LMFDB - Embedded newform 4027.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, 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("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53459 q^{2} +2.56413 q^{3} +4.42415 q^{4} -2.01095 q^{5} -6.49903 q^{6} -2.72523 q^{7} -6.14422 q^{8} +3.57478 q^{9} +O(q^{10})$	\(q-2.53459 q^{2} +2.56413 q^{3} +4.42415 q^{4} -2.01095 q^{5} -6.49903 q^{6} -2.72523 q^{7} -6.14422 q^{8} +3.57478 q^{9} +5.09695 q^{10} -5.31951 q^{11} +11.3441 q^{12} -4.97223 q^{13} +6.90734 q^{14} -5.15635 q^{15} +6.72478 q^{16} +5.38535 q^{17} -9.06060 q^{18} -4.08068 q^{19} -8.89676 q^{20} -6.98785 q^{21} +13.4828 q^{22} -3.66483 q^{23} -15.7546 q^{24} -0.956062 q^{25} +12.6026 q^{26} +1.47381 q^{27} -12.0568 q^{28} +4.17497 q^{29} +13.0692 q^{30} +3.40622 q^{31} -4.75613 q^{32} -13.6399 q^{33} -13.6496 q^{34} +5.48031 q^{35} +15.8153 q^{36} -0.551233 q^{37} +10.3428 q^{38} -12.7495 q^{39} +12.3557 q^{40} +0.256698 q^{41} +17.7113 q^{42} +1.62862 q^{43} -23.5343 q^{44} -7.18872 q^{45} +9.28884 q^{46} +8.56541 q^{47} +17.2432 q^{48} +0.426869 q^{49} +2.42322 q^{50} +13.8087 q^{51} -21.9979 q^{52} -1.26818 q^{53} -3.73550 q^{54} +10.6973 q^{55} +16.7444 q^{56} -10.4634 q^{57} -10.5818 q^{58} -2.84160 q^{59} -22.8125 q^{60} +4.17697 q^{61} -8.63337 q^{62} -9.74209 q^{63} -1.39472 q^{64} +9.99893 q^{65} +34.5716 q^{66} -9.17328 q^{67} +23.8256 q^{68} -9.39711 q^{69} -13.8903 q^{70} -4.31676 q^{71} -21.9642 q^{72} +2.53212 q^{73} +1.39715 q^{74} -2.45147 q^{75} -18.0535 q^{76} +14.4969 q^{77} +32.3146 q^{78} +6.09135 q^{79} -13.5232 q^{80} -6.94530 q^{81} -0.650623 q^{82} +6.95608 q^{83} -30.9153 q^{84} -10.8297 q^{85} -4.12788 q^{86} +10.7052 q^{87} +32.6842 q^{88} -2.68794 q^{89} +18.2204 q^{90} +13.5505 q^{91} -16.2137 q^{92} +8.73400 q^{93} -21.7098 q^{94} +8.20606 q^{95} -12.1954 q^{96} -10.1869 q^{97} -1.08194 q^{98} -19.0161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * 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 $

$2$	−2.53459	−1.79223	−0.896113	−	0.443826i	$-0.853621\pi$
$2$	−2.53459	−1.79223	−0.896113	+	0.443826i	$0.853621\pi$
$3$	2.56413	1.48040	0.740201	−	0.672385i	$-0.234730\pi$
$3$	2.56413	1.48040	0.740201	+	0.672385i	$0.234730\pi$
$4$	4.42415	2.21207
$5$	−2.01095	−0.899326	−0.449663	−	0.893198i	$-0.648456\pi$
$5$	−2.01095	−0.899326	−0.449663	+	0.893198i	$0.648456\pi$
$6$	−6.49903	−2.65322
$7$	−2.72523	−1.03004	−0.515020	−	0.857178i	$-0.672215\pi$
$7$	−2.72523	−1.03004	−0.515020	+	0.857178i	$0.672215\pi$
$8$	−6.14422	−2.17231
$9$	3.57478	1.19159
$10$	5.09695	1.61180
$11$	−5.31951	−1.60389	−0.801947	−	0.597396i	$-0.796202\pi$
$11$	−5.31951	−1.60389	−0.801947	+	0.597396i	$0.796202\pi$
$12$	11.3441	3.27476
$13$	−4.97223	−1.37905	−0.689524	−	0.724263i	$-0.742180\pi$
$13$	−4.97223	−1.37905	−0.689524	+	0.724263i	$0.742180\pi$
$14$	6.90734	1.84606
$15$	−5.15635	−1.33137
$16$	6.72478	1.68120
$17$	5.38535	1.30614	0.653069	−	0.757298i	$-0.273481\pi$
$17$	5.38535	1.30614	0.653069	+	0.757298i	$0.273481\pi$
$18$	−9.06060	−2.13560
$19$	−4.08068	−0.936172	−0.468086	−	0.883683i	$-0.655056\pi$
$19$	−4.08068	−0.936172	−0.468086	+	0.883683i	$0.655056\pi$
$20$	−8.89676	−1.98938
$21$	−6.98785	−1.52487
$22$	13.4828	2.87454
$23$	−3.66483	−0.764170	−0.382085	−	0.924127i	$-0.624794\pi$
$23$	−3.66483	−0.764170	−0.382085	+	0.924127i	$0.624794\pi$
$24$	−15.7546	−3.21589
$25$	−0.956062	−0.191212
$26$	12.6026	2.47157
$27$	1.47381	0.283634
$28$	−12.0568	−2.27852
$29$	4.17497	0.775272	0.387636	−	0.921812i	$-0.373292\pi$
$29$	4.17497	0.775272	0.387636	+	0.921812i	$0.373292\pi$
$30$	13.0692	2.38611
$31$	3.40622	0.611775	0.305888	−	0.952068i	$-0.401047\pi$
$31$	3.40622	0.611775	0.305888	+	0.952068i	$0.401047\pi$
$32$	−4.75613	−0.840773
$33$	−13.6399	−2.37441
$34$	−13.6496	−2.34090
$35$	5.48031	0.926341
$36$	15.8153	2.63589
$37$	−0.551233	−0.0906221	−0.0453110	−	0.998973i	$-0.514428\pi$
$37$	−0.551233	−0.0906221	−0.0453110	+	0.998973i	$0.514428\pi$
$38$	10.3428	1.67783
$39$	−12.7495	−2.04155
$40$	12.3557	1.95361
$41$	0.256698	0.0400894	0.0200447	−	0.999799i	$-0.493619\pi$
$41$	0.256698	0.0400894	0.0200447	+	0.999799i	$0.493619\pi$
$42$	17.7113	2.73292
$43$	1.62862	0.248362	0.124181	−	0.992260i	$-0.460370\pi$
$43$	1.62862	0.248362	0.124181	+	0.992260i	$0.460370\pi$
$44$	−23.5343	−3.54793
$45$	−7.18872	−1.07163
$46$	9.28884	1.36957
$47$	8.56541	1.24939	0.624697	−	0.780867i	$-0.285223\pi$
$47$	8.56541	1.24939	0.624697	+	0.780867i	$0.285223\pi$
$48$	17.2432	2.48885
$49$	0.426869	0.0609813
$50$	2.42322	0.342696
$51$	13.8087	1.93361
$52$	−21.9979	−3.05056
$53$	−1.26818	−0.174199	−0.0870993	−	0.996200i	$-0.527760\pi$
$53$	−1.26818	−0.174199	−0.0870993	+	0.996200i	$0.527760\pi$
$54$	−3.73550	−0.508337
$55$	10.6973	1.44242
$56$	16.7444	2.23756
$57$	−10.4634	−1.38591
$58$	−10.5818	−1.38946
$59$	−2.84160	−0.369945	−0.184973	−	0.982744i	$-0.559220\pi$
$59$	−2.84160	−0.369945	−0.184973	+	0.982744i	$0.559220\pi$
$60$	−22.8125	−2.94508
$61$	4.17697	0.534806	0.267403	−	0.963585i	$-0.413835\pi$
$61$	4.17697	0.534806	0.267403	+	0.963585i	$0.413835\pi$
$62$	−8.63337	−1.09644
$63$	−9.74209	−1.22739
$64$	−1.39472	−0.174340
$65$	9.99893	1.24021
$66$	34.5716	4.25548
$67$	−9.17328	−1.12069	−0.560347	−	0.828258i	$-0.689332\pi$
$67$	−9.17328	−1.12069	−0.560347	+	0.828258i	$0.689332\pi$
$68$	23.8256	2.88927
$69$	−9.39711	−1.13128
$70$	−13.8903	−1.66021
$71$	−4.31676	−0.512305	−0.256153	−	0.966636i	$-0.582455\pi$
$71$	−4.31676	−0.512305	−0.256153	+	0.966636i	$0.582455\pi$
