0.129183
$439$	24.2048	1.15523	0.577616	−	0.816308i	$-0.303983\pi$
$439$	24.2048	1.15523	0.577616	+	0.816308i	$0.303983\pi$
$440$	3.72578	0.177619
$441$	14.2862	0.680296
$442$	16.7110	0.794861
$443$	2.98360	0.141755	0.0708775	−	0.997485i	$-0.477420\pi$
$443$	2.98360	0.141755	0.0708775	+	0.997485i	$0.477420\pi$
$444$	8.23988	0.391048
$445$	7.17232	0.340000
$446$	−4.04328	−0.191455
$447$	4.50712	0.213179
$448$	−1.04704	−0.0494681
$449$	11.0148	0.519823	0.259911	−	0.965632i	$-0.416307\pi$
$449$	11.0148	0.519823	0.259911	+	0.965632i	$0.416307\pi$
$450$	11.0249	0.519720
$451$	15.1523	0.713492
$452$	18.0034	0.846808
$453$	2.79871	0.131495
$454$	6.90052	0.323857
$455$	−3.94228	−0.184817
$456$	−5.36147	−0.251074
$457$	28.8630	1.35016	0.675078	−	0.737747i	$-0.264110\pi$
$457$	28.8630	1.35016	0.675078	+	0.737747i	$0.264110\pi$
$458$	14.9265	0.697468
$459$	−12.2085	−0.569846
$460$	5.22387	0.243564
$461$	−17.1765	−0.799990	−0.399995	−	0.916517i	$-0.630988\pi$
$461$	−17.1765	−0.799990	−0.399995	+	0.916517i	$0.630988\pi$
$462$	−4.45910	−0.207456
$463$	−38.8759	−1.80672	−0.903358	−	0.428887i	$-0.858906\pi$
$463$	−38.8759	−1.80672	−0.903358	+	0.428887i	$0.858906\pi$
$464$	−6.27325	−0.291228
$465$	2.80859	0.130245
$466$	−9.07074	−0.420194
$467$	2.22089	0.102770	0.0513852	−	0.998679i	$-0.483636\pi$
$467$	2.22089	0.102770	0.0513852	+	0.998679i	$0.483636\pi$
$468$	−13.6735	−0.632060
$469$	14.7556	0.681349
$470$	3.25682	0.150226
$471$	1.00736	0.0464165
$472$	1.28571	0.0591794
$473$	−52.4571	−2.41198
$474$	6.09568	0.279984
$475$	32.0705	1.47150
$476$	−3.09655	−0.141930
$477$	−9.64536	−0.441631
$478$	−5.66975	−0.259328
$479$	12.6800	0.579362	0.289681	−	0.957123i	$-0.406451\pi$
$479$	12.6800	0.579362	0.289681	+	0.957123i	$0.406451\pi$
$480$	0.507523	0.0231651
$481$	61.1292	2.78725
$482$	3.75268	0.170930
$483$	−6.25206	−0.284478
$484$	20.2640	0.921092
$485$	1.60905	0.0730630
$486$	15.5188	0.703949
$487$	18.4031	0.833924	0.416962	−	0.908924i	$-0.363095\pi$
$487$	18.4031	0.833924	0.416962	+	0.908924i	$0.363095\pi$
$488$	−2.84008	−0.128564
$489$	−7.00896	−0.316956
$490$	−3.93386	−0.177714
$491$	−4.52337	−0.204137	−0.102068	−	0.994777i	$-0.532546\pi$
$491$	−4.52337	−0.204137	−0.102068	+	0.994777i	$0.532546\pi$
$492$	2.06403	0.0930536
$493$	−18.5527	−0.835571
$494$	−39.7751	−1.78957
$495$	−9.01591	−0.405235
$496$	5.53392	0.248481
$497$	−15.4848	−0.694588
$498$	−0.397054	−0.0177924
$499$	43.5028	1.94745	0.973726	−	0.227722i	$-0.0731277\pi$
$499$	43.5028	1.94745	0.973726	+	0.227722i	$0.0731277\pi$
$500$	−6.36752	−0.284764
$501$	4.53444	0.202584
$502$	−14.7879	−0.660014
$503$	16.1436	0.719810	0.359905	−	0.932989i	$-0.382809\pi$
$503$	16.1436	0.719810	0.359905	+	0.932989i	$0.382809\pi$
$504$	2.53371	0.112860
$505$	−4.74011	−0.210932
$506$	43.8349	1.94870
$507$	14.4170	0.640280
$508$	2.94717	0.130760
$509$	−24.2281	−1.07389	−0.536946	−	0.843617i	$-0.680422\pi$
$509$	−24.2281	−1.07389	−0.536946	+	0.843617i	$0.680422\pi$
