LMFDB - Embedded newform 4003.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, 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("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45287 q^{2} -0.154053 q^{3} +4.01656 q^{4} -1.18015 q^{5} +0.377872 q^{6} +4.09823 q^{7} -4.94635 q^{8} -2.97627 q^{9} +O(q^{10})$	\(q-2.45287 q^{2} -0.154053 q^{3} +4.01656 q^{4} -1.18015 q^{5} +0.377872 q^{6} +4.09823 q^{7} -4.94635 q^{8} -2.97627 q^{9} +2.89476 q^{10} +5.48058 q^{11} -0.618764 q^{12} -3.18906 q^{13} -10.0524 q^{14} +0.181806 q^{15} +4.09963 q^{16} -0.192870 q^{17} +7.30039 q^{18} +6.80476 q^{19} -4.74015 q^{20} -0.631346 q^{21} -13.4431 q^{22} -2.66990 q^{23} +0.762001 q^{24} -3.60724 q^{25} +7.82234 q^{26} +0.920663 q^{27} +16.4608 q^{28} -9.24117 q^{29} -0.445946 q^{30} +4.63160 q^{31} -0.163149 q^{32} -0.844301 q^{33} +0.473085 q^{34} -4.83654 q^{35} -11.9544 q^{36} -5.89403 q^{37} -16.6912 q^{38} +0.491285 q^{39} +5.83745 q^{40} +4.56265 q^{41} +1.54861 q^{42} -4.29737 q^{43} +22.0131 q^{44} +3.51245 q^{45} +6.54892 q^{46} -5.19678 q^{47} -0.631561 q^{48} +9.79553 q^{49} +8.84809 q^{50} +0.0297123 q^{51} -12.8090 q^{52} -7.66747 q^{53} -2.25826 q^{54} -6.46792 q^{55} -20.2713 q^{56} -1.04830 q^{57} +22.6674 q^{58} -7.73668 q^{59} +0.730235 q^{60} +1.67991 q^{61} -11.3607 q^{62} -12.1974 q^{63} -7.79908 q^{64} +3.76357 q^{65} +2.07096 q^{66} -1.81328 q^{67} -0.774674 q^{68} +0.411307 q^{69} +11.8634 q^{70} -6.15697 q^{71} +14.7217 q^{72} -4.56558 q^{73} +14.4573 q^{74} +0.555707 q^{75} +27.3317 q^{76} +22.4607 q^{77} -1.20506 q^{78} +9.09484 q^{79} -4.83819 q^{80} +8.78697 q^{81} -11.1916 q^{82} -15.1678 q^{83} -2.53584 q^{84} +0.227616 q^{85} +10.5409 q^{86} +1.42363 q^{87} -27.1089 q^{88} -7.31368 q^{89} -8.61557 q^{90} -13.0695 q^{91} -10.7238 q^{92} -0.713512 q^{93} +12.7470 q^{94} -8.03065 q^{95} +0.0251336 q^{96} +2.45124 q^{97} -24.0271 q^{98} -16.3117 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * 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 $

$2$	−2.45287	−1.73444	−0.867220	−	0.497926i	$-0.834095\pi$
$2$	−2.45287	−1.73444	−0.867220	+	0.497926i	$0.834095\pi$
$3$	−0.154053	−0.0889426	−0.0444713	−	0.999011i	$-0.514160\pi$
$3$	−0.154053	−0.0889426	−0.0444713	+	0.999011i	$0.514160\pi$
$4$	4.01656	2.00828
$5$	−1.18015	−0.527780	−0.263890	−	0.964553i	$-0.585006\pi$
$5$	−1.18015	−0.527780	−0.263890	+	0.964553i	$0.585006\pi$
$6$	0.377872	0.154266
$7$	4.09823	1.54899	0.774494	−	0.632582i	$-0.218005\pi$
$7$	4.09823	1.54899	0.774494	+	0.632582i	$0.218005\pi$
$8$	−4.94635	−1.74880
$9$	−2.97627	−0.992089
$10$	2.89476	0.915402
$11$	5.48058	1.65246	0.826229	−	0.563335i	$-0.190482\pi$
$11$	5.48058	1.65246	0.826229	+	0.563335i	$0.190482\pi$
$12$	−0.618764	−0.178622
$13$	−3.18906	−0.884486	−0.442243	−	0.896895i	$-0.645817\pi$
$13$	−3.18906	−0.884486	−0.442243	+	0.896895i	$0.645817\pi$
$14$	−10.0524	−2.68662
$15$	0.181806	0.0469421
$16$	4.09963	1.02491
$17$	−0.192870	−0.0467779	−0.0233889	−	0.999726i	$-0.507446\pi$
$17$	−0.192870	−0.0467779	−0.0233889	+	0.999726i	$0.507446\pi$
$18$	7.30039	1.72072
$19$	6.80476	1.56112	0.780560	−	0.625081i	$-0.214934\pi$
$19$	6.80476	1.56112	0.780560	+	0.625081i	$0.214934\pi$
$20$	−4.74015	−1.05993
$21$	−0.631346	−0.137771
$22$	−13.4431	−2.86609
$23$	−2.66990	−0.556713	−0.278357	−	0.960478i	$-0.589790\pi$
$23$	−2.66990	−0.556713	−0.278357	+	0.960478i	$0.589790\pi$
$24$	0.762001	0.155543
$25$	−3.60724	−0.721448
$26$	7.82234	1.53409
$27$	0.920663	0.177182
$28$	16.4608	3.11080
$29$	−9.24117	−1.71604	−0.858022	−	0.513614i	$-0.828306\pi$
$29$	−9.24117	−1.71604	−0.858022	+	0.513614i	$0.828306\pi$
$30$	−0.445946	−0.0814183
$31$	4.63160	0.831859	0.415930	−	0.909397i	$-0.363456\pi$
$31$	4.63160	0.831859	0.415930	+	0.909397i	$0.363456\pi$
$32$	−0.163149	−0.0288409
$33$	−0.844301	−0.146974
$34$	0.473085	0.0811334
$35$	−4.83654	−0.817524
$36$	−11.9544	−1.99239
$37$	−5.89403	−0.968973	−0.484486	−	0.874799i	$-0.660994\pi$
$37$	−5.89403	−0.968973	−0.484486	+	0.874799i	$0.660994\pi$
$38$	−16.6912	−2.70767
$39$	0.491285	0.0786685
$40$	5.83745	0.922982
$41$	4.56265	0.712566	0.356283	−	0.934378i	$-0.384044\pi$
$41$	4.56265	0.712566	0.356283	+	0.934378i	$0.384044\pi$
$42$	1.54861	0.238955
$43$	−4.29737	−0.655344	−0.327672	−	0.944792i	$-0.606264\pi$
$43$	−4.29737	−0.655344	−0.327672	+	0.944792i	$0.606264\pi$
$44$	22.0131	3.31860
$45$	3.51245	0.523605
$46$	6.54892	0.965586
$47$	−5.19678	−0.758029	−0.379014	−	0.925391i	$-0.623737\pi$
$47$	−5.19678	−0.758029	−0.379014	+	0.925391i	$0.623737\pi$
$48$	−0.631561	−0.0911580
$49$	9.79553	1.39936
$50$	8.84809	1.25131
$51$	0.0297123	0.00416055
$52$	−12.8090	−1.77630
$53$	−7.66747	−1.05321	−0.526604	−	0.850111i	$-0.676535\pi$
$53$	−7.66747	−1.05321	−0.526604	+	0.850111i	$0.676535\pi$
$54$	−2.25826	−0.307311
$55$	−6.46792	−0.872134
$56$	−20.2713	−2.70887
$57$	−1.04830	−0.138850
$58$	22.6674	2.97637
$59$	−7.73668	−1.00723	−0.503615	−	0.863928i	$-0.667997\pi$
$59$	−7.73668	−1.00723	−0.503615	+	0.863928i	$0.667997\pi$
$60$	0.730235	0.0942729
$61$	1.67991	0.215091	0.107545	−	0.994200i	$-0.465701\pi$
$61$	1.67991	0.215091	0.107545	+	0.994200i	$0.465701\pi$
$62$	−11.3607	−1.44281
$63$	−12.1974	−1.53673
$64$	−7.79908	−0.974885
$65$	3.76357	0.466814
$66$	2.07096	0.254917
$67$	−1.81328	−0.221528	−0.110764	−	0.993847i	$-0.535330\pi$
$67$	−1.81328	−0.221528	−0.110764	+	0.993847i	$0.535330\pi$
$68$	−0.774674	−0.0939431
$69$	0.411307	0.0495156
$70$	11.8634	1.41795
$71$	−6.15697	−0.730698	−0.365349	−	0.930871i	$-0.619050\pi$
