LMFDB - Embedded newform 4019.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21437 q^{2} +0.176199 q^{3} +2.90346 q^{4} +3.35713 q^{5} -0.390170 q^{6} +0.00990688 q^{7} -2.00059 q^{8} -2.96895 q^{9} +O(q^{10})$	\(q-2.21437 q^{2} +0.176199 q^{3} +2.90346 q^{4} +3.35713 q^{5} -0.390170 q^{6} +0.00990688 q^{7} -2.00059 q^{8} -2.96895 q^{9} -7.43394 q^{10} -0.392889 q^{11} +0.511585 q^{12} -1.15909 q^{13} -0.0219376 q^{14} +0.591521 q^{15} -1.37686 q^{16} -5.09337 q^{17} +6.57438 q^{18} -2.83746 q^{19} +9.74727 q^{20} +0.00174558 q^{21} +0.870004 q^{22} -0.717103 q^{23} -0.352501 q^{24} +6.27031 q^{25} +2.56667 q^{26} -1.05172 q^{27} +0.0287642 q^{28} +4.62982 q^{29} -1.30985 q^{30} +2.91239 q^{31} +7.05005 q^{32} -0.0692265 q^{33} +11.2786 q^{34} +0.0332587 q^{35} -8.62023 q^{36} +2.11454 q^{37} +6.28320 q^{38} -0.204231 q^{39} -6.71624 q^{40} +2.30501 q^{41} -0.00386536 q^{42} +11.2877 q^{43} -1.14074 q^{44} -9.96716 q^{45} +1.58794 q^{46} +0.624900 q^{47} -0.242600 q^{48} -6.99990 q^{49} -13.8848 q^{50} -0.897444 q^{51} -3.36538 q^{52} -11.5233 q^{53} +2.32890 q^{54} -1.31898 q^{55} -0.0198196 q^{56} -0.499956 q^{57} -10.2522 q^{58} +2.20073 q^{59} +1.71745 q^{60} +4.89909 q^{61} -6.44911 q^{62} -0.0294131 q^{63} -12.8578 q^{64} -3.89123 q^{65} +0.153293 q^{66} -5.77083 q^{67} -14.7884 q^{68} -0.126352 q^{69} -0.0736472 q^{70} +2.96015 q^{71} +5.93966 q^{72} +11.0843 q^{73} -4.68239 q^{74} +1.10482 q^{75} -8.23844 q^{76} -0.00389231 q^{77} +0.452243 q^{78} -14.1501 q^{79} -4.62228 q^{80} +8.72155 q^{81} -5.10416 q^{82} -14.8114 q^{83} +0.00506821 q^{84} -17.0991 q^{85} -24.9953 q^{86} +0.815767 q^{87} +0.786011 q^{88} +6.96676 q^{89} +22.0710 q^{90} -0.0114830 q^{91} -2.08208 q^{92} +0.513158 q^{93} -1.38376 q^{94} -9.52572 q^{95} +1.24221 q^{96} +6.53784 q^{97} +15.5004 q^{98} +1.16647 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.21437	−1.56580	−0.782900	−	0.622148i	$-0.786260\pi$
$2$	−2.21437	−1.56580	−0.782900	+	0.622148i	$0.786260\pi$
$3$	0.176199	0.101728	0.0508641	−	0.998706i	$-0.483802\pi$
$3$	0.176199	0.101728	0.0508641	+	0.998706i	$0.483802\pi$
$4$	2.90346	1.45173
$5$	3.35713	1.50135	0.750677	−	0.660670i	$-0.229728\pi$
$5$	3.35713	1.50135	0.750677	+	0.660670i	$0.229728\pi$
$6$	−0.390170	−0.159286
$7$	0.00990688	0.00374445	0.00187223	−	0.999998i	$-0.499404\pi$
$7$	0.00990688	0.00374445	0.00187223	+	0.999998i	$0.499404\pi$
$8$	−2.00059	−0.707315
$9$	−2.96895	−0.989651
$10$	−7.43394	−2.35082
$11$	−0.392889	−0.118461	−0.0592303	−	0.998244i	$-0.518865\pi$
$11$	−0.392889	−0.118461	−0.0592303	+	0.998244i	$0.518865\pi$
$12$	0.511585	0.147682
$13$	−1.15909	−0.321475	−0.160737	−	0.986997i	$-0.551387\pi$
$13$	−1.15909	−0.321475	−0.160737	+	0.986997i	$0.551387\pi$
$14$	−0.0219376	−0.00586306
$15$	0.591521	0.152730
$16$	−1.37686	−0.344214
$17$	−5.09337	−1.23532	−0.617662	−	0.786444i	$-0.711920\pi$
$17$	−5.09337	−1.23532	−0.617662	+	0.786444i	$0.711920\pi$
$18$	6.57438	1.54960
$19$	−2.83746	−0.650958	−0.325479	−	0.945549i	$-0.605526\pi$
$19$	−2.83746	−0.650958	−0.325479	+	0.945549i	$0.605526\pi$
$20$	9.74727	2.17956
$21$	0.00174558	0.000380916 0
$22$	0.870004	0.185486
$23$	−0.717103	−0.149526	−0.0747632	−	0.997201i	$-0.523820\pi$
$23$	−0.717103	−0.149526	−0.0747632	+	0.997201i	$0.523820\pi$
$24$	−0.352501	−0.0719539
$25$	6.27031	1.25406
$26$	2.56667	0.503365
$27$	−1.05172	−0.202404
$28$	0.0287642	0.00543592
$29$	4.62982	0.859736	0.429868	−	0.902892i	$-0.358560\pi$
$29$	4.62982	0.859736	0.429868	+	0.902892i	$0.358560\pi$
$30$	−1.30985	−0.239145
$31$	2.91239	0.523080	0.261540	−	0.965193i	$-0.415770\pi$
$31$	2.91239	0.523080	0.261540	+	0.965193i	$0.415770\pi$
$32$	7.05005	1.24629
$33$	−0.0692265	−0.0120508
$34$	11.2786	1.93427
$35$	0.0332587	0.00562174
$36$	−8.62023	−1.43670
$37$	2.11454	0.347629	0.173814	−	0.984778i	$-0.444391\pi$
$37$	2.11454	0.347629	0.173814	+	0.984778i	$0.444391\pi$
$38$	6.28320	1.01927
$39$	−0.204231	−0.0327031
$40$	−6.71624	−1.06193
$41$	2.30501	0.359982	0.179991	−	0.983668i	$-0.442393\pi$
$41$	2.30501	0.359982	0.179991	+	0.983668i	$0.442393\pi$
$42$	−0.00386536	−0.000596439 0
$43$	11.2877	1.72136	0.860681	−	0.509145i	$-0.170038\pi$
$43$	11.2877	1.72136	0.860681	+	0.509145i	$0.170038\pi$
$44$	−1.14074	−0.171973
$45$	−9.96716	−1.48582
$46$	1.58794	0.234128
$47$	0.624900	0.0911511	0.0455755	−	0.998961i	$-0.485488\pi$
$47$	0.624900	0.0911511	0.0455755	+	0.998961i	$0.485488\pi$
$48$	−0.242600	−0.0350163
$49$	−6.99990	−0.999986
$50$	−13.8848	−1.96361
$51$	−0.897444	−0.125667
$52$	−3.36538	−0.466694
$53$	−11.5233	−1.58285	−0.791425	−	0.611266i	$-0.790661\pi$
$53$	−11.5233	−1.58285	−0.791425	+	0.611266i	$0.790661\pi$
$54$	2.32890	0.316924
$55$	−1.31898	−0.177851
$56$	−0.0198196	−0.00264851
$57$	−0.499956	−0.0662208
$58$	−10.2522	−1.34617
$59$	2.20073	0.286511	0.143256	−	0.989686i	$-0.454243\pi$
$59$	2.20073	0.286511	0.143256	+	0.989686i	$0.454243\pi$
$60$	1.71745	0.221722
$61$	4.89909	0.627264	0.313632	−	0.949545i	$-0.398454\pi$
$61$	4.89909	0.627264	0.313632	+	0.949545i	$0.398454\pi$
$62$	−6.44911	−0.819038
$63$	−0.0294131	−0.00370570
$64$	−12.8578	−1.60722
$65$	−3.89123	−0.482647
$66$	0.153293	0.0188691
$67$	−5.77083	−0.705019	−0.352509	−	0.935808i	$-0.614672\pi$
$67$	−5.77083	−0.705019	−0.352509	+	0.935808i	$0.614672\pi$
$68$	−14.7884	−1.79335
$69$	−0.126352	−0.0152111
$70$	−0.0736472	−0.00880252
$71$	2.96015	0.351305	0.175652	−	0.984452i	$-0.443797\pi$
$71$	2.96015	0.351305	0.175652	+	0.984452i	$0.443797\pi$
$72$	5.93966	0.699996
$73$	11.0843	1.29731	0.648657	−	0.761081i	$-0.275331\pi$
$73$	11.0843	1.29731	0.648657	+	0.761081i	$0.275331\pi$