$510$	1.50096	0.0664636
$511$	3.71660	0.164413
$512$	1.00000	0.0441942
$513$	29.0585	1.28296
$514$	−27.9458	−1.23264
$515$	7.98337	0.351789
$516$	−7.14566	−0.314570
$517$	27.3289	1.20192
$518$	−11.3272	−0.497691
$519$	8.87728	0.389670
$520$	3.76515	0.165113
$521$	21.1461	0.926426	0.463213	−	0.886247i	$-0.346696\pi$
$521$	21.1461	0.926426	0.463213	+	0.886247i	$0.346696\pi$
$522$	15.1805	0.664432
$523$	−23.7701	−1.03940	−0.519698	−	0.854350i	$-0.673955\pi$
$523$	−23.7701	−1.03940	−0.519698	+	0.854350i	$0.673955\pi$
$524$	7.32746	0.320102
$525$	3.63336	0.158573
$526$	−4.30098	−0.187532
$527$	16.3662	0.712922
$528$	4.25876	0.185339
$529$	38.4604	1.67219
$530$	2.65595	0.115367
$531$	−3.11125	−0.135017
$532$	7.37033	0.319544
$533$	15.3124	0.663254
$534$	8.19834	0.354777
$535$	−7.17226	−0.310084
$536$	−14.0926	−0.608708
$537$	2.12598	0.0917430
$538$	−1.00842	−0.0434761
$539$	−33.0101	−1.42185
$540$	−2.75071	−0.118372
$541$	−12.6751	−0.544945	−0.272473	−	0.962164i	$-0.587841\pi$
$541$	−12.6751	−0.544945	−0.272473	+	0.962164i	$0.587841\pi$
$542$	−19.7572	−0.848644
$543$	−13.4922	−0.579006
$544$	2.95743	0.126799
$545$	−1.20217	−0.0514951
$546$	−4.50623	−0.192849
$547$	−8.35543	−0.357252	−0.178626	−	0.983917i	$-0.557165\pi$
$547$	−8.35543	−0.357252	−0.178626	+	0.983917i	$0.557165\pi$
$548$	−3.30748	−0.141288
$549$	6.87264	0.293317
$550$	−25.4745	−1.08624
$551$	44.1586	1.88122
$552$	5.97116	0.254149
$553$	−8.37965	−0.356339
$554$	−28.6740	−1.21824
$555$	5.49055	0.233061
$556$	−14.0592	−0.596244
$557$	−25.5790	−1.08382	−0.541908	−	0.840438i	$-0.682298\pi$
$557$	−25.5790	−1.08382	−0.541908	+	0.840438i	$0.682298\pi$
$558$	−13.3914	−0.566903
$559$	−53.0115	−2.24215
$560$	−0.697684	−0.0294825
$561$	12.5950	0.531760
$562$	16.1533	0.681385
$563$	40.2010	1.69427	0.847135	−	0.531378i	$-0.178326\pi$
$563$	40.2010	1.69427	0.847135	+	0.531378i	$0.178326\pi$
$564$	3.72272	0.156755
$565$	11.9963	0.504689
$566$	−29.4514	−1.23794
$567$	−4.30902	−0.180962
$568$	14.7891	0.620536
$569$	6.19765	0.259819	0.129909	−	0.991526i	$-0.458531\pi$
$569$	6.19765	0.259819	0.129909	+	0.991526i	$0.458531\pi$
$570$	−3.57255	−0.149638
$571$	7.06289	0.295573	0.147786	−	0.989019i	$-0.452785\pi$
$571$	7.06289	0.295573	0.147786	+	0.989019i	$0.452785\pi$
$572$	31.5944	1.32103
$573$	14.7014	0.614159
$574$	−2.83739	−0.118430
$575$	−35.7175	−1.48952
$576$	−2.41987	−0.100828
$577$	18.8456	0.784553	0.392276	−	0.919847i	$-0.371688\pi$
$577$	18.8456	0.784553	0.392276	+	0.919847i	$0.371688\pi$
$578$	−8.25363	−0.343306
$579$	−19.1726	−0.796788
$580$	−4.18011	−0.173569
$581$	0.545824	0.0226446
$582$	1.83923	0.0762384
$583$	22.2868	0.923025
$584$	−3.54962	−0.146884
$585$	−9.11120	−0.376702
$586$	1.74817	0.0722164
$587$	32.3480	1.33515	0.667573	−	0.744544i	$-0.267333\pi$
$587$	32.3480	1.33515	0.667573	+	0.744544i	$0.267333\pi$
$588$	−4.49661	−0.185437
$589$	−38.9544	−1.60509
$590$	0.856714	0.0352704
$591$	−7.56224	−0.311069
$592$	10.8183	0.444631