$71$	−6.15697	−0.730698	−0.365349	+	0.930871i	$0.619050\pi$
$72$	14.7217	1.73497
$73$	−4.56558	−0.534360	−0.267180	−	0.963647i	$-0.586092\pi$
$73$	−4.56558	−0.534360	−0.267180	+	0.963647i	$0.586092\pi$
$74$	14.4573	1.68062
$75$	0.555707	0.0641675
$76$	27.3317	3.13517
$77$	22.4607	2.55963
$78$	−1.20506	−0.136446
$79$	9.09484	1.02325	0.511625	−	0.859209i	$-0.329044\pi$
$79$	9.09484	1.02325	0.511625	+	0.859209i	$0.329044\pi$
$80$	−4.83819	−0.540926
$81$	8.78697	0.976330
$82$	−11.1916	−1.23590
$83$	−15.1678	−1.66489	−0.832444	−	0.554109i	$-0.813059\pi$
$83$	−15.1678	−1.66489	−0.832444	+	0.554109i	$0.813059\pi$
$84$	−2.53584	−0.276683
$85$	0.227616	0.0246884
$86$	10.5409	1.13665
$87$	1.42363	0.152629
$88$	−27.1089	−2.88982
$89$	−7.31368	−0.775248	−0.387624	−	0.921817i	$-0.626704\pi$
$89$	−7.31368	−0.775248	−0.387624	+	0.921817i	$0.626704\pi$
$90$	−8.61557	−0.908161
$91$	−13.0695	−1.37006
$92$	−10.7238	−1.11804
$93$	−0.713512	−0.0739877
$94$	12.7470	1.31475
$95$	−8.03065	−0.823928
$96$	0.0251336	0.00256519
$97$	2.45124	0.248886	0.124443	−	0.992227i	$-0.460286\pi$
$97$	2.45124	0.248886	0.124443	+	0.992227i	$0.460286\pi$
$98$	−24.0271	−2.42711
$99$	−16.3117	−1.63938
$100$	−14.4887	−1.44887
$101$	−18.7995	−1.87062	−0.935308	−	0.353834i	$-0.884878\pi$
$101$	−18.7995	−1.87062	−0.935308	+	0.353834i	$0.884878\pi$
$102$	−0.0728802	−0.00721622
$103$	0.771377	0.0760060	0.0380030	−	0.999278i	$-0.487900\pi$
$103$	0.771377	0.0760060	0.0380030	+	0.999278i	$0.487900\pi$
$104$	15.7742	1.54679
$105$	0.745084	0.0727128
$106$	18.8073	1.82673
$107$	6.21860	0.601175	0.300588	−	0.953754i	$-0.402817\pi$
$107$	6.21860	0.601175	0.300588	+	0.953754i	$0.402817\pi$
$108$	3.69790	0.355830
$109$	−10.9029	−1.04431	−0.522153	−	0.852852i	$-0.674871\pi$
$109$	−10.9029	−1.04431	−0.522153	+	0.852852i	$0.674871\pi$
$110$	15.8649	1.51266
$111$	0.907994	0.0861830
$112$	16.8013	1.58757
$113$	18.5806	1.74791	0.873957	−	0.486003i	$-0.161546\pi$
$113$	18.5806	1.74791	0.873957	+	0.486003i	$0.161546\pi$
$114$	2.57133	0.240827
$115$	3.15089	0.293822
$116$	−37.1177	−3.44629
$117$	9.49149	0.877489
$118$	18.9770	1.74698
$119$	−0.790427	−0.0724583
$120$	−0.899277	−0.0820924
$121$	19.0368	1.73061
$122$	−4.12060	−0.373062
$123$	−0.702890	−0.0633775
$124$	18.6031	1.67061
$125$	10.1579	0.908546
$126$	29.9187	2.66537
$127$	−8.00695	−0.710502	−0.355251	−	0.934771i	$-0.615605\pi$
$127$	−8.00695	−0.710502	−0.355251	+	0.934771i	$0.615605\pi$
$128$	19.4564	1.71972
$129$	0.662024	0.0582880
$130$	−9.23155	−0.809660
$131$	−7.53027	−0.657923	−0.328961	−	0.944343i	$-0.606699\pi$
$131$	−7.53027	−0.657923	−0.328961	+	0.944343i	$0.606699\pi$
$132$	−3.39118	−0.295165
$133$	27.8875	2.41815
$134$	4.44774	0.384226
$135$	−1.08652	−0.0935129
$136$	0.954004	0.0818052
$137$	−7.41725	−0.633698	−0.316849	−	0.948476i	$-0.602625\pi$
$137$	−7.41725	−0.633698	−0.316849	+	0.948476i	$0.602625\pi$
$138$	−1.00888	−0.0858817
$139$	5.13575	0.435609	0.217805	−	0.975992i	$-0.430110\pi$
$139$	5.13575	0.435609	0.217805	+	0.975992i	$0.430110\pi$
$140$	−19.4262	−1.64182
$141$	0.800581	0.0674211
$142$	15.1022	1.26735
$143$	−17.4779	−1.46158
$144$	−12.2016	−1.01680
$145$	10.9060	0.905693
$146$	11.1988	0.926816
$147$	−1.50903	−0.124463
$148$	−23.6737	−1.94597
$149$	−0.175622	−0.0143875	−0.00719377	−	0.999974i	$-0.502290\pi$
$149$	−0.175622	−0.0143875	−0.00719377	+	0.999974i	$0.502290\pi$
$150$	−1.36308	−0.111295
$151$	11.8629	0.965388	0.482694	−	0.875789i	$-0.339658\pi$
$151$	11.8629	0.965388	0.482694	+	0.875789i	$0.339658\pi$
$152$	−33.6588	−2.73009
$153$	0.574033	0.0464078
$154$	−55.0931	−4.43953
$155$	−5.46599	−0.439039
$156$	1.97327	0.157988
$157$	9.01649	0.719594	0.359797	−	0.933031i	$-0.382846\pi$
$157$	9.01649	0.719594	0.359797	+	0.933031i	$0.382846\pi$
$158$	−22.3084	−1.77476
$159$	1.18120	0.0936751
$160$	0.192541	0.0152217
$161$	−10.9419	−0.862342
$162$	−21.5533	−1.69339
$163$	8.57431	0.671592	0.335796	−	0.941935i	$-0.390995\pi$
$163$	8.57431	0.671592	0.335796	+	0.941935i	$0.390995\pi$
$164$	18.3262	1.43103
$165$	0.996403	0.0775699
$166$	37.2047	2.88765
$167$	−19.3151	−1.49465	−0.747324	−	0.664460i	$-0.768662\pi$
$167$	−19.3151	−1.49465	−0.747324	+	0.664460i	$0.768662\pi$
$168$	3.12286	0.240934
$169$	−2.82990	−0.217685
$170$	−0.558312	−0.0428206
$171$	−20.2528	−1.54877
$172$	−17.2607	−1.31611
$173$	−13.7794	−1.04763	−0.523815	−	0.851832i	$-0.675492\pi$
$173$	−13.7794	−1.04763	−0.523815	+	0.851832i	$0.675492\pi$
$174$	−3.49198	−0.264726
$175$	−14.7833	−1.11751
$176$	22.4684	1.69362
$177$	1.19186	0.0895856
$178$	17.9395	1.34462
$179$	3.01303	0.225204	0.112602	−	0.993640i	$-0.464081\pi$
$179$	3.01303	0.225204	0.112602	+	0.993640i	$0.464081\pi$
$180$	14.1080	1.05154
$181$	12.3330	0.916706	0.458353	−	0.888770i	$-0.348440\pi$
$181$	12.3330	0.916706	0.458353	+	0.888770i	$0.348440\pi$
$182$	32.0578	2.37628
$183$	−0.258796	−0.0191307
$184$	13.2063	0.973581
$185$	6.95585	0.511404
$186$	1.75015	0.128327
$187$	−1.05704	−0.0772984
$188$	−20.8732	−1.52233
$189$	3.77309	0.274452
$190$	19.6981	1.42905
$191$	9.79911	0.709039	0.354519	−	0.935049i	$-0.384644\pi$
$191$	9.79911	0.709039	0.354519	+	0.935049i	$0.384644\pi$
$192$	1.20147	0.0867089
$193$	−9.11411	−0.656048	−0.328024	−	0.944669i	$-0.606383\pi$
$193$	−9.11411	−0.656048	−0.328024	+	0.944669i	$0.606383\pi$
$194$	−6.01256	−0.431677
$195$	−0.579790	−0.0415197
$196$	39.3443	2.81031
$197$	23.5975	1.68125	0.840625	−	0.541618i	$-0.182188\pi$
$197$	23.5975	1.68125	0.840625	+	0.541618i	$0.182188\pi$
$198$	40.0104	2.84341
$199$	−12.0048	−0.850997	−0.425499	−	0.904959i	$-0.639901\pi$
