LMFDB - Embedded newform 4022.2.a.f.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.61133 q^{3} +1.00000 q^{4} -0.740567 q^{5} -2.61133 q^{6} -2.94518 q^{7} +1.00000 q^{8} +3.81902 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.61133 q^{3} +1.00000 q^{4} -0.740567 q^{5} -2.61133 q^{6} -2.94518 q^{7} +1.00000 q^{8} +3.81902 q^{9} -0.740567 q^{10} +3.23119 q^{11} -2.61133 q^{12} +2.51123 q^{13} -2.94518 q^{14} +1.93386 q^{15} +1.00000 q^{16} -1.46304 q^{17} +3.81902 q^{18} -1.61548 q^{19} -0.740567 q^{20} +7.69082 q^{21} +3.23119 q^{22} +4.93290 q^{23} -2.61133 q^{24} -4.45156 q^{25} +2.51123 q^{26} -2.13874 q^{27} -2.94518 q^{28} -6.62984 q^{29} +1.93386 q^{30} +0.600367 q^{31} +1.00000 q^{32} -8.43769 q^{33} -1.46304 q^{34} +2.18110 q^{35} +3.81902 q^{36} -8.64629 q^{37} -1.61548 q^{38} -6.55764 q^{39} -0.740567 q^{40} -1.90400 q^{41} +7.69082 q^{42} -0.328707 q^{43} +3.23119 q^{44} -2.82824 q^{45} +4.93290 q^{46} -6.46338 q^{47} -2.61133 q^{48} +1.67406 q^{49} -4.45156 q^{50} +3.82046 q^{51} +2.51123 q^{52} +8.34326 q^{53} -2.13874 q^{54} -2.39292 q^{55} -2.94518 q^{56} +4.21853 q^{57} -6.62984 q^{58} +8.62235 q^{59} +1.93386 q^{60} +9.21625 q^{61} +0.600367 q^{62} -11.2477 q^{63} +1.00000 q^{64} -1.85974 q^{65} -8.43769 q^{66} -10.1156 q^{67} -1.46304 q^{68} -12.8814 q^{69} +2.18110 q^{70} -6.89263 q^{71} +3.81902 q^{72} +15.1379 q^{73} -8.64629 q^{74} +11.6245 q^{75} -1.61548 q^{76} -9.51643 q^{77} -6.55764 q^{78} +6.92343 q^{79} -0.740567 q^{80} -5.87213 q^{81} -1.90400 q^{82} +9.15716 q^{83} +7.69082 q^{84} +1.08348 q^{85} -0.328707 q^{86} +17.3127 q^{87} +3.23119 q^{88} -4.53954 q^{89} -2.82824 q^{90} -7.39602 q^{91} +4.93290 q^{92} -1.56775 q^{93} -6.46338 q^{94} +1.19637 q^{95} -2.61133 q^{96} +3.81477 q^{97} +1.67406 q^{98} +12.3400 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) $ 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.61133	−1.50765	−0.753825	−	0.657075i	$-0.771793\pi$
$3$	−2.61133	−1.50765	−0.753825	+	0.657075i	$0.771793\pi$
$4$	1.00000	0.500000
$5$	−0.740567	−0.331192	−0.165596	−	0.986194i	$-0.552955\pi$
$5$	−0.740567	−0.331192	−0.165596	+	0.986194i	$0.552955\pi$
$6$	−2.61133	−1.06607
$7$	−2.94518	−1.11317	−0.556586	−	0.830790i	$-0.687889\pi$
$7$	−2.94518	−1.11317	−0.556586	+	0.830790i	$0.687889\pi$
$8$	1.00000	0.353553
$9$	3.81902	1.27301
$10$	−0.740567	−0.234188
$11$	3.23119	0.974241	0.487120	−	0.873335i	$-0.338047\pi$
$11$	3.23119	0.974241	0.487120	+	0.873335i	$0.338047\pi$
$12$	−2.61133	−0.753825
$13$	2.51123	0.696490	0.348245	−	0.937404i	$-0.386778\pi$
$13$	2.51123	0.696490	0.348245	+	0.937404i	$0.386778\pi$
$14$	−2.94518	−0.787131
$15$	1.93386	0.499321
$16$	1.00000	0.250000
$17$	−1.46304	−0.354838	−0.177419	−	0.984135i	$-0.556775\pi$
$17$	−1.46304	−0.354838	−0.177419	+	0.984135i	$0.556775\pi$
$18$	3.81902	0.900152
$19$	−1.61548	−0.370615	−0.185308	−	0.982681i	$-0.559328\pi$
$19$	−1.61548	−0.370615	−0.185308	+	0.982681i	$0.559328\pi$
$20$	−0.740567	−0.165596
$21$	7.69082	1.67827
$22$	3.23119	0.688892
$23$	4.93290	1.02858	0.514290	−	0.857616i	$-0.328055\pi$
$23$	4.93290	1.02858	0.514290	+	0.857616i	$0.328055\pi$
$24$	−2.61133	−0.533035
$25$	−4.45156	−0.890312
$26$	2.51123	0.492493
$27$	−2.13874	−0.411600
$28$	−2.94518	−0.556586
$29$	−6.62984	−1.23113	−0.615565	−	0.788086i	$-0.711072\pi$
$29$	−6.62984	−1.23113	−0.615565	+	0.788086i	$0.711072\pi$
$30$	1.93386	0.353073
$31$	0.600367	0.107829	0.0539146	−	0.998546i	$-0.482830\pi$
$31$	0.600367	0.107829	0.0539146	+	0.998546i	$0.482830\pi$
$32$	1.00000	0.176777
$33$	−8.43769	−1.46881
$34$	−1.46304	−0.250909
$35$	2.18110	0.368673
$36$	3.81902	0.636504
$37$	−8.64629	−1.42144	−0.710721	−	0.703474i	$-0.751631\pi$
$37$	−8.64629	−1.42144	−0.710721	+	0.703474i	$0.751631\pi$
$38$	−1.61548	−0.262065
$39$	−6.55764	−1.05006
$40$	−0.740567	−0.117094
$41$	−1.90400	−0.297354	−0.148677	−	0.988886i	$-0.547502\pi$
$41$	−1.90400	−0.297354	−0.148677	+	0.988886i	$0.547502\pi$
$42$	7.69082	1.18672
$43$	−0.328707	−0.0501274	−0.0250637	−	0.999686i	$-0.507979\pi$
$43$	−0.328707	−0.0501274	−0.0250637	+	0.999686i	$0.507979\pi$
$44$	3.23119	0.487120
$45$	−2.82824	−0.421610
$46$	4.93290	0.727316
$47$	−6.46338	−0.942781	−0.471391	−	0.881924i	$-0.656248\pi$
$47$	−6.46338	−0.942781	−0.471391	+	0.881924i	$0.656248\pi$
$48$	−2.61133	−0.376912
$49$	1.67406	0.239152
$50$	−4.45156	−0.629546
$51$	3.82046	0.534972
$52$	2.51123	0.348245
$53$	8.34326	1.14603	0.573017	−	0.819543i	$-0.305773\pi$
$53$	8.34326	1.14603	0.573017	+	0.819543i	$0.305773\pi$
$54$	−2.13874	−0.291045
$55$	−2.39292	−0.322661
$56$	−2.94518	−0.393566
$57$	4.21853	0.558758
$58$	−6.62984	−0.870540
$59$	8.62235	1.12253	0.561267	−	0.827635i	$-0.310314\pi$
$59$	8.62235	1.12253	0.561267	+	0.827635i	$0.310314\pi$
$60$	1.93386	0.249661
$61$	9.21625	1.18002	0.590010	−	0.807396i	$-0.299124\pi$
$61$	9.21625	1.18002	0.590010	+	0.807396i	$0.299124\pi$
$62$	0.600367	0.0762467
$63$	−11.2477	−1.41708
$64$	1.00000	0.125000
$65$	−1.85974	−0.230672
$66$	−8.43769	−1.03861
$67$	−10.1156	−1.23581	−0.617906	−	0.786252i	$-0.712019\pi$
$67$	−10.1156	−1.23581	−0.617906	+	0.786252i	$0.712019\pi$
$68$	−1.46304	−0.177419
$69$	−12.8814	−1.55074
$70$	2.18110	0.260691
$71$	−6.89263	−0.818004	−0.409002	−	0.912533i	$-0.634123\pi$
$71$	−6.89263	−0.818004	−0.409002	+	0.912533i	$0.634123\pi$
$72$	3.81902	0.450076
$73$	15.1379	1.77175	0.885877	−	0.463921i	$-0.153558\pi$
$73$	15.1379	1.77175	0.885877	+	0.463921i	$0.153558\pi$
$74$	−8.64629	−1.00511
$75$	11.6245	1.34228
$76$	−1.61548	−0.185308
$77$	−9.51643	−1.08450
$78$	−6.55764	−0.742507
$79$	6.92343	0.778947	0.389474	−	0.921038i	$-0.372657\pi$
$79$	6.92343	0.778947	0.389474	+	0.921038i	$0.372657\pi$
$80$	−0.740567	−0.0827980
$81$	−5.87213	−0.652459
$82$	−1.90400	−0.210261