$593$	−32.0776	−1.31727	−0.658634	−	0.752463i	$-0.728865\pi$
$593$	−32.0776	−1.31727	−0.658634	+	0.752463i	$0.728865\pi$
$594$	−23.0820	−0.947064
$595$	−2.06335	−0.0845890
$596$	5.91750	0.242390
$597$	2.81539	0.115226
$598$	44.2982	1.81149
$599$	37.5812	1.53552	0.767762	−	0.640735i	$-0.221370\pi$
$599$	37.5812	1.53552	0.767762	+	0.640735i	$0.221370\pi$
$600$	−3.47012	−0.141667
$601$	−2.86134	−0.116716	−0.0583582	−	0.998296i	$-0.518587\pi$
$601$	−2.86134	−0.116716	−0.0583582	+	0.998296i	$0.518587\pi$
$602$	9.82303	0.400357
$603$	34.1024	1.38876
$604$	3.67450	0.149513
$605$	13.5027	0.548962
$606$	−5.41820	−0.220099
$607$	35.0684	1.42338	0.711690	−	0.702493i	$-0.247930\pi$
$607$	35.0684	1.42338	0.711690	+	0.702493i	$0.247930\pi$
$608$	−7.03919	−0.285477
$609$	5.00285	0.202726
$610$	−1.89245	−0.0766232
$611$	27.6177	1.11729
$612$	−7.15660	−0.289288
$613$	−9.37554	−0.378674	−0.189337	−	0.981912i	$-0.560634\pi$
$613$	−9.37554	−0.378674	−0.189337	+	0.981912i	$0.560634\pi$
$614$	−0.989292	−0.0399246
$615$	1.37534	0.0554591
$616$	−5.85446	−0.235883
$617$	−33.5515	−1.35073	−0.675366	−	0.737483i	$-0.736014\pi$
$617$	−33.5515	−1.35073	−0.675366	+	0.737483i	$0.736014\pi$
$618$	9.12541	0.367078
$619$	9.41015	0.378226	0.189113	−	0.981955i	$-0.439439\pi$
$619$	9.41015	0.378226	0.189113	+	0.981955i	$0.439439\pi$
$620$	3.68746	0.148092
$621$	−32.3629	−1.29868
$622$	33.9195	1.36005
$623$	−11.2701	−0.451529
$624$	4.30377	0.172289
$625$	18.5371	0.741482
$626$	−6.28253	−0.251101
$627$	−29.9782	−1.19722
$628$	1.32258	0.0527767
$629$	31.9944	1.27570
$630$	1.68831	0.0672638
$631$	−30.1556	−1.20048	−0.600238	−	0.799822i	$-0.704927\pi$
$631$	−30.1556	−1.20048	−0.600238	+	0.799822i	$0.704927\pi$
$632$	8.00316	0.318349
$633$	2.35443	0.0935803
$634$	−1.01507	−0.0403134
$635$	1.96381	0.0779315
$636$	3.03589	0.120381
$637$	−33.3590	−1.32173
$638$	−35.0764	−1.38869
$639$	−35.7877	−1.41574
$640$	0.666338	0.0263393
$641$	−42.4609	−1.67710	−0.838552	−	0.544822i	$-0.816597\pi$
$641$	−42.4609	−1.67710	−0.838552	+	0.544822i	$0.816597\pi$
$642$	−8.19828	−0.323560
$643$	−22.2961	−0.879273	−0.439637	−	0.898176i	$-0.644893\pi$
$643$	−22.2961	−0.879273	−0.439637	+	0.898176i	$0.644893\pi$
$644$	−8.20847	−0.323459
$645$	−4.76142	−0.187481
$646$	−20.8179	−0.819069
$647$	24.3101	0.955728	0.477864	−	0.878434i	$-0.341411\pi$
$647$	24.3101	0.955728	0.477864	+	0.878434i	$0.341411\pi$
$648$	4.11542	0.161669
$649$	7.18892	0.282190
$650$	−25.7437	−1.00975
$651$	−4.41325	−0.172969
$652$	−9.20222	−0.360387
$653$	−4.14117	−0.162057	−0.0810283	−	0.996712i	$-0.525820\pi$
$653$	−4.14117	−0.162057	−0.0810283	+	0.996712i	$0.525820\pi$
$654$	−1.37414	−0.0537331
$655$	4.88257	0.190778
$656$	2.70991	0.105804
$657$	8.58963	0.335113
$658$	−5.11756	−0.199503
$659$	12.9339	0.503832	0.251916	−	0.967749i	$-0.418939\pi$
$659$	12.9339	0.503832	0.251916	+	0.967749i	$0.418939\pi$
$660$	2.83777	0.110460
$661$	−36.0697	−1.40295	−0.701475	−	0.712694i	$-0.747475\pi$