$199$	−12.0048	−0.850997	−0.425499	+	0.904959i	$0.639901\pi$
$200$	17.8427	1.26167
$201$	0.279342	0.0197033
$202$	46.1126	3.24447
$203$	−37.8725	−2.65813
$204$	0.119341	0.00835554
$205$	−5.38462	−0.376078
$206$	−1.89209	−0.131828
$207$	7.94635	0.552309
$208$	−13.0740	−0.906517
$209$	37.2941	2.57968
$210$	−1.82759	−0.126116
$211$	4.08280	0.281071	0.140536	−	0.990076i	$-0.455118\pi$
$211$	4.08280	0.281071	0.140536	+	0.990076i	$0.455118\pi$
$212$	−30.7969	−2.11514
$213$	0.948500	0.0649902
$214$	−15.2534	−1.04270
$215$	5.07155	0.345877
$216$	−4.55392	−0.309855
$217$	18.9814	1.28854
$218$	26.7433	1.81129
$219$	0.703342	0.0475274
$220$	−25.9788	−1.75149
$221$	0.615074	0.0413744
$222$	−2.22719	−0.149479
$223$	13.9434	0.933719	0.466860	−	0.884331i	$-0.345385\pi$
$223$	13.9434	0.933719	0.466860	+	0.884331i	$0.345385\pi$
$224$	−0.668623	−0.0446742
$225$	10.7361	0.715741
$226$	−45.5757	−3.03165
$227$	7.01701	0.465735	0.232868	−	0.972508i	$-0.425189\pi$
$227$	7.01701	0.465735	0.232868	+	0.972508i	$0.425189\pi$
$228$	−4.21054	−0.278850
$229$	−21.7982	−1.44046	−0.720232	−	0.693733i	$-0.755965\pi$
$229$	−21.7982	−1.44046	−0.720232	+	0.693733i	$0.755965\pi$
$230$	−7.72872	−0.509617
$231$	−3.46014	−0.227661
$232$	45.7101	3.00102
$233$	3.49397	0.228898	0.114449	−	0.993429i	$-0.463490\pi$
$233$	3.49397	0.228898	0.114449	+	0.993429i	$0.463490\pi$
$234$	−23.2814	−1.52195
$235$	6.13299	0.400072
$236$	−31.0748	−2.02280
$237$	−1.40109	−0.0910105
$238$	1.93881	0.125675
$239$	−5.25990	−0.340235	−0.170117	−	0.985424i	$-0.554415\pi$
$239$	−5.25990	−0.340235	−0.170117	+	0.985424i	$0.554415\pi$
$240$	0.745338	0.0481114
$241$	22.9316	1.47715	0.738576	−	0.674170i	$-0.235499\pi$
$241$	22.9316	1.47715	0.738576	+	0.674170i	$0.235499\pi$
$242$	−46.6946	−3.00165
$243$	−4.11565	−0.264019
$244$	6.74746	0.431962
$245$	−11.5602	−0.738555
$246$	1.72410	0.109924
$247$	−21.7008	−1.38079
$248$	−22.9095	−1.45476
$249$	2.33665	0.148079
$250$	−24.9159	−1.57582
$251$	15.8844	1.00261	0.501307	−	0.865270i	$-0.332853\pi$
$251$	15.8844	1.00261	0.501307	+	0.865270i	$0.332853\pi$
$252$	−48.9918	−3.08619
$253$	−14.6326	−0.919945
$254$	19.6400	1.23232
$255$	−0.0350650	−0.00219585
$256$	−32.1259	−2.00787
$257$	6.40882	0.399772	0.199886	−	0.979819i	$-0.435943\pi$
$257$	6.40882	0.399772	0.199886	+	0.979819i	$0.435943\pi$
$258$	−1.62386	−0.101097
$259$	−24.1551	−1.50093
$260$	15.1166	0.937493
$261$	27.5042	1.70247
$262$	18.4708	1.14113
$263$	−20.9579	−1.29232	−0.646161	−	0.763201i	$-0.723627\pi$
$263$	−20.9579	−1.29232	−0.646161	+	0.763201i	$0.723627\pi$
$264$	4.17621	0.257028
$265$	9.04878	0.555862
$266$	−68.4044	−4.19414
$267$	1.12670	0.0689526
$268$	−7.28316	−0.444890
$269$	1.52770	0.0931453	0.0465726	−	0.998915i	$-0.485170\pi$
$269$	1.52770	0.0931453	0.0465726	+	0.998915i	$0.485170\pi$
$270$	2.66509	0.162192
$271$	−8.25345	−0.501361	−0.250681	−	0.968070i	$-0.580654\pi$
$271$	−8.25345	−0.501361	−0.250681	+	0.968070i	$0.580654\pi$
$272$	−0.790697	−0.0479430
$273$	2.01340	0.121856
$274$	18.1935	1.09911
$275$	−19.7698	−1.19216
$276$	1.65204	0.0994411
$277$	−21.2202	−1.27500	−0.637500	−	0.770451i	$-0.720031\pi$
$277$	−21.2202	−1.27500	−0.637500	+	0.770451i	$0.720031\pi$
$278$	−12.5973	−0.755537
$279$	−13.7849	−0.825278
$280$	23.9232	1.42969
$281$	23.2045	1.38426	0.692132	−	0.721771i	$-0.256672\pi$
$281$	23.2045	1.38426	0.692132	+	0.721771i	$0.256672\pi$
$282$	−1.96372	−0.116938
$283$	3.64808	0.216856	0.108428	−	0.994104i	$-0.465418\pi$
$283$	3.64808	0.216856	0.108428	+	0.994104i	$0.465418\pi$
$284$	−24.7298	−1.46745
$285$	1.23715	0.0732823
$286$	42.8710	2.53501
$287$	18.6988	1.10376
$288$	0.485575	0.0286128
$289$	−16.9628	−0.997812
$290$	−26.7509	−1.57087
$291$	−0.377621	−0.0221365
$292$	−18.3379	−1.07315
$293$	−19.9772	−1.16708	−0.583541	−	0.812083i	$-0.698333\pi$
$293$	−19.9772	−1.16708	−0.583541	+	0.812083i	$0.698333\pi$
$294$	3.70146	0.215873
$295$	9.13045	0.531596
$296$	29.1540	1.69454
$297$	5.04577	0.292785
$298$	0.430778	0.0249543
$299$	8.51448	0.492405
$300$	2.23203	0.128866
$301$	−17.6117	−1.01512
$302$	−29.0981	−1.67441
$303$	2.89612	0.166378
$304$	27.8970	1.60000
$305$	−1.98255	−0.113520
$306$	−1.40803	−0.0804916
$307$	−4.63766	−0.264685	−0.132342	−	0.991204i	$-0.542250\pi$
$307$	−4.63766	−0.264685	−0.132342	+	0.991204i	$0.542250\pi$
$308$	90.2148	5.14046
$309$	−0.118833	−0.00676018
$310$	13.4073	0.761486
$311$	−0.0269580	−0.00152865	−0.000764325	−	1.00000i	$-0.500243\pi$
$311$	−0.0269580	−0.00152865	−0.000764325		1.00000i	$0.500243\pi$
$312$	−2.43007	−0.137576
$313$	0.0974778	0.00550977	0.00275489	−	0.999996i	$-0.499123\pi$
$313$	0.0974778	0.00550977	0.00275489	+	0.999996i	$0.499123\pi$
$314$	−22.1163	−1.24809
$315$	14.3948	0.811057
$316$	36.5300	2.05497
$317$	19.1623	1.07626	0.538131	−	0.842861i	$-0.319131\pi$
$317$	19.1623	1.07626	0.538131	+	0.842861i	$0.319131\pi$
$318$	−2.89732	−0.162474
$319$	−50.6470	−2.83569
$320$	9.20410	0.514525
$321$	−0.957995	−0.0534701
$322$	26.8390	1.49568
$323$	−1.31244	−0.0730259
$324$	35.2934	1.96074
$325$	11.5037	0.638111
$326$	−21.0317	−1.16484
$327$	1.67962	0.0928834
$328$	−22.5685	−1.24614
$329$	−21.2976	−1.17418
$330$	−2.44404	−0.134540
$331$	27.4329	1.50785	0.753924	−	0.656962i	$-0.228159\pi$
$331$	27.4329	1.50785	0.753924	+	0.656962i	$0.228159\pi$
$332$	−60.9226	−3.34356
$333$	17.5422	0.961308
$334$	47.3774	2.59238
$335$	2.13995	0.116918
$336$	−2.58829	−0.141203
$337$	−26.6037	−1.44919	−0.724597	−	0.689173i	$-0.757974\pi$
$337$	−26.6037	−1.44919	−0.724597	+	0.689173i	$0.757974\pi$
$338$	6.94137	0.377561
$339$	−2.86240	−0.155464