$72$	−21.9642	−2.58851
$73$	2.53212	0.296362	0.148181	−	0.988960i	$-0.452658\pi$
$73$	2.53212	0.296362	0.148181	+	0.988960i	$0.452658\pi$
$74$	1.39715	0.162415
$75$	−2.45147	−0.283071
$76$	−18.0535	−2.07088
$77$	14.4969	1.65207
$78$	32.3146	3.65891
$79$	6.09135	0.685330	0.342665	−	0.939458i	$-0.388670\pi$
$79$	6.09135	0.685330	0.342665	+	0.939458i	$0.388670\pi$
$80$	−13.5232	−1.51194
$81$	−6.94530	−0.771700
$82$	−0.650623	−0.0718493
$83$	6.95608	0.763529	0.381764	−	0.924260i	$-0.375317\pi$
$83$	6.95608	0.763529	0.381764	+	0.924260i	$0.375317\pi$
$84$	−30.9153	−3.37313
$85$	−10.8297	−1.17464
$86$	−4.12788	−0.445121
$87$	10.7052	1.14772
$88$	32.6842	3.48415
$89$	−2.68794	−0.284921	−0.142461	−	0.989800i	$-0.545501\pi$
$89$	−2.68794	−0.284921	−0.142461	+	0.989800i	$0.545501\pi$
$90$	18.2204	1.92060
$91$	13.5505	1.42047
$92$	−16.2137	−1.69040
$93$	8.73400	0.905674
$94$	−21.7098	−2.23920
$95$	8.20606	0.841924
$96$	−12.1954	−1.24468
$97$	−10.1869	−1.03433	−0.517163	−	0.855887i	$-0.673012\pi$
$97$	−10.1869	−1.03433	−0.517163	+	0.855887i	$0.673012\pi$
$98$	−1.08194	−0.109292
$99$	−19.0161	−1.91119
$100$	−4.22976	−0.422976
$101$	10.7100	1.06569	0.532843	−	0.846214i	$-0.321124\pi$
$101$	10.7100	1.06569	0.532843	+	0.846214i	$0.321124\pi$
$102$	−34.9995	−3.46547
$103$	−1.68724	−0.166249	−0.0831245	−	0.996539i	$-0.526490\pi$
$103$	−1.68724	−0.166249	−0.0831245	+	0.996539i	$0.526490\pi$
$104$	30.5505	2.99572
$105$	14.0522	1.37136
$106$	3.21433	0.312203
$107$	15.3667	1.48555	0.742775	−	0.669541i	$-0.233509\pi$
$107$	15.3667	1.48555	0.742775	+	0.669541i	$0.233509\pi$
$108$	6.52034	0.627420
$109$	−6.36460	−0.609618	−0.304809	−	0.952413i	$-0.598593\pi$
$109$	−6.36460	−0.609618	−0.304809	+	0.952413i	$0.598593\pi$
$110$	−27.1133	−2.58515
$111$	−1.41343	−0.134157
$112$	−18.3266	−1.73170
$113$	−7.23314	−0.680437	−0.340218	−	0.940346i	$-0.610501\pi$
$113$	−7.23314	−0.680437	−0.340218	+	0.940346i	$0.610501\pi$
$114$	26.5204	2.48387
$115$	7.36981	0.687238
$116$	18.4707	1.71496
$117$	−17.7746	−1.64326
$118$	7.20230	0.663025
$119$	−14.6763	−1.34537
$120$	31.6818	2.89214
$121$	17.2972	1.57247
$122$	−10.5869	−0.958493
$123$	0.658207	0.0593485
$124$	15.0696	1.35329
$125$	11.9774	1.07129
$126$	24.6922	2.19976
$127$	−14.7645	−1.31014	−0.655069	−	0.755569i	$-0.727360\pi$
$127$	−14.7645	−1.31014	−0.655069	+	0.755569i	$0.727360\pi$
$128$	13.0473	1.15323
$129$	4.17599	0.367676
$130$	−25.3432	−2.22274
$131$	6.82979	0.596722	0.298361	−	0.954453i	$-0.403560\pi$
$131$	6.82979	0.596722	0.298361	+	0.954453i	$0.403560\pi$
$132$	−60.3451	−5.25237
$133$	11.1208	0.964294
$134$	23.2505	2.00854
$135$	−2.96376	−0.255080
$136$	−33.0888	−2.83734
$137$	14.1299	1.20720	0.603601	−	0.797287i	$-0.293732\pi$
$137$	14.1299	1.20720	0.603601	+	0.797287i	$0.293732\pi$
$138$	23.8178	2.02751
$139$	3.79122	0.321567	0.160784	−	0.986990i	$-0.448598\pi$
$139$	3.79122	0.321567	0.160784	+	0.986990i	$0.448598\pi$
$140$	24.2457	2.04914
$141$	21.9629	1.84961
$142$	10.9412	0.918166
$143$	26.4498	2.21185
$144$	24.0396	2.00330
$145$	−8.39567	−0.697223
$146$	−6.41788	−0.531148
$147$	1.09455	0.0902768
$148$	−2.43873	−0.200463
$149$	−1.68530	−0.138065	−0.0690326	−	0.997614i	$-0.521991\pi$
$149$	−1.68530	−0.138065	−0.0690326	+	0.997614i	$0.521991\pi$
$150$	6.21347	0.507328
$151$	16.5292	1.34513	0.672564	−	0.740039i	$-0.265193\pi$
$151$	16.5292	1.34513	0.672564	+	0.740039i	$0.265193\pi$
$152$	25.0726	2.03366
$153$	19.2514	1.55639
$154$	−36.7437	−2.96089
$155$	−6.84975	−0.550185
$156$	−56.4055	−4.51605
$157$	23.7652	1.89667	0.948334	−	0.317273i	$-0.102767\pi$
$157$	23.7652	1.89667	0.948334	+	0.317273i	$0.102767\pi$
$158$	−15.4391	−1.22827
$159$	−3.25179	−0.257884
$160$	9.56436	0.756129
$161$	9.98750	0.787125
$162$	17.6035	1.38306
$163$	13.4732	1.05530	0.527652	−	0.849460i	$-0.323072\pi$
$163$	13.4732	1.05530	0.527652	+	0.849460i	$0.323072\pi$
$164$	1.13567	0.0886807
$165$	27.4293	2.13537
$166$	−17.6308	−1.36842
$167$	20.7333	1.60439	0.802195	−	0.597062i	$-0.203665\pi$
$167$	20.7333	1.60439	0.802195	+	0.597062i	$0.203665\pi$
$168$	42.9349	3.31250
$169$	11.7231	0.901774
$170$	27.4488	2.10523
$171$	−14.5875	−1.11554
$172$	7.20525	0.549395
$173$	5.84549	0.444424	0.222212	−	0.974998i	$-0.428672\pi$
$173$	5.84549	0.444424	0.222212	+	0.974998i	$0.428672\pi$
$174$	−27.1332	−2.05697
$175$	2.60549	0.196956
$176$	−35.7726	−2.69646
$177$	−7.28625	−0.547668
$178$	6.81283	0.510643
$179$	−19.6199	−1.46646	−0.733231	−	0.679980i	$-0.761988\pi$
$179$	−19.6199	−1.46646	−0.733231	+	0.679980i	$0.761988\pi$
$180$	−31.8039	−2.37053
$181$	13.3320	0.990962	0.495481	−	0.868619i	$-0.334992\pi$
$181$	13.3320	0.990962	0.495481	+	0.868619i	$0.334992\pi$
$182$	−34.3449	−2.54581
$183$	10.7103	0.791728
$184$	22.5175	1.66001
$185$	1.10850	0.0814988
$186$	−22.1371	−1.62317
$187$	−28.6474	−2.09491
$188$	37.8946	2.76375
$189$	−4.01646	−0.292155
$190$	−20.7990	−1.50892
$191$	6.86299	0.496589	0.248294	−	0.968685i	$-0.420130\pi$
$191$	6.86299	0.496589	0.248294	+	0.968685i	$0.420130\pi$
$192$	−3.57626	−0.258094
$193$	−7.87184	−0.566628	−0.283314	−	0.959027i	$-0.591434\pi$
$193$	−7.87184	−0.566628	−0.283314	+	0.959027i	$0.591434\pi$
$194$	25.8197	1.85374
$195$	25.6386	1.83602
$196$	1.88853	0.134895
$197$	3.95538	0.281809	0.140905	−	0.990023i	$-0.454999\pi$
$197$	3.95538	0.281809	0.140905	+	0.990023i	$0.454999\pi$
$198$	48.1980	3.42528
$199$	8.97566	0.636267	0.318134	−	0.948046i	$-0.396944\pi$
$199$	8.97566	0.636267	0.318134	+	0.948046i	$0.396944\pi$