$83$	9.15716	1.00513	0.502564	−	0.864540i	$-0.332390\pi$
$83$	9.15716	1.00513	0.502564	+	0.864540i	$0.332390\pi$
$84$	7.69082	0.839137
$85$	1.08348	0.117520
$86$	−0.328707	−0.0354454
$87$	17.3127	1.85611
$88$	3.23119	0.344446
$89$	−4.53954	−0.481191	−0.240595	−	0.970626i	$-0.577343\pi$
$89$	−4.53954	−0.481191	−0.240595	+	0.970626i	$0.577343\pi$
$90$	−2.82824	−0.298123
$91$	−7.39602	−0.775313
$92$	4.93290	0.514290
$93$	−1.56775	−0.162569
$94$	−6.46338	−0.666647
$95$	1.19637	0.122745
$96$	−2.61133	−0.266517
$97$	3.81477	0.387332	0.193666	−	0.981068i	$-0.437962\pi$
$97$	3.81477	0.387332	0.193666	+	0.981068i	$0.437962\pi$
$98$	1.67406	0.169106
$99$	12.3400	1.24022
$100$	−4.45156	−0.445156
$101$	7.44282	0.740589	0.370294	−	0.928914i	$-0.379257\pi$
$101$	7.44282	0.740589	0.370294	+	0.928914i	$0.379257\pi$
$102$	3.82046	0.378282
$103$	14.3014	1.40916	0.704580	−	0.709625i	$-0.251135\pi$
$103$	14.3014	1.40916	0.704580	+	0.709625i	$0.251135\pi$
$104$	2.51123	0.246246
$105$	−5.69557	−0.555830
$106$	8.34326	0.810369
$107$	12.4057	1.19930	0.599652	−	0.800261i	$-0.295306\pi$
$107$	12.4057	1.19930	0.599652	+	0.800261i	$0.295306\pi$
$108$	−2.13874	−0.205800
$109$	−19.4964	−1.86741	−0.933707	−	0.358038i	$-0.883446\pi$
$109$	−19.4964	−1.86741	−0.933707	+	0.358038i	$0.883446\pi$
$110$	−2.39292	−0.228156
$111$	22.5783	2.14304
$112$	−2.94518	−0.278293
$113$	17.0861	1.60732	0.803662	−	0.595086i	$-0.202882\pi$
$113$	17.0861	1.60732	0.803662	+	0.595086i	$0.202882\pi$
$114$	4.21853	0.395102
$115$	−3.65314	−0.340657
$116$	−6.62984	−0.615565
$117$	9.59045	0.886637
$118$	8.62235	0.793751
$119$	4.30890	0.394996
$120$	1.93386	0.176537
$121$	−0.559400	−0.0508546
$122$	9.21625	0.834400
$123$	4.97196	0.448306
$124$	0.600367	0.0539146
$125$	6.99952	0.626056
$126$	−11.2477	−1.00202
$127$	−3.00574	−0.266716	−0.133358	−	0.991068i	$-0.542576\pi$
$127$	−3.00574	−0.266716	−0.133358	+	0.991068i	$0.542576\pi$
$128$	1.00000	0.0883883
$129$	0.858361	0.0755745
$130$	−1.85974	−0.163110
$131$	7.77607	0.679398	0.339699	−	0.940534i	$-0.389675\pi$
$131$	7.77607	0.679398	0.339699	+	0.940534i	$0.389675\pi$
$132$	−8.43769	−0.734407
$133$	4.75786	0.412559
$134$	−10.1156	−0.873851
$135$	1.58388	0.136319
$136$	−1.46304	−0.125454
$137$	18.3385	1.56676	0.783382	−	0.621541i	$-0.213493\pi$
$137$	18.3385	1.56676	0.783382	+	0.621541i	$0.213493\pi$
$138$	−12.8814	−1.09654
$139$	23.2131	1.96891	0.984455	−	0.175638i	$-0.0561990\pi$
$139$	23.2131	1.96891	0.984455	+	0.175638i	$0.0561990\pi$
$140$	2.18110	0.184337
$141$	16.8780	1.42138
$142$	−6.89263	−0.578416
$143$	8.11427	0.678549
$144$	3.81902	0.318252
$145$	4.90984	0.407740
$146$	15.1379	1.25282
$147$	−4.37152	−0.360557
$148$	−8.64629	−0.710721
$149$	8.17325	0.669579	0.334790	−	0.942293i	$-0.391335\pi$
$149$	8.17325	0.669579	0.334790	+	0.942293i	$0.391335\pi$
$150$	11.6245	0.949134
$151$	−15.1133	−1.22991	−0.614953	−	0.788564i	$-0.710825\pi$
$151$	−15.1133	−1.22991	−0.614953	+	0.788564i	$0.710825\pi$
$152$	−1.61548	−0.131032
$153$	−5.58737	−0.451712
$154$	−9.51643	−0.766856
$155$	−0.444612	−0.0357121
$156$	−6.55764	−0.525032
$157$	15.5828	1.24364	0.621820	−	0.783161i	$-0.286394\pi$
$157$	15.5828	1.24364	0.621820	+	0.783161i	$0.286394\pi$
$158$	6.92343	0.550799
$159$	−21.7870	−1.72782
$160$	−0.740567	−0.0585470
$161$	−14.5283	−1.14499
$162$	−5.87213	−0.461358
$163$	20.4890	1.60482	0.802410	−	0.596773i	$-0.203551\pi$
$163$	20.4890	1.60482	0.802410	+	0.596773i	$0.203551\pi$
$164$	−1.90400	−0.148677
$165$	6.24868	0.486459
$166$	9.15716	0.710733
$167$	12.6431	0.978356	0.489178	−	0.872184i	$-0.337297\pi$
$167$	12.6431	0.978356	0.489178	+	0.872184i	$0.337297\pi$
$168$	7.69082	0.593359
$169$	−6.69372	−0.514901
$170$	1.08348	0.0830989
$171$	−6.16954	−0.471796
$172$	−0.328707	−0.0250637
$173$	−25.5056	−1.93915	−0.969577	−	0.244788i	$-0.921282\pi$
$173$	−25.5056	−1.93915	−0.969577	+	0.244788i	$0.921282\pi$
$174$	17.3127	1.31247
$175$	13.1106	0.991070
$176$	3.23119	0.243560
$177$	−22.5158	−1.69239
$178$	−4.53954	−0.340253
$179$	−15.7507	−1.17726	−0.588630	−	0.808403i	$-0.700332\pi$
$179$	−15.7507	−1.17726	−0.588630	+	0.808403i	$0.700332\pi$
$180$	−2.82824	−0.210805
$181$	−9.82618	−0.730374	−0.365187	−	0.930934i	$-0.618995\pi$
$181$	−9.82618	−0.730374	−0.365187	+	0.930934i	$0.618995\pi$
$182$	−7.39602	−0.548229
$183$	−24.0666	−1.77906
$184$	4.93290	0.363658
$185$	6.40316	0.470770
$186$	−1.56775	−0.114953
$187$	−4.72735	−0.345698
$188$	−6.46338	−0.471391
$189$	6.29896	0.458182
$190$	1.19637	0.0867937
$191$	23.9877	1.73569	0.867843	−	0.496838i	$-0.165506\pi$
$191$	23.9877	1.73569	0.867843	+	0.496838i	$0.165506\pi$
$192$	−2.61133	−0.188456
$193$	4.50929	0.324586	0.162293	−	0.986743i	$-0.448111\pi$
$193$	4.50929	0.324586	0.162293	+	0.986743i	$0.448111\pi$
$194$	3.81477	0.273885
$195$	4.85638	0.347772
$196$	1.67406	0.119576
$197$	−1.09564	−0.0780611	−0.0390305	−	0.999238i	$-0.512427\pi$
$197$	−1.09564	−0.0780611	−0.0390305	+	0.999238i	$0.512427\pi$
$198$	12.3400	0.876965
$199$	−12.7965	−0.907120	−0.453560	−	0.891226i	$-0.649846\pi$
$199$	−12.7965	−0.907120	−0.453560	+	0.891226i	$0.649846\pi$
$200$	−4.45156	−0.314773
$201$	26.4150	1.86317
$202$	7.44282	0.523675
$203$	19.5260	1.37046
$204$	3.82046	0.267486
$205$	1.41004	0.0984813
$206$	14.3014	0.996426
$207$	18.8388	1.30939
$208$	2.51123	0.174123
$209$	−5.21991	−0.361069
$210$	−5.69557	−0.393031
$211$	−11.5656	−0.796209	−0.398104	−	0.917340i	$-0.630332\pi$
$211$	−11.5656	−0.796209	−0.398104	+	0.917340i	$0.630332\pi$
$212$	8.34326	0.573017
$213$	17.9989	1.23326
$214$	12.4057	0.848036
$215$	0.243430	0.0166018
$216$	−2.13874	−0.145523
$217$	−1.76819	−0.120032
$218$	−19.4964	−1.32046
$219$	−39.5299	−2.67118
$220$	−2.39292	−0.161330
$221$	−3.67402	−0.247141
$222$	22.5783	1.51536
$223$	25.4935	1.70717	0.853586	−	0.520952i	$-0.174423\pi$