$340$	0.914234	0.0495813
$341$	25.3838	1.37461
$342$	49.6774	2.68625
$343$	11.4567	0.618605
$344$	21.2563	1.14606
$345$	−0.485405	−0.0261333
$346$	33.7991	1.81705
$347$	−7.03327	−0.377566	−0.188783	−	0.982019i	$-0.560454\pi$
$347$	−7.03327	−0.377566	−0.188783	+	0.982019i	$0.560454\pi$
$348$	5.71810	0.306523
$349$	0.0147714	0.000790697 0	0.000395349	−	1.00000i	$-0.499874\pi$
$349$	0.0147714	0.000790697 0	0.000395349		1.00000i	$0.499874\pi$
$350$	36.2615	1.93826
$351$	−2.93605	−0.156715
$352$	−0.894151	−0.0476584
$353$	−34.8482	−1.85478	−0.927392	−	0.374090i	$-0.877955\pi$
$353$	−34.8482	−1.85478	−0.927392	+	0.374090i	$0.877955\pi$
$354$	−2.92347	−0.155381
$355$	7.26616	0.385648
$356$	−29.3758	−1.55692
$357$	0.121768	0.00644463
$358$	−7.39056	−0.390603
$359$	−36.5280	−1.92787	−0.963936	−	0.266133i	$-0.914254\pi$
$359$	−36.5280	−1.92787	−0.963936	+	0.266133i	$0.914254\pi$
$360$	−17.3738	−0.915680
$361$	27.3048	1.43710
$362$	−30.2512	−1.58997
$363$	−2.93267	−0.153925
$364$	−52.4945	−2.75146
$365$	5.38807	0.282025
$366$	0.634791	0.0331811
$367$	−1.89373	−0.0988519	−0.0494259	−	0.998778i	$-0.515739\pi$
$367$	−1.89373	−0.0988519	−0.0494259	+	0.998778i	$0.515739\pi$
$368$	−10.9456	−0.570580
$369$	−13.5797	−0.706929
$370$	−17.0618	−0.887000
$371$	−31.4231	−1.63141
$372$	−2.86586	−0.148588
$373$	29.4413	1.52441	0.762206	−	0.647334i	$-0.224116\pi$
$373$	29.4413	1.52441	0.762206	+	0.647334i	$0.224116\pi$
$374$	2.59278	0.134069
$375$	−1.56485	−0.0808085
$376$	25.7051	1.32564
$377$	29.4707	1.51782
$378$	−9.25490	−0.476021
$379$	−11.1366	−0.572051	−0.286025	−	0.958222i	$-0.592334\pi$
$379$	−11.1366	−0.572051	−0.286025	+	0.958222i	$0.592334\pi$
$380$	−32.2556	−1.65468
$381$	1.23350	0.0631939
$382$	−24.0359	−1.22979
$383$	−0.293213	−0.0149825	−0.00749123	−	0.999972i	$-0.502385\pi$
$383$	−0.293213	−0.0149825	−0.00749123	+	0.999972i	$0.502385\pi$
$384$	−2.99732	−0.152956
$385$	−26.5070	−1.35092
$386$	22.3557	1.13788
$387$	12.7901	0.650159
$388$	9.84554	0.499832
$389$	−24.2789	−1.23099	−0.615494	−	0.788141i	$-0.711044\pi$
$389$	−24.2789	−1.23099	−0.615494	+	0.788141i	$0.711044\pi$
$390$	1.42215	0.0720133
$391$	0.514945	0.0260419
$392$	−48.4521	−2.44720
$393$	1.16006	0.0585174
$394$	−57.8815	−2.91603
$395$	−10.7333	−0.540050
$396$	−65.5168	−3.29234
$397$	−12.7662	−0.640717	−0.320358	−	0.947296i	$-0.603803\pi$
$397$	−12.7662	−0.640717	−0.320358	+	0.947296i	$0.603803\pi$
$398$	29.4462	1.47600
$399$	−4.29616	−0.215077
$400$	−14.7884	−0.739418
$401$	−0.156996	−0.00784002	−0.00392001	−	0.999992i	$-0.501248\pi$
$401$	−0.156996	−0.00784002	−0.00392001	+	0.999992i	$0.501248\pi$
$402$	−0.685189	−0.0341741
$403$	−14.7704	−0.735768
$404$	−75.5092	−3.75672
$405$	−10.3700	−0.515288
$406$	92.8962	4.61036
$407$	−32.3027	−1.60119
$408$	−0.146967	−0.00727597
$409$	9.35103	0.462379	0.231189	−	0.972909i	$-0.425738\pi$
$409$	9.35103	0.462379	0.231189	+	0.972909i	$0.425738\pi$
$410$	13.2078	0.652285
$411$	1.14265	0.0563628
$412$	3.09828	0.152641
$413$	−31.7067	−1.56019
$414$	−19.4913	−0.957947
$415$	17.9004	0.878694
$416$	0.520292	0.0255094
$417$	−0.791179	−0.0387442
$418$	−91.4774	−4.47430
$419$	−26.8069	−1.30960	−0.654800	−	0.755802i	$-0.727247\pi$
$419$	−26.8069	−1.30960	−0.654800	+	0.755802i	$0.727247\pi$
$420$	2.99267	0.146028
$421$	−2.74086	−0.133581	−0.0667906	−	0.997767i	$-0.521276\pi$
$421$	−2.74086	−0.133581	−0.0667906	+	0.997767i	$0.521276\pi$
$422$	−10.0146	−0.487501
$423$	15.4670	0.752032
$424$	37.9260	1.84185
$425$	0.695729	0.0337478
$426$	−2.32655	−0.112722
$427$	6.88467	0.333172
$428$	24.9774	1.20733
$429$	2.69252	0.129996
$430$	−12.4399	−0.599903
$431$	6.83256	0.329113	0.164556	−	0.986368i	$-0.447381\pi$
$431$	6.83256	0.329113	0.164556	+	0.986368i	$0.447381\pi$
$432$	3.77438	0.181595
$433$	−10.9181	−0.524689	−0.262345	−	0.964974i	$-0.584496\pi$
$433$	−10.9181	−0.524689	−0.262345	+	0.964974i	$0.584496\pi$
$434$	−46.5588	−2.23489
$435$	−1.68010	−0.0805547
$436$	−43.7921	−2.09726
$437$	−18.1681	−0.869096
$438$	−1.72520	−0.0824334
$439$	36.1942	1.72745	0.863727	−	0.503959i	$-0.168124\pi$
$439$	36.1942	1.72745	0.863727	+	0.503959i	$0.168124\pi$
$440$	31.9926	1.52519
$441$	−29.1541	−1.38829
$442$	−1.50870	−0.0717614
$443$	17.3906	0.826251	0.413126	−	0.910674i	$-0.364437\pi$
$443$	17.3906	0.826251	0.413126	+	0.910674i	$0.364437\pi$
$444$	3.64701	0.173080
$445$	8.63125	0.409161
$446$	−34.2013	−1.61948
$447$	0.0270552	0.00127967
$448$	−31.9625	−1.51009
$449$	−6.52024	−0.307709	−0.153855	−	0.988094i	$-0.549169\pi$
$449$	−6.52024	−0.307709	−0.153855	+	0.988094i	$0.549169\pi$
$450$	−26.3343	−1.24141
$451$	25.0060	1.17748
$452$	74.6300	3.51030
$453$	−1.82751	−0.0858641
$454$	−17.2118	−0.807789
$455$	15.4240	0.723089
$456$	5.18524	0.242821
$457$	−14.9429	−0.698999	−0.349499	−	0.936937i	$-0.613648\pi$
$457$	−14.9429	−0.698999	−0.349499	+	0.936937i	$0.613648\pi$
$458$	53.4681	2.49840
$459$	−0.177568	−0.00828818
$460$	12.6557	0.590077
$461$	−17.3974	−0.810276	−0.405138	−	0.914255i	$-0.632777\pi$
$461$	−17.3974	−0.810276	−0.405138	+	0.914255i	$0.632777\pi$
$462$	8.48727	0.394864
$463$	−1.81386	−0.0842972	−0.0421486	−	0.999111i	$-0.513420\pi$
$463$	−1.81386	−0.0842972	−0.0421486	+	0.999111i	$0.513420\pi$
$464$	−37.8854	−1.75879
$465$	0.842052	0.0390492
$466$	−8.57025	−0.397009
$467$	−21.8978	−1.01331	−0.506655	−	0.862149i	$-0.669118\pi$
$467$	−21.8978	−1.01331	−0.506655	+	0.862149i	$0.669118\pi$
$468$	38.1232	1.76224
$469$	−7.43126	−0.343144
$470$	−15.0434	−0.693901
$471$	−1.38902	−0.0640026
$472$	38.2683	1.76144
$473$	−23.5521	−1.08293