$74$	−4.68239	−0.544317
$75$	1.10482	0.127574
$76$	−8.23844	−0.945014
$77$	−0.00389231	−0.000443570 0
$78$	0.452243	0.0512064
$79$	−14.1501	−1.59202	−0.796008	−	0.605286i	$-0.793059\pi$
$79$	−14.1501	−1.59202	−0.796008	+	0.605286i	$0.793059\pi$
$80$	−4.62228	−0.516787
$81$	8.72155	0.969061
$82$	−5.10416	−0.563660
$83$	−14.8114	−1.62577	−0.812884	−	0.582426i	$-0.802104\pi$
$83$	−14.8114	−1.62577	−0.812884	+	0.582426i	$0.802104\pi$
$84$	0.00506821	0.000552987 0
$85$	−17.0991	−1.85466
$86$	−24.9953	−2.69531
$87$	0.815767	0.0874594
$88$	0.786011	0.0837890
$89$	6.96676	0.738475	0.369237	−	0.929335i	$-0.379619\pi$
$89$	6.96676	0.738475	0.369237	+	0.929335i	$0.379619\pi$
$90$	22.0710	2.32649
$91$	−0.0114830	−0.00120375
$92$	−2.08208	−0.217072
$93$	0.513158	0.0532120
$94$	−1.38376	−0.142724
$95$	−9.52572	−0.977318
$96$	1.24221	0.126782
$97$	6.53784	0.663817	0.331908	−	0.943312i	$-0.392308\pi$
$97$	6.53784	0.663817	0.331908	+	0.943312i	$0.392308\pi$
$98$	15.5004	1.56578
$99$	1.16647	0.117235
$100$	18.2056	1.82056
$101$	−12.9103	−1.28462	−0.642311	−	0.766444i	$-0.722024\pi$
$101$	−12.9103	−1.28462	−0.642311	+	0.766444i	$0.722024\pi$
$102$	1.98728	0.196770
$103$	1.28956	0.127064	0.0635319	−	0.997980i	$-0.479764\pi$
$103$	1.28956	0.127064	0.0635319	+	0.997980i	$0.479764\pi$
$104$	2.31887	0.227384
$105$	0.00586013	0.000571890 0
$106$	25.5170	2.47843
$107$	−6.83416	−0.660683	−0.330341	−	0.943861i	$-0.607164\pi$
$107$	−6.83416	−0.660683	−0.330341	+	0.943861i	$0.607164\pi$
$108$	−3.05362	−0.293835
$109$	−17.8669	−1.71134	−0.855668	−	0.517525i	$-0.826854\pi$
$109$	−17.8669	−1.71134	−0.855668	+	0.517525i	$0.826854\pi$
$110$	2.92072	0.278479
$111$	0.372580	0.0353637
$112$	−0.0136404	−0.00128889
$113$	−10.5715	−0.994487	−0.497244	−	0.867611i	$-0.665654\pi$
$113$	−10.5715	−0.994487	−0.497244	+	0.867611i	$0.665654\pi$
$114$	1.10709	0.103689
$115$	−2.40741	−0.224492
$116$	13.4425	1.24810
$117$	3.44130	0.318148
$118$	−4.87325	−0.448619
$119$	−0.0504594	−0.00462561
$120$	−1.18339	−0.108028
$121$	−10.8456	−0.985967
$122$	−10.8484	−0.982170
$123$	0.406140	0.0366204
$124$	8.45598	0.759370
$125$	4.26459	0.381437
$126$	0.0651316	0.00580238
$127$	−15.5425	−1.37917	−0.689587	−	0.724203i	$-0.742208\pi$
$127$	−15.5425	−1.37917	−0.689587	+	0.724203i	$0.742208\pi$
$128$	14.3718	1.27030
$129$	1.98888	0.175111
$130$	8.61663	0.755729
$131$	1.56290	0.136551	0.0682754	−	0.997667i	$-0.478250\pi$
$131$	1.56290	0.136551	0.0682754	+	0.997667i	$0.478250\pi$
$132$	−0.200996	−0.0174945
$133$	−0.0281104	−0.00243748
$134$	12.7788	1.10392
$135$	−3.53076	−0.303880
$136$	10.1897	0.873764
$137$	17.6122	1.50471	0.752357	−	0.658756i	$-0.228917\pi$
$137$	17.6122	1.50471	0.752357	+	0.658756i	$0.228917\pi$
$138$	0.279792	0.0238175
$139$	−10.4142	−0.883319	−0.441659	−	0.897183i	$-0.645610\pi$
$139$	−10.4142	−0.883319	−0.441659	+	0.897183i	$0.645610\pi$
$140$	0.0965651	0.00816124
$141$	0.110106	0.00927264
$142$	−6.55488	−0.550073
$143$	0.455396	0.0380821
$144$	4.08782	0.340652
$145$	15.5429	1.29077
$146$	−24.5447	−2.03133
$147$	−1.23337	−0.101727
$148$	6.13949	0.504663
$149$	−9.92104	−0.812764	−0.406382	−	0.913703i	$-0.633210\pi$
$149$	−9.92104	−0.812764	−0.406382	+	0.913703i	$0.633210\pi$
$150$	−2.44648	−0.199755
$151$	0.579498	0.0471589	0.0235794	−	0.999722i	$-0.492494\pi$
$151$	0.579498	0.0471589	0.0235794	+	0.999722i	$0.492494\pi$
$152$	5.67659	0.460433
$153$	15.1220	1.22254
$154$	0.00861903	0.000694541 0
$155$	9.77725	0.785328
$156$	−0.592974	−0.0474759
$157$	0.154332	0.0123170	0.00615851	−	0.999981i	$-0.498040\pi$
$157$	0.154332	0.0123170	0.00615851	+	0.999981i	$0.498040\pi$
$158$	31.3337	2.49278
$159$	−2.03039	−0.161021
$160$	23.6679	1.87111
$161$	−0.00710426	−0.000559894 0
$162$	−19.3128	−1.51736
$163$	−22.6373	−1.77309	−0.886545	−	0.462642i	$-0.846901\pi$
$163$	−22.6373	−1.77309	−0.886545	+	0.462642i	$0.846901\pi$
$164$	6.69250	0.522597
$165$	−0.232402	−0.0180925
$166$	32.7981	2.54563
$167$	−1.58385	−0.122562	−0.0612810	−	0.998121i	$-0.519519\pi$
$167$	−1.58385	−0.122562	−0.0612810	+	0.998121i	$0.519519\pi$
$168$	−0.00349219	−0.000269428 0
$169$	−11.6565	−0.896654
$170$	37.8638	2.90402
$171$	8.42429	0.644222
$172$	32.7734	2.49895
$173$	−12.3744	−0.940808	−0.470404	−	0.882451i	$-0.655892\pi$
$173$	−12.3744	−0.940808	−0.470404	+	0.882451i	$0.655892\pi$
$174$	−1.80641	−0.136944
$175$	0.0621192	0.00469577
$176$	0.540952	0.0407758
$177$	0.387766	0.0291463
$178$	−15.4270	−1.15630
$179$	−16.7092	−1.24890	−0.624452	−	0.781063i	$-0.714678\pi$
$179$	−16.7092	−1.24890	−0.624452	+	0.781063i	$0.714678\pi$
$180$	−28.9392	−2.15700
$181$	−6.24715	−0.464347	−0.232174	−	0.972674i	$-0.574584\pi$
$181$	−6.24715	−0.464347	−0.232174	+	0.972674i	$0.574584\pi$
$182$	0.0254277	0.00188483
$183$	0.863212	0.0638105
$184$	1.43463	0.105762
$185$	7.09880	0.521914
$186$	−1.13632	−0.0833193
$187$	2.00113	0.146337
$188$	1.81437	0.132327
$189$	−0.0104193	−0.000757891 0
$190$	21.0935	1.53028
$191$	−15.6600	−1.13311	−0.566557	−	0.824022i	$-0.691725\pi$
$191$	−15.6600	−1.13311	−0.566557	+	0.824022i	$0.691725\pi$
$192$	−2.26552	−0.163500
$193$	−19.0820	−1.37355	−0.686777	−	0.726868i	$-0.740975\pi$
$193$	−19.0820	−1.37355	−0.686777	+	0.726868i	$0.740975\pi$
$194$	−14.4772	−1.03940
$195$	−0.685628	−0.0490989
$196$	−20.3239	−1.45171
$197$	26.2010	1.86674	0.933371	−	0.358913i	$-0.116853\pi$
$197$	26.2010	1.86674	0.933371	+	0.358913i	$0.116853\pi$
$198$	−2.58300	−0.183566
$199$	6.42761	0.455641	0.227820	−	0.973703i	$-0.426840\pi$
$199$	6.42761	0.455641	0.227820	+	0.973703i	$0.426840\pi$
$200$	−12.5443	−0.887017
$201$	−1.01681	−0.0717203