$661$	−36.0697	−1.40295	−0.701475	+	0.712694i	$0.747475\pi$
$662$	−21.0786	−0.819244
$663$	12.7281	0.494318
$664$	−0.521301	−0.0202304
$665$	4.91113	0.190446
$666$	−26.1790	−1.01442
$667$	−49.1802	−1.90427
$668$	5.95338	0.230343
$669$	−3.07960	−0.119064
$670$	−9.39045	−0.362785
$671$	−15.8801	−0.613045
$672$	−0.797490	−0.0307638
$673$	−2.40775	−0.0928118	−0.0464059	−	0.998923i	$-0.514777\pi$
$673$	−2.40775	−0.0928118	−0.0464059	+	0.998923i	$0.514777\pi$
$674$	−17.8275	−0.686689
$675$	18.8076	0.723905
$676$	18.9284	0.728014
$677$	−39.5256	−1.51909	−0.759547	−	0.650452i	$-0.774579\pi$
$677$	−39.5256	−1.51909	−0.759547	+	0.650452i	$0.774579\pi$
$678$	13.7124	0.526623
$679$	−2.52836	−0.0970294
$680$	1.97065	0.0755708
$681$	5.25585	0.201404
$682$	30.9425	1.18485
$683$	2.87598	0.110046	0.0550231	−	0.998485i	$-0.482477\pi$
$683$	2.87598	0.110046	0.0550231	+	0.998485i	$0.482477\pi$
$684$	17.0340	0.651310
$685$	−2.20390	−0.0842066
$686$	13.5107	0.515842
$687$	11.3689	0.433750
$688$	−9.38170	−0.357674
$689$	22.5224	0.858033
$690$	3.97881	0.151471
$691$	−11.7448	−0.446795	−0.223397	−	0.974727i	$-0.571715\pi$
$691$	−11.7448	−0.446795	−0.223397	+	0.974727i	$0.571715\pi$
$692$	11.6552	0.443064
$693$	14.1671	0.538162
$694$	−20.3991	−0.774338
$695$	−9.36820	−0.355356
$696$	−4.77808	−0.181113
$697$	8.01436	0.303566
$698$	−30.5134	−1.15495
$699$	−6.90882	−0.261315
$700$	4.77032	0.180301
$701$	−37.2560	−1.40714	−0.703570	−	0.710626i	$-0.748412\pi$
$701$	−37.2560	−1.40714	−0.703570	+	0.710626i	$0.748412\pi$
$702$	−23.3259	−0.880379
$703$	−76.1523	−2.87214
$704$	5.59142	0.210735
$705$	2.48059	0.0934243
$706$	−9.66357	−0.363693
$707$	7.44832	0.280123
$708$	0.979270	0.0368032
$709$	−44.9012	−1.68630	−0.843150	−	0.537679i	$-0.819301\pi$
$709$	−44.9012	−1.68630	−0.843150	+	0.537679i	$0.819301\pi$
$710$	9.85452	0.369834
$711$	−19.3666	−0.726306
$712$	10.7638	0.403390
$713$	43.3841	1.62475
$714$	−2.35852	−0.0882653
$715$	21.0526	0.787322
$716$	2.79125	0.104314
$717$	−4.31842	−0.161274
$718$	−33.1792	−1.23824
$719$	−31.3925	−1.17074	−0.585372	−	0.810765i	$-0.699052\pi$
$719$	−31.3925	−1.17074	−0.585372	+	0.810765i	$0.699052\pi$
$720$	−1.61245	−0.0600926
$721$	−12.5446	−0.467184
$722$	30.5502	1.13696
$723$	2.85826	0.106300
$724$	−17.7142	−0.658345
$725$	28.5809	1.06147
$726$	15.4343	0.572820
$727$	−22.7270	−0.842898	−0.421449	−	0.906852i	$-0.638478\pi$
$727$	−22.7270	−0.842898	−0.421449	+	0.906852i	$0.638478\pi$
$728$	−5.91633	−0.219274
$729$	−0.526182	−0.0194882
$730$	−2.36524	−0.0875416
$731$	−27.7457	−1.02621
$732$	−2.16318	−0.0799533
$733$	−22.0263	−0.813559	−0.406780	−	0.913526i	$-0.633348\pi$
$733$	−22.0263	−0.813559	−0.406780	+	0.913526i	$0.633348\pi$
$734$	8.02979	0.296385
$735$	−2.99626	−0.110519
$736$	7.83967	0.288974
$737$	−78.7978	−2.90255
$738$	−6.55764	−0.241390
$739$	6.14363	0.225997	0.112999	−	0.993595i	$-0.463954\pi$
$739$	6.14363	0.225997	0.112999	+	0.993595i	$0.463954\pi$
$740$	7.20866	0.264996
$741$	−30.2951	−1.11292