$200$	5.87425	0.415372
$201$	−23.5215	−1.65908
$202$	−27.1455	−1.90995
$203$	−11.3777	−0.798561
$204$	61.0919	4.27729
$205$	−0.516207	−0.0360535
$206$	4.27647	0.297956
$207$	−13.1010	−0.910579
$208$	−33.4372	−2.31845
$209$	21.7072	1.50152
$210$	−35.6167	−2.45778
$211$	−12.3541	−0.850489	−0.425245	−	0.905078i	$-0.639812\pi$
$211$	−12.3541	−0.850489	−0.425245	+	0.905078i	$0.639812\pi$
$212$	−5.61064	−0.385340
$213$	−11.0687	−0.758418
$214$	−38.9482	−2.66244
$215$	−3.27508	−0.223358
$216$	−9.05539	−0.616142
$217$	−9.28273	−0.630152
$218$	16.1317	1.09257
$219$	6.49269	0.438735
$220$	47.3264	3.19075
$221$	−26.7772	−1.80123
$222$	3.58248	0.240440
$223$	−24.6174	−1.64850	−0.824252	−	0.566224i	$-0.808404\pi$
$223$	−24.6174	−1.64850	−0.824252	+	0.566224i	$0.808404\pi$
$224$	12.9615	0.866030
$225$	−3.41771	−0.227847
$226$	18.3330	1.21950
$227$	1.91492	0.127097	0.0635487	−	0.997979i	$-0.479758\pi$
$227$	1.91492	0.127097	0.0635487	+	0.997979i	$0.479758\pi$
$228$	−46.2916	−3.06574
$229$	17.5825	1.16189	0.580943	−	0.813945i	$-0.302684\pi$
$229$	17.5825	1.16189	0.580943	+	0.813945i	$0.302684\pi$
$230$	−18.6794	−1.23169
$231$	37.1719	2.44573
$232$	−25.6519	−1.68413
$233$	−0.582736	−0.0381763	−0.0190882	−	0.999818i	$-0.506076\pi$
$233$	−0.582736	−0.0381763	−0.0190882	+	0.999818i	$0.506076\pi$
$234$	45.0514	2.94510
$235$	−17.2247	−1.12361
$236$	−12.5717	−0.818346
$237$	15.6190	1.01456
$238$	37.1984	2.41121
$239$	17.0557	1.10324	0.551620	−	0.834096i	$-0.314010\pi$
$239$	17.0557	1.10324	0.551620	+	0.834096i	$0.314010\pi$
$240$	−34.6754	−2.23829
$241$	−28.3989	−1.82934	−0.914668	−	0.404207i	$-0.867548\pi$
$241$	−28.3989	−1.82934	−0.914668	+	0.404207i	$0.867548\pi$
$242$	−43.8413	−2.81823
$243$	−22.2301	−1.42606
$244$	18.4795	1.18303
$245$	−0.858414	−0.0548421
$246$	−1.66828	−0.106366
$247$	20.2901	1.29103
$248$	−20.9286	−1.32896
$249$	17.8363	1.13033
$250$	−30.3577	−1.91999
$251$	−18.9155	−1.19394	−0.596969	−	0.802264i	$-0.703629\pi$
$251$	−18.9155	−1.19394	−0.596969	+	0.802264i	$0.703629\pi$
$252$	−43.1004	−2.71507
$253$	19.4951	1.22565
$254$	37.4220	2.34806
$255$	−27.7688	−1.73895
$256$	−30.2801	−1.89251
$257$	9.03146	0.563367	0.281683	−	0.959507i	$-0.409107\pi$
$257$	9.03146	0.563367	0.281683	+	0.959507i	$0.409107\pi$
$258$	−10.5844	−0.658958
$259$	1.50223	0.0933443
$260$	44.2367	2.74344
$261$	14.9246	0.923809
$262$	−17.3107	−1.06946
$263$	21.2681	1.31145	0.655723	−	0.755002i	$-0.272364\pi$
$263$	21.2681	1.31145	0.655723	+	0.755002i	$0.272364\pi$
$264$	83.8068	5.15795
$265$	2.55026	0.156661
$266$	−28.1866	−1.72823
$267$	−6.89224	−0.421798
$268$	−40.5839	−2.47906
$269$	−13.2904	−0.810331	−0.405166	−	0.914243i	$-0.632786\pi$
$269$	−13.2904	−0.810331	−0.405166	+	0.914243i	$0.632786\pi$
$270$	7.51191	0.457161
$271$	−30.0848	−1.82752	−0.913760	−	0.406254i	$-0.866835\pi$
$271$	−30.0848	−1.82752	−0.913760	+	0.406254i	$0.866835\pi$
$272$	36.2153	2.19588
$273$	34.7452	2.10287
$274$	−35.8136	−2.16358
$275$	5.08578	0.306684
$276$	−41.5742	−2.50247
$277$	23.9839	1.44105	0.720527	−	0.693427i	$-0.243900\pi$
$277$	23.9839	1.44105	0.720527	+	0.693427i	$0.243900\pi$
$278$	−9.60920	−0.576321
$279$	12.1765	0.728987
$280$	−33.6722	−2.01230
$281$	12.7082	0.758109	0.379055	−	0.925374i	$-0.376249\pi$
$281$	12.7082	0.758109	0.379055	+	0.925374i	$0.376249\pi$
$282$	−55.6668	−3.31491
$283$	−11.1050	−0.660122	−0.330061	−	0.943960i	$-0.607069\pi$
$283$	−11.1050	−0.660122	−0.330061	+	0.943960i	$0.607069\pi$
$284$	−19.0980	−1.13326
$285$	21.0414	1.24639
$286$	−67.0395	−3.96413
$287$	−0.699559	−0.0412937
$288$	−17.0021	−1.00186
$289$	12.0020	0.705998
$290$	21.2796	1.24958
$291$	−26.1206	−1.53122
$292$	11.2025	0.655575
$293$	−8.06426	−0.471119	−0.235560	−	0.971860i	$-0.575692\pi$
$293$	−8.06426	−0.471119	−0.235560	+	0.971860i	$0.575692\pi$
$294$	−2.77423	−0.161797
$295$	5.71433	0.332701
$296$	3.38689	0.196859
$297$	−7.83993	−0.454919
$298$	4.27155	0.247444
$299$	18.2224	1.05383
$300$	−10.8457	−0.626175
$301$	−4.43836	−0.255823
$302$	−41.8948	−2.41077
$303$	27.4619	1.57764
$304$	−27.4417	−1.57389
$305$	−8.39969	−0.480965
$306$	−48.7945	−2.78939
$307$	−33.3364	−1.90261	−0.951304	−	0.308253i	$-0.900256\pi$
$307$	−33.3364	−1.90261	−0.951304	+	0.308253i	$0.900256\pi$
$308$	64.1363	3.65451
$309$	−4.32631	−0.246115
$310$	17.3613	0.986056
$311$	−18.2611	−1.03549	−0.517747	−	0.855534i	$-0.673229\pi$
$311$	−18.2611	−1.03549	−0.517747	+	0.855534i	$0.673229\pi$
$312$	78.3355	4.43487
$313$	−6.78381	−0.383443	−0.191722	−	0.981449i	$-0.561407\pi$
$313$	−6.78381	−0.383443	−0.191722	+	0.981449i	$0.561407\pi$
$314$	−60.2350	−3.39926
$315$	19.5909	1.10382
$316$	26.9490	1.51600
$317$	7.60501	0.427140	0.213570	−	0.976928i	$-0.431491\pi$
$317$	7.60501	0.427140	0.213570	+	0.976928i	$0.431491\pi$
$318$	8.24197	0.462187
$319$	−22.2088	−1.24345
$320$	2.80473	0.156789
$321$	39.4022	2.19921
$322$	−25.3142	−1.41071
$323$	−21.9759	−1.22277
$324$	−30.7270	−1.70706
$325$	4.75376	0.263691
$326$	−34.1491	−1.89134
$327$	−16.3197	−0.902481
$328$	−1.57721	−0.0870866
$329$	−23.3427	−1.28692
$330$	−69.5220	−3.82706
$331$	21.7815	1.19722	0.598610	−	0.801041i	$-0.295720\pi$
$331$	21.7815	1.19722	0.598610	+	0.801041i	$0.295720\pi$
$332$	30.7747	1.68898
$333$	−1.97053	−0.107985
$334$	−52.5504	−2.87543
$335$	18.4470	1.00787
$336$	−46.9918	−2.56361
$337$	−19.4266	−1.05823	−0.529117	−	0.848549i	$-0.677477\pi$
$337$	−19.4266	−1.05823	−0.529117	+	0.848549i	$0.677477\pi$
$338$	−29.7131	−1.61618
$339$	−18.5467	−1.00732