$202$	28.5882	2.01146
$203$	0.0458671	0.00321924
$204$	−2.60569	−0.182435
$205$	7.73822	0.540461
$206$	−2.85556	−0.198956
$207$	2.12905	0.147979
$208$	1.59590	0.110656
$209$	1.11481	0.0771129
$210$	−0.0129765	−0.000895465 0
$211$	17.9281	1.23422	0.617111	−	0.786876i	$-0.288303\pi$
$211$	17.9281	1.23422	0.617111	+	0.786876i	$0.288303\pi$
$212$	−33.4575	−2.29787
$213$	0.521574	0.0357376
$214$	15.1334	1.03450
$215$	37.8943	2.58437
$216$	2.10406	0.143163
$217$	0.0288527	0.00195865
$218$	39.5640	2.67961
$219$	1.95303	0.131973
$220$	−3.82960	−0.258192
$221$	5.90369	0.397125
$222$	−0.825031	−0.0553724
$223$	11.3876	0.762570	0.381285	−	0.924457i	$-0.375482\pi$
$223$	11.3876	0.762570	0.381285	+	0.924457i	$0.375482\pi$
$224$	0.0698441	0.00466665
$225$	−18.6163	−1.24108
$226$	23.4094	1.55717
$227$	24.5440	1.62905	0.814523	−	0.580132i	$-0.196999\pi$
$227$	24.5440	1.62905	0.814523	+	0.580132i	$0.196999\pi$
$228$	−1.45160	−0.0961346
$229$	−4.95428	−0.327388	−0.163694	−	0.986511i	$-0.552341\pi$
$229$	−4.95428	−0.327388	−0.163694	+	0.986511i	$0.552341\pi$
$230$	5.33090	0.351509
$231$	−0.000685819 0	−4.51236e−5 0
$232$	−9.26237	−0.608104
$233$	−10.2232	−0.669745	−0.334873	−	0.942263i	$-0.608693\pi$
$233$	−10.2232	−0.669745	−0.334873	+	0.942263i	$0.608693\pi$
$234$	−7.62032	−0.498156
$235$	2.09787	0.136850
$236$	6.38973	0.415936
$237$	−2.49324	−0.161953
$238$	0.111736	0.00724278
$239$	−12.6494	−0.818225	−0.409112	−	0.912484i	$-0.634162\pi$
$239$	−12.6494	−0.818225	−0.409112	+	0.912484i	$0.634162\pi$
$240$	−0.814439	−0.0525718
$241$	3.76691	0.242648	0.121324	−	0.992613i	$-0.461286\pi$
$241$	3.76691	0.242648	0.121324	+	0.992613i	$0.461286\pi$
$242$	24.0163	1.54383
$243$	4.69189	0.300985
$244$	14.2243	0.910617
$245$	−23.4996	−1.50133
$246$	−0.899346	−0.0573402
$247$	3.28888	0.209267
$248$	−5.82649	−0.369982
$249$	−2.60975	−0.165386
$250$	−9.44341	−0.597254
$251$	26.5769	1.67752	0.838760	−	0.544501i	$-0.183281\pi$
$251$	26.5769	1.67752	0.838760	+	0.544501i	$0.183281\pi$
$252$	−0.0853996	−0.00537967
$253$	0.281742	0.0177130
$254$	34.4169	2.15951
$255$	−3.01284	−0.188671
$256$	−6.10899	−0.381812
$257$	−0.684730	−0.0427123	−0.0213561	−	0.999772i	$-0.506798\pi$
$257$	−0.684730	−0.0427123	−0.0213561	+	0.999772i	$0.506798\pi$
$258$	−4.40413	−0.274189
$259$	0.0209485	0.00130168
$260$	−11.2980	−0.700672
$261$	−13.7457	−0.850839
$262$	−3.46084	−0.213811
$263$	21.0292	1.29672	0.648359	−	0.761335i	$-0.275456\pi$
$263$	21.0292	1.29672	0.648359	+	0.761335i	$0.275456\pi$
$264$	0.138494	0.00852371
$265$	−38.6853	−2.37642
$266$	0.0622469	0.00381660
$267$	1.22753	0.0751237
$268$	−16.7553	−1.02350
$269$	31.9372	1.94725	0.973624	−	0.228159i	$-0.0732707\pi$
$269$	31.9372	1.94725	0.973624	+	0.228159i	$0.0732707\pi$
$270$	7.81843	0.475814
$271$	4.87593	0.296192	0.148096	−	0.988973i	$-0.452686\pi$
$271$	4.87593	0.296192	0.148096	+	0.988973i	$0.452686\pi$
$272$	7.01284	0.425216
$273$	−0.00202329	−0.000122455 0
$274$	−39.0001	−2.35608
$275$	−2.46354	−0.148557
$276$	−0.366859	−0.0220823
$277$	−17.2749	−1.03795	−0.518973	−	0.854791i	$-0.673685\pi$
$277$	−17.2749	−1.03795	−0.518973	+	0.854791i	$0.673685\pi$
$278$	23.0609	1.38310
$279$	−8.64674	−0.517667
$280$	−0.0665370	−0.00397634
$281$	−2.48882	−0.148470	−0.0742352	−	0.997241i	$-0.523652\pi$
$281$	−2.48882	−0.148470	−0.0742352	+	0.997241i	$0.523652\pi$
$282$	−0.243817	−0.0145191
$283$	−21.9988	−1.30770	−0.653848	−	0.756626i	$-0.726846\pi$
$283$	−21.9988	−1.30770	−0.653848	+	0.756626i	$0.726846\pi$
$284$	8.59466	0.509999
$285$	−1.67842	−0.0994209
$286$	−1.00842	−0.0596289
$287$	0.0228355	0.00134794
$288$	−20.9313	−1.23339
$289$	8.94243	0.526025
$290$	−34.4178	−2.02108
$291$	1.15196	0.0675289
$292$	32.1826	1.88335
$293$	−18.5724	−1.08501	−0.542505	−	0.840053i	$-0.682524\pi$
$293$	−18.5724	−1.08501	−0.542505	+	0.840053i	$0.682524\pi$
$294$	2.73115	0.159284
$295$	7.38814	0.430154
$296$	−4.23034	−0.245883
$297$	0.413210	0.0239769
$298$	21.9689	1.27262
$299$	0.831190	0.0480689
$300$	3.20779	0.185202
$301$	0.111826	0.00644555
$302$	−1.28323	−0.0738414
$303$	−2.27477	−0.130682
$304$	3.90677	0.224069
$305$	16.4469	0.941745
$306$	−33.4857	−1.91425
$307$	−8.40640	−0.479778	−0.239889	−	0.970800i	$-0.577111\pi$
$307$	−8.40640	−0.479778	−0.239889	+	0.970800i	$0.577111\pi$
$308$	−0.0113011	−0.000643943 0
$309$	0.227218	0.0129260
$310$	−21.6505	−1.22967
$311$	−11.6850	−0.662597	−0.331299	−	0.943526i	$-0.607487\pi$
$311$	−11.6850	−0.662597	−0.331299	+	0.943526i	$0.607487\pi$
$312$	0.408582	0.0231314
$313$	−34.7328	−1.96321	−0.981607	−	0.190911i	$-0.938856\pi$
$313$	−34.7328	−1.96321	−0.981607	+	0.190911i	$0.938856\pi$
$314$	−0.341749	−0.0192860
$315$	−0.0987435	−0.00556357
$316$	−41.0843	−2.31117
$317$	−23.4805	−1.31880	−0.659398	−	0.751794i	$-0.729189\pi$
$317$	−23.4805	−1.31880	−0.659398	+	0.751794i	$0.729189\pi$
$318$	4.49605	0.252126
$319$	−1.81901	−0.101845
$320$	−43.1651	−2.41300
$321$	−1.20417	−0.0672101
$322$	0.0157315	0.000876682 0
$323$	14.4522	0.804144
$324$	25.3226	1.40681
$325$	−7.26788	−0.403149
$326$	50.1275	2.77630
$327$	−3.14812	−0.174091
$328$	−4.61138	−0.254621
$329$	0.00619081	0.000341311 0
$330$	0.514626	0.0283292
$331$	1.37150	0.0753844	0.0376922	−	0.999289i	$-0.487999\pi$
$331$	1.37150	0.0753844	0.0376922	+	0.999289i	$0.487999\pi$
$332$	−43.0044	−2.36017
$333$	−6.27799	−0.344031
$334$	3.50723	0.191907
$335$	−19.3734	−1.05848
$336$	−0.00240341	−0.000131117 0
$337$	3.94336	0.214809	0.107404	−	0.994215i	$-0.465746\pi$
$337$	3.94336	0.214809	0.107404	+	0.994215i	$0.465746\pi$
$338$	25.8119	1.40398
$339$	−1.86269	−0.101167
$340$	−49.6465	−2.69246
$341$	−1.14425	−0.0619644