$223$	25.4935	1.70717	0.853586	+	0.520952i	$0.174423\pi$
$224$	−2.94518	−0.196783
$225$	−17.0006	−1.13337
$226$	17.0861	1.13655
$227$	18.0343	1.19698	0.598490	−	0.801130i	$-0.295767\pi$
$227$	18.0343	1.19698	0.598490	+	0.801130i	$0.295767\pi$
$228$	4.21853	0.279379
$229$	−26.8304	−1.77301	−0.886503	−	0.462723i	$-0.846872\pi$
$229$	−26.8304	−1.77301	−0.886503	+	0.462723i	$0.846872\pi$
$230$	−3.65314	−0.240881
$231$	24.8505	1.63504
$232$	−6.62984	−0.435270
$233$	−13.8381	−0.906561	−0.453281	−	0.891368i	$-0.649746\pi$
$233$	−13.8381	−0.906561	−0.453281	+	0.891368i	$0.649746\pi$
$234$	9.59045	0.626947
$235$	4.78657	0.312241
$236$	8.62235	0.561267
$237$	−18.0793	−1.17438
$238$	4.30890	0.279304
$239$	−18.6974	−1.20943	−0.604716	−	0.796441i	$-0.706713\pi$
$239$	−18.6974	−1.20943	−0.604716	+	0.796441i	$0.706713\pi$
$240$	1.93386	0.124830
$241$	11.3111	0.728615	0.364307	−	0.931279i	$-0.381306\pi$
$241$	11.3111	0.728615	0.364307	+	0.931279i	$0.381306\pi$
$242$	−0.559400	−0.0359596
$243$	21.7503	1.39528
$244$	9.21625	0.590010
$245$	−1.23976	−0.0792051
$246$	4.97196	0.317000
$247$	−4.05683	−0.258130
$248$	0.600367	0.0381234
$249$	−23.9123	−1.51538
$250$	6.99952	0.442688
$251$	19.4199	1.22577	0.612887	−	0.790170i	$-0.290008\pi$
$251$	19.4199	1.22577	0.612887	+	0.790170i	$0.290008\pi$
$252$	−11.2477	−0.708538
$253$	15.9391	1.00208
$254$	−3.00574	−0.188597
$255$	−2.82931	−0.177178
$256$	1.00000	0.0625000
$257$	−3.07300	−0.191688	−0.0958441	−	0.995396i	$-0.530555\pi$
$257$	−3.07300	−0.191688	−0.0958441	+	0.995396i	$0.530555\pi$
$258$	0.858361	0.0534393
$259$	25.4649	1.58231
$260$	−1.85974	−0.115336
$261$	−25.3195	−1.56724
$262$	7.77607	0.480407
$263$	8.65961	0.533974	0.266987	−	0.963700i	$-0.413972\pi$
$263$	8.65961	0.533974	0.266987	+	0.963700i	$0.413972\pi$
$264$	−8.43769	−0.519304
$265$	−6.17875	−0.379557
$266$	4.75786	0.291723
$267$	11.8542	0.725467
$268$	−10.1156	−0.617906
$269$	13.4968	0.822915	0.411458	−	0.911429i	$-0.365020\pi$
$269$	13.4968	0.822915	0.411458	+	0.911429i	$0.365020\pi$
$270$	1.58388	0.0963918
$271$	18.6003	1.12989	0.564944	−	0.825129i	$-0.308898\pi$
$271$	18.6003	1.12989	0.564944	+	0.825129i	$0.308898\pi$
$272$	−1.46304	−0.0887096
$273$	19.3134	1.16890
$274$	18.3385	1.10787
$275$	−14.3838	−0.867378
$276$	−12.8814	−0.775369
$277$	18.0584	1.08503	0.542513	−	0.840047i	$-0.317473\pi$
$277$	18.0584	1.08503	0.542513	+	0.840047i	$0.317473\pi$
$278$	23.2131	1.39223
$279$	2.29282	0.137267
$280$	2.18110	0.130346
$281$	−29.6396	−1.76815	−0.884076	−	0.467343i	$-0.845211\pi$
$281$	−29.6396	−1.76815	−0.884076	+	0.467343i	$0.845211\pi$
$282$	16.8780	1.00507
$283$	14.8706	0.883966	0.441983	−	0.897023i	$-0.354275\pi$
$283$	14.8706	0.883966	0.441983	+	0.897023i	$0.354275\pi$
$284$	−6.89263	−0.409002
$285$	−3.12411	−0.185056
$286$	8.11427	0.479807
$287$	5.60761	0.331007
$288$	3.81902	0.225038
$289$	−14.8595	−0.874090
$290$	4.90984	0.288316
$291$	−9.96162	−0.583960
$292$	15.1379	0.885877
$293$	−19.6836	−1.14993	−0.574963	−	0.818179i	$-0.694984\pi$
$293$	−19.6836	−1.14993	−0.574963	+	0.818179i	$0.694984\pi$
$294$	−4.37152	−0.254952
$295$	−6.38543	−0.371774
$296$	−8.64629	−0.502556
$297$	−6.91067	−0.400998
$298$	8.17325	0.473464
$299$	12.3876	0.716396
$300$	11.6245	0.671139
$301$	0.968100	0.0558004
$302$	−15.1133	−0.869675
$303$	−19.4356	−1.11655
$304$	−1.61548	−0.0926539
$305$	−6.82525	−0.390813
$306$	−5.58737	−0.319409
$307$	−20.6546	−1.17882	−0.589411	−	0.807833i	$-0.700640\pi$
$307$	−20.6546	−1.17882	−0.589411	+	0.807833i	$0.700640\pi$
$308$	−9.51643	−0.542249
$309$	−37.3456	−2.12452
$310$	−0.444612	−0.0252523
$311$	14.6703	0.831874	0.415937	−	0.909393i	$-0.363454\pi$
$311$	14.6703	0.831874	0.415937	+	0.909393i	$0.363454\pi$
$312$	−6.55764	−0.371253
$313$	3.37831	0.190953	0.0954766	−	0.995432i	$-0.469562\pi$
$313$	3.37831	0.190953	0.0954766	+	0.995432i	$0.469562\pi$
$314$	15.5828	0.879386
$315$	8.32968	0.469324
$316$	6.92343	0.389474
$317$	6.31465	0.354666	0.177333	−	0.984151i	$-0.443253\pi$
$317$	6.31465	0.354666	0.177333	+	0.984151i	$0.443253\pi$
$318$	−21.7870	−1.22175
$319$	−21.4223	−1.19942
$320$	−0.740567	−0.0413990
$321$	−32.3953	−1.80813
$322$	−14.5283	−0.809628
$323$	2.36350	0.131509
$324$	−5.87213	−0.326230
$325$	−11.1789	−0.620094
$326$	20.4890	1.13478
$327$	50.9114	2.81541
$328$	−1.90400	−0.105131
$329$	19.0358	1.04948
$330$	6.24868	0.343979
$331$	16.4757	0.905584	0.452792	−	0.891616i	$-0.350428\pi$
$331$	16.4757	0.905584	0.452792	+	0.891616i	$0.350428\pi$
$332$	9.15716	0.502564
$333$	−33.0204	−1.80951
$334$	12.6431	0.691802
$335$	7.49125	0.409291
$336$	7.69082	0.419568
$337$	19.3246	1.05268	0.526339	−	0.850275i	$-0.323564\pi$
$337$	19.3246	1.05268	0.526339	+	0.850275i	$0.323564\pi$
$338$	−6.69372	−0.364090
$339$	−44.6174	−2.42328
$340$	1.08348	0.0587598
$341$	1.93990	0.105052
$342$	−6.16954	−0.333610
$343$	15.6858	0.846955
$344$	−0.328707	−0.0177227
$345$	9.53955	0.513592
$346$	−25.5056	−1.37119
$347$	19.1992	1.03067	0.515334	−	0.856989i	$-0.327668\pi$
$347$	19.1992	1.03067	0.515334	+	0.856989i	$0.327668\pi$
$348$	17.3127	0.928056
$349$	15.1578	0.811381	0.405690	−	0.914011i	$-0.367031\pi$
$349$	15.1578	0.811381	0.405690	+	0.914011i	$0.367031\pi$
$350$	13.1106	0.700793
$351$	−5.37086	−0.286675
$352$	3.23119	0.172223
$353$	−6.11908	−0.325686	−0.162843	−	0.986652i	$-0.552066\pi$
$353$	−6.11908	−0.325686	−0.162843	+	0.986652i	$0.552066\pi$
$354$	−22.5158	−1.19670
$355$	5.10445	0.270916
$356$	−4.53954	−0.240595
$357$	−11.2519	−0.595516
$358$	−15.7507	−0.832448
$359$	30.6879	1.61964	0.809822	−	0.586675i	$-0.199564\pi$
$359$	30.6879	1.61964	0.809822	+	0.586675i	$0.199564\pi$
$360$	−2.82824	−0.149062
$361$	−16.3902	−0.862644
$362$	−9.82618	−0.516452
$363$	1.46078	0.0766709
$364$	−7.39602	−0.387657
$365$	−11.2106	−0.586790
$366$	−24.0666	−1.25798