$340$	−47.9121	−2.59840
$341$	−18.1194	−0.981222
$342$	36.9734	1.99929
$343$	17.9133	0.967226
$344$	−10.0066	−0.539519
$345$	18.8972	1.01739
$346$	−14.8159	−0.796508
$347$	−16.3367	−0.877003	−0.438501	−	0.898731i	$-0.644491\pi$
$347$	−16.3367	−0.877003	−0.438501	+	0.898731i	$0.644491\pi$
$348$	47.3613	2.53883
$349$	21.4882	1.15024	0.575119	−	0.818070i	$-0.304956\pi$
$349$	21.4882	1.15024	0.575119	+	0.818070i	$0.304956\pi$
$350$	−6.60384	−0.352990
$351$	−7.32811	−0.391145
$352$	25.3003	1.34851
$353$	33.7957	1.79876	0.899382	−	0.437163i	$-0.144017\pi$
$353$	33.7957	1.79876	0.899382	+	0.437163i	$0.144017\pi$
$354$	18.4677	0.981545
$355$	8.68081	0.460729
$356$	−11.8918	−0.630266
$357$	−37.6320	−1.99170
$358$	49.7284	2.62823
$359$	28.8856	1.52452	0.762261	−	0.647270i	$-0.224089\pi$
$359$	28.8856	1.52452	0.762261	+	0.647270i	$0.224089\pi$
$360$	44.1690	2.32791
$361$	−2.34806	−0.123582
$362$	−33.7912	−1.77603
$363$	44.3523	2.32789
$364$	59.9492	3.14219
$365$	−5.09198	−0.266526
$366$	−27.1462	−1.41896
$367$	−24.3881	−1.27305	−0.636525	−	0.771256i	$-0.719629\pi$
$367$	−24.3881	−1.27305	−0.636525	+	0.771256i	$0.719629\pi$
$368$	−24.6452	−1.28472
$369$	0.917637	0.0477703
$370$	−2.80960	−0.146064
$371$	3.45609	0.179431
$372$	38.6405	2.00342
$373$	4.89725	0.253570	0.126785	−	0.991930i	$-0.459534\pi$
$373$	4.89725	0.253570	0.126785	+	0.991930i	$0.459534\pi$
$374$	72.6095	3.75455
$375$	30.7116	1.58594
$376$	−52.6278	−2.71407
$377$	−20.7589	−1.06914
$378$	10.1801	0.523607
$379$	−0.658380	−0.0338187	−0.0169094	−	0.999857i	$-0.505383\pi$
$379$	−0.658380	−0.0338187	−0.0169094	+	0.999857i	$0.505383\pi$
$380$	36.3048	1.86240
$381$	−37.8582	−1.93953
$382$	−17.3949	−0.889999
$383$	−32.7314	−1.67250	−0.836249	−	0.548350i	$-0.815256\pi$
$383$	−32.7314	−1.67250	−0.836249	+	0.548350i	$0.815256\pi$
$384$	33.4551	1.70725
$385$	−29.1526	−1.48575
$386$	19.9519	1.01552
$387$	5.82195	0.295946
$388$	−45.0684	−2.28800
$389$	13.1409	0.666268	0.333134	−	0.942879i	$-0.391894\pi$
$389$	13.1409	0.666268	0.333134	+	0.942879i	$0.391894\pi$
$390$	−64.9833	−3.29056
$391$	−19.7364	−0.998112
$392$	−2.62278	−0.132470
$393$	17.5125	0.883388
$394$	−10.0253	−0.505066
$395$	−12.2494	−0.616335
$396$	−84.1299	−4.22769
$397$	39.3440	1.97462	0.987309	−	0.158813i	$-0.0507666\pi$
$397$	39.3440	1.97462	0.987309	+	0.158813i	$0.0507666\pi$
$398$	−22.7496	−1.14034
$399$	28.5152	1.42754
$400$	−6.42931	−0.321465
$401$	−35.6424	−1.77989	−0.889947	−	0.456064i	$-0.849259\pi$
$401$	−35.6424	−1.77989	−0.889947	+	0.456064i	$0.849259\pi$
$402$	59.6174	2.97345
$403$	−16.9365	−0.843667
$404$	47.3826	2.35737
$405$	13.9667	0.694010
$406$	28.8379	1.43120
$407$	2.93229	0.145348
$408$	−84.8440	−4.20040
$409$	−9.10168	−0.450049	−0.225025	−	0.974353i	$-0.572246\pi$
$409$	−9.10168	−0.450049	−0.225025	+	0.974353i	$0.572246\pi$
$410$	1.30837	0.0646160
$411$	36.2310	1.78714
$412$	−7.46461	−0.367755
$413$	7.74402	0.381058
$414$	33.2056	1.63196
$415$	−13.9884	−0.686661
$416$	23.6486	1.15947
$417$	9.72120	0.476049
$418$	−55.0189	−2.69106
$419$	−0.525874	−0.0256906	−0.0128453	−	0.999917i	$-0.504089\pi$
$419$	−0.525874	−0.0256906	−0.0128453	+	0.999917i	$0.504089\pi$
$420$	62.1692	3.03355
$421$	24.4813	1.19315	0.596573	−	0.802559i	$-0.296529\pi$
$421$	24.4813	1.19315	0.596573	+	0.802559i	$0.296529\pi$
$422$	31.3125	1.52427
$423$	30.6194	1.48877
$424$	7.79201	0.378413
$425$	−5.14873	−0.249750
$426$	28.0547	1.35926
$427$	−11.3832	−0.550871
$428$	67.9844	3.28615
$429$	67.8209	3.27442
$430$	8.30098	0.400309
$431$	7.44823	0.358769	0.179384	−	0.983779i	$-0.442589\pi$
$431$	7.44823	0.358769	0.179384	+	0.983779i	$0.442589\pi$
$432$	9.91103	0.476845
$433$	−3.03056	−0.145640	−0.0728198	−	0.997345i	$-0.523200\pi$
$433$	−3.03056	−0.145640	−0.0728198	+	0.997345i	$0.523200\pi$
$434$	23.5279	1.12938
$435$	−21.5276	−1.03217
$436$	−28.1579	−1.34852
$437$	14.9550	0.715395
$438$	−16.4563	−0.786313
$439$	18.5097	0.883419	0.441710	−	0.897158i	$-0.354372\pi$
$439$	18.5097	0.883419	0.441710	+	0.897158i	$0.354372\pi$
$440$	−65.7265	−3.13339
$441$	1.52596	0.0726648
$442$	67.8692	3.22821
$443$	7.84447	0.372702	0.186351	−	0.982483i	$-0.440334\pi$
$443$	7.84447	0.372702	0.186351	+	0.982483i	$0.440334\pi$
$444$	−6.25324	−0.296766
$445$	5.40533	0.256237
$446$	62.3950	2.95449
$447$	−4.32134	−0.204392
$448$	3.80094	0.179578
$449$	−0.568702	−0.0268387	−0.0134193	−	0.999910i	$-0.504272\pi$
$449$	−0.568702	−0.0268387	−0.0134193	+	0.999910i	$0.504272\pi$
$450$	8.66249	0.408354
$451$	−1.36551	−0.0642991
$452$	−32.0005	−1.50518
$453$	42.3831	1.99133
$454$	−4.85353	−0.227787
$455$	−27.2494	−1.27747
$456$	64.2895	3.01063
$457$	31.8862	1.49157	0.745786	−	0.666186i	$-0.232074\pi$
$457$	31.8862	1.49157	0.745786	+	0.666186i	$0.232074\pi$
$458$	−44.5645	−2.08236
$459$	7.93696	0.370466
$460$	32.6051	1.52022
$461$	−14.6034	−0.680148	−0.340074	−	0.940399i	$-0.610452\pi$
$461$	−14.6034	−0.680148	−0.340074	+	0.940399i	$0.610452\pi$
$462$	−94.2156	−4.38331
$463$	−14.4255	−0.670410	−0.335205	−	0.942145i	$-0.608806\pi$
$463$	−14.4255	−0.670410	−0.335205	+	0.942145i	$0.608806\pi$
$464$	28.0758	1.30338
$465$	−17.5637	−0.814496
$466$	1.47700	0.0684206
$467$	32.6772	1.51212	0.756060	−	0.654502i	$-0.227122\pi$
$467$	32.6772	1.51212	0.756060	+	0.654502i	$0.227122\pi$
$468$	−78.6375	−3.63502
$469$	24.9993	1.15436
$470$	43.6574	2.01377
$471$	60.9371	2.80783
$472$	17.4594	0.803635
$473$	−8.66345	−0.398346
$474$	−39.5878	−1.81833
$475$	3.90138	0.179008
$476$	−64.9301	−2.97607