$342$	−18.6545	−1.00872
$343$	−0.138695	−0.00748885
$344$	−22.5821	−1.21755
$345$	−0.424182	−0.0228372
$346$	27.4015	1.47312
$347$	−28.0126	−1.50380	−0.751899	−	0.659279i	$-0.770862\pi$
$347$	−28.0126	−1.50380	−0.751899	+	0.659279i	$0.770862\pi$
$348$	2.36854	0.126967
$349$	−3.12741	−0.167406	−0.0837032	−	0.996491i	$-0.526675\pi$
$349$	−3.12741	−0.167406	−0.0837032	+	0.996491i	$0.526675\pi$
$350$	−0.137555	−0.00735264
$351$	1.21904	0.0650677
$352$	−2.76989	−0.147636
$353$	−8.58629	−0.457002	−0.228501	−	0.973544i	$-0.573382\pi$
$353$	−8.58629	−0.457002	−0.228501	+	0.973544i	$0.573382\pi$
$354$	−0.858659	−0.0456372
$355$	9.93760	0.527433
$356$	20.2277	1.07206
$357$	−0.00889088	−0.000470555 0
$358$	37.0004	1.95553
$359$	−29.6572	−1.56525	−0.782623	−	0.622496i	$-0.786119\pi$
$359$	−29.6572	−1.56525	−0.782623	+	0.622496i	$0.786119\pi$
$360$	19.9402	1.05094
$361$	−10.9488	−0.576254
$362$	13.8335	0.727074
$363$	−1.91099	−0.100301
$364$	−0.0333404	−0.00174751
$365$	37.2113	1.94773
$366$	−1.91148	−0.0999144
$367$	−11.7277	−0.612181	−0.306091	−	0.952002i	$-0.599021\pi$
$367$	−11.7277	−0.612181	−0.306091	+	0.952002i	$0.599021\pi$
$368$	0.987348	0.0514691
$369$	−6.84348	−0.356257
$370$	−15.7194	−0.817213
$371$	−0.114160	−0.00592690
$372$	1.48993	0.0772494
$373$	−31.3579	−1.62365	−0.811825	−	0.583901i	$-0.801525\pi$
$373$	−31.3579	−1.62365	−0.811825	+	0.583901i	$0.801525\pi$
$374$	−4.43126	−0.229135
$375$	0.751415	0.0388029
$376$	−1.25017	−0.0644725
$377$	−5.36639	−0.276383
$378$	0.0230722	0.00118670
$379$	−27.9813	−1.43730	−0.718652	−	0.695370i	$-0.755240\pi$
$379$	−27.9813	−1.43730	−0.718652	+	0.695370i	$0.755240\pi$
$380$	−27.6575	−1.41880
$381$	−2.73856	−0.140301
$382$	34.6770	1.77423
$383$	31.1064	1.58946	0.794731	−	0.606962i	$-0.207612\pi$
$383$	31.1064	1.58946	0.794731	+	0.606962i	$0.207612\pi$
$384$	2.53228	0.129225
$385$	−0.0130670	−0.000665955 0
$386$	42.2548	2.15071
$387$	−33.5127	−1.70355
$388$	18.9823	0.963681
$389$	−1.74917	−0.0886867	−0.0443433	−	0.999016i	$-0.514120\pi$
$389$	−1.74917	−0.0886867	−0.0443433	+	0.999016i	$0.514120\pi$
$390$	1.51824	0.0768790
$391$	3.65247	0.184713
$392$	14.0039	0.707305
$393$	0.275380	0.0138911
$394$	−58.0188	−2.92294
$395$	−47.5039	−2.39018
$396$	3.38680	0.170193
$397$	21.1984	1.06392	0.531959	−	0.846770i	$-0.321456\pi$
$397$	21.1984	1.06392	0.531959	+	0.846770i	$0.321456\pi$
$398$	−14.2331	−0.713442
$399$	−0.00495301	−0.000247961 0
$400$	−8.63331	−0.431666
$401$	−16.3436	−0.816160	−0.408080	−	0.912946i	$-0.633802\pi$
$401$	−16.3436	−0.816160	−0.408080	+	0.912946i	$0.633802\pi$
$402$	2.25160	0.112300
$403$	−3.37573	−0.168157
$404$	−37.4844	−1.86492
$405$	29.2794	1.45490
$406$	−0.101567	−0.00504068
$407$	−0.830782	−0.0411803
$408$	1.79542	0.0888864
$409$	10.7972	0.533885	0.266943	−	0.963712i	$-0.413987\pi$
$409$	10.7972	0.533885	0.266943	+	0.963712i	$0.413987\pi$
$410$	−17.1353	−0.846253
$411$	3.10325	0.153072
$412$	3.74417	0.184462
$413$	0.0218024	0.00107283
$414$	−4.71451	−0.231705
$415$	−49.7239	−2.44085
$416$	−8.17167	−0.400649
$417$	−1.83496	−0.0898584
$418$	−2.46860	−0.120743
$419$	37.0084	1.80798	0.903990	−	0.427554i	$-0.140625\pi$
$419$	37.0084	1.80798	0.903990	+	0.427554i	$0.140625\pi$
$420$	0.0170146	0.000830229 0
$421$	−13.8399	−0.674517	−0.337259	−	0.941412i	$-0.609500\pi$
$421$	−13.8399	−0.674517	−0.337259	+	0.941412i	$0.609500\pi$
$422$	−39.6995	−1.93254
$423$	−1.85530	−0.0902078
$424$	23.0534	1.11957
$425$	−31.9370	−1.54917
$426$	−1.15496	−0.0559580
$427$	0.0485347	0.00234876
$428$	−19.8427	−0.959132
$429$	0.0802400	0.00387402
$430$	−83.9123	−4.04661
$431$	28.0540	1.35131	0.675657	−	0.737216i	$-0.263860\pi$
$431$	28.0540	1.35131	0.675657	+	0.737216i	$0.263860\pi$
$432$	1.44807	0.0696702
$433$	−14.5729	−0.700330	−0.350165	−	0.936688i	$-0.613875\pi$
$433$	−14.5729	−0.700330	−0.350165	+	0.936688i	$0.613875\pi$
$434$	−0.0638906	−0.00306685
$435$	2.73863	0.131307
$436$	−51.8757	−2.48440
$437$	2.03475	0.0973354
$438$	−4.32474	−0.206644
$439$	−32.0839	−1.53128	−0.765641	−	0.643268i	$-0.777578\pi$
$439$	−32.0839	−1.53128	−0.765641	+	0.643268i	$0.777578\pi$
$440$	2.63874	0.125797
$441$	20.7824	0.989637
$442$	−13.0730	−0.621819
$443$	16.5229	0.785027	0.392514	−	0.919746i	$-0.371606\pi$
$443$	16.5229	0.785027	0.392514	+	0.919746i	$0.371606\pi$
$444$	1.08177	0.0513384
$445$	23.3883	1.10871
$446$	−25.2164	−1.19403
$447$	−1.74807	−0.0826810
$448$	−0.127380	−0.00601815
$449$	−28.0904	−1.32567	−0.662834	−	0.748767i	$-0.730646\pi$
$449$	−28.0904	−1.32567	−0.662834	+	0.748767i	$0.730646\pi$
$450$	41.2234	1.94329
$451$	−0.905615	−0.0426437
$452$	−30.6940	−1.44372
$453$	0.102107	0.00479739
$454$	−54.3497	−2.55076
$455$	−0.0385499	−0.00180725
$456$	1.00021	0.0468390
$457$	20.9523	0.980109	0.490054	−	0.871692i	$-0.336977\pi$
$457$	20.9523	0.980109	0.490054	+	0.871692i	$0.336977\pi$
$458$	10.9706	0.512624
$459$	5.35680	0.250034
$460$	−6.98980	−0.325901
$461$	−11.5088	−0.536016	−0.268008	−	0.963417i	$-0.586365\pi$
$461$	−11.5088	−0.536016	−0.268008	+	0.963417i	$0.586365\pi$
$462$	0.00151866	7.06545e−5 0
$463$	35.5352	1.65146	0.825731	−	0.564064i	$-0.190763\pi$
$463$	35.5352	1.65146	0.825731	+	0.564064i	$0.190763\pi$
$464$	−6.37459	−0.295933
$465$	1.72274	0.0798900
$466$	22.6380	1.04869
$467$	16.0790	0.744048	0.372024	−	0.928223i	$-0.378664\pi$
$467$	16.0790	0.744048	0.372024	+	0.928223i	$0.378664\pi$
$468$	9.99165	0.461864
$469$	−0.0571709	−0.00263991
$470$	−4.64547	−0.214280
$471$	0.0271930	0.00125299
$472$	−4.40276	−0.202654
$473$	−4.43483	−0.203914
$474$	5.52096	0.253586
$475$	−17.7918	−0.816342
$476$	−0.146507	−0.00671513