$367$	0.762925	0.0398243	0.0199122	−	0.999802i	$-0.493661\pi$
$367$	0.762925	0.0398243	0.0199122	+	0.999802i	$0.493661\pi$
$368$	4.93290	0.257145
$369$	−7.27141	−0.378534
$370$	6.40316	0.332885
$371$	−24.5724	−1.27573
$372$	−1.56775	−0.0812843
$373$	−6.86255	−0.355329	−0.177665	−	0.984091i	$-0.556854\pi$
$373$	−6.86255	−0.355329	−0.177665	+	0.984091i	$0.556854\pi$
$374$	−4.72735	−0.244445
$375$	−18.2780	−0.943873
$376$	−6.46338	−0.333324
$377$	−16.6491	−0.857470
$378$	6.29896	0.323983
$379$	17.9496	0.922010	0.461005	−	0.887398i	$-0.347489\pi$
$379$	17.9496	0.922010	0.461005	+	0.887398i	$0.347489\pi$
$380$	1.19637	0.0613724
$381$	7.84897	0.402115
$382$	23.9877	1.22732
$383$	31.1966	1.59407	0.797036	−	0.603931i	$-0.206400\pi$
$383$	31.1966	1.59407	0.797036	+	0.603931i	$0.206400\pi$
$384$	−2.61133	−0.133259
$385$	7.04756	0.359177
$386$	4.50929	0.229517
$387$	−1.25534	−0.0638125
$388$	3.81477	0.193666
$389$	16.7747	0.850509	0.425255	−	0.905074i	$-0.360185\pi$
$389$	16.7747	0.850509	0.425255	+	0.905074i	$0.360185\pi$
$390$	4.85638	0.245912
$391$	−7.21701	−0.364980
$392$	1.67406	0.0845529
$393$	−20.3058	−1.02429
$394$	−1.09564	−0.0551975
$395$	−5.12727	−0.257981
$396$	12.3400	0.620108
$397$	−7.79954	−0.391448	−0.195724	−	0.980659i	$-0.562706\pi$
$397$	−7.79954	−0.391448	−0.195724	+	0.980659i	$0.562706\pi$
$398$	−12.7965	−0.641431
$399$	−12.4243	−0.621994
$400$	−4.45156	−0.222578
$401$	−13.6285	−0.680577	−0.340288	−	0.940321i	$-0.610525\pi$
$401$	−13.6285	−0.680577	−0.340288	+	0.940321i	$0.610525\pi$
$402$	26.4150	1.31746
$403$	1.50766	0.0751019
$404$	7.44282	0.370294
$405$	4.34871	0.216089
$406$	19.5260	0.969061
$407$	−27.9378	−1.38483
$408$	3.82046	0.189141
$409$	−15.3973	−0.761348	−0.380674	−	0.924709i	$-0.624308\pi$
$409$	−15.3973	−0.761348	−0.380674	+	0.924709i	$0.624308\pi$
$410$	1.41004	0.0696368
$411$	−47.8878	−2.36213
$412$	14.3014	0.704580
$413$	−25.3943	−1.24957
$414$	18.8388	0.925879
$415$	−6.78149	−0.332890
$416$	2.51123	0.123123
$417$	−60.6170	−2.96843
$418$	−5.21991	−0.255314
$419$	−3.51716	−0.171825	−0.0859123	−	0.996303i	$-0.527381\pi$
$419$	−3.51716	−0.171825	−0.0859123	+	0.996303i	$0.527381\pi$
$420$	−5.69557	−0.277915
$421$	24.5683	1.19739	0.598693	−	0.800978i	$-0.295687\pi$
$421$	24.5683	1.19739	0.598693	+	0.800978i	$0.295687\pi$
$422$	−11.5656	−0.563005
$423$	−24.6838	−1.20017
$424$	8.34326	0.405185
$425$	6.51279	0.315917
$426$	17.9989	0.872049
$427$	−27.1435	−1.31356
$428$	12.4057	0.599652
$429$	−21.1890	−1.02301
$430$	0.243430	0.0117392
$431$	5.42444	0.261286	0.130643	−	0.991429i	$-0.458296\pi$
$431$	5.42444	0.261286	0.130643	+	0.991429i	$0.458296\pi$
$432$	−2.13874	−0.102900
$433$	−22.8656	−1.09885	−0.549426	−	0.835543i	$-0.685153\pi$
$433$	−22.8656	−1.09885	−0.549426	+	0.835543i	$0.685153\pi$
$434$	−1.76819	−0.0848757
$435$	−12.8212	−0.614729
$436$	−19.4964	−0.933707
$437$	−7.96897	−0.381208
$438$	−39.5299	−1.88881
$439$	−18.5377	−0.884755	−0.442377	−	0.896829i	$-0.645865\pi$
$439$	−18.5377	−0.884755	−0.442377	+	0.896829i	$0.645865\pi$
$440$	−2.39292	−0.114078
$441$	6.39328	0.304442
$442$	−3.67402	−0.174755
$443$	−1.84496	−0.0876566	−0.0438283	−	0.999039i	$-0.513955\pi$
$443$	−1.84496	−0.0876566	−0.0438283	+	0.999039i	$0.513955\pi$
$444$	22.5783	1.07152
$445$	3.36184	0.159366
$446$	25.4935	1.20715
$447$	−21.3430	−1.00949
$448$	−2.94518	−0.139146
$449$	14.8240	0.699587	0.349794	−	0.936827i	$-0.386252\pi$
$449$	14.8240	0.699587	0.349794	+	0.936827i	$0.386252\pi$
$450$	−17.0006	−0.801416
$451$	−6.15218	−0.289695
$452$	17.0861	0.803662
$453$	39.4658	1.85427
$454$	18.0343	0.846393
$455$	5.47725	0.256777
$456$	4.21853	0.197551
$457$	35.8345	1.67627	0.838133	−	0.545466i	$-0.183647\pi$
$457$	35.8345	1.67627	0.838133	+	0.545466i	$0.183647\pi$
$458$	−26.8304	−1.25370
$459$	3.12905	0.146052
$460$	−3.65314	−0.170329
$461$	−11.0473	−0.514526	−0.257263	−	0.966341i	$-0.582821\pi$
$461$	−11.0473	−0.514526	−0.257263	+	0.966341i	$0.582821\pi$
$462$	24.8505	1.15615
$463$	−19.2655	−0.895344	−0.447672	−	0.894198i	$-0.647747\pi$
$463$	−19.2655	−0.895344	−0.447672	+	0.894198i	$0.647747\pi$
$464$	−6.62984	−0.307783
$465$	1.16103	0.0538414
$466$	−13.8381	−0.641036
$467$	−34.3508	−1.58957	−0.794783	−	0.606894i	$-0.792415\pi$
$467$	−34.3508	−1.58957	−0.794783	+	0.606894i	$0.792415\pi$
$468$	9.59045	0.443319
$469$	29.7921	1.37567
$470$	4.78657	0.220788
$471$	−40.6916	−1.87497
$472$	8.62235	0.396876
$473$	−1.06212	−0.0488361
$474$	−18.0793	−0.830412
$475$	7.19138	0.329963
$476$	4.30890	0.197498
$477$	31.8631	1.45891
$478$	−18.6974	−0.855197
$479$	8.97709	0.410174	0.205087	−	0.978744i	$-0.434252\pi$
$479$	8.97709	0.410174	0.205087	+	0.978744i	$0.434252\pi$
$480$	1.93386	0.0882684
$481$	−21.7128	−0.990020
$482$	11.3111	0.515208
$483$	37.9380	1.72624
$484$	−0.559400	−0.0254273
$485$	−2.82510	−0.128281
$486$	21.7503	0.986612
$487$	−32.4591	−1.47086	−0.735431	−	0.677600i	$-0.763020\pi$
$487$	−32.4591	−1.47086	−0.735431	+	0.677600i	$0.763020\pi$
$488$	9.21625	0.417200
$489$	−53.5034	−2.41951
$490$	−1.23976	−0.0560065
$491$	−5.97991	−0.269870	−0.134935	−	0.990854i	$-0.543082\pi$
$491$	−5.97991	−0.269870	−0.134935	+	0.990854i	$0.543082\pi$
$492$	4.97196	0.224153
$493$	9.69969	0.436852
$494$	−4.05683	−0.182525
$495$	−9.13860	−0.410749
$496$	0.600367	0.0269573
$497$	20.3000	0.910579
$498$	−23.9123	−1.07154
$499$	−2.14662	−0.0960961	−0.0480481	−	0.998845i	$-0.515300\pi$
$499$	−2.14662	−0.0960961	−0.0480481	+	0.998845i	$0.515300\pi$
$500$	6.99952	0.313028
$501$	−33.0154	−1.47502
$502$	19.4199	0.866753
$503$	30.7220	1.36983	0.684913	−	0.728625i	$-0.259840\pi$
$503$	30.7220	1.36983	0.684913	+	0.728625i	$0.259840\pi$
$504$	−11.2477	−0.501012
$505$	−5.51191	−0.245277
$506$	15.9391	0.708581
$507$	17.4795	0.776291
$508$	−3.00574	−0.133358