$477$	−4.53348	−0.207574
$478$	−43.2291	−1.97725
$479$	−12.1253	−0.554020	−0.277010	−	0.960867i	$-0.589344\pi$
$479$	−12.1253	−0.554020	−0.277010	+	0.960867i	$0.589344\pi$
$480$	24.5243	1.11938
$481$	2.74085	0.124972
$482$	71.9796	3.27858
$483$	25.6093	1.16526
$484$	76.5254	3.47843
$485$	20.4854	0.930196
$486$	56.3442	2.55582
$487$	−6.72766	−0.304859	−0.152430	−	0.988314i	$-0.548710\pi$
$487$	−6.72766	−0.304859	−0.152430	+	0.988314i	$0.548710\pi$
$488$	−25.6642	−1.16176
$489$	34.5472	1.56228
$490$	2.17573	0.0982893
$491$	28.5022	1.28629	0.643143	−	0.765746i	$-0.277630\pi$
$491$	28.5022	1.28629	0.643143	+	0.765746i	$0.277630\pi$
$492$	2.91200	0.131283
$493$	22.4837	1.01261
$494$	−51.4270	−2.31381
$495$	38.2405	1.71878
$496$	22.9061	1.02851
$497$	11.7642	0.527694
$498$	−45.2077	−2.02581
$499$	−7.27892	−0.325849	−0.162925	−	0.986639i	$-0.552093\pi$
$499$	−7.27892	−0.325849	−0.162925	+	0.986639i	$0.552093\pi$
$500$	52.9896	2.36977
$501$	53.1629	2.37514
$502$	47.9432	2.13981
$503$	9.40468	0.419334	0.209667	−	0.977773i	$-0.432762\pi$
$503$	9.40468	0.419334	0.209667	+	0.977773i	$0.432762\pi$
$504$	59.8575	2.66627
$505$	−21.5373	−0.958398
$506$	−49.4121	−2.19664
$507$	30.0595	1.33499
$508$	−65.3203	−2.89812
$509$	−1.34232	−0.0594974	−0.0297487	−	0.999557i	$-0.509471\pi$
$509$	−1.34232	−0.0594974	−0.0297487	+	0.999557i	$0.509471\pi$
$510$	70.3824	3.11659
$511$	−6.90060	−0.305265
$512$	50.6531	2.23857
$513$	−6.01413	−0.265531
$514$	−22.8910	−1.00968
$515$	3.39297	0.149512
$516$	18.4752	0.813326
$517$	−45.5638	−2.00389
$518$	−3.80755	−0.167294
$519$	14.9886	0.657927
$520$	−61.4356	−2.69413
$521$	−13.6515	−0.598084	−0.299042	−	0.954240i	$-0.596667\pi$
$521$	−13.6515	−0.598084	−0.299042	+	0.954240i	$0.596667\pi$
$522$	−37.8277	−1.65567
$523$	0.598206	0.0261577	0.0130789	−	0.999914i	$-0.495837\pi$
$523$	0.598206	0.0261577	0.0130789	+	0.999914i	$0.495837\pi$
$524$	30.2160	1.31999
$525$	6.68081	0.291575
$526$	−53.9058	−2.35041
$527$	18.3437	0.799063
$528$	−91.7256	−3.99185
$529$	−9.56902	−0.416044
$530$	−6.46387	−0.280773
$531$	−10.1581	−0.440824
$532$	49.2000	2.13309
$533$	−1.27636	−0.0552852
$534$	17.4690	0.755957
$535$	−30.9017	−1.33599
$536$	56.3626	2.43450
$537$	−50.3081	−2.17095
$538$	33.6858	1.45230
$539$	−2.27073	−0.0978074
$540$	−13.1121	−0.564255
$541$	−21.9071	−0.941860	−0.470930	−	0.882171i	$-0.656082\pi$
$541$	−21.9071	−0.941860	−0.470930	+	0.882171i	$0.656082\pi$
$542$	76.2526	3.27533
$543$	34.1851	1.46702
$544$	−25.6134	−1.09817
$545$	12.7989	0.548246
$546$	−88.0648	−3.76882
$547$	11.2969	0.483020	0.241510	−	0.970398i	$-0.422357\pi$
$547$	11.2969	0.483020	0.241510	+	0.970398i	$0.422357\pi$
$548$	62.5129	2.67042
$549$	14.9317	0.637271
$550$	−12.8904	−0.549647
$551$	−17.0367	−0.725788
$552$	57.7379	2.45749
$553$	−16.6003	−0.705917
$554$	−60.7894	−2.58269
$555$	2.84235	0.120651
$556$	16.7729	0.711331
$557$	−29.7616	−1.26104	−0.630521	−	0.776172i	$-0.717159\pi$
$557$	−29.7616	−1.26104	−0.630521	+	0.776172i	$0.717159\pi$
$558$	−30.8624	−1.30651
$559$	−8.09786	−0.342503
$560$	36.8539	1.55736
$561$	−73.4558	−3.10131
$562$	−32.2102	−1.35870
$563$	42.4340	1.78838	0.894190	−	0.447688i	$-0.147753\pi$
$563$	42.4340	1.78838	0.894190	+	0.447688i	$0.147753\pi$
$564$	97.1669	4.09146
$565$	14.5455	0.611935
$566$	28.1466	1.18309
$567$	18.9275	0.794881
$568$	26.5231	1.11289
$569$	−16.6322	−0.697257	−0.348629	−	0.937261i	$-0.613353\pi$
$569$	−16.6322	−0.697257	−0.348629	+	0.937261i	$0.613353\pi$
$570$	−53.3314	−2.23381
$571$	6.07093	0.254061	0.127030	−	0.991899i	$-0.459455\pi$
$571$	6.07093	0.254061	0.127030	+	0.991899i	$0.459455\pi$
$572$	117.018	4.89277
$573$	17.5976	0.735151
$574$	1.77310	0.0740076
$575$	3.50380	0.146119
$576$	−4.98583	−0.207743
$577$	27.1115	1.12867	0.564333	−	0.825547i	$-0.309133\pi$
$577$	27.1115	1.12867	0.564333	+	0.825547i	$0.309133\pi$
$578$	−30.4201	−1.26531
$579$	−20.1844	−0.838837
$580$	−37.1437	−1.54231
$581$	−18.9569	−0.786465
$582$	66.2051	2.74429
$583$	6.74612	0.279396
$584$	−15.5579	−0.643790
$585$	35.7439	1.47783
$586$	20.4396	0.844352
$587$	−19.6491	−0.811005	−0.405502	−	0.914094i	$-0.632903\pi$
$587$	−19.6491	−0.811005	−0.405502	+	0.914094i	$0.632903\pi$
$588$	4.84244	0.199699
$589$	−13.8997	−0.572727
$590$	−14.4835	−0.596276
$591$	10.1421	0.417191
$592$	−3.70692	−0.152353
$593$	24.4317	1.00329	0.501645	−	0.865073i	$-0.332728\pi$
$593$	24.4317	1.00329	0.501645	+	0.865073i	$0.332728\pi$
$594$	19.8710	0.815318
$595$	29.5134	1.20993
$596$	−7.45602	−0.305411
$597$	23.0148	0.941932
$598$	−46.1863	−1.88870
$599$	−22.9622	−0.938208	−0.469104	−	0.883143i	$-0.655423\pi$
$599$	−22.9622	−0.938208	−0.469104	+	0.883143i	$0.655423\pi$
$600$	15.0624	0.614919
$601$	−1.52929	−0.0623812	−0.0311906	−	0.999513i	$-0.509930\pi$
$601$	−1.52929	−0.0623812	−0.0311906	+	0.999513i	$0.509930\pi$
$602$	11.2494	0.458492
$603$	−32.7924	−1.33541
$604$	73.1277	2.97552
$605$	−34.7839	−1.41417
$606$	−69.6046	−2.82749
$607$	−42.8062	−1.73745	−0.868725	−	0.495295i	$-0.835060\pi$
$607$	−42.8062	−1.73745	−0.868725	+	0.495295i	$0.835060\pi$
$608$	19.4082	0.787108
$609$	−29.1741	−1.18219
$610$	21.2898	0.861997
$611$	−42.5892	−1.72297
$612$	85.1711	3.44284
$613$	40.7951	1.64770	0.823848	−	0.566810i	$-0.191823\pi$
$613$	40.7951	1.64770	0.823848	+	0.566810i	$0.191823\pi$
$614$	84.4941	3.40990
$615$	−1.32362	−0.0533737
$616$	−89.0720	−3.58881
$617$	40.2711	1.62125	0.810627	−	0.585563i	$-0.199127\pi$
$617$	40.2711	1.62125	0.810627	+	0.585563i	$0.199127\pi$