$477$	34.2122	1.56647
$478$	28.0106	1.28118
$479$	11.8163	0.539900	0.269950	−	0.962874i	$-0.412993\pi$
$479$	11.8163	0.539900	0.269950	+	0.962874i	$0.412993\pi$
$480$	4.17026	0.190345
$481$	−2.45095	−0.111754
$482$	−8.34135	−0.379938
$483$	−0.00125176	−5.69570e−5 0
$484$	−31.4898	−1.43136
$485$	21.9484	0.996624
$486$	−10.3896	−0.471282
$487$	33.0153	1.49606	0.748032	−	0.663663i	$-0.230999\pi$
$487$	33.0153	1.49606	0.748032	+	0.663663i	$0.230999\pi$
$488$	−9.80107	−0.443674
$489$	−3.98866	−0.180373
$490$	52.0369	2.35079
$491$	−8.82942	−0.398466	−0.199233	−	0.979952i	$-0.563845\pi$
$491$	−8.82942	−0.398466	−0.199233	+	0.979952i	$0.563845\pi$
$492$	1.17921	0.0531628
$493$	−23.5814	−1.06205
$494$	−7.28282	−0.327669
$495$	3.91599	0.176011
$496$	−4.00994	−0.180051
$497$	0.0293258	0.00131544
$498$	5.77898	0.258962
$499$	19.6249	0.878530	0.439265	−	0.898358i	$-0.355239\pi$
$499$	19.6249	0.878530	0.439265	+	0.898358i	$0.355239\pi$
$500$	12.3821	0.553743
$501$	−0.279072	−0.0124680
$502$	−58.8513	−2.62666
$503$	27.8033	1.23969	0.619844	−	0.784725i	$-0.287196\pi$
$503$	27.8033	1.23969	0.619844	+	0.784725i	$0.287196\pi$
$504$	0.0588435	0.00262110
$505$	−43.3415	−1.92867
$506$	−0.623883	−0.0277350
$507$	−2.05386	−0.0912150
$508$	−45.1269	−2.00218
$509$	41.0189	1.81813	0.909065	−	0.416653i	$-0.136797\pi$
$509$	41.0189	1.81813	0.909065	+	0.416653i	$0.136797\pi$
$510$	6.67155	0.295421
$511$	0.109810	0.00485773
$512$	−15.2160	−0.672457
$513$	2.98422	0.131756
$514$	1.51625	0.0668788
$515$	4.32920	0.190768
$516$	5.77463	0.254214
$517$	−0.245517	−0.0107978
$518$	−0.0463879	−0.00203817
$519$	−2.18035	−0.0957067
$520$	7.78475	0.341384
$521$	−39.8195	−1.74452	−0.872261	−	0.489040i	$-0.837347\pi$
$521$	−39.8195	−1.74452	−0.872261	+	0.489040i	$0.837347\pi$
$522$	30.4382	1.33224
$523$	7.32821	0.320440	0.160220	−	0.987081i	$-0.448780\pi$
$523$	7.32821	0.320440	0.160220	+	0.987081i	$0.448780\pi$
$524$	4.53780	0.198235
$525$	0.0109453	0.000477693 0
$526$	−46.5666	−2.03040
$527$	−14.8339	−0.646173
$528$	0.0953150	0.00414805
$529$	−22.4858	−0.977642
$530$	85.6637	3.72099
$531$	−6.53388	−0.283546
$532$	−0.0816173	−0.00353856
$533$	−2.67173	−0.115725
$534$	−2.71822	−0.117629
$535$	−22.9431	−0.991919
$536$	11.5451	0.498671
$537$	−2.94414	−0.127049
$538$	−70.7210	−3.04900
$539$	2.75019	0.118459
$540$	−10.2514	−0.441150
$541$	5.76647	0.247920	0.123960	−	0.992287i	$-0.460441\pi$
$541$	5.76647	0.247920	0.123960	+	0.992287i	$0.460441\pi$
$542$	−10.7971	−0.463777
$543$	−1.10074	−0.0472372
$544$	−35.9085	−1.53957
$545$	−59.9814	−2.56932
$546$	0.00448032	0.000191740 0
$547$	19.7510	0.844491	0.422246	−	0.906481i	$-0.361242\pi$
$547$	19.7510	0.844491	0.422246	+	0.906481i	$0.361242\pi$
$548$	51.1363	2.18443
$549$	−14.5452	−0.620773
$550$	5.45520	0.232610
$551$	−13.1369	−0.559652
$552$	0.252779	0.0107590
$553$	−0.140184	−0.00596123
$554$	38.2530	1.62522
$555$	1.25080	0.0530934
$556$	−30.2371	−1.28234
$557$	22.6785	0.960921	0.480460	−	0.877016i	$-0.340470\pi$
$557$	22.6785	0.960921	0.480460	+	0.877016i	$0.340470\pi$
$558$	19.1471	0.810562
$559$	−13.0835	−0.553374
$560$	−0.0457924	−0.00193508
$561$	0.352596	0.0148866
$562$	5.51118	0.232475
$563$	−19.6806	−0.829438	−0.414719	−	0.909950i	$-0.636120\pi$
$563$	−19.6806	−0.829438	−0.414719	+	0.909950i	$0.636120\pi$
$564$	0.319689	0.0134613
$565$	−35.4900	−1.49308
$566$	48.7137	2.04759
$567$	0.0864034	0.00362860
$568$	−5.92204	−0.248483
$569$	−0.391729	−0.0164221	−0.00821106	−	0.999966i	$-0.502614\pi$
$569$	−0.391729	−0.0164221	−0.00821106	+	0.999966i	$0.502614\pi$
$570$	3.71665	0.155673
$571$	−31.5883	−1.32193	−0.660965	−	0.750417i	$-0.729853\pi$
$571$	−31.5883	−1.32193	−0.660965	+	0.750417i	$0.729853\pi$
$572$	1.32222	0.0552848
$573$	−2.75926	−0.115270
$574$	−0.0505663	−0.00211060
$575$	−4.49646	−0.187515
$576$	38.1741	1.59059
$577$	0.238407	0.00992501	0.00496251	−	0.999988i	$-0.498420\pi$
$577$	0.238407	0.00992501	0.00496251	+	0.999988i	$0.498420\pi$
$578$	−19.8019	−0.823650
$579$	−3.36222	−0.139729
$580$	45.1281	1.87384
$581$	−0.146735	−0.00608761
$582$	−2.55086	−0.105737
$583$	4.52739	0.187505
$584$	−22.1750	−0.917610
$585$	11.5529	0.477652
$586$	41.1262	1.69891
$587$	40.5801	1.67492	0.837460	−	0.546498i	$-0.184040\pi$
$587$	40.5801	1.67492	0.837460	+	0.546498i	$0.184040\pi$
$588$	−3.58104	−0.147680
$589$	−8.26378	−0.340503
$590$	−16.3601	−0.673535
$591$	4.61657	0.189900
$592$	−2.91142	−0.119659
$593$	23.5493	0.967054	0.483527	−	0.875330i	$-0.339356\pi$
$593$	23.5493	0.967054	0.483527	+	0.875330i	$0.339356\pi$
$594$	−0.915002	−0.0375430
$595$	−0.169399	−0.00694467
$596$	−28.8053	−1.17991
$597$	1.13253	0.0463516
$598$	−1.84057	−0.0752663
$599$	−12.2918	−0.502227	−0.251114	−	0.967958i	$-0.580797\pi$
$599$	−12.2918	−0.502227	−0.251114	+	0.967958i	$0.580797\pi$
$600$	−2.21029	−0.0902347
$601$	−24.5463	−1.00126	−0.500632	−	0.865660i	$-0.666899\pi$
$601$	−24.5463	−1.00126	−0.500632	+	0.865660i	$0.666899\pi$
$602$	−0.247625	−0.0100924
$603$	17.1333	0.697723
$604$	1.68255	0.0684619
$605$	−36.4102	−1.48029
$606$	5.03720	0.204622
$607$	−11.7312	−0.476154	−0.238077	−	0.971246i	$-0.576517\pi$
$607$	−11.7312	−0.476154	−0.238077	+	0.971246i	$0.576517\pi$
$608$	−20.0043	−0.811280
$609$	0.00808171	0.000327487 0
$610$	−36.4195	−1.47458
$611$	−0.724318	−0.0293028
$612$	43.9060	1.77480
$613$	17.6960	0.714734	0.357367	−	0.933964i	$-0.383675\pi$
$613$	17.6960	0.714734	0.357367	+	0.933964i	$0.383675\pi$
$614$	18.6149	0.751237
$615$	1.36346	0.0549801
$616$	0.00778692	0.000313744 0
$617$	26.9991	1.08694	0.543472	−	0.839428i	$-0.317110\pi$
$617$	26.9991	1.08694	0.543472	+	0.839428i	$0.317110\pi$