$509$	21.0925	0.934909	0.467455	−	0.884017i	$-0.345171\pi$
$509$	21.0925	0.934909	0.467455	+	0.884017i	$0.345171\pi$
$510$	−2.82931	−0.125284
$511$	−44.5837	−1.97227
$512$	1.00000	0.0441942
$513$	3.45508	0.152545
$514$	−3.07300	−0.135544
$515$	−10.5912	−0.466702
$516$	0.858361	0.0377873
$517$	−20.8844	−0.918496
$518$	25.4649	1.11886
$519$	66.6034	2.92356
$520$	−1.85974	−0.0815548
$521$	14.3048	0.626706	0.313353	−	0.949637i	$-0.398548\pi$
$521$	14.3048	0.626706	0.313353	+	0.949637i	$0.398548\pi$
$522$	−25.3195	−1.10820
$523$	4.48816	0.196254	0.0981269	−	0.995174i	$-0.468715\pi$
$523$	4.48816	0.196254	0.0981269	+	0.995174i	$0.468715\pi$
$524$	7.77607	0.339699
$525$	−34.2361	−1.49419
$526$	8.65961	0.377577
$527$	−0.878359	−0.0382619
$528$	−8.43769	−0.367204
$529$	1.33347	0.0579770
$530$	−6.17875	−0.268388
$531$	32.9289	1.42899
$532$	4.75786	0.206279
$533$	−4.78138	−0.207104
$534$	11.8542	0.512983
$535$	−9.18725	−0.397199
$536$	−10.1156	−0.436926
$537$	41.1301	1.77490
$538$	13.4968	0.581889
$539$	5.40922	0.232992
$540$	1.58388	0.0681593
$541$	45.5182	1.95698	0.978490	−	0.206296i	$-0.0661411\pi$
$541$	45.5182	1.95698	0.978490	+	0.206296i	$0.0661411\pi$
$542$	18.6003	0.798952
$543$	25.6594	1.10115
$544$	−1.46304	−0.0627272
$545$	14.4384	0.618472
$546$	19.3134	0.826538
$547$	−14.0924	−0.602549	−0.301274	−	0.953537i	$-0.597412\pi$
$547$	−14.0924	−0.602549	−0.301274	+	0.953537i	$0.597412\pi$
$548$	18.3385	0.783382
$549$	35.1971	1.50217
$550$	−14.3838	−0.613329
$551$	10.7103	0.456276
$552$	−12.8814	−0.548269
$553$	−20.3907	−0.867102
$554$	18.0584	0.767230
$555$	−16.7207	−0.709756
$556$	23.2131	0.984455
$557$	−28.2190	−1.19568	−0.597838	−	0.801617i	$-0.703974\pi$
$557$	−28.2190	−1.19568	−0.597838	+	0.801617i	$0.703974\pi$
$558$	2.29282	0.0970627
$559$	−0.825460	−0.0349132
$560$	2.18110	0.0921684
$561$	12.3447	0.521192
$562$	−29.6396	−1.25027
$563$	−45.5887	−1.92134	−0.960668	−	0.277699i	$-0.910428\pi$
$563$	−45.5887	−1.92134	−0.960668	+	0.277699i	$0.910428\pi$
$564$	16.8780	0.710692
$565$	−12.6534	−0.532333
$566$	14.8706	0.625059
$567$	17.2945	0.726299
$568$	−6.89263	−0.289208
$569$	22.5281	0.944429	0.472214	−	0.881484i	$-0.343455\pi$
$569$	22.5281	0.944429	0.472214	+	0.881484i	$0.343455\pi$
$570$	−3.12411	−0.130854
$571$	−40.1421	−1.67990	−0.839948	−	0.542667i	$-0.817415\pi$
$571$	−40.1421	−1.67990	−0.839948	+	0.542667i	$0.817415\pi$
$572$	8.11427	0.339275
$573$	−62.6396	−2.61681
$574$	5.60761	0.234057
$575$	−21.9591	−0.915757
$576$	3.81902	0.159126
$577$	26.0907	1.08617	0.543084	−	0.839678i	$-0.317256\pi$
$577$	26.0907	1.08617	0.543084	+	0.839678i	$0.317256\pi$
$578$	−14.8595	−0.618075
$579$	−11.7752	−0.489361
$580$	4.90984	0.203870
$581$	−26.9694	−1.11888
$582$	−9.96162	−0.412922
$583$	26.9587	1.11651
$584$	15.1379	0.626409
$585$	−7.10237	−0.293647
$586$	−19.6836	−0.813121
$587$	8.36754	0.345365	0.172683	−	0.984978i	$-0.444756\pi$
$587$	8.36754	0.345365	0.172683	+	0.984978i	$0.444756\pi$
$588$	−4.37152	−0.180279
$589$	−0.969879	−0.0399631
$590$	−6.38543	−0.262884
$591$	2.86107	0.117689
$592$	−8.64629	−0.355360
$593$	1.28135	0.0526186	0.0263093	−	0.999654i	$-0.491625\pi$
$593$	1.28135	0.0526186	0.0263093	+	0.999654i	$0.491625\pi$
$594$	−6.91067	−0.283548
$595$	−3.19103	−0.130819
$596$	8.17325	0.334790
$597$	33.4158	1.36762
$598$	12.3876	0.506568
$599$	−16.8837	−0.689851	−0.344925	−	0.938630i	$-0.612096\pi$
$599$	−16.8837	−0.689851	−0.344925	+	0.938630i	$0.612096\pi$
$600$	11.6245	0.474567
$601$	20.1512	0.821984	0.410992	−	0.911639i	$-0.365182\pi$
$601$	20.1512	0.821984	0.410992	+	0.911639i	$0.365182\pi$
$602$	0.968100	0.0394568
$603$	−38.6316	−1.57320
$604$	−15.1133	−0.614953
$605$	0.414273	0.0168426
$606$	−19.4356	−0.789519
$607$	24.8657	1.00927	0.504634	−	0.863333i	$-0.331627\pi$
$607$	24.8657	1.00927	0.504634	+	0.863333i	$0.331627\pi$
$608$	−1.61548	−0.0655162
$609$	−50.9889	−2.06617
$610$	−6.82525	−0.276346
$611$	−16.2310	−0.656638
$612$	−5.58737	−0.225856
$613$	31.5045	1.27245	0.636227	−	0.771502i	$-0.280494\pi$
$613$	31.5045	1.27245	0.636227	+	0.771502i	$0.280494\pi$
$614$	−20.6546	−0.833553
$615$	−3.68207	−0.148475
$616$	−9.51643	−0.383428
$617$	−24.5170	−0.987017	−0.493508	−	0.869741i	$-0.664286\pi$
$617$	−24.5170	−0.987017	−0.493508	+	0.869741i	$0.664286\pi$
$618$	−37.3456	−1.50226
$619$	36.5863	1.47053	0.735263	−	0.677782i	$-0.237059\pi$
$619$	36.5863	1.47053	0.735263	+	0.677782i	$0.237059\pi$
$620$	−0.444612	−0.0178561
$621$	−10.5502	−0.423364
$622$	14.6703	0.588224
$623$	13.3698	0.535648
$624$	−6.55764	−0.262516
$625$	17.0742	0.682967
$626$	3.37831	0.135024
$627$	13.6309	0.544365
$628$	15.5828	0.621820
$629$	12.6498	0.504382
$630$	8.32968	0.331862
$631$	35.6300	1.41841	0.709203	−	0.705004i	$-0.249055\pi$
$631$	35.6300	1.41841	0.709203	+	0.705004i	$0.249055\pi$
$632$	6.92343	0.275399
$633$	30.2016	1.20040
$634$	6.31465	0.250787
$635$	2.22595	0.0883343
$636$	−21.7870	−0.863910
$637$	4.20396	0.166567
$638$	−21.4223	−0.848116
$639$	−26.3231	−1.04133
$640$	−0.740567	−0.0292735
$641$	45.5686	1.79985	0.899926	−	0.436043i	$-0.143621\pi$
$641$	45.5686	1.79985	0.899926	+	0.436043i	$0.143621\pi$
$642$	−32.3953	−1.27854
$643$	−3.05250	−0.120379	−0.0601894	−	0.998187i	$-0.519170\pi$
$643$	−3.05250	−0.120379	−0.0601894	+	0.998187i	$0.519170\pi$
$644$	−14.5283	−0.572493
$645$	−0.635675	−0.0250297
$646$	2.36350	0.0929906
$647$	2.05622	0.0808383	0.0404192	−	0.999183i	$-0.487131\pi$
$647$	2.05622	0.0808383	0.0404192	+	0.999183i	$0.487131\pi$
$648$	−5.87213	−0.230679
$649$	27.8605	1.09362
$650$	−11.1789	−0.438472
$651$	4.61731	0.180967
$652$	20.4890	0.802410
$653$	−36.4955	−1.42818	−0.714089	−	0.700055i	$-0.753159\pi$
$653$	−36.4955	−1.42818	−0.714089	+	0.700055i	$0.753159\pi$
$654$	50.9114	1.99079
$655$	−5.75870	−0.225011
$656$	−1.90400	−0.0743386
$657$	57.8119	2.25546