$618$	10.9654	0.441094
$619$	−22.9423	−0.922130	−0.461065	−	0.887366i	$-0.652533\pi$
$619$	−22.9423	−0.922130	−0.461065	+	0.887366i	$0.652533\pi$
$620$	−30.3043	−1.21705
$621$	−5.40125	−0.216745
$622$	46.2845	1.85584
$623$	7.32525	0.293480
$624$	−85.7373	−3.43224
$625$	−19.3056	−0.772225
$626$	17.1942	0.687217
$627$	55.6602	2.22285
$628$	105.141	4.19557
$629$	−2.96858	−0.118365
$630$	−49.6549	−1.97830
$631$	5.65218	0.225010	0.112505	−	0.993651i	$-0.464113\pi$
$631$	5.65218	0.225010	0.112505	+	0.993651i	$0.464113\pi$
$632$	−37.4266	−1.48875
$633$	−31.6775	−1.25907
$634$	−19.2756	−0.765531
$635$	29.6908	1.17824
$636$	−14.3864	−0.570459
$637$	−2.12249	−0.0840961
$638$	56.2902	2.22855
$639$	−15.4315	−0.610459
$640$	−26.2376	−1.03713
$641$	−22.1634	−0.875402	−0.437701	−	0.899121i	$-0.644207\pi$
$641$	−22.1634	−0.875402	−0.437701	+	0.899121i	$0.644207\pi$
$642$	−99.8683	−3.94149
$643$	27.7299	1.09356	0.546780	−	0.837276i	$-0.315853\pi$
$643$	27.7299	1.09356	0.546780	+	0.837276i	$0.315853\pi$
$644$	44.1862	1.74118
$645$	−8.39773	−0.330660
$646$	55.6998	2.19148
$647$	−33.7906	−1.32844	−0.664222	−	0.747535i	$-0.731237\pi$
$647$	−33.7906	−1.32844	−0.664222	+	0.747535i	$0.731237\pi$
$648$	42.6734	1.67637
$649$	15.1159	0.593353
$650$	−12.0488	−0.472594
$651$	−23.8021	−0.932880
$652$	59.6076	2.33441
$653$	−11.4793	−0.449218	−0.224609	−	0.974449i	$-0.572110\pi$
$653$	−11.4793	−0.449218	−0.224609	+	0.974449i	$0.572110\pi$
$654$	41.3637	1.61745
$655$	−13.7344	−0.536647
$656$	1.72624	0.0673982
$657$	9.05176	0.353143
$658$	59.1642	2.30646
$659$	16.9988	0.662179	0.331089	−	0.943599i	$-0.392584\pi$
$659$	16.9988	0.662179	0.331089	+	0.943599i	$0.392584\pi$
$660$	121.351	4.72359
$661$	−6.37293	−0.247878	−0.123939	−	0.992290i	$-0.539553\pi$
$661$	−6.37293	−0.247878	−0.123939	+	0.992290i	$0.539553\pi$
$662$	−55.2072	−2.14569
$663$	−68.6603	−2.66654
$664$	−42.7397	−1.65862
$665$	−22.3634	−0.867215
$666$	4.99450	0.193533
$667$	−15.3006	−0.592440
$668$	91.7271	3.54903
$669$	−63.1223	−2.44045
$670$	−46.7557	−1.80633
$671$	−22.2194	−0.857771
$672$	33.2351	1.28207
$673$	47.6245	1.83579	0.917895	−	0.396823i	$-0.129887\pi$
$673$	47.6245	1.83579	0.917895	+	0.396823i	$0.129887\pi$
$674$	49.2384	1.89659
$675$	−1.40905	−0.0542344
$676$	51.8645	1.99479
$677$	10.1943	0.391797	0.195898	−	0.980624i	$-0.437238\pi$
$677$	10.1943	0.391797	0.195898	+	0.980624i	$0.437238\pi$
$678$	47.0084	1.80535
$679$	27.7617	1.06540
$680$	66.5400	2.55169
$681$	4.91010	0.188155
$682$	45.9253	1.75857
$683$	−15.5480	−0.594927	−0.297464	−	0.954733i	$-0.596141\pi$
$683$	−15.5480	−0.594927	−0.297464	+	0.954733i	$0.596141\pi$
$684$	−64.5373	−2.46765
$685$	−28.4146	−1.08567
$686$	−45.4028	−1.73349
$687$	45.0839	1.72006
$688$	10.9521	0.417545
$689$	6.30571	0.240228
$690$	−47.8966	−1.82339
$691$	−30.7649	−1.17035	−0.585175	−	0.810907i	$-0.698974\pi$
$691$	−30.7649	−1.17035	−0.585175	+	0.810907i	$0.698974\pi$
$692$	25.8613	0.983099
$693$	51.8231	1.96860
$694$	41.4070	1.57179
$695$	−7.62398	−0.289194
$696$	−65.7750	−2.49319
$697$	1.38241	0.0523623
$698$	−54.4638	−2.06149
$699$	−1.49421	−0.0565163
$700$	11.5271	0.435682
$701$	22.8103	0.861532	0.430766	−	0.902464i	$-0.358243\pi$
$701$	22.8103	0.861532	0.430766	+	0.902464i	$0.358243\pi$
$702$	18.5737	0.701021
$703$	2.24940	0.0848379
$704$	7.41925	0.279623
$705$	−44.1663	−1.66340
$706$	−85.6583	−3.22379
$707$	−29.1872	−1.09770
$708$	−32.2354	−1.21148
$709$	−31.4901	−1.18264	−0.591318	−	0.806439i	$-0.701392\pi$
$709$	−31.4901	−1.18264	−0.591318	+	0.806439i	$0.701392\pi$
$710$	−22.0023	−0.825731
$711$	21.7752	0.816634
$712$	16.5153	0.618937
$713$	−12.4832	−0.467500
$714$	95.3817	3.56957
$715$	−53.1894	−1.98917
$716$	−86.8014	−3.24392
$717$	43.7330	1.63324
$718$	−73.2130	−2.73229
$719$	−48.7555	−1.81827	−0.909137	−	0.416497i	$-0.863258\pi$
$719$	−48.7555	−1.81827	−0.909137	+	0.416497i	$0.863258\pi$
$720$	−48.3426	−1.80162
$721$	4.59812	0.171243
$722$	5.95136	0.221487
$723$	−72.8186	−2.70815
$724$	58.9829	2.19208
$725$	−3.99153	−0.148242
$726$	−112.415	−4.17211
$727$	−19.8875	−0.737588	−0.368794	−	0.929511i	$-0.620229\pi$
$727$	−19.8875	−0.737588	−0.368794	+	0.929511i	$0.620229\pi$
$728$	−83.2570	−3.08571
$729$	−36.1650	−1.33944
$730$	12.9061	0.477675
$731$	8.77067	0.324395
$732$	47.3839	1.75136
$733$	−6.38470	−0.235824	−0.117912	−	0.993024i	$-0.537620\pi$
$733$	−6.38470	−0.235824	−0.117912	+	0.993024i	$0.537620\pi$
$734$	61.8139	2.28159
$735$	−2.20109	−0.0811883
$736$	17.4304	0.642494
$737$	48.7974	1.79747
$738$	−2.32583	−0.0856151
$739$	49.5631	1.82321	0.911605	−	0.411068i	$-0.134844\pi$
$739$	49.5631	1.82321	0.911605	+	0.411068i	$0.134844\pi$
$740$	4.90418	0.180281
$741$	52.0264	1.91124
$742$	−8.75978	−0.321582
$743$	−7.81432	−0.286680	−0.143340	−	0.989674i	$-0.545784\pi$
$743$	−7.81432	−0.286680	−0.143340	+	0.989674i	$0.545784\pi$
$744$	−53.6636	−1.96740
$745$	3.38907	0.124166
$746$	−12.4125	−0.454455
$747$	24.8664	0.909815
$748$	−126.740	−4.63409
$749$	−41.8777	−1.53018
$750$	−77.8412	−2.84236
$751$	35.4501	1.29359	0.646796	−	0.762663i	$-0.276109\pi$
$751$	35.4501	1.29359	0.646796	+	0.762663i	$0.276109\pi$
$752$	57.6005	2.10048
$753$	−48.5020	−1.76751
$754$	52.6153	1.91614
$755$	−33.2395	−1.20971
$756$	−17.7694	−0.646267
$757$	20.1642	0.732882	0.366441	−	0.930441i	$-0.380576\pi$
$757$	20.1642	0.732882	0.366441	+	0.930441i	$0.380576\pi$
$758$	1.66872	0.0606108
$759$	49.9881	1.81445
$760$	−50.4198	−1.82892
$761$	−16.4203	−0.595237	−0.297618	−	0.954685i	$-0.596192\pi$