$474$	3.43668	0.157852
$475$	−24.5464	−1.12627
$476$	−3.17480	−0.145517
$477$	22.8205	1.04488
$478$	12.9018	0.590117
$479$	7.21751	0.329776	0.164888	−	0.986312i	$-0.447274\pi$
$479$	7.21751	0.329776	0.164888	+	0.986312i	$0.447274\pi$
$480$	−0.0296615	−0.00135385
$481$	18.7964	0.857043
$482$	−56.2481	−2.56203
$483$	1.68563	0.0766990
$484$	76.4623	3.47556
$485$	−2.89283	−0.131357
$486$	10.0951	0.457925
$487$	−27.3996	−1.24160	−0.620798	−	0.783971i	$-0.713191\pi$
$487$	−27.3996	−1.24160	−0.620798	+	0.783971i	$0.713191\pi$
$488$	−8.30943	−0.376150
$489$	−1.32090	−0.0597332
$490$	28.3557	1.28098
$491$	−33.6499	−1.51860	−0.759300	−	0.650740i	$-0.774459\pi$
$491$	−33.6499	−1.51860	−0.759300	+	0.650740i	$0.774459\pi$
$492$	−2.82320	−0.127280
$493$	1.78235	0.0802729
$494$	53.2292	2.39489
$495$	19.2503	0.865234
$496$	18.9878	0.852579
$497$	−25.2327	−1.13184
$498$	−5.73150	−0.256835
$499$	5.45861	0.244361	0.122181	−	0.992508i	$-0.461011\pi$
$499$	5.45861	0.244361	0.122181	+	0.992508i	$0.461011\pi$
$500$	40.7996	1.82461
$501$	2.97555	0.132938
$502$	−38.9623	−1.73897
$503$	−34.3253	−1.53049	−0.765244	−	0.643740i	$-0.777382\pi$
$503$	−34.3253	−1.53049	−0.765244	+	0.643740i	$0.777382\pi$
$504$	60.3329	2.68744
$505$	22.1862	0.987274
$506$	35.8919	1.59559
$507$	0.435955	0.0193614
$508$	−32.1604	−1.42689
$509$	−4.96106	−0.219895	−0.109948	−	0.993937i	$-0.535068\pi$
$509$	−4.96106	−0.219895	−0.109948	+	0.993937i	$0.535068\pi$
$510$	0.0860097	0.00380858
$511$	−18.7108	−0.827717
$512$	39.8876	1.76280
$513$	6.26489	0.276602
$514$	−15.7200	−0.693379
$515$	−0.910342	−0.0401145
$516$	2.65906	0.117059
$517$	−28.4814	−1.25261
$518$	59.2493	2.60327
$519$	2.12276	0.0931790
$520$	−18.6160	−0.816364
$521$	−18.2186	−0.798172	−0.399086	−	0.916914i	$-0.630672\pi$
$521$	−18.2186	−0.798172	−0.399086	+	0.916914i	$0.630672\pi$
$522$	−67.4642	−2.95283
$523$	−20.2083	−0.883649	−0.441825	−	0.897101i	$-0.645669\pi$
$523$	−20.2083	−0.883649	−0.441825	+	0.897101i	$0.645669\pi$
$524$	−30.2458	−1.32129
$525$	2.27742	0.0993946
$526$	51.4071	2.24145
$527$	−0.893296	−0.0389126
$528$	−3.46132	−0.150635
$529$	−15.8716	−0.690070
$530$	−22.1955	−0.964110
$531$	23.0264	0.999262
$532$	112.012	4.85633
$533$	−14.5506	−0.630255
$534$	−2.76363	−0.119594
$535$	−7.33890	−0.317288
$536$	8.96914	0.387408
$537$	−0.464167	−0.0200303
$538$	−3.74724	−0.161555
$539$	53.6852	2.31238
$540$	−4.36408	−0.187800
$541$	−45.7308	−1.96612	−0.983060	−	0.183282i	$-0.941328\pi$
$541$	−45.7308	−1.96612	−0.983060	+	0.183282i	$0.941328\pi$
$542$	20.2446	0.869581
$543$	−1.89994	−0.0815342
$544$	0.0314666	0.00134912
$545$	12.8671	0.551164
$546$	−4.93860	−0.211353
$547$	−12.0802	−0.516514	−0.258257	−	0.966076i	$-0.583148\pi$
$547$	−12.0802	−0.516514	−0.258257	+	0.966076i	$0.583148\pi$
$548$	−29.7918	−1.27264
$549$	−4.99986	−0.213389
$550$	48.4926	2.06773
$551$	−62.8840	−2.67895
$552$	−2.03447	−0.0865928
$553$	37.2728	1.58500
$554$	52.0504	2.21141
$555$	−1.07157	−0.0454857
$556$	20.6281	0.874825
$557$	−32.4836	−1.37637	−0.688187	−	0.725533i	$-0.741593\pi$
$557$	−32.4836	−1.37637	−0.688187	+	0.725533i	$0.741593\pi$
$558$	33.8125	1.43140
$559$	13.7046	0.579642
$560$	−19.8280	−0.837887
$561$	0.162840	0.00687513
$562$	−56.9176	−2.40092
$563$	7.29351	0.307385	0.153692	−	0.988119i	$-0.450884\pi$
$563$	7.29351	0.307385	0.153692	+	0.988119i	$0.450884\pi$
$564$	3.21558	0.135400
$565$	−21.9279	−0.922514
$566$	−8.94827	−0.376124
$567$	36.0111	1.51232
$568$	30.4546	1.27784
$569$	−4.49709	−0.188528	−0.0942638	−	0.995547i	$-0.530050\pi$
$569$	−4.49709	−0.188528	−0.0942638	+	0.995547i	$0.530050\pi$
$570$	−3.03456	−0.127104
$571$	20.8980	0.874554	0.437277	−	0.899327i	$-0.355943\pi$
$571$	20.8980	0.874554	0.437277	+	0.899327i	$0.355943\pi$
$572$	−70.2010	−2.93525
$573$	−1.50958	−0.0630638
$574$	−45.8657	−1.91440
$575$	9.63099	0.401640
$576$	23.2122	0.967173
$577$	−24.8696	−1.03534	−0.517668	−	0.855582i	$-0.673200\pi$
$577$	−24.8696	−1.03534	−0.517668	+	0.855582i	$0.673200\pi$
$578$	41.6075	1.73064
$579$	1.40406	0.0583506
$580$	43.8046	1.81889
$581$	−62.1614	−2.57889
$582$	0.926254	0.0383945
$583$	−42.0222	−1.74038
$584$	22.5830	0.934490
$585$	−11.2014	−0.463121
$586$	49.0015	2.02423
$587$	42.8556	1.76884	0.884421	−	0.466691i	$-0.154554\pi$
$587$	42.8556	1.76884	0.884421	+	0.466691i	$0.154554\pi$
$588$	−6.06112	−0.249956
$589$	31.5169	1.29863
$590$	−22.3958	−0.922020
$591$	−3.63526	−0.149535
$592$	−24.1634	−0.993108
$593$	37.5717	1.54288	0.771442	−	0.636299i	$-0.219536\pi$
$593$	37.5717	1.54288	0.771442	+	0.636299i	$0.219536\pi$
$594$	−12.3766	−0.507818
$595$	0.932824	0.0382421
$596$	−0.705398	−0.0288942
$597$	1.84938	0.0756899
$598$	−20.8849	−0.854047
$599$	−6.82934	−0.279039	−0.139520	−	0.990219i	$-0.544556\pi$
$599$	−6.82934	−0.279039	−0.139520	+	0.990219i	$0.544556\pi$
$600$	−2.74872	−0.112216
$601$	−0.673297	−0.0274643	−0.0137322	−	0.999906i	$-0.504371\pi$
$601$	−0.673297	−0.0274643	−0.0137322	+	0.999906i	$0.504371\pi$
$602$	43.1990	1.76066
$603$	5.39681	0.219775
$604$	47.6480	1.93877
$605$	−22.4663	−0.913384
$606$	−7.10379	−0.288572
$607$	−19.9964	−0.811627	−0.405814	−	0.913956i	$-0.633012\pi$
$607$	−19.9964	−0.811627	−0.405814	+	0.913956i	$0.633012\pi$
$608$	−1.11019	−0.0450241
$609$	5.83438	0.236421
$610$	4.86293	0.196894
$611$	16.5728	0.670466
$612$	2.30564	0.0931999
$613$	−3.20002	−0.129248	−0.0646238	−	0.997910i	$-0.520585\pi$
$613$	−3.20002	−0.129248	−0.0646238	+	0.997910i	$0.520585\pi$
$614$	11.3756	0.459080
$615$	0.829517	0.0334494
$616$	−111.099	−4.47629
$617$	48.3916	1.94817	0.974086	−	0.226177i	$-0.0726226\pi$