$658$	19.0358	0.742093
$659$	−25.1504	−0.979722	−0.489861	−	0.871801i	$-0.662952\pi$
$659$	−25.1504	−0.979722	−0.489861	+	0.871801i	$0.662952\pi$
$660$	6.24868	0.243230
$661$	2.56783	0.0998771	0.0499386	−	0.998752i	$-0.484097\pi$
$661$	2.56783	0.0998771	0.0499386	+	0.998752i	$0.484097\pi$
$662$	16.4757	0.640345
$663$	9.59407	0.372603
$664$	9.15716	0.355367
$665$	−3.52352	−0.136636
$666$	−33.0204	−1.27951
$667$	−32.7043	−1.26632
$668$	12.6431	0.489178
$669$	−66.5719	−2.57382
$670$	7.49125	0.289412
$671$	29.7795	1.14962
$672$	7.69082	0.296680
$673$	28.6539	1.10453	0.552263	−	0.833670i	$-0.313764\pi$
$673$	28.6539	1.10453	0.552263	+	0.833670i	$0.313764\pi$
$674$	19.3246	0.744355
$675$	9.52071	0.366452
$676$	−6.69372	−0.257451
$677$	−32.6163	−1.25355	−0.626773	−	0.779202i	$-0.715625\pi$
$677$	−32.6163	−1.25355	−0.626773	+	0.779202i	$0.715625\pi$
$678$	−44.6174	−1.71352
$679$	−11.2352	−0.431167
$680$	1.08348	0.0415494
$681$	−47.0935	−1.80463
$682$	1.93990	0.0742827
$683$	−32.9135	−1.25940	−0.629700	−	0.776838i	$-0.716822\pi$
$683$	−32.9135	−1.25940	−0.629700	+	0.776838i	$0.716822\pi$
$684$	−6.16954	−0.235898
$685$	−13.5809	−0.518899
$686$	15.6858	0.598888
$687$	70.0630	2.67307
$688$	−0.328707	−0.0125318
$689$	20.9519	0.798202
$690$	9.53955	0.363164
$691$	−14.3696	−0.546644	−0.273322	−	0.961923i	$-0.588122\pi$
$691$	−14.3696	−0.546644	−0.273322	+	0.961923i	$0.588122\pi$
$692$	−25.5056	−0.969577
$693$	−36.3435	−1.38057
$694$	19.1992	0.728793
$695$	−17.1909	−0.652087
$696$	17.3127	0.656235
$697$	2.78562	0.105513
$698$	15.1578	0.573733
$699$	36.1357	1.36678
$700$	13.1106	0.495535
$701$	−43.4401	−1.64071	−0.820355	−	0.571854i	$-0.806224\pi$
$701$	−43.4401	−1.64071	−0.820355	+	0.571854i	$0.806224\pi$
$702$	−5.37086	−0.202710
$703$	13.9679	0.526808
$704$	3.23119	0.121780
$705$	−12.4993	−0.470751
$706$	−6.11908	−0.230294
$707$	−21.9204	−0.824402
$708$	−22.5158	−0.846194
$709$	−25.4569	−0.956053	−0.478026	−	0.878346i	$-0.658648\pi$
$709$	−25.4569	−0.956053	−0.478026	+	0.878346i	$0.658648\pi$
$710$	5.10445	0.191567
$711$	26.4408	0.991606
$712$	−4.53954	−0.170127
$713$	2.96155	0.110911
$714$	−11.2519	−0.421093
$715$	−6.00916	−0.224730
$716$	−15.7507	−0.588630
$717$	48.8249	1.82340
$718$	30.6879	1.14526
$719$	5.79521	0.216125	0.108062	−	0.994144i	$-0.465535\pi$
$719$	5.79521	0.216125	0.108062	+	0.994144i	$0.465535\pi$
$720$	−2.82824	−0.105402
$721$	−42.1202	−1.56864
$722$	−16.3902	−0.609982
$723$	−29.5371	−1.09850
$724$	−9.82618	−0.365187
$725$	29.5131	1.09609
$726$	1.46078	0.0542145
$727$	−43.9176	−1.62882	−0.814408	−	0.580293i	$-0.802938\pi$
$727$	−43.9176	−1.62882	−0.814408	+	0.580293i	$0.802938\pi$
$728$	−7.39602	−0.274115
$729$	−39.1806	−1.45113
$730$	−11.2106	−0.414923
$731$	0.480910	0.0177871
$732$	−24.0666	−0.889528
$733$	1.09587	0.0404770	0.0202385	−	0.999795i	$-0.493557\pi$
$733$	1.09587	0.0404770	0.0202385	+	0.999795i	$0.493557\pi$
$734$	0.762925	0.0281601
$735$	3.23741	0.119414
$736$	4.93290	0.181829
$737$	−32.6853	−1.20398
$738$	−7.27141	−0.267664
$739$	43.8959	1.61474	0.807368	−	0.590048i	$-0.200891\pi$
$739$	43.8959	1.61474	0.807368	+	0.590048i	$0.200891\pi$
$740$	6.40316	0.235385
$741$	10.5937	0.389170
$742$	−24.5724	−0.902080
$743$	39.5668	1.45156	0.725782	−	0.687925i	$-0.241478\pi$
$743$	39.5668	1.45156	0.725782	+	0.687925i	$0.241478\pi$
$744$	−1.56775	−0.0574767
$745$	−6.05284	−0.221759
$746$	−6.86255	−0.251256
$747$	34.9714	1.27954
$748$	−4.72735	−0.172849
$749$	−36.5369	−1.33503
$750$	−18.2780	−0.667419
$751$	−37.9719	−1.38561	−0.692806	−	0.721124i	$-0.743626\pi$
$751$	−37.9719	−1.38561	−0.692806	+	0.721124i	$0.743626\pi$
$752$	−6.46338	−0.235695
$753$	−50.7117	−1.84804
$754$	−16.6491	−0.606323
$755$	11.1924	0.407335
$756$	6.29896	0.229091
$757$	17.3498	0.630589	0.315294	−	0.948994i	$-0.397897\pi$
$757$	17.3498	0.630589	0.315294	+	0.948994i	$0.397897\pi$
$758$	17.9496	0.651960
$759$	−41.6223	−1.51079
$760$	1.19637	0.0433968
$761$	−16.3944	−0.594298	−0.297149	−	0.954831i	$-0.596036\pi$
$761$	−16.3944	−0.594298	−0.297149	+	0.954831i	$0.596036\pi$
$762$	7.84897	0.284338
$763$	57.4203	2.07875
$764$	23.9877	0.867843
$765$	4.13782	0.149603
$766$	31.1966	1.12718
$767$	21.6527	0.781834
$768$	−2.61133	−0.0942281
$769$	32.9884	1.18959	0.594796	−	0.803877i	$-0.297233\pi$
$769$	32.9884	1.18959	0.594796	+	0.803877i	$0.297233\pi$
$770$	7.04756	0.253976
$771$	8.02459	0.288999
$772$	4.50929	0.162293
$773$	−7.12644	−0.256320	−0.128160	−	0.991753i	$-0.540907\pi$
$773$	−7.12644	−0.256320	−0.128160	+	0.991753i	$0.540907\pi$
$774$	−1.25534	−0.0451223
$775$	−2.67257	−0.0960016
$776$	3.81477	0.136942
$777$	−66.4970	−2.38557
$778$	16.7747	0.601401
$779$	3.07586	0.110204
$780$	4.85638	0.173886
$781$	−22.2714	−0.796933
$782$	−7.21701	−0.258080
$783$	14.1795	0.506733
$784$	1.67406	0.0597880
$785$	−11.5401	−0.411883
$786$	−20.3058	−0.724286
$787$	50.0013	1.78235	0.891177	−	0.453655i	$-0.149880\pi$
$787$	50.0013	1.78235	0.891177	+	0.453655i	$0.149880\pi$
$788$	−1.09564	−0.0390305
$789$	−22.6131	−0.805046
$790$	−5.12727	−0.182420
$791$	−50.3216	−1.78923
$792$	12.3400	0.438483
$793$	23.1441	0.821872
$794$	−7.79954	−0.276795
$795$	16.1347	0.572240
$796$	−12.7965	−0.453560
$797$	−9.68997	−0.343236	−0.171618	−	0.985164i	$-0.554900\pi$
$797$	−9.68997	−0.343236	−0.171618	+	0.985164i	$0.554900\pi$
$798$	−12.4243	−0.439816
$799$	9.45616	0.334535
$800$	−4.45156	−0.157386
$801$	−17.3366	−0.612559
$802$	−13.6285	−0.481240
$803$	48.9133	1.72611
$804$	26.4150	0.931586
$805$	10.7591	0.379210
$806$	1.50766	0.0531051
$807$	−35.2446	−1.24067
$808$	7.44282	0.261838
$809$	44.1686	1.55289	0.776443	−	0.630187i	$-0.217022\pi$
$809$	44.1686	1.55289	0.776443	+	0.630187i	$0.217022\pi$
$810$	4.34871	0.152798
$811$	−49.6953	−1.74504	−0.872519	−	0.488580i	$-0.837515\pi$