$761$	−16.4203	−0.595237	−0.297618	+	0.954685i	$0.596192\pi$
$762$	95.9549	3.47608
$763$	17.3450	0.627931
$764$	30.3629	1.09849
$765$	−38.7137	−1.39970
$766$	82.9608	2.99749
$767$	14.1291	0.510172
$768$	−77.6423	−2.80168
$769$	22.4424	0.809293	0.404647	−	0.914473i	$-0.367395\pi$
$769$	22.4424	0.809293	0.404647	+	0.914473i	$0.367395\pi$
$770$	73.8898	2.66280
$771$	23.1579	0.834010
$772$	−34.8262	−1.25342
$773$	21.7861	0.783591	0.391796	−	0.920052i	$-0.371854\pi$
$773$	21.7861	0.783591	0.391796	+	0.920052i	$0.371854\pi$
$774$	−14.7563	−0.530402
$775$	−3.25656	−0.116979
$776$	62.5907	2.24687
$777$	3.85193	0.138187
$778$	−33.3067	−1.19410
$779$	−1.04750	−0.0375306
$780$	113.429	4.06140
$781$	22.9631	0.821683
$782$	50.0237	1.78884
$783$	6.15310	0.219894
$784$	2.87060	0.102521
$785$	−47.7907	−1.70572
$786$	−44.3870	−1.58323
$787$	43.5528	1.55249	0.776246	−	0.630431i	$-0.217122\pi$
$787$	43.5528	1.55249	0.776246	+	0.630431i	$0.217122\pi$
$788$	17.4992	0.623383
$789$	54.5342	1.94147
$790$	31.0473	1.10461
$791$	19.7120	0.700877
$792$	116.839	4.15169
$793$	−20.7688	−0.737523
$794$	−99.7208	−3.53896
$795$	6.53921	0.231922
$796$	39.7096	1.40747
$797$	26.6815	0.945107	0.472553	−	0.881302i	$-0.343332\pi$
$797$	26.6815	0.945107	0.472553	+	0.881302i	$0.343332\pi$
$798$	−72.2743	−2.55848
$799$	46.1277	1.63188
$800$	4.54716	0.160766
$801$	−9.60879	−0.339510
$802$	90.3388	3.18997
$803$	−13.4696	−0.475333
$804$	−104.063	−3.67001
$805$	−20.0844	−0.707882
$806$	42.9271	1.51204
$807$	−34.0784	−1.19962
$808$	−65.8046	−2.31500
$809$	15.7917	0.555207	0.277603	−	0.960696i	$-0.410460\pi$
$809$	15.7917	0.555207	0.277603	+	0.960696i	$0.410460\pi$
$810$	−35.3998	−1.24382
$811$	−1.00853	−0.0354144	−0.0177072	−	0.999843i	$-0.505637\pi$
$811$	−1.00853	−0.0354144	−0.0177072	+	0.999843i	$0.505637\pi$
$812$	−50.3368	−1.76648
$813$	−77.1414	−2.70547
$814$	−7.43215	−0.260497
$815$	−27.0941	−0.949063
$816$	92.8608	3.25078
$817$	−6.64587	−0.232509
$818$	23.0690	0.806590
$819$	48.4399	1.69263
$820$	−2.28378	−0.0797529
$821$	−35.6536	−1.24432	−0.622160	−	0.782890i	$-0.713745\pi$
$821$	−35.6536	−1.24432	−0.622160	+	0.782890i	$0.713745\pi$
$822$	−91.8308	−3.20297
$823$	0.677853	0.0236285	0.0118142	−	0.999930i	$-0.496239\pi$
$823$	0.677853	0.0236285	0.0118142	+	0.999930i	$0.496239\pi$
$824$	10.3668	0.361144
$825$	13.0406	0.454016
$826$	−19.6279	−0.682942
$827$	20.1792	0.701699	0.350849	−	0.936432i	$-0.385893\pi$
$827$	20.1792	0.701699	0.350849	+	0.936432i	$0.385893\pi$
$828$	−57.9606	−2.01427
$829$	−3.24765	−0.112796	−0.0563978	−	0.998408i	$-0.517962\pi$
$829$	−3.24765	−0.112796	−0.0563978	+	0.998408i	$0.517962\pi$
$830$	35.4547	1.23065
$831$	61.4980	2.13334
$832$	6.93488	0.240424
$833$	2.29884	0.0796500
$834$	−24.6393	−0.853188
$835$	−41.6937	−1.44287
$836$	96.0359	3.32147
$837$	5.02011	0.173520
$838$	1.33288	0.0460434
$839$	51.2298	1.76865	0.884324	−	0.466874i	$-0.154620\pi$
$839$	51.2298	1.76865	0.884324	+	0.466874i	$0.154620\pi$
$840$	−86.3401	−2.97902
$841$	−11.5696	−0.398953
$842$	−62.0501	−2.13839
$843$	32.5856	1.12231
$844$	−54.6562	−1.88134
$845$	−23.5745	−0.810989
$846$	−77.6077	−2.66821
$847$	−47.1388	−1.61971
$848$	−8.52827	−0.292862
$849$	−28.4746	−0.977247
$850$	13.0499	0.447608
$851$	2.02017	0.0692507
$852$	−48.9698	−1.67768
$853$	35.2658	1.20748	0.603740	−	0.797181i	$-0.293677\pi$
$853$	35.2658	1.20748	0.603740	+	0.797181i	$0.293677\pi$
$854$	28.8517	0.987285
$855$	29.3348	1.00323
$856$	−94.4161	−3.22708
$857$	−38.8801	−1.32812	−0.664059	−	0.747680i	$-0.731168\pi$
$857$	−38.8801	−1.32812	−0.664059	+	0.747680i	$0.731168\pi$
$858$	−171.898	−5.86851
$859$	−5.28982	−0.180486	−0.0902432	−	0.995920i	$-0.528764\pi$
$859$	−5.28982	−0.180486	−0.0902432	+	0.995920i	$0.528764\pi$
$860$	−14.4894	−0.494085
$861$	−1.79376	−0.0611313
$862$	−18.8782	−0.642994
$863$	−20.6293	−0.702228	−0.351114	−	0.936333i	$-0.614197\pi$
$863$	−20.6293	−0.702228	−0.351114	+	0.936333i	$0.614197\pi$
$864$	−7.00962	−0.238472
$865$	−11.7550	−0.399682
$866$	7.68124	0.261019
$867$	30.7746	1.04516
$868$	−41.0681	−1.39394
$869$	−32.4030	−1.09920
$870$	54.5637	1.84988
$871$	45.6116	1.54549
$872$	39.1055	1.32428
$873$	−36.4160	−1.23249
$874$	−37.9048	−1.28215
$875$	−32.6411	−1.10347
$876$	28.7246	0.970515
$877$	−48.9826	−1.65403	−0.827013	−	0.562183i	$-0.809961\pi$
$877$	−48.9826	−1.65403	−0.827013	+	0.562183i	$0.809961\pi$
$878$	−46.9145	−1.58329
$879$	−20.6778	−0.697446
$880$	71.9370	2.42500
$881$	23.4578	0.790313	0.395156	−	0.918614i	$-0.370690\pi$
$881$	23.4578	0.790313	0.395156	+	0.918614i	$0.370690\pi$
$882$	−3.86769	−0.130232
$883$	8.82855	0.297104	0.148552	−	0.988905i	$-0.452539\pi$
$883$	8.82855	0.297104	0.148552	+	0.988905i	$0.452539\pi$
$884$	−118.466	−3.98445
$885$	14.6523	0.492532
$886$	−19.8825	−0.667966
$887$	12.1826	0.409053	0.204526	−	0.978861i	$-0.434435\pi$
$887$	12.1826	0.409053	0.204526	+	0.978861i	$0.434435\pi$
$888$	8.68445	0.291431
$889$	40.2366	1.34949
$890$	−13.7003	−0.459235
$891$	36.9456	1.23772
$892$	−108.911	−3.64661
$893$	−34.9527	−1.16965
$894$	10.9528	0.366317
$895$	39.4548	1.31883
$896$	−35.5569	−1.18787
$897$	46.7246	1.56009
$898$	1.44143	0.0481010
$899$	14.2209	0.474292
$900$	−15.1204	−0.504015
$901$	−6.82962	−0.227528
$902$	3.46100	0.115239
$903$	−11.3805	−0.378720
$904$	44.4420	1.47812
$905$	−26.8101	−0.891198
$906$	−107.424	−3.56892
$907$	39.9599	1.32685	0.663424	−	0.748244i	$-0.269103\pi$
$907$	39.9599	1.32685	0.663424	+	0.748244i	$0.269103\pi$
$908$	8.47187	0.281149