$742$	−4.17340	−0.153210
$743$	−16.7051	−0.612851	−0.306425	−	0.951895i	$-0.599133\pi$
$743$	−16.7051	−0.612851	−0.306425	+	0.951895i	$0.599133\pi$
$744$	4.21497	0.154528
$745$	3.94305	0.144462
$746$	−33.3927	−1.22259
$747$	1.26148	0.0461553
$748$	16.5362	0.604624
$749$	11.2701	0.411799
$750$	−4.84988	−0.177093
$751$	−31.4036	−1.14593	−0.572966	−	0.819579i	$-0.694207\pi$
$751$	−31.4036	−1.14593	−0.572966	+	0.819579i	$0.694207\pi$
$752$	4.88764	0.178234
$753$	−11.2633	−0.410458
$754$	−35.4471	−1.29091
$755$	2.44846	0.0891084
$756$	4.32229	0.157200
$757$	23.7799	0.864297	0.432148	−	0.901803i	$-0.357756\pi$
$757$	23.7799	0.864297	0.432148	+	0.901803i	$0.357756\pi$
$758$	3.83439	0.139271
$759$	33.3873	1.21188
$760$	−4.69048	−0.170142
$761$	−2.40185	−0.0870670	−0.0435335	−	0.999052i	$-0.513862\pi$
$761$	−2.40185	−0.0870670	−0.0435335	+	0.999052i	$0.513862\pi$
$762$	2.24474	0.0813184
$763$	1.88901	0.0683867
$764$	19.3018	0.698313
$765$	−4.76871	−0.172413
$766$	−26.5822	−0.960453
$767$	7.26490	0.262320
$768$	0.761659	0.0274840
$769$	6.86260	0.247472	0.123736	−	0.992315i	$-0.460512\pi$
$769$	6.86260	0.247472	0.123736	+	0.992315i	$0.460512\pi$
$770$	−3.90105	−0.140584
$771$	−21.2852	−0.766567
$772$	−25.1722	−0.905967
$773$	14.3988	0.517890	0.258945	−	0.965892i	$-0.416625\pi$
$773$	14.3988	0.517890	0.258945	+	0.965892i	$0.416625\pi$
$774$	22.7025	0.816026
$775$	−25.2125	−0.905661
$776$	2.41476	0.0866849
$777$	−8.62751	−0.309510
$778$	33.3124	1.19431
$779$	−19.0756	−0.683454
$780$	2.86777	0.102682
$781$	82.6920	2.95895
$782$	23.1852	0.829103
$783$	25.8966	0.925469
$784$	−5.90370	−0.210847
$785$	0.881286	0.0314544
$786$	5.58103	0.199069
$787$	−2.08160	−0.0742012	−0.0371006	−	0.999312i	$-0.511812\pi$
$787$	−2.08160	−0.0742012	−0.0371006	+	0.999312i	$0.511812\pi$
$788$	−9.92864	−0.353693
$789$	−3.27588	−0.116625
$790$	5.33281	0.189733
$791$	−18.8503	−0.670239
$792$	−13.5305	−0.480787
$793$	−16.0479	−0.569879
$794$	−6.20757	−0.220299
$795$	2.02293	0.0717459
$796$	3.69638	0.131015
$797$	45.1832	1.60047	0.800235	−	0.599686i	$-0.204708\pi$
$797$	45.1832	1.60047	0.800235	+	0.599686i	$0.204708\pi$
$798$	5.61368	0.198722
$799$	14.4548	0.511375
$800$	−4.55599	−0.161079
$801$	−26.0470	−0.920326
$802$	7.34814	0.259472
$803$	−19.8474	−0.700400
$804$	−10.7338	−0.378551
$805$	−5.46961	−0.192778
$806$	31.2695	1.10142
$807$	−0.768074	−0.0270375
$808$	−7.11368	−0.250258
$809$	−43.0440	−1.51335	−0.756673	−	0.653794i	$-0.773176\pi$
$809$	−43.0440	−1.51335	−0.756673	+	0.653794i	$0.773176\pi$
$810$	2.74226	0.0963532
$811$	45.6549	1.60316	0.801581	−	0.597887i	$-0.203993\pi$
$811$	45.6549	1.60316	0.801581	+	0.597887i	$0.203993\pi$
$812$	6.56836	0.230504
$813$	−15.0483	−0.527765
$814$	60.4899	2.12017
$815$	−6.13179	−0.214787
$816$	2.25255	0.0788551
$817$	66.0396	2.31043
$818$	−34.0224	−1.18956
$819$	14.3168	0.500269
$820$	1.80572	0.0630583
$821$	0.521464	0.0181992	0.00909961	−	0.999959i	$-0.497103\pi$