$618$	−0.503145	−0.0202395
$619$	4.05087	0.162818	0.0814091	−	0.996681i	$-0.474058\pi$
$619$	4.05087	0.162818	0.0814091	+	0.996681i	$0.474058\pi$
$620$	28.3878	1.14008
$621$	0.754192	0.0302647
$622$	25.8750	1.03749
$623$	0.0690189	0.00276518
$624$	0.281196	0.0112569
$625$	−17.0348	−0.681390
$626$	76.9115	3.07400
$627$	0.196428	0.00784456
$628$	0.448096	0.0178810
$629$	−10.7702	−0.429434
$630$	0.218655	0.00871143
$631$	−0.0296850	−0.00118174	−0.000590870	−	1.00000i	$-0.500188\pi$
$631$	−0.0296850	−0.00118174	−0.000590870		1.00000i	$0.500188\pi$
$632$	28.3086	1.12606
$633$	3.15890	0.125555
$634$	51.9946	2.06497
$635$	−52.1781	−2.07063
$636$	−5.89515	−0.233758
$637$	8.11354	0.321470
$638$	4.02796	0.159469
$639$	−8.78854	−0.347669
$640$	48.2479	1.90717
$641$	46.8884	1.85198	0.925991	−	0.377546i	$-0.123232\pi$
$641$	46.8884	1.85198	0.925991	+	0.377546i	$0.123232\pi$
$642$	2.66648	0.105238
$643$	1.58317	0.0624343	0.0312171	−	0.999513i	$-0.490062\pi$
$643$	1.58317	0.0624343	0.0312171	+	0.999513i	$0.490062\pi$
$644$	−0.0206269	−0.000812814 0
$645$	6.67693	0.262904
$646$	−32.0027	−1.25913
$647$	33.0554	1.29954	0.649771	−	0.760130i	$-0.274865\pi$
$647$	33.0554	1.29954	0.649771	+	0.760130i	$0.274865\pi$
$648$	−17.4482	−0.685432
$649$	−0.864645	−0.0339403
$650$	16.0938	0.631251
$651$	0.00508380	0.000199250 0
$652$	−65.7264	−2.57404
$653$	31.4874	1.23220	0.616098	−	0.787669i	$-0.288712\pi$
$653$	31.4874	1.23220	0.616098	+	0.787669i	$0.288712\pi$
$654$	6.97111	0.272592
$655$	5.24684	0.205011
$656$	−3.17367	−0.123911
$657$	−32.9086	−1.28389
$658$	−0.0137088	−0.000534424 0
$659$	−10.4164	−0.405766	−0.202883	−	0.979203i	$-0.565031\pi$
$659$	−10.4164	−0.405766	−0.202883	+	0.979203i	$0.565031\pi$
$660$	−0.674770	−0.0262654
$661$	−28.0877	−1.09248	−0.546242	−	0.837628i	$-0.683942\pi$
$661$	−28.0877	−1.09248	−0.546242	+	0.837628i	$0.683942\pi$
$662$	−3.03701	−0.118037
$663$	1.04022	0.0403989
$664$	29.6316	1.14993
$665$	−0.0943702	−0.00365952
$666$	13.9018	0.538684
$667$	−3.32006	−0.128553
$668$	−4.59864	−0.177927
$669$	2.00648	0.0775749
$670$	42.9000	1.65737
$671$	−1.92480	−0.0743061
$672$	0.0123064	0.000474731 0
$673$	48.8502	1.88304	0.941519	−	0.336961i	$-0.109399\pi$
$673$	48.8502	1.88304	0.941519	+	0.336961i	$0.109399\pi$
$674$	−8.73209	−0.336347
$675$	−6.59462	−0.253827
$676$	−33.8441	−1.30170
$677$	−3.65329	−0.140407	−0.0702037	−	0.997533i	$-0.522365\pi$
$677$	−3.65329	−0.140407	−0.0702037	+	0.997533i	$0.522365\pi$
$678$	4.12469	0.158408
$679$	0.0647696	0.00248563
$680$	34.2083	1.31183
$681$	4.32462	0.165720
$682$	2.53379	0.0970238
$683$	25.0933	0.960170	0.480085	−	0.877222i	$-0.340606\pi$
$683$	25.0933	0.960170	0.480085	+	0.877222i	$0.340606\pi$
$684$	24.4596	0.935234
$685$	59.1265	2.25911
$686$	0.307124	0.0117260
$687$	−0.872937	−0.0333046
$688$	−15.5416	−0.592517
$689$	13.3566	0.508846
$690$	0.939297	0.0357584
$691$	−12.8057	−0.487150	−0.243575	−	0.969882i	$-0.578320\pi$
$691$	−12.8057	−0.487150	−0.243575	+	0.969882i	$0.578320\pi$
$692$	−35.9285	−1.36580
$693$	0.0115561	0.000438980 0
$694$	62.0305	2.35464
$695$	−34.9617	−1.32617
$696$	−1.63202	−0.0618614
$697$	−11.7403	−0.444695
$698$	6.92526	0.262125
$699$	−1.80132	−0.0681320
$700$	0.180360	0.00681698
$701$	−8.19048	−0.309350	−0.154675	−	0.987965i	$-0.549433\pi$
$701$	−8.19048	−0.309350	−0.154675	+	0.987965i	$0.549433\pi$
$702$	−2.69942	−0.101883
$703$	−5.99994	−0.226292
$704$	5.05167	0.190392
$705$	0.369642	0.0139215
$706$	19.0133	0.715574
$707$	−0.127901	−0.00481020
$708$	1.12586	0.0423125
$709$	−17.3676	−0.652255	−0.326128	−	0.945326i	$-0.605744\pi$
$709$	−17.3676	−0.652255	−0.326128	+	0.945326i	$0.605744\pi$
$710$	−22.0056	−0.825854
$711$	42.0111	1.57554
$712$	−13.9376	−0.522334
$713$	−2.08848	−0.0782142
$714$	0.0196877	0.000736795 0
$715$	1.52882	0.0571747
$716$	−48.5144	−1.81307
$717$	−2.22881	−0.0832366
$718$	65.6721	2.45086
$719$	14.8594	0.554163	0.277081	−	0.960846i	$-0.410633\pi$
$719$	14.8594	0.554163	0.277081	+	0.960846i	$0.410633\pi$
$720$	13.7233	0.511439
$721$	0.0127755	0.000475784 0
$722$	24.2448	0.902298
$723$	0.663724	0.0246842
$724$	−18.1383	−0.674106
$725$	29.0304	1.07816
$726$	4.23164	0.157051
$727$	19.1523	0.710320	0.355160	−	0.934806i	$-0.384426\pi$
$727$	19.1523	0.710320	0.355160	+	0.934806i	$0.384426\pi$
$728$	0.0229728	0.000851428 0
$729$	−25.3379	−0.938443
$730$	−82.3997	−3.04975
$731$	−57.4926	−2.12644
$732$	2.50630	0.0926355
$733$	−30.6639	−1.13260	−0.566298	−	0.824201i	$-0.691625\pi$
$733$	−30.6639	−1.13260	−0.566298	+	0.824201i	$0.691625\pi$
$734$	25.9695	0.958553
$735$	−4.14059	−0.152728
$736$	−5.05562	−0.186352
$737$	2.26730	0.0835170
$738$	15.1540	0.557827
$739$	32.8622	1.20885	0.604427	−	0.796660i	$-0.293402\pi$
$739$	32.8622	1.20885	0.604427	+	0.796660i	$0.293402\pi$
$740$	20.6110	0.757677
$741$	0.579496	0.0212883
$742$	0.252794	0.00928034
$743$	−25.4278	−0.932855	−0.466428	−	0.884559i	$-0.654459\pi$
$743$	−25.4278	−0.932855	−0.466428	+	0.884559i	$0.654459\pi$
$744$	−1.02662	−0.0376377
$745$	−33.3062	−1.22025
$746$	69.4381	2.54231
$747$	43.9745	1.60894
$748$	5.81020	0.212442
$749$	−0.0677052	−0.00247389
$750$	−1.66391	−0.0607576
$751$	35.6667	1.30150	0.650749	−	0.759293i	$-0.274455\pi$
$751$	35.6667	1.30150	0.650749	+	0.759293i	$0.274455\pi$
$752$	−0.860397	−0.0313755
$753$	4.68281	0.170651
$754$	11.8832	0.432761
$755$	1.94545	0.0708022
$756$	−0.0302519	−0.00110025
$757$	0.703651	0.0255746	0.0127873	−	0.999918i	$-0.495930\pi$
$757$	0.703651	0.0255746	0.0127873	+	0.999918i	$0.495930\pi$
$758$	61.9611	2.25053
$759$	0.0496426	0.00180191
$760$	19.0571	0.691272