$909$	38.2859	1.26986
$910$	69.0659	2.28951
$911$	−19.4942	−0.645872	−0.322936	−	0.946421i	$-0.604670\pi$
$911$	−19.4942	−0.645872	−0.322936	+	0.946421i	$0.604670\pi$
$912$	−70.3641	−2.32999
$913$	−37.0029	−1.22462
$914$	−80.8183	−2.67323
$915$	−21.5379	−0.712022
$916$	77.7876	2.57018
$917$	−18.6127	−0.614647
$918$	−20.1170	−0.663958
$919$	−9.36735	−0.309000	−0.154500	−	0.987993i	$-0.549377\pi$
$919$	−9.36735	−0.309000	−0.154500	+	0.987993i	$0.549377\pi$
$920$	−45.2817	−1.49289
$921$	−85.4789	−2.81663
$922$	37.0136	1.21898
$923$	21.4639	0.706493
$924$	164.454	5.41014
$925$	0.527012	0.0173281
$926$	36.5628	1.20153
$927$	−6.03152	−0.198101
$928$	−19.8567	−0.651828
$929$	−35.6904	−1.17096	−0.585482	−	0.810685i	$-0.699095\pi$
$929$	−35.6904	−1.17096	−0.585482	+	0.810685i	$0.699095\pi$
$930$	44.5167	1.45976
$931$	−1.74192	−0.0570890
$932$	−2.57811	−0.0844488
$933$	−46.8240	−1.53295
$934$	−82.8233	−2.71006
$935$	57.6087	1.88400
$936$	109.211	3.56968
$937$	52.0532	1.70050	0.850252	−	0.526375i	$-0.176449\pi$
$937$	52.0532	1.70050	0.850252	+	0.526375i	$0.176449\pi$
$938$	−63.3629	−2.06887
$939$	−17.3946	−0.567651
$940$	−76.2044	−2.48551
$941$	−37.7244	−1.22978	−0.614891	−	0.788612i	$-0.710800\pi$
$941$	−37.7244	−1.22978	−0.614891	+	0.788612i	$0.710800\pi$
$942$	−154.451	−5.03227
$943$	−0.940753	−0.0306351
$944$	−19.1092	−0.621950
$945$	8.07692	0.262742
$946$	21.9583	0.713926
$947$	−24.2687	−0.788627	−0.394313	−	0.918976i	$-0.629018\pi$
$947$	−24.2687	−0.788627	−0.394313	+	0.918976i	$0.629018\pi$
$948$	69.1009	2.24429
$949$	−12.5903	−0.408698
$950$	−9.88840	−0.320822
$951$	19.5002	0.632339
$952$	90.1744	2.92257
$953$	−40.3241	−1.30623	−0.653113	−	0.757260i	$-0.726537\pi$
$953$	−40.3241	−1.30623	−0.653113	+	0.757260i	$0.726537\pi$
$954$	11.4905	0.372019
$955$	−13.8012	−0.446595
$956$	75.4568	2.44045
$957$	−56.9463	−1.84081
$958$	30.7327	0.992930
$959$	−38.5073	−1.24346
$960$	7.19169	0.232111
$961$	−19.3977	−0.625731
$962$	−6.94694	−0.223978
$963$	54.9324	1.77017
$964$	−125.641	−4.04662
$965$	15.8299	0.509583
$966$	−64.9090	−2.08841
$967$	12.3319	0.396567	0.198283	−	0.980145i	$-0.436463\pi$
$967$	12.3319	0.396567	0.198283	+	0.980145i	$0.436463\pi$
$968$	−106.278	−3.41590
$969$	−56.3491	−1.81019
$970$	−51.9222	−1.66712
$971$	−44.3784	−1.42417	−0.712085	−	0.702093i	$-0.752249\pi$
$971$	−44.3784	−1.42417	−0.712085	+	0.702093i	$0.752249\pi$
$972$	−98.3492	−3.15455
$973$	−10.3319	−0.331227
$974$	17.0519	0.546377
$975$	12.1893	0.390369
$976$	28.0892	0.899113
$977$	6.74466	0.215781	0.107890	−	0.994163i	$-0.465590\pi$
$977$	6.74466	0.215781	0.107890	+	0.994163i	$0.465590\pi$
$978$	−87.5629	−2.79995
$979$	14.2985	0.456983
$980$	−3.79775	−0.121315
$981$	−22.7520	−0.726417
$982$	−72.2414	−2.30532
$983$	33.3640	1.06415	0.532074	−	0.846698i	$-0.321413\pi$
$983$	33.3640	1.06415	0.532074	+	0.846698i	$0.321413\pi$
$984$	−4.04417	−0.128923
$985$	−7.95410	−0.253439
$986$	−56.9869	−1.81483
$987$	−59.8538	−1.90517
$988$	89.7663	2.85585
$989$	−5.96861	−0.189791
$990$	−96.9239	−3.08044
$991$	27.8321	0.884116	0.442058	−	0.896987i	$-0.354249\pi$
$991$	27.8321	0.884116	0.442058	+	0.896987i	$0.354249\pi$
$992$	−16.2004	−0.514364
$993$	55.8507	1.77237
$994$	−29.8173	−0.945748
$995$	−18.0496	−0.572212
$996$	78.9104	2.50037
$997$	−48.9314	−1.54967	−0.774837	−	0.632161i	$-0.782168\pi$
$997$	−48.9314	−1.54967	−0.774837	+	0.632161i	$0.782168\pi$
$998$	18.4491	0.583995
$999$	−0.812411	−0.0257035

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.9	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.9	✓	174	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:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53459 q^{2} +2.56413 q^{3} +4.42415 q^{4} -2.01095 q^{5} -6.49903 q^{6} -2.72523 q^{7} -6.14422 q^{8} +3.57478 q^{9} +O(q^{10})\)	\(q-2.53459 q^{2} +2.56413 q^{3} +4.42415 q^{4} -2.01095 q^{5} -6.49903 q^{6} -2.72523 q^{7} -6.14422 q^{8} +3.57478 q^{9} +5.09695 q^{10} -5.31951 q^{11} +11.3441 q^{12} -4.97223 q^{13} +6.90734 q^{14} -5.15635 q^{15} +6.72478 q^{16} +5.38535 q^{17} -9.06060 q^{18} -4.08068 q^{19} -8.89676 q^{20} -6.98785 q^{21} +13.4828 q^{22} -3.66483 q^{23} -15.7546 q^{24} -0.956062 q^{25} +12.6026 q^{26} +1.47381 q^{27} -12.0568 q^{28} +4.17497 q^{29} +13.0692 q^{30} +3.40622 q^{31} -4.75613 q^{32} -13.6399 q^{33} -13.6496 q^{34} +5.48031 q^{35} +15.8153 q^{36} -0.551233 q^{37} +10.3428 q^{38} -12.7495 q^{39} +12.3557 q^{40} +0.256698 q^{41} +17.7113 q^{42} +1.62862 q^{43} -23.5343 q^{44} -7.18872 q^{45} +9.28884 q^{46} +8.56541 q^{47} +17.2432 q^{48} +0.426869 q^{49} +2.42322 q^{50} +13.8087 q^{51} -21.9979 q^{52} -1.26818 q^{53} -3.73550 q^{54} +10.6973 q^{55} +16.7444 q^{56} -10.4634 q^{57} -10.5818 q^{58} -2.84160 q^{59} -22.8125 q^{60} +4.17697 q^{61} -8.63337 q^{62} -9.74209 q^{63} -1.39472 q^{64} +9.99893 q^{65} +34.5716 q^{66} -9.17328 q^{67} +23.8256 q^{68} -9.39711 q^{69} -13.8903 q^{70} -4.31676 q^{71} -21.9642 q^{72} +2.53212 q^{73} +1.39715 q^{74} -2.45147 q^{75} -18.0535 q^{76} +14.4969 q^{77} +32.3146 q^{78} +6.09135 q^{79} -13.5232 q^{80} -6.94530 q^{81} -0.650623 q^{82} +6.95608 q^{83} -30.9153 q^{84} -10.8297 q^{85} -4.12788 q^{86} +10.7052 q^{87} +32.6842 q^{88} -2.68794 q^{89} +18.2204 q^{90} +13.5505 q^{91} -16.2137 q^{92} +8.73400 q^{93} -21.7098 q^{94} +8.20606 q^{95} -12.1954 q^{96} -10.1869 q^{97} -1.08194 q^{98} -19.0161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

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