$821$	0.521464	0.0181992	0.00909961	+	0.999959i	$0.497103\pi$
$822$	−2.51917	−0.0878662
$823$	−15.6542	−0.545669	−0.272835	−	0.962061i	$-0.587961\pi$
$823$	−15.6542	−0.545669	−0.272835	+	0.962061i	$0.587961\pi$
$824$	11.9810	0.417377
$825$	−19.4029	−0.675522
$826$	−1.34619	−0.0468399
$827$	41.7664	1.45236	0.726180	−	0.687505i	$-0.241294\pi$
$827$	41.7664	1.45236	0.726180	+	0.687505i	$0.241294\pi$
$828$	−18.9710	−0.659289
$829$	55.8440	1.93954	0.969772	−	0.244013i	$-0.0784639\pi$
$829$	55.8440	1.93954	0.969772	+	0.244013i	$0.0784639\pi$
$830$	−0.347363	−0.0120571
$831$	−21.8398	−0.757616
$832$	5.65052	0.195896
$833$	−17.4598	−0.604945
$834$	−10.7083	−0.370800
$835$	3.96696	0.137282
$836$	−39.3591	−1.36126
$837$	−22.8446	−0.789624
$838$	−29.8923	−1.03261
$839$	−6.06892	−0.209522	−0.104761	−	0.994497i	$-0.533408\pi$
$839$	−6.06892	−0.209522	−0.104761	+	0.994497i	$0.533408\pi$
$840$	−0.531398	−0.0183350
$841$	10.3537	0.357025
$842$	31.7449	1.09400
$843$	12.3033	0.423748
$844$	3.09119	0.106403
$845$	12.6127	0.433890
$846$	−11.8275	−0.406637
$847$	−21.2173	−0.729035
$848$	3.98589	0.136876
$849$	−22.4320	−0.769863
$850$	−13.4740	−0.462155
$851$	84.8121	2.90732
$852$	11.2642	0.385907
$853$	37.4421	1.28199	0.640996	−	0.767544i	$-0.278522\pi$
$853$	37.4421	1.28199	0.640996	+	0.767544i	$0.278522\pi$
$854$	2.97369	0.101757
$855$	11.3504	0.388175
$856$	−10.7637	−0.367896
$857$	−14.5521	−0.497092	−0.248546	−	0.968620i	$-0.579953\pi$
$857$	−14.5521	−0.497092	−0.248546	+	0.968620i	$0.579953\pi$
$858$	24.0642	0.821539
$859$	−42.7404	−1.45828	−0.729141	−	0.684363i	$-0.760080\pi$
$859$	−42.7404	−1.45828	−0.729141	+	0.684363i	$0.760080\pi$
$860$	−6.25138	−0.213170
$861$	−2.16113	−0.0736510
$862$	−28.3601	−0.965950
$863$	32.6558	1.11162	0.555808	−	0.831310i	$-0.312409\pi$
$863$	32.6558	1.11162	0.555808	+	0.831310i	$0.312409\pi$
$864$	−4.12810	−0.140441
$865$	7.76629	0.264062
$866$	35.0024	1.18943
$867$	−6.28645	−0.213499
$868$	−5.79425	−0.196670
$869$	44.7491	1.51801
$870$	−3.18382	−0.107942
$871$	−79.6306	−2.69818
$872$	−1.80414	−0.0610958
$873$	−5.84342	−0.197770
$874$	−55.1850	−1.86666
$875$	6.66706	0.225388
$876$	−2.70360	−0.0913461
$877$	−20.8502	−0.704061	−0.352031	−	0.935988i	$-0.614509\pi$
$877$	−20.8502	−0.704061	−0.352031	+	0.935988i	$0.614509\pi$
$878$	24.2048	0.816873
$879$	1.33151	0.0449108
$880$	3.72578	0.125596
$881$	−0.118535	−0.00399356	−0.00199678	−	0.999998i	$-0.500636\pi$
$881$	−0.118535	−0.00399356	−0.00199678	+	0.999998i	$0.500636\pi$
$882$	14.2862	0.481042
$883$	46.9582	1.58027	0.790135	−	0.612933i	$-0.210010\pi$
$883$	46.9582	1.58027	0.790135	+	0.612933i	$0.210010\pi$
$884$	16.7110	0.562052
$885$	0.652524	0.0219344
$886$	2.98360	0.100236
$887$	21.3344	0.716340	0.358170	−	0.933656i	$-0.383401\pi$
$887$	21.3344	0.716340	0.358170	+	0.933656i	$0.383401\pi$
$888$	8.23988	0.276512
$889$	−3.08581	−0.103495
$890$	7.17232	0.240417
$891$	23.0111	0.770899
$892$	−4.04328	−0.135379
$893$	−34.4050	−1.15132