$811$	−49.6953	−1.74504	−0.872519	+	0.488580i	$0.837515\pi$
$812$	19.5260	0.685230
$813$	−48.5715	−1.70348
$814$	−27.9378	−0.979220
$815$	−15.1735	−0.531504
$816$	3.82046	0.133743
$817$	0.531018	0.0185780
$818$	−15.3973	−0.538355
$819$	−28.2456	−0.986980
$820$	1.41004	0.0492407
$821$	−28.9218	−1.00938	−0.504688	−	0.863302i	$-0.668393\pi$
$821$	−28.9218	−1.00938	−0.504688	+	0.863302i	$0.668393\pi$
$822$	−47.8878	−1.67028
$823$	−32.7237	−1.14068	−0.570339	−	0.821410i	$-0.693188\pi$
$823$	−32.7237	−1.14068	−0.570339	+	0.821410i	$0.693188\pi$
$824$	14.3014	0.498213
$825$	37.5609	1.30770
$826$	−25.3943	−0.883582
$827$	−10.9165	−0.379602	−0.189801	−	0.981823i	$-0.560784\pi$
$827$	−10.9165	−0.379602	−0.189801	+	0.981823i	$0.560784\pi$
$828$	18.8388	0.654695
$829$	−35.3160	−1.22658	−0.613288	−	0.789859i	$-0.710153\pi$
$829$	−35.3160	−1.22658	−0.613288	+	0.789859i	$0.710153\pi$
$830$	−6.78149	−0.235389
$831$	−47.1565	−1.63584
$832$	2.51123	0.0870613
$833$	−2.44921	−0.0848603
$834$	−60.6170	−2.09899
$835$	−9.36310	−0.324024
$836$	−5.21991	−0.180534
$837$	−1.28403	−0.0443825
$838$	−3.51716	−0.121498
$839$	15.3181	0.528840	0.264420	−	0.964408i	$-0.414819\pi$
$839$	15.3181	0.528840	0.264420	+	0.964408i	$0.414819\pi$
$840$	−5.69557	−0.196516
$841$	14.9548	0.515681
$842$	24.5683	0.846680
$843$	77.3987	2.66575
$844$	−11.5656	−0.398104
$845$	4.95715	0.170531
$846$	−24.6838	−0.848647
$847$	1.64753	0.0566099
$848$	8.34326	0.286509
$849$	−38.8320	−1.33271
$850$	6.51279	0.223387
$851$	−42.6513	−1.46207
$852$	17.9989	0.616632
$853$	−40.3264	−1.38075	−0.690375	−	0.723451i	$-0.742555\pi$
$853$	−40.3264	−1.38075	−0.690375	+	0.723451i	$0.742555\pi$
$854$	−27.1435	−0.928830
$855$	4.56896	0.156255
$856$	12.4057	0.424018
$857$	−5.64563	−0.192851	−0.0964255	−	0.995340i	$-0.530741\pi$
$857$	−5.64563	−0.192851	−0.0964255	+	0.995340i	$0.530741\pi$
$858$	−21.1890	−0.723381
$859$	31.6858	1.08111	0.540553	−	0.841310i	$-0.318215\pi$
$859$	31.6858	1.08111	0.540553	+	0.841310i	$0.318215\pi$
$860$	0.243430	0.00830089
$861$	−14.6433	−0.499042
$862$	5.42444	0.184757
$863$	11.6695	0.397233	0.198617	−	0.980077i	$-0.436355\pi$
$863$	11.6695	0.397233	0.198617	+	0.980077i	$0.436355\pi$
$864$	−2.13874	−0.0727613
$865$	18.8886	0.642232
$866$	−22.8656	−0.777005
$867$	38.8031	1.31782
$868$	−1.76819	−0.0600162
$869$	22.3709	0.758882
$870$	−12.8212	−0.434679
$871$	−25.4025	−0.860731
$872$	−19.4964	−0.660231
$873$	14.5687	0.493076
$874$	−7.96897	−0.269555
$875$	−20.6148	−0.696908
$876$	−39.5299	−1.33559
$877$	−19.0709	−0.643979	−0.321989	−	0.946743i	$-0.604352\pi$
$877$	−19.0709	−0.643979	−0.321989	+	0.946743i	$0.604352\pi$
$878$	−18.5377	−0.625616
$879$	51.4002	1.73369
$880$	−2.39292	−0.0806652
$881$	−30.6985	−1.03426	−0.517130	−	0.855907i	$-0.673000\pi$
$881$	−30.6985	−1.03426	−0.517130	+	0.855907i	$0.673000\pi$
$882$	6.39328	0.215273
$883$	−10.2115	−0.343643	−0.171822	−	0.985128i	$-0.554965\pi$
$883$	−10.2115	−0.343643	−0.171822	+	0.985128i	$0.554965\pi$
$884$	−3.67402	−0.123571
$885$	16.6744	0.560505
$886$	−1.84496	−0.0619826
$887$	11.6566	0.391390	0.195695	−	0.980665i	$-0.437304\pi$
$887$	11.6566	0.391390	0.195695	+	0.980665i	$0.437304\pi$
$888$	22.5783	0.757678
$889$	8.85244	0.296901
$890$	3.36184	0.112689
$891$	−18.9740	−0.635652
$892$	25.4935	0.853586
$893$	10.4414	0.349409
$894$	−21.3430	−0.713818
$895$	11.6644	0.389899
$896$	−2.94518	−0.0983914
$897$	−32.3482	−1.08007
$898$	14.8240	0.494683
$899$	−3.98034	−0.132752
$900$	−17.0006	−0.566687
$901$	−12.2065	−0.406657
$902$	−6.15218	−0.204845
$903$	−2.52803	−0.0841274
$904$	17.0861	0.568275
$905$	7.27695	0.241894
$906$	39.4658	1.31116
$907$	−50.8214	−1.68750	−0.843749	−	0.536738i	$-0.819656\pi$
$907$	−50.8214	−1.68750	−0.843749	+	0.536738i	$0.819656\pi$
$908$	18.0343	0.598490
$909$	28.4243	0.942775
$910$	5.47725	0.181569
$911$	9.38796	0.311037	0.155519	−	0.987833i	$-0.450295\pi$
$911$	9.38796	0.311037	0.155519	+	0.987833i	$0.450295\pi$
$912$	4.21853	0.139690
$913$	29.5885	0.979238
$914$	35.8345	1.18530
$915$	17.8230	0.589209
$916$	−26.8304	−0.886503
$917$	−22.9019	−0.756287
$918$	3.12905	0.103274
$919$	9.14536	0.301678	0.150839	−	0.988558i	$-0.451803\pi$
$919$	9.14536	0.301678	0.150839	+	0.988558i	$0.451803\pi$
$920$	−3.65314	−0.120441
$921$	53.9360	1.77725
$922$	−11.0473	−0.363825
$923$	−17.3090	−0.569732
$924$	24.8505	0.817521
$925$	38.4895	1.26553
$926$	−19.2655	−0.633104
$927$	54.6174	1.79387
$928$	−6.62984	−0.217635
$929$	15.5493	0.510157	0.255078	−	0.966920i	$-0.417899\pi$
$929$	15.5493	0.510157	0.255078	+	0.966920i	$0.417899\pi$
$930$	1.16103	0.0380716
$931$	−2.70441	−0.0886334
$932$	−13.8381	−0.453281
$933$	−38.3088	−1.25417
$934$	−34.3508	−1.12399
$935$	3.50092	0.114492
$936$	9.59045	0.313474
$937$	2.84630	0.0929847	0.0464923	−	0.998919i	$-0.485196\pi$
$937$	2.84630	0.0929847	0.0464923	+	0.998919i	$0.485196\pi$
$938$	29.7921	0.972747
$939$	−8.82186	−0.287891
$940$	4.78657	0.156121
$941$	44.4865	1.45022	0.725110	−	0.688634i	$-0.241789\pi$
$941$	44.4865	1.45022	0.725110	+	0.688634i	$0.241789\pi$
$942$	−40.6916	−1.32581
$943$	−9.39222	−0.305853
$944$	8.62235	0.280633
$945$	−4.66480	−0.151746
$946$	−1.06212	−0.0345324
$947$	25.2006	0.818910	0.409455	−	0.912330i	$-0.365719\pi$
$947$	25.2006	0.818910	0.409455	+	0.912330i	$0.365719\pi$
$948$	−18.0793	−0.587190
$949$	38.0147	1.23401
$950$	7.19138	0.233319
$951$	−16.4896	−0.534713
$952$	4.30890	0.139652
$953$	−23.2844	−0.754257	−0.377128	−	0.926161i	$-0.623088\pi$
$953$	−23.2844	−0.754257	−0.377128	+	0.926161i	$0.623088\pi$
$954$	31.8631	1.03161
$955$	−17.7645	−0.574845
$956$	−18.6974	−0.604716
$957$	55.9406	1.80830
$958$	8.97709	0.290037
$959$	−54.0101	−1.74408
$960$	1.93386	0.0624152
$961$	−30.6396	−0.988373
$962$	−21.7128	−0.700050
$963$	47.3776	1.52672
$964$	11.3111	0.364307
$965$	−3.33943	−0.107500