$617$	48.3916	1.94817	0.974086	+	0.226177i	$0.0726226\pi$
$618$	0.291482	0.0117251
$619$	3.61406	0.145261	0.0726306	−	0.997359i	$-0.476861\pi$
$619$	3.61406	0.145261	0.0726306	+	0.997359i	$0.476861\pi$
$620$	−21.9545	−0.881712
$621$	−2.45808	−0.0986394
$622$	0.0661245	0.00265135
$623$	−29.9732	−1.20085
$624$	2.01409	0.0806280
$625$	6.04840	0.241936
$626$	−0.239100	−0.00955636
$627$	−5.74527	−0.229444
$628$	36.2153	1.44515
$629$	1.13678	0.0453265
$630$	−35.3086	−1.40673
$631$	−9.82783	−0.391240	−0.195620	−	0.980680i	$-0.562672\pi$
$631$	−9.82783	−0.391240	−0.195620	+	0.980680i	$0.562672\pi$
$632$	−44.9863	−1.78946
$633$	−0.628968	−0.0249992
$634$	−47.0026	−1.86671
$635$	9.44942	0.374989
$636$	4.74435	0.188126
$637$	−31.2385	−1.23772
$638$	124.230	4.91833
$639$	18.3248	0.724917
$640$	−22.9615	−0.907634
$641$	−3.71444	−0.146712	−0.0733558	−	0.997306i	$-0.523371\pi$
$641$	−3.71444	−0.146712	−0.0733558	+	0.997306i	$0.523371\pi$
$642$	2.34984	0.0927406
$643$	−35.9366	−1.41720	−0.708601	−	0.705609i	$-0.750673\pi$
$643$	−35.9366	−1.41720	−0.708601	+	0.705609i	$0.750673\pi$
$644$	−43.9488	−1.73182
$645$	−0.781289	−0.0307632
$646$	3.21923	0.126659
$647$	−28.7054	−1.12853	−0.564263	−	0.825595i	$-0.690839\pi$
$647$	−28.7054	−1.12853	−0.564263	+	0.825595i	$0.690839\pi$
$648$	−43.4635	−1.70741
$649$	−42.4015	−1.66440
$650$	−28.2171	−1.10676
$651$	−2.92414	−0.114606
$652$	34.4392	1.34874
$653$	−3.77911	−0.147888	−0.0739440	−	0.997262i	$-0.523559\pi$
$653$	−3.77911	−0.147888	−0.0739440	+	0.997262i	$0.523559\pi$
$654$	−4.11989	−0.161101
$655$	8.88687	0.347239
$656$	18.7052	0.730315
$657$	13.5884	0.530133
$658$	52.2403	2.03654
$659$	17.4480	0.679678	0.339839	−	0.940484i	$-0.389627\pi$
$659$	17.4480	0.679678	0.339839	+	0.940484i	$0.389627\pi$
$660$	4.00211	0.155782
$661$	−47.2122	−1.83634	−0.918172	−	0.396183i	$-0.870335\pi$
$661$	−47.2122	−1.83634	−0.918172	+	0.396183i	$0.870335\pi$
$662$	−67.2892	−2.61527
$663$	−0.0947541	−0.00367995
$664$	75.0256	2.91156
$665$	−32.9115	−1.27625
$666$	−43.0287	−1.66733
$667$	24.6730	0.955344
$668$	−77.5803	−3.00167
$669$	−2.14803	−0.0830474
$670$	−5.24901	−0.202787
$671$	9.20689	0.355428
$672$	0.103003	0.00397344
$673$	26.5048	1.02169	0.510843	−	0.859674i	$-0.329333\pi$
$673$	26.5048	1.02169	0.510843	+	0.859674i	$0.329333\pi$
$674$	65.2553	2.51354
$675$	−3.32105	−0.127827
$676$	−11.3665	−0.437172
$677$	−41.5900	−1.59843	−0.799216	−	0.601044i	$-0.794752\pi$
$677$	−41.5900	−1.59843	−0.799216	+	0.601044i	$0.794752\pi$
$678$	7.02108	0.269643
$679$	10.0457	0.385520
$680$	−1.12587	−0.0431751
$681$	−1.08099	−0.0414237
$682$	−62.2632	−2.38418
$683$	37.9879	1.45357	0.726784	−	0.686866i	$-0.241014\pi$
$683$	37.9879	1.45357	0.726784	+	0.686866i	$0.241014\pi$
$684$	−81.3466	−3.11036
$685$	8.75348	0.334453
$686$	−28.1018	−1.07293
$687$	3.35808	0.128119
$688$	−17.6177	−0.671667
$689$	24.4520	0.931548
$690$	1.19063	0.0453267
$691$	−32.6194	−1.24090	−0.620450	−	0.784246i	$-0.713050\pi$
$691$	−32.6194	−1.24090	−0.620450	+	0.784246i	$0.713050\pi$
$692$	−55.3459	−2.10394
$693$	−66.8491	−2.53939
$694$	17.2517	0.654865
$695$	−6.06097	−0.229906
$696$	−7.04179	−0.266918
$697$	−0.879999	−0.0333323
$698$	−0.0362324	−0.00137142
$699$	−0.538257	−0.0203588
$700$	−59.3781	−2.24428
$701$	33.4148	1.26206	0.631029	−	0.775759i	$-0.282633\pi$
$701$	33.4148	1.26206	0.631029	+	0.775759i	$0.282633\pi$
$702$	7.20174	0.271812
$703$	−40.1075	−1.51268
$704$	−42.7435	−1.61096
$705$	−0.944807	−0.0355835
$706$	85.4781	3.21701
$707$	−77.0446	−2.89756
$708$	4.78717	0.179913
$709$	3.88843	0.146033	0.0730166	−	0.997331i	$-0.476737\pi$
$709$	3.88843	0.146033	0.0730166	+	0.997331i	$0.476737\pi$
$710$	−17.8229	−0.668882
$711$	−27.0687	−1.01515
$712$	36.1760	1.35575
$713$	−12.3659	−0.463107
$714$	−0.298680	−0.0111778
$715$	20.6266	0.771390
$716$	12.1020	0.452273
$717$	0.810304	0.0302614
$718$	89.5983	3.34378
$719$	33.0481	1.23249	0.616244	−	0.787555i	$-0.288654\pi$
$719$	33.0481	1.23249	0.616244	+	0.787555i	$0.288654\pi$
$720$	14.3997	0.536647
$721$	3.16128	0.117732
$722$	−66.9751	−2.49255
$723$	−3.53268	−0.131382
$724$	49.5363	1.84100
$725$	33.3352	1.23804
$726$	7.19346	0.266974
$727$	39.1541	1.45215	0.726073	−	0.687618i	$-0.241343\pi$
$727$	39.1541	1.45215	0.726073	+	0.687618i	$0.241343\pi$
$728$	64.6464	2.39596
$729$	−25.7269	−0.952848
$730$	−13.2162	−0.489155
$731$	0.828835	0.0306556
$732$	−1.03947	−0.0384198
$733$	−28.0029	−1.03431	−0.517155	−	0.855892i	$-0.673009\pi$
$733$	−28.0029	−1.03431	−0.517155	+	0.855892i	$0.673009\pi$
$734$	4.64507	0.171453
$735$	1.78089	0.0656890
$736$	0.435592	0.0160561
$737$	−9.93784	−0.366065
$738$	33.3091	1.22613
$739$	50.6121	1.86179	0.930897	−	0.365281i	$-0.119027\pi$
$739$	50.6121	1.86179	0.930897	+	0.365281i	$0.119027\pi$
$740$	27.9386	1.02704
$741$	3.34308	0.122811
$742$	77.0767	2.82958
$743$	−45.8270	−1.68123	−0.840615	−	0.541633i	$-0.817806\pi$
$743$	−45.8270	−1.68123	−0.840615	+	0.541633i	$0.817806\pi$
$744$	3.52928	0.129390
$745$	0.207261	0.00759346
$746$	−72.2156	−2.64400
$747$	45.1436	1.65172
$748$	−4.24567	−0.155237
$749$	25.4853	0.931212
$750$	3.83837	0.140157
$751$	13.0035	0.474506	0.237253	−	0.971448i	$-0.423753\pi$
$751$	13.0035	0.474506	0.237253	+	0.971448i	$0.423753\pi$
$752$	−21.3049	−0.776910
$753$	−2.44704	−0.0891751
$754$	−72.2876	−2.63256
$755$	−14.0000	−0.509512
$756$	15.1549	0.551177
$757$	12.8466	0.466917	0.233458	−	0.972367i	$-0.424996\pi$
$757$	12.8466	0.466917	0.233458	+	0.972367i	$0.424996\pi$
$758$	27.3167	0.992188
$759$	2.25420	0.0818223
$760$	39.7225	1.44089