$894$	4.50712	0.150741
$895$	1.85992	0.0621702
$896$	−1.04704	−0.0349792
$897$	33.7401	1.12655
$898$	11.0148	0.367570
$899$	−34.7157	−1.15783
$900$	11.0249	0.367498
$901$	11.7880	0.392715
$902$	15.1523	0.504515
$903$	7.48181	0.248979
$904$	18.0034	0.598783
$905$	−11.8037	−0.392367
$906$	2.79871	0.0929811
$907$	−43.4282	−1.44201	−0.721005	−	0.692930i	$-0.756320\pi$
$907$	−43.4282	−1.44201	−0.721005	+	0.692930i	$0.756320\pi$
$908$	6.90052	0.229002
$909$	17.2142	0.570960
$910$	−3.94228	−0.130685
$911$	31.9107	1.05725	0.528624	−	0.848856i	$-0.322708\pi$
$911$	31.9107	1.05725	0.528624	+	0.848856i	$0.322708\pi$
$912$	−5.36147	−0.177536
$913$	−2.91481	−0.0964663
$914$	28.8630	0.954704
$915$	−1.44141	−0.0476514
$916$	14.9265	0.493184
$917$	−7.67216	−0.253357
$918$	−12.2085	−0.402942
$919$	24.1285	0.795927	0.397963	−	0.917401i	$-0.369717\pi$
$919$	24.1285	0.795927	0.397963	+	0.917401i	$0.369717\pi$
$920$	5.22387	0.172226
$921$	−0.753504	−0.0248288
$922$	−17.1765	−0.565679
$923$	83.5660	2.75061
$924$	−4.45910	−0.146694
$925$	−49.2882	−1.62059
$926$	−38.8759	−1.27754
$927$	−28.9924	−0.952236
$928$	−6.27325	−0.205930
$929$	−44.0424	−1.44498	−0.722492	−	0.691380i	$-0.757003\pi$
$929$	−44.0424	−1.44498	−0.722492	+	0.691380i	$0.757003\pi$
$930$	2.80859	0.0920973
$931$	41.5573	1.36199
$932$	−9.07074	−0.297122
$933$	25.8351	0.845803
$934$	2.22089	0.0726697
$935$	11.0187	0.360350
$936$	−13.6735	−0.446934
$937$	2.20423	0.0720092	0.0360046	−	0.999352i	$-0.488537\pi$
$937$	2.20423	0.0720092	0.0360046	+	0.999352i	$0.488537\pi$
$938$	14.7556	0.481786
$939$	−4.78515	−0.156158
$940$	3.25682	0.106226
$941$	−13.0209	−0.424468	−0.212234	−	0.977219i	$-0.568074\pi$
$941$	−13.0209	−0.424468	−0.212234	+	0.977219i	$0.568074\pi$
$942$	1.00736	0.0328214
$943$	21.2448	0.691826
$944$	1.28571	0.0418461
$945$	2.88011	0.0936899
$946$	−52.4571	−1.70553
$947$	−18.9339	−0.615270	−0.307635	−	0.951504i	$-0.599538\pi$
$947$	−18.9339	−0.615270	−0.307635	+	0.951504i	$0.599538\pi$
$948$	6.09568	0.197979
$949$	−20.0572	−0.651083
$950$	32.0705	1.04051
$951$	−0.773134	−0.0250706
$952$	−3.09655	−0.100360
$953$	21.5972	0.699603	0.349801	−	0.936824i	$-0.386249\pi$
$953$	21.5972	0.699603	0.349801	+	0.936824i	$0.386249\pi$
$954$	−9.64536	−0.312280
$955$	12.8615	0.416188
$956$	−5.66975	−0.183373
$957$	−26.7163	−0.863615
$958$	12.6800	0.409671
$959$	3.46307	0.111828
$960$	0.507523	0.0163802
$961$	−0.375683	−0.0121188
$962$	61.1292	1.97088
$963$	26.0468	0.839347
$964$	3.75268	0.120866
$965$	−16.7732	−0.539948
$966$	−6.25206	−0.201157
$967$	10.5639	0.339713	0.169857	−	0.985469i	$-0.445670\pi$
$967$	10.5639	0.339713	0.169857	+	0.985469i	$0.445670\pi$
$968$	20.2640	0.651310
$969$	−15.8561	−0.509373
$970$	1.60905	0.0516634
$971$	−50.3719	−1.61651	−0.808255	−	0.588832i	$-0.799588\pi$
$971$	−50.3719	−1.61651	−0.808255	+	0.588832i	$0.799588\pi$
$972$	15.5188	0.497767
$973$	14.7206	0.471921
$974$	18.4031	0.589673
$975$	−19.6080	−0.627957
$976$	−2.84008	−0.0909088