$761$	−5.57300	−0.202021	−0.101010	−	0.994885i	$-0.532208\pi$
$761$	−5.57300	−0.202021	−0.101010	+	0.994885i	$0.532208\pi$
$762$	6.06421	0.219683
$763$	−0.177005	−0.00640801
$764$	−45.4680	−1.64497
$765$	50.7664	1.83546
$766$	−68.8812	−2.48878
$767$	−2.55086	−0.0921061
$768$	−1.07639	−0.0388410
$769$	20.4209	0.736397	0.368199	−	0.929747i	$-0.379975\pi$
$769$	20.4209	0.736397	0.368199	+	0.929747i	$0.379975\pi$
$770$	0.0289352	0.00104275
$771$	−0.120648	−0.00434504
$772$	−55.4038	−1.99403
$773$	19.5894	0.704581	0.352291	−	0.935891i	$-0.385403\pi$
$773$	19.5894	0.704581	0.352291	+	0.935891i	$0.385403\pi$
$774$	74.2098	2.66741
$775$	18.2616	0.655975
$776$	−13.0795	−0.469528
$777$	0.00369110	0.000132418 0
$778$	3.87333	0.138866
$779$	−6.54038	−0.234333
$780$	−1.99069	−0.0712782
$781$	−1.16301	−0.0416158
$782$	−8.08794	−0.289224
$783$	−4.86928	−0.174014
$784$	9.63786	0.344209
$785$	0.518112	0.0184922
$786$	−0.609794	−0.0217506
$787$	12.3450	0.440051	0.220026	−	0.975494i	$-0.429386\pi$
$787$	12.3450	0.440051	0.220026	+	0.975494i	$0.429386\pi$
$788$	76.0734	2.71000
$789$	3.70532	0.131913
$790$	105.191	3.74254
$791$	−0.104731	−0.00372381
$792$	−2.33363	−0.0829219
$793$	−5.67850	−0.201650
$794$	−46.9412	−1.66588
$795$	−6.81629	−0.241749
$796$	18.6623	0.661467
$797$	47.3485	1.67717	0.838585	−	0.544770i	$-0.183383\pi$
$797$	47.3485	1.67717	0.838585	+	0.544770i	$0.183383\pi$
$798$	0.0109678	0.000388257 0
$799$	−3.18285	−0.112601
$800$	44.2060	1.56292
$801$	−20.6840	−0.730833
$802$	36.1908	1.27794
$803$	−4.35489	−0.153681
$804$	−2.95227	−0.104118
$805$	−0.0238499	−0.000840599 0
$806$	7.47513	0.263300
$807$	5.62729	0.198090
$808$	25.8282	0.908632
$809$	−40.0479	−1.40801	−0.704005	−	0.710195i	$-0.748607\pi$
$809$	−40.0479	−1.40801	−0.704005	+	0.710195i	$0.748607\pi$
$810$	−64.8355	−2.27809
$811$	−19.6923	−0.691490	−0.345745	−	0.938329i	$-0.612374\pi$
$811$	−19.6923	−0.691490	−0.345745	+	0.938329i	$0.612374\pi$
$812$	0.133173	0.00467346
$813$	0.859132	0.0301311
$814$	1.83966	0.0644802
$815$	−75.9963	−2.66203
$816$	1.23565	0.0432565
$817$	−32.0285	−1.12053
$818$	−23.9090	−0.835957
$819$	0.0340925	0.00119129
$820$	22.4676	0.784602
$821$	30.7174	1.07205	0.536023	−	0.844204i	$-0.319926\pi$
$821$	30.7174	1.07205	0.536023	+	0.844204i	$0.319926\pi$
$822$	−6.87175	−0.239680
$823$	−35.3037	−1.23061	−0.615305	−	0.788289i	$-0.710967\pi$
$823$	−35.3037	−1.23061	−0.615305	+	0.788289i	$0.710967\pi$
$824$	−2.57987	−0.0898741
$825$	−0.434072	−0.0151124
$826$	−0.0482787	−0.00167983
$827$	11.5059	0.400100	0.200050	−	0.979786i	$-0.435890\pi$
$827$	11.5059	0.400100	0.200050	+	0.979786i	$0.435890\pi$
$828$	6.18159	0.214825
$829$	31.7873	1.10402	0.552009	−	0.833838i	$-0.313861\pi$
$829$	31.7873	1.10402	0.552009	+	0.833838i	$0.313861\pi$
$830$	110.107	3.82188
$831$	−3.04381	−0.105588
$832$	14.9033	0.516680
$833$	35.6531	1.23531
$834$	4.06329	0.140700
$835$	−5.31718	−0.184009
$836$	3.23680	0.111947
$837$	−3.06302	−0.105873
$838$	−81.9505	−2.83093
$839$	47.0740	1.62518	0.812588	−	0.582838i	$-0.198058\pi$
$839$	47.0740	1.62518	0.812588	+	0.582838i	$0.198058\pi$
$840$	−0.0117237	−0.000404507 0
$841$	−7.56479	−0.260855
$842$	30.6468	1.05616
$843$	−0.438526	−0.0151036
$844$	52.0534	1.79175
$845$	−39.1324	−1.34619
$846$	4.10833	0.141247
$847$	−0.107446	−0.00369190
$848$	15.8660	0.544839
$849$	−3.87616	−0.133030
$850$	70.7205	2.42569
$851$	−1.51635	−0.0519797
$852$	1.51437	0.0518813
$853$	21.9371	0.751113	0.375556	−	0.926800i	$-0.377452\pi$
$853$	21.9371	0.751113	0.375556	+	0.926800i	$0.377452\pi$
$854$	−0.107474	−0.00367769
$855$	28.2814	0.967204
$856$	13.6723	0.467311
$857$	1.27332	0.0434957	0.0217478	−	0.999763i	$-0.493077\pi$
$857$	1.27332	0.0434957	0.0217478	+	0.999763i	$0.493077\pi$
$858$	−0.177681	−0.00606595
$859$	−27.8458	−0.950088	−0.475044	−	0.879962i	$-0.657568\pi$
$859$	−27.8458	−0.950088	−0.475044	+	0.879962i	$0.657568\pi$
$860$	110.025	3.75181
$861$	0.00402358	0.000137123 0
$862$	−62.1221	−2.11589
$863$	39.2540	1.33622	0.668111	−	0.744061i	$-0.267103\pi$
$863$	39.2540	1.33622	0.668111	+	0.744061i	$0.267103\pi$
$864$	−7.41469	−0.252253
$865$	−41.5424	−1.41248
$866$	32.2699	1.09658
$867$	1.57564	0.0535116
$868$	0.0837725	0.00284342
$869$	5.55944	0.188591
$870$	−6.06436	−0.205601
$871$	6.68893	0.226646
$872$	35.7443	1.21045
$873$	−19.4105	−0.656947
$874$	−4.50570	−0.152408
$875$	0.0422488	0.00142827
$876$	5.67053	0.191590
$877$	9.15700	0.309210	0.154605	−	0.987976i	$-0.450590\pi$
$877$	9.15700	0.309210	0.154605	+	0.987976i	$0.450590\pi$
$878$	71.0459	2.39768
$879$	−3.27242	−0.110376
$880$	1.81605	0.0612189
$881$	6.52474	0.219824	0.109912	−	0.993941i	$-0.464943\pi$
$881$	6.52474	0.219824	0.109912	+	0.993941i	$0.464943\pi$
$882$	−46.0200	−1.54957
$883$	−46.7878	−1.57454	−0.787268	−	0.616612i	$-0.788505\pi$
$883$	−46.7878	−1.57454	−0.787268	+	0.616612i	$0.788505\pi$
$884$	17.1411	0.576518
$885$	1.30178	0.0437589
$886$	−36.5879	−1.22920
$887$	25.8215	0.867001	0.433501	−	0.901153i	$-0.357278\pi$
$887$	25.8215	0.867001	0.433501	+	0.901153i	$0.357278\pi$
$888$	−0.745379	−0.0250133
$889$	−0.153978	−0.00516425
$890$	−51.7905	−1.73602
$891$	−3.42660	−0.114796
$892$	33.0634	1.10704
$893$	−1.77313	−0.0593355
$894$	3.87089	0.129462
$895$	−56.0950	−1.87505
$896$	0.142379	0.00475656
$897$	0.146454	0.00488997
$898$	62.2027	2.07573
$899$	13.4838	0.449711
$900$	−54.0515	−1.80172
$901$	58.6926	1.95533
$902$	2.00537	0.0667716
$903$	0.0197036	0.000655695 0
$904$	21.1493	0.703416
$905$	−20.9725	−0.697149
$906$	−0.226103	−0.00751175
$907$	24.9248	0.827614	0.413807	−	0.910365i	$-0.364199\pi$
$907$	24.9248	0.827614	0.413807	+	0.910365i	$0.364199\pi$