$761$	5.92289	0.214704	0.107352	−	0.994221i	$-0.465763\pi$
$761$	5.92289	0.214704	0.107352	+	0.994221i	$0.465763\pi$
$762$	−3.02560	−0.109606
$763$	−44.6826	−1.61762
$764$	39.3587	1.42395
$765$	−0.677446	−0.0244931
$766$	0.719212	0.0259862
$767$	24.6727	0.890880
$768$	4.94909	0.178585
$769$	−31.8209	−1.14749	−0.573746	−	0.819033i	$-0.694510\pi$
$769$	−31.8209	−1.14749	−0.573746	+	0.819033i	$0.694510\pi$
$770$	65.0183	2.34310
$771$	−0.987300	−0.0355567
$772$	−36.6074	−1.31753
$773$	53.0471	1.90797	0.953986	−	0.299851i	$-0.0969370\pi$
$773$	53.0471	1.90797	0.953986	+	0.299851i	$0.0969370\pi$
$774$	−31.3725	−1.12766
$775$	−16.7073	−0.600143
$776$	−12.1247	−0.435251
$777$	3.72117	0.133496
$778$	59.5529	2.13508
$779$	31.0477	1.11240
$780$	−2.32876	−0.0833831
$781$	−33.7438	−1.20745
$782$	−1.26309	−0.0451681
$783$	−8.50801	−0.304051
$784$	40.1581	1.43422
$785$	−10.6408	−0.379787
$786$	−2.84548	−0.101495
$787$	−37.7856	−1.34691	−0.673455	−	0.739228i	$-0.735191\pi$
$787$	−37.7856	−1.34691	−0.673455	+	0.739228i	$0.735191\pi$
$788$	94.7806	3.37642
$789$	3.22864	0.114943
$790$	26.3273	0.936685
$791$	76.1476	2.70750
$792$	80.6833	2.86696
$793$	−5.35734	−0.190245
$794$	31.3138	1.11128
$795$	−1.39399	−0.0494399
$796$	−48.2180	−1.70904
$797$	12.2357	0.433411	0.216706	−	0.976237i	$-0.430469\pi$
$797$	12.2357	0.433411	0.216706	+	0.976237i	$0.430469\pi$
$798$	10.5379	0.373038
$799$	1.00230	0.0354590
$800$	0.588518	0.0208072
$801$	21.7675	0.769116
$802$	0.385091	0.0135980
$803$	−25.0220	−0.883008
$804$	1.12199	0.0395697
$805$	12.9131	0.455127
$806$	36.2299	1.27614
$807$	−0.235346	−0.00828458
$808$	92.9888	3.27133
$809$	17.0387	0.599050	0.299525	−	0.954088i	$-0.403172\pi$
$809$	17.0387	0.599050	0.299525	+	0.954088i	$0.403172\pi$
$810$	25.4361	0.893735
$811$	29.3552	1.03080	0.515400	−	0.856950i	$-0.327644\pi$
$811$	29.3552	1.03080	0.515400	+	0.856950i	$0.327644\pi$
$812$	−152.117	−5.33827
$813$	1.27147	0.0445924
$814$	79.2343	2.77716
$815$	−10.1190	−0.354453
$816$	0.121809	0.00426418
$817$	−29.2426	−1.02307
$818$	−22.9368	−0.801967
$819$	38.8984	1.35922
$820$	−21.6276	−0.755270
$821$	52.4593	1.83084	0.915421	−	0.402497i	$-0.131858\pi$
$821$	52.4593	1.83084	0.915421	+	0.402497i	$0.131858\pi$
$822$	−2.80277	−0.0977578
$823$	22.6140	0.788276	0.394138	−	0.919051i	$-0.371043\pi$
$823$	22.6140	0.788276	0.394138	+	0.919051i	$0.371043\pi$
$824$	−3.81550	−0.132919
$825$	3.04560	0.106034
$826$	77.7724	2.70605
$827$	−0.426064	−0.0148157	−0.00740785	−	0.999973i	$-0.502358\pi$
$827$	−0.426064	−0.0148157	−0.00740785	+	0.999973i	$0.502358\pi$
$828$	31.9170	1.10919
$829$	27.4947	0.954930	0.477465	−	0.878651i	$-0.341556\pi$
$829$	27.4947	0.954930	0.477465	+	0.878651i	$0.341556\pi$
$830$	−43.9072	−1.52404
$831$	3.26904	0.113402
$832$	24.8717	0.862272
$833$	−1.88926	−0.0654591
$834$	1.94066	0.0671995
$835$	22.7948	0.788845
$836$	149.794	5.18073
$837$	4.26414	0.147390
$838$	65.7537	2.27142
$839$	18.4382	0.636558	0.318279	−	0.947997i	$-0.396895\pi$
$839$	18.4382	0.636558	0.318279	+	0.947997i	$0.396895\pi$
$840$	−3.68545	−0.127160
$841$	56.3993	1.94480
$842$	6.72296	0.231688
$843$	−3.57473	−0.123120
$844$	16.3988	0.564470
$845$	3.33971	0.114890
$846$	−37.9385	−1.30435
$847$	78.0171	2.68070
$848$	−31.4338	−1.07944
$849$	−0.561999	−0.0192877
$850$	−1.70653	−0.0585336
$851$	15.7365	0.539440
$852$	3.80971	0.130518
$853$	−21.4491	−0.734404	−0.367202	−	0.930141i	$-0.619684\pi$
$853$	−21.4491	−0.734404	−0.367202	+	0.930141i	$0.619684\pi$
$854$	−16.8872	−0.577867
$855$	23.9014	0.817410
$856$	−30.7594	−1.05134
$857$	−12.9996	−0.444056	−0.222028	−	0.975040i	$-0.571268\pi$
$857$	−12.9996	−0.444056	−0.222028	+	0.975040i	$0.571268\pi$
$858$	−6.60441	−0.225471
$859$	3.77899	0.128938	0.0644688	−	0.997920i	$-0.479465\pi$
$859$	3.77899	0.128938	0.0644688	+	0.997920i	$0.479465\pi$
$860$	20.3702	0.694618
$861$	−2.88061	−0.0981709
$862$	−16.7594	−0.570826
$863$	26.5162	0.902621	0.451311	−	0.892367i	$-0.350957\pi$
$863$	26.5162	0.902621	0.451311	+	0.892367i	$0.350957\pi$
$864$	−0.150205	−0.00511008
$865$	16.2618	0.552918
$866$	26.7806	0.910041
$867$	2.61317	0.0887480
$868$	76.2398	2.58775
$869$	49.8450	1.69088
$870$	4.12107	0.139717
$871$	5.78267	0.195938
$872$	53.9295	1.82628
$873$	−7.29554	−0.246917
$874$	44.5639	1.50740
$875$	41.6293	1.40733
$876$	2.82501	0.0954484
$877$	11.9881	0.404811	0.202405	−	0.979302i	$-0.435124\pi$
$877$	11.9881	0.404811	0.202405	+	0.979302i	$0.435124\pi$
$878$	−88.7796	−2.99617
$879$	3.07756	0.103803
$880$	−26.5161	−0.893857
$881$	12.2562	0.412923	0.206462	−	0.978455i	$-0.433805\pi$
$881$	12.2562	0.412923	0.206462	+	0.978455i	$0.433805\pi$
$882$	71.5112	2.40791
$883$	−9.64087	−0.324441	−0.162221	−	0.986755i	$-0.551866\pi$
$883$	−9.64087	−0.324441	−0.162221	+	0.986755i	$0.551866\pi$
$884$	2.47048	0.0830913
$885$	−1.40658	−0.0472815
$886$	−42.6568	−1.43308
$887$	8.66172	0.290832	0.145416	−	0.989371i	$-0.453548\pi$
$887$	8.66172	0.290832	0.145416	+	0.989371i	$0.453548\pi$
$888$	−4.49126	−0.150717
$889$	−32.8144	−1.10056
$890$	−21.1713	−0.709664
$891$	48.1577	1.61334
$892$	56.0045	1.87517
$893$	−35.3629	−1.18337
$894$	−0.0663628	−0.00221950
$895$	−3.55583	−0.118858
$896$	79.7370	2.66383
$897$	−1.31168	−0.0437958
$898$	15.9933	0.533703
$899$	−42.8014	−1.42751
$900$	43.1223	1.43741
$901$	1.47883	0.0492669
$902$	−61.3363	−2.04228
$903$	2.71313	0.0902873
$904$	−91.9061	−3.05675
$905$	−14.5548	−0.483819
$906$	4.48265	0.148926
$907$	−26.1870	−0.869525	−0.434762	−	0.900545i	$-0.643168\pi$
$907$	−26.1870	−0.869525	−0.434762	+	0.900545i	$0.643168\pi$