$977$	8.71944	0.278960	0.139480	−	0.990225i	$-0.455457\pi$
$977$	8.71944	0.278960	0.139480	+	0.990225i	$0.455457\pi$
$978$	−7.00896	−0.224122
$979$	60.1849	1.92352
$980$	−3.93386	−0.125663
$981$	4.36579	0.139389
$982$	−4.52337	−0.144347
$983$	0.130362	0.00415790	0.00207895	−	0.999998i	$-0.499338\pi$
$983$	0.130362	0.00415790	0.00207895	+	0.999998i	$0.499338\pi$
$984$	2.06403	0.0657988
$985$	−6.61583	−0.210798
$986$	−18.5527	−0.590838
$987$	−3.89784	−0.124070
$988$	−39.7751	−1.26541
$989$	−73.5494	−2.33874
$990$	−9.01591	−0.286545
$991$	−2.66998	−0.0848146	−0.0424073	−	0.999100i	$-0.513503\pi$
$991$	−2.66998	−0.0848146	−0.0424073	+	0.999100i	$0.513503\pi$
$992$	5.53392	0.175702
$993$	−16.0547	−0.509481
$994$	−15.4848	−0.491148
$995$	2.46304	0.0780836
$996$	−0.397054	−0.0125811
$997$	10.0845	0.319378	0.159689	−	0.987167i	$-0.448951\pi$
$997$	10.0845	0.319378	0.159689	+	0.987167i	$0.448951\pi$
$998$	43.5028	1.37706
$999$	−44.6591	−1.41295

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.28	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.28	✓	50	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.761659 q^{3} +1.00000 q^{4} +0.666338 q^{5} +0.761659 q^{6} -1.04704 q^{7} +1.00000 q^{8} -2.41987 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.761659 q^{3} +1.00000 q^{4} +0.666338 q^{5} +0.761659 q^{6} -1.04704 q^{7} +1.00000 q^{8} -2.41987 q^{9} +0.666338 q^{10} +5.59142 q^{11} +0.761659 q^{12} +5.65052 q^{13} -1.04704 q^{14} +0.507523 q^{15} +1.00000 q^{16} +2.95743 q^{17} -2.41987 q^{18} -7.03919 q^{19} +0.666338 q^{20} -0.797490 q^{21} +5.59142 q^{22} +7.83967 q^{23} +0.761659 q^{24} -4.55599 q^{25} +5.65052 q^{26} -4.12810 q^{27} -1.04704 q^{28} -6.27325 q^{29} +0.507523 q^{30} +5.53392 q^{31} +1.00000 q^{32} +4.25876 q^{33} +2.95743 q^{34} -0.697684 q^{35} -2.41987 q^{36} +10.8183 q^{37} -7.03919 q^{38} +4.30377 q^{39} +0.666338 q^{40} +2.70991 q^{41} -0.797490 q^{42} -9.38170 q^{43} +5.59142 q^{44} -1.61245 q^{45} +7.83967 q^{46} +4.88764 q^{47} +0.761659 q^{48} -5.90370 q^{49} -4.55599 q^{50} +2.25255 q^{51} +5.65052 q^{52} +3.98589 q^{53} -4.12810 q^{54} +3.72578 q^{55} -1.04704 q^{56} -5.36147 q^{57} -6.27325 q^{58} +1.28571 q^{59} +0.507523 q^{60} -2.84008 q^{61} +5.53392 q^{62} +2.53371 q^{63} +1.00000 q^{64} +3.76515 q^{65} +4.25876 q^{66} -14.0926 q^{67} +2.95743 q^{68} +5.97116 q^{69} -0.697684 q^{70} +14.7891 q^{71} -2.41987 q^{72} -3.54962 q^{73} +10.8183 q^{74} -3.47012 q^{75} -7.03919 q^{76} -5.85446 q^{77} +4.30377 q^{78} +8.00316 q^{79} +0.666338 q^{80} +4.11542 q^{81} +2.70991 q^{82} -0.521301 q^{83} -0.797490 q^{84} +1.97065 q^{85} -9.38170 q^{86} -4.77808 q^{87} +5.59142 q^{88} +10.7638 q^{89} -1.61245 q^{90} -5.91633 q^{91} +7.83967 q^{92} +4.21497 q^{93} +4.88764 q^{94} -4.69048 q^{95} +0.761659 q^{96} +2.41476 q^{97} -5.90370 q^{98} -13.5305 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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