$908$	71.2626	2.36493
$909$	38.3300	1.27133
$910$	0.0853640	0.00282979
$911$	−43.2387	−1.43256	−0.716281	−	0.697812i	$-0.754157\pi$
$911$	−43.2387	−1.43256	−0.716281	+	0.697812i	$0.754157\pi$
$912$	0.688368	0.0227941
$913$	5.81926	0.192589
$914$	−46.3963	−1.53465
$915$	2.89791	0.0958021
$916$	−14.3845	−0.475279
$917$	0.0154834	0.000511308 0
$918$	−11.8620	−0.391503
$919$	33.6677	1.11060	0.555298	−	0.831651i	$-0.312604\pi$
$919$	33.6677	1.11060	0.555298	+	0.831651i	$0.312604\pi$
$920$	4.81623	0.158787
$921$	−1.48119	−0.0488070
$922$	25.4847	0.839294
$923$	−3.43109	−0.112936
$924$	−0.00199125	−6.55072e−5 0
$925$	13.2588	0.435948
$926$	−78.6883	−2.58586
$927$	−3.82863	−0.125749
$928$	32.6405	1.07148
$929$	−25.4364	−0.834542	−0.417271	−	0.908782i	$-0.637013\pi$
$929$	−25.4364	−0.834542	−0.417271	+	0.908782i	$0.637013\pi$
$930$	−3.81479	−0.125092
$931$	19.8619	0.650949
$932$	−29.6827	−0.972288
$933$	−2.05888	−0.0674049
$934$	−35.6050	−1.16503
$935$	6.71806	0.219704
$936$	−6.88462	−0.225031
$937$	−60.4769	−1.97569	−0.987846	−	0.155433i	$-0.950323\pi$
$937$	−60.4769	−1.97569	−0.987846	+	0.155433i	$0.950323\pi$
$938$	0.126598	0.00413357
$939$	−6.11987	−0.199714
$940$	6.09107	0.198669
$941$	−6.87289	−0.224050	−0.112025	−	0.993705i	$-0.535734\pi$
$941$	−6.87289	−0.224050	−0.112025	+	0.993705i	$0.535734\pi$
$942$	−0.0602156	−0.00196193
$943$	−1.65293	−0.0538269
$944$	−3.03009	−0.0986211
$945$	−0.0349788	−0.00113786
$946$	9.82037	0.319288
$947$	−3.58627	−0.116538	−0.0582690	−	0.998301i	$-0.518558\pi$
$947$	−3.58627	−0.116538	−0.0582690	+	0.998301i	$0.518558\pi$
$948$	−7.23900	−0.235112
$949$	−12.8477	−0.417054
$950$	39.3976	1.27823
$951$	−4.13723	−0.134159
$952$	0.100949	0.00327176
$953$	−36.0682	−1.16836	−0.584181	−	0.811623i	$-0.698584\pi$
$953$	−36.0682	−1.16836	−0.584181	+	0.811623i	$0.698584\pi$
$954$	−75.7587	−2.45278
$955$	−52.5725	−1.70121
$956$	−36.7271	−1.18784
$957$	−0.320506	−0.0103605
$958$	−26.1657	−0.845375
$959$	0.174482	0.00563433
$960$	−7.60563	−0.245471
$961$	−22.5180	−0.726387
$962$	5.42733	0.174984
$963$	20.2903	0.653846
$964$	10.9371	0.352259
$965$	−64.0608	−2.06219
$966$	0.00277186	8.91833e−5 0
$967$	46.2237	1.48645	0.743226	−	0.669040i	$-0.233295\pi$
$967$	46.2237	1.48645	0.743226	+	0.669040i	$0.233295\pi$
$968$	21.6977	0.697390
$969$	2.54646	0.0818042
$970$	−48.6019	−1.56051
$971$	16.6348	0.533837	0.266918	−	0.963719i	$-0.413995\pi$
$971$	16.6348	0.533837	0.266918	+	0.963719i	$0.413995\pi$
$972$	13.6227	0.436948
$973$	−0.103172	−0.00330754
$974$	−73.1082	−2.34254
$975$	−1.28059	−0.0410117
$976$	−6.74534	−0.215913
$977$	28.4101	0.908921	0.454460	−	0.890767i	$-0.349832\pi$
$977$	28.4101	0.908921	0.454460	+	0.890767i	$0.349832\pi$
$978$	8.83238	0.282429
$979$	−2.73716	−0.0874802
$980$	−68.2300	−2.17953
$981$	53.0459	1.69363
$982$	19.5517	0.623918
$983$	−5.48735	−0.175019	−0.0875096	−	0.996164i	$-0.527891\pi$
$983$	−5.48735	−0.175019	−0.0875096	+	0.996164i	$0.527891\pi$
$984$	−0.812519	−0.0259022
$985$	87.9600	2.80264
$986$	52.2180	1.66296
$987$	0.00109081	3.47209e−5 0
$988$	9.54912	0.303798
$989$	−8.09446	−0.257389
$990$	−8.67147	−0.275597
$991$	10.2495	0.325585	0.162792	−	0.986660i	$-0.447950\pi$
$991$	10.2495	0.325585	0.162792	+	0.986660i	$0.447950\pi$
$992$	20.5325	0.651907
$993$	0.241656	0.00766872
$994$	−0.0649384	−0.00205972
$995$	21.5783	0.684078
$996$	−7.57731	−0.240096
$997$	−41.5059	−1.31451	−0.657253	−	0.753670i	$-0.728282\pi$
$997$	−41.5059	−1.31451	−0.657253	+	0.753670i	$0.728282\pi$
$998$	−43.4568	−1.37560
$999$	−2.22391	−0.0703614

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.20	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.20	✓	149	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21437 q^{2} +0.176199 q^{3} +2.90346 q^{4} +3.35713 q^{5} -0.390170 q^{6} +0.00990688 q^{7} -2.00059 q^{8} -2.96895 q^{9} +O(q^{10})\)	\(q-2.21437 q^{2} +0.176199 q^{3} +2.90346 q^{4} +3.35713 q^{5} -0.390170 q^{6} +0.00990688 q^{7} -2.00059 q^{8} -2.96895 q^{9} -7.43394 q^{10} -0.392889 q^{11} +0.511585 q^{12} -1.15909 q^{13} -0.0219376 q^{14} +0.591521 q^{15} -1.37686 q^{16} -5.09337 q^{17} +6.57438 q^{18} -2.83746 q^{19} +9.74727 q^{20} +0.00174558 q^{21} +0.870004 q^{22} -0.717103 q^{23} -0.352501 q^{24} +6.27031 q^{25} +2.56667 q^{26} -1.05172 q^{27} +0.0287642 q^{28} +4.62982 q^{29} -1.30985 q^{30} +2.91239 q^{31} +7.05005 q^{32} -0.0692265 q^{33} +11.2786 q^{34} +0.0332587 q^{35} -8.62023 q^{36} +2.11454 q^{37} +6.28320 q^{38} -0.204231 q^{39} -6.71624 q^{40} +2.30501 q^{41} -0.00386536 q^{42} +11.2877 q^{43} -1.14074 q^{44} -9.96716 q^{45} +1.58794 q^{46} +0.624900 q^{47} -0.242600 q^{48} -6.99990 q^{49} -13.8848 q^{50} -0.897444 q^{51} -3.36538 q^{52} -11.5233 q^{53} +2.32890 q^{54} -1.31898 q^{55} -0.0198196 q^{56} -0.499956 q^{57} -10.2522 q^{58} +2.20073 q^{59} +1.71745 q^{60} +4.89909 q^{61} -6.44911 q^{62} -0.0294131 q^{63} -12.8578 q^{64} -3.89123 q^{65} +0.153293 q^{66} -5.77083 q^{67} -14.7884 q^{68} -0.126352 q^{69} -0.0736472 q^{70} +2.96015 q^{71} +5.93966 q^{72} +11.0843 q^{73} -4.68239 q^{74} +1.10482 q^{75} -8.23844 q^{76} -0.00389231 q^{77} +0.452243 q^{78} -14.1501 q^{79} -4.62228 q^{80} +8.72155 q^{81} -5.10416 q^{82} -14.8114 q^{83} +0.00506821 q^{84} -17.0991 q^{85} -24.9953 q^{86} +0.815767 q^{87} +0.786011 q^{88} +6.96676 q^{89} +22.0710 q^{90} -0.0114830 q^{91} -2.08208 q^{92} +0.513158 q^{93} -1.38376 q^{94} -9.52572 q^{95} +1.24221 q^{96} +6.53784 q^{97} +15.5004 q^{98} +1.16647 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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