$908$	28.1842	0.935326
$909$	55.9522	1.85582
$910$	−37.8331	−1.25415
$911$	39.6510	1.31370	0.656848	−	0.754023i	$-0.271889\pi$
$911$	39.6510	1.31370	0.656848	+	0.754023i	$0.271889\pi$
$912$	−4.29763	−0.142309
$913$	−83.1286	−2.75116
$914$	36.6529	1.21237
$915$	0.305418	0.0100968
$916$	−87.5537	−2.89286
$917$	−30.8608	−1.01911
$918$	0.435552	0.0143753
$919$	44.1429	1.45614	0.728069	−	0.685503i	$-0.240418\pi$
$919$	44.1429	1.45614	0.728069	+	0.685503i	$0.240418\pi$
$920$	−15.5854	−0.513836
$921$	0.714445	0.0235418
$922$	42.6734	1.40538
$923$	19.6349	0.646292
$924$	−13.8979	−0.457206
$925$	21.2612	0.699064
$926$	4.44916	0.146208
$927$	−2.29582	−0.0754048
$928$	1.50769	0.0494923
$929$	26.8196	0.879921	0.439961	−	0.898017i	$-0.354992\pi$
$929$	26.8196	0.879921	0.439961	+	0.898017i	$0.354992\pi$
$930$	−2.06544	−0.0677285
$931$	66.6562	2.18457
$932$	14.0337	0.459691
$933$	0.00415297	0.000135962 0
$934$	53.7124	1.75752
$935$	1.24747	0.0407966
$936$	−46.9483	−1.53455
$937$	39.5638	1.29249	0.646246	−	0.763129i	$-0.276338\pi$
$937$	39.5638	1.29249	0.646246	+	0.763129i	$0.276338\pi$
$938$	18.2279	0.595162
$939$	−0.0150168	−0.000490053 0
$940$	24.6335	0.803457
$941$	−18.0284	−0.587709	−0.293854	−	0.955850i	$-0.594938\pi$
$941$	−18.0284	−0.587709	−0.293854	+	0.955850i	$0.594938\pi$
$942$	3.40708	0.111009
$943$	−12.1818	−0.396695
$944$	−31.7175	−1.03232
$945$	−4.45282	−0.144850
$946$	57.7702	1.87827
$947$	−14.3579	−0.466568	−0.233284	−	0.972409i	$-0.574947\pi$
$947$	−14.3579	−0.466568	−0.233284	+	0.972409i	$0.574947\pi$
$948$	−5.62755	−0.182774
$949$	14.5599	0.472634
$950$	60.2091	1.95344
$951$	−2.95201	−0.0957256
$952$	3.90973	0.126715
$953$	−17.8983	−0.579784	−0.289892	−	0.957059i	$-0.593619\pi$
$953$	−17.8983	−0.579784	−0.289892	+	0.957059i	$0.593619\pi$
$954$	−55.9756	−1.81228
$955$	−11.5644	−0.374217
$956$	−21.1267	−0.683287
$957$	7.80233	0.252213
$958$	−17.7036	−0.571977
$959$	−30.3976	−0.981590
$960$	−1.41792	−0.0457632
$961$	−9.54833	−0.308011
$962$	−46.1051	−1.48649
$963$	−18.5082	−0.596419
$964$	92.1060	2.96654
$965$	10.7560	0.346249
$966$	−4.13463	−0.133030
$967$	−45.4824	−1.46261	−0.731307	−	0.682048i	$-0.761090\pi$
$967$	−45.4824	−1.46261	−0.731307	+	0.682048i	$0.761090\pi$
$968$	−94.1625	−3.02650
$969$	0.202185	0.00649511
$970$	7.09574	0.227830
$971$	−37.2870	−1.19660	−0.598299	−	0.801273i	$-0.704156\pi$
$971$	−37.2870	−1.19660	−0.598299	+	0.801273i	$0.704156\pi$
$972$	−16.5308	−0.530224
$973$	21.0475	0.674753
$974$	67.2076	2.15347
$975$	−1.77218	−0.0567553
$976$	6.88702	0.220448
$977$	54.3149	1.73769	0.868844	−	0.495086i	$-0.164864\pi$
$977$	54.3149	1.73769	0.868844	+	0.495086i	$0.164864\pi$
$978$	3.23999	0.103604
$979$	−40.0832	−1.28106
$980$	−46.4323	−1.48322
$981$	32.4499	1.03605
$982$	82.5389	2.63392
$983$	−28.5523	−0.910677	−0.455339	−	0.890318i	$-0.650482\pi$
$983$	−28.5523	−0.910677	−0.455339	+	0.890318i	$0.650482\pi$
$984$	3.47674	0.110835
$985$	−27.8486	−0.887330
$986$	−4.37186	−0.139228
$987$	3.28097	0.104434
$988$	−87.1625	−2.77301
$989$	11.4736	0.364839
$990$	−47.2183	−1.50070
$991$	−28.2039	−0.895928	−0.447964	−	0.894052i	$-0.647851\pi$
$991$	−28.2039	−0.895928	−0.447964	+	0.894052i	$0.647851\pi$
$992$	−0.755640	−0.0239916
$993$	−4.22612	−0.134112
$994$	61.8925	1.96311
$995$	14.1675	0.449139
$996$	9.38531	0.297385
$997$	32.1059	1.01680	0.508402	−	0.861120i	$-0.330237\pi$
$997$	32.1059	1.01680	0.508402	+	0.861120i	$0.330237\pi$
$998$	−13.3893	−0.423829
$999$	−5.42642	−0.171684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.13	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.13	✓	152	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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45287 q^{2} -0.154053 q^{3} +4.01656 q^{4} -1.18015 q^{5} +0.377872 q^{6} +4.09823 q^{7} -4.94635 q^{8} -2.97627 q^{9} +O(q^{10})\)	\(q-2.45287 q^{2} -0.154053 q^{3} +4.01656 q^{4} -1.18015 q^{5} +0.377872 q^{6} +4.09823 q^{7} -4.94635 q^{8} -2.97627 q^{9} +2.89476 q^{10} +5.48058 q^{11} -0.618764 q^{12} -3.18906 q^{13} -10.0524 q^{14} +0.181806 q^{15} +4.09963 q^{16} -0.192870 q^{17} +7.30039 q^{18} +6.80476 q^{19} -4.74015 q^{20} -0.631346 q^{21} -13.4431 q^{22} -2.66990 q^{23} +0.762001 q^{24} -3.60724 q^{25} +7.82234 q^{26} +0.920663 q^{27} +16.4608 q^{28} -9.24117 q^{29} -0.445946 q^{30} +4.63160 q^{31} -0.163149 q^{32} -0.844301 q^{33} +0.473085 q^{34} -4.83654 q^{35} -11.9544 q^{36} -5.89403 q^{37} -16.6912 q^{38} +0.491285 q^{39} +5.83745 q^{40} +4.56265 q^{41} +1.54861 q^{42} -4.29737 q^{43} +22.0131 q^{44} +3.51245 q^{45} +6.54892 q^{46} -5.19678 q^{47} -0.631561 q^{48} +9.79553 q^{49} +8.84809 q^{50} +0.0297123 q^{51} -12.8090 q^{52} -7.66747 q^{53} -2.25826 q^{54} -6.46792 q^{55} -20.2713 q^{56} -1.04830 q^{57} +22.6674 q^{58} -7.73668 q^{59} +0.730235 q^{60} +1.67991 q^{61} -11.3607 q^{62} -12.1974 q^{63} -7.79908 q^{64} +3.76357 q^{65} +2.07096 q^{66} -1.81328 q^{67} -0.774674 q^{68} +0.411307 q^{69} +11.8634 q^{70} -6.15697 q^{71} +14.7217 q^{72} -4.56558 q^{73} +14.4573 q^{74} +0.555707 q^{75} +27.3317 q^{76} +22.4607 q^{77} -1.20506 q^{78} +9.09484 q^{79} -4.83819 q^{80} +8.78697 q^{81} -11.1916 q^{82} -15.1678 q^{83} -2.53584 q^{84} +0.227616 q^{85} +10.5409 q^{86} +1.42363 q^{87} -27.1089 q^{88} -7.31368 q^{89} -8.61557 q^{90} -13.0695 q^{91} -10.7238 q^{92} -0.713512 q^{93} +12.7470 q^{94} -8.03065 q^{95} +0.0251336 q^{96} +2.45124 q^{97} -24.0271 q^{98} -16.3117 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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