$966$	37.9380	1.22064
$967$	17.4048	0.559699	0.279850	−	0.960044i	$-0.409715\pi$
$967$	17.4048	0.559699	0.279850	+	0.960044i	$0.409715\pi$
$968$	−0.559400	−0.0179798
$969$	−6.17187	−0.198269
$970$	−2.82510	−0.0907084
$971$	−50.3775	−1.61669	−0.808346	−	0.588707i	$-0.799637\pi$
$971$	−50.3775	−1.61669	−0.808346	+	0.588707i	$0.799637\pi$
$972$	21.7503	0.697640
$973$	−68.3667	−2.19173
$974$	−32.4591	−1.04006
$975$	29.1917	0.934884
$976$	9.21625	0.295005
$977$	7.83781	0.250754	0.125377	−	0.992109i	$-0.459986\pi$
$977$	7.83781	0.250754	0.125377	+	0.992109i	$0.459986\pi$
$978$	−53.5034	−1.71085
$979$	−14.6681	−0.468796
$980$	−1.23976	−0.0396026
$981$	−74.4571	−2.37723
$982$	−5.97991	−0.190827
$983$	36.9611	1.17888	0.589438	−	0.807814i	$-0.299349\pi$
$983$	36.9611	1.17888	0.589438	+	0.807814i	$0.299349\pi$
$984$	4.97196	0.158500
$985$	0.811395	0.0258532
$986$	9.69969	0.308901
$987$	−49.7087	−1.58224
$988$	−4.05683	−0.129065
$989$	−1.62148	−0.0515600
$990$	−9.13860	−0.290444
$991$	60.9407	1.93584	0.967922	−	0.251250i	$-0.0808417\pi$
$991$	60.9407	1.93584	0.967922	+	0.251250i	$0.0808417\pi$
$992$	0.600367	0.0190617
$993$	−43.0233	−1.36530
$994$	20.3000	0.643877
$995$	9.47667	0.300431
$996$	−23.9123	−0.757691
$997$	8.73128	0.276522	0.138261	−	0.990396i	$-0.455849\pi$
$997$	8.73128	0.276522	0.138261	+	0.990396i	$0.455849\pi$
$998$	−2.14662	−0.0679502
$999$	18.4921	0.585066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.f.1.4	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.f.1.4	✓	50	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.61133 q^{3} +1.00000 q^{4} -0.740567 q^{5} -2.61133 q^{6} -2.94518 q^{7} +1.00000 q^{8} +3.81902 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.61133 q^{3} +1.00000 q^{4} -0.740567 q^{5} -2.61133 q^{6} -2.94518 q^{7} +1.00000 q^{8} +3.81902 q^{9} -0.740567 q^{10} +3.23119 q^{11} -2.61133 q^{12} +2.51123 q^{13} -2.94518 q^{14} +1.93386 q^{15} +1.00000 q^{16} -1.46304 q^{17} +3.81902 q^{18} -1.61548 q^{19} -0.740567 q^{20} +7.69082 q^{21} +3.23119 q^{22} +4.93290 q^{23} -2.61133 q^{24} -4.45156 q^{25} +2.51123 q^{26} -2.13874 q^{27} -2.94518 q^{28} -6.62984 q^{29} +1.93386 q^{30} +0.600367 q^{31} +1.00000 q^{32} -8.43769 q^{33} -1.46304 q^{34} +2.18110 q^{35} +3.81902 q^{36} -8.64629 q^{37} -1.61548 q^{38} -6.55764 q^{39} -0.740567 q^{40} -1.90400 q^{41} +7.69082 q^{42} -0.328707 q^{43} +3.23119 q^{44} -2.82824 q^{45} +4.93290 q^{46} -6.46338 q^{47} -2.61133 q^{48} +1.67406 q^{49} -4.45156 q^{50} +3.82046 q^{51} +2.51123 q^{52} +8.34326 q^{53} -2.13874 q^{54} -2.39292 q^{55} -2.94518 q^{56} +4.21853 q^{57} -6.62984 q^{58} +8.62235 q^{59} +1.93386 q^{60} +9.21625 q^{61} +0.600367 q^{62} -11.2477 q^{63} +1.00000 q^{64} -1.85974 q^{65} -8.43769 q^{66} -10.1156 q^{67} -1.46304 q^{68} -12.8814 q^{69} +2.18110 q^{70} -6.89263 q^{71} +3.81902 q^{72} +15.1379 q^{73} -8.64629 q^{74} +11.6245 q^{75} -1.61548 q^{76} -9.51643 q^{77} -6.55764 q^{78} +6.92343 q^{79} -0.740567 q^{80} -5.87213 q^{81} -1.90400 q^{82} +9.15716 q^{83} +7.69082 q^{84} +1.08348 q^{85} -0.328707 q^{86} +17.3127 q^{87} +3.23119 q^{88} -4.53954 q^{89} -2.82824 q^{90} -7.39602 q^{91} +4.93290 q^{92} -1.56775 q^{93} -6.46338 q^{94} +1.19637 q^{95} -2.61133 q^{96} +3.81477 q^{97} +1.67406 q^{98} +12.3400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9}+O(q^{10}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9	\( 50 q + 50 q^{2} + 18 q^{3} + 50 q^{4} + 11 q^{5} + 18 q^{6} + 30 q^{7} + 50 q^{8} + 66 q^{9} + 11 q^{10} + 21 q^{11} + 18 q^{12} + 26 q^{13} + 30 q^{14} + 17 q^{15} + 50 q^{16} + 24 q^{17} + 66 q^{18} + 39 q^{19} + 11 q^{20} - q^{21} + 21 q^{22} + 28 q^{23} + 18 q^{24} + 79 q^{25} + 26 q^{26} + 66 q^{27} + 30 q^{28} - 5 q^{29} + 17 q^{30} + 60 q^{31} + 50 q^{32} + 37 q^{33} + 24 q^{34} + 38 q^{35} + 66 q^{36} + 35 q^{37} + 39 q^{38} + 37 q^{39} + 11 q^{40} + 42 q^{41} - q^{42} + 44 q^{43} + 21 q^{44} + 31 q^{45} + 28 q^{46} + 60 q^{47} + 18 q^{48} + 92 q^{49} + 79 q^{50} + 26 q^{51} + 26 q^{52} - 2 q^{53} + 66 q^{54} + 33 q^{55} + 30 q^{56} + 15 q^{57} - 5 q^{58} + 65 q^{59} + 17 q^{60} + 15 q^{61} + 60 q^{62} + 56 q^{63} + 50 q^{64} + 6 q^{65} + 37 q^{66} + 48 q^{67} + 24 q^{68} - 9 q^{69} + 38 q^{70} + 34 q^{71} + 66 q^{72} + 91 q^{73} + 35 q^{74} + 54 q^{75} + 39 q^{76} - 6 q^{77} + 37 q^{78} + 29 q^{79} + 11 q^{80} + 66 q^{81} + 42 q^{82} + 43 q^{83} - q^{84} + 44 q^{86} + 32 q^{87} + 21 q^{88} + 38 q^{89} + 31 q^{90} + 55 q^{91} + 28 q^{92} - 15 q^{93} + 60 q^{94} + 9 q^{95} + 18 q^{96} + 80 q^{97} + 92 q^{98} + 20 q^{99}+O(q^{100}) \) 50 * q + 50 * q^2 + 18 * q^3 + 50 * q^4 + 11 * q^5 + 18 * q^6 + 30 * q^7 + 50 * q^8 + 66 * q^9 + 11 * q^10 + 21 * q^11 + 18 * q^12 + 26 * q^13 + 30 * q^14 + 17 * q^15 + 50 * q^16 + 24 * q^17 + 66 * q^18 + 39 * q^19 + 11 * q^20 - q^21 + 21 * q^22 + 28 * q^23 + 18 * q^24 + 79 * q^25 + 26 * q^26 + 66 * q^27 + 30 * q^28 - 5 * q^29 + 17 * q^30 + 60 * q^31 + 50 * q^32 + 37 * q^33 + 24 * q^34 + 38 * q^35 + 66 * q^36 + 35 * q^37 + 39 * q^38 + 37 * q^39 + 11 * q^40 + 42 * q^41 - q^42 + 44 * q^43 + 21 * q^44 + 31 * q^45 + 28 * q^46 + 60 * q^47 + 18 * q^48 + 92 * q^49 + 79 * q^50 + 26 * q^51 + 26 * q^52 - 2 * q^53 + 66 * q^54 + 33 * q^55 + 30 * q^56 + 15 * q^57 - 5 * q^58 + 65 * q^59 + 17 * q^60 + 15 * q^61 + 60 * q^62 + 56 * q^63 + 50 * q^64 + 6 * q^65 + 37 * q^66 + 48 * q^67 + 24 * q^68 - 9 * q^69 + 38 * q^70 + 34 * q^71 + 66 * q^72 + 91 * q^73 + 35 * q^74 + 54 * q^75 + 39 * q^76 - 6 * q^77 + 37 * q^78 + 29 * q^79 + 11 * q^80 + 66 * q^81 + 42 * q^82 + 43 * q^83 - q^84 + 44 * q^86 + 32 * q^87 + 21 * q^88 + 38 * q^89 + 31 * q^90 + 55 * q^91 + 28 * q^92 - 15 * q^93 + 60 * q^94 + 9 * q^95 + 18 * q^96 + 80 * q^97 + 92 * q^98 + 20 * q^99

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