LMFDB - Embedded newform 6015.2.a.b.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.60756 q^{2} +1.00000 q^{3} +0.584262 q^{4} +1.00000 q^{5} +1.60756 q^{6} +0.859599 q^{7} -2.27589 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.60756 q^{2} +1.00000 q^{3} +0.584262 q^{4} +1.00000 q^{5} +1.60756 q^{6} +0.859599 q^{7} -2.27589 q^{8} +1.00000 q^{9} +1.60756 q^{10} -4.75256 q^{11} +0.584262 q^{12} +0.281045 q^{13} +1.38186 q^{14} +1.00000 q^{15} -4.82716 q^{16} -1.54849 q^{17} +1.60756 q^{18} -1.69205 q^{19} +0.584262 q^{20} +0.859599 q^{21} -7.64004 q^{22} +0.956268 q^{23} -2.27589 q^{24} +1.00000 q^{25} +0.451798 q^{26} +1.00000 q^{27} +0.502231 q^{28} -7.66583 q^{29} +1.60756 q^{30} -2.13187 q^{31} -3.20819 q^{32} -4.75256 q^{33} -2.48930 q^{34} +0.859599 q^{35} +0.584262 q^{36} -3.76872 q^{37} -2.72008 q^{38} +0.281045 q^{39} -2.27589 q^{40} +0.653307 q^{41} +1.38186 q^{42} +4.50506 q^{43} -2.77674 q^{44} +1.00000 q^{45} +1.53726 q^{46} -5.23238 q^{47} -4.82716 q^{48} -6.26109 q^{49} +1.60756 q^{50} -1.54849 q^{51} +0.164204 q^{52} +3.80161 q^{53} +1.60756 q^{54} -4.75256 q^{55} -1.95635 q^{56} -1.69205 q^{57} -12.3233 q^{58} -2.17545 q^{59} +0.584262 q^{60} -9.72745 q^{61} -3.42711 q^{62} +0.859599 q^{63} +4.49695 q^{64} +0.281045 q^{65} -7.64004 q^{66} +4.08866 q^{67} -0.904723 q^{68} +0.956268 q^{69} +1.38186 q^{70} +3.22877 q^{71} -2.27589 q^{72} -15.3277 q^{73} -6.05845 q^{74} +1.00000 q^{75} -0.988600 q^{76} -4.08529 q^{77} +0.451798 q^{78} +11.7326 q^{79} -4.82716 q^{80} +1.00000 q^{81} +1.05023 q^{82} -13.5950 q^{83} +0.502231 q^{84} -1.54849 q^{85} +7.24217 q^{86} -7.66583 q^{87} +10.8163 q^{88} +10.1045 q^{89} +1.60756 q^{90} +0.241586 q^{91} +0.558711 q^{92} -2.13187 q^{93} -8.41139 q^{94} -1.69205 q^{95} -3.20819 q^{96} -7.41676 q^{97} -10.0651 q^{98} -4.75256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * 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 $

$2$	1.60756	1.13672	0.568360	−	0.822780i	$-0.307578\pi$
$2$	1.60756	1.13672	0.568360	+	0.822780i	$0.307578\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.584262	0.292131
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.60756	0.656285
$7$	0.859599	0.324898	0.162449	−	0.986717i	$-0.448061\pi$
$7$	0.859599	0.324898	0.162449	+	0.986717i	$0.448061\pi$
$8$	−2.27589	−0.804649
$9$	1.00000	0.333333
$10$	1.60756	0.508356
$11$	−4.75256	−1.43295	−0.716475	−	0.697613i	$-0.754246\pi$
$11$	−4.75256	−1.43295	−0.716475	+	0.697613i	$0.754246\pi$
$12$	0.584262	0.168662
$13$	0.281045	0.0779479	0.0389739	−	0.999240i	$-0.487591\pi$
$13$	0.281045	0.0779479	0.0389739	+	0.999240i	$0.487591\pi$
$14$	1.38186	0.369318
$15$	1.00000	0.258199
$16$	−4.82716	−1.20679
$17$	−1.54849	−0.375564	−0.187782	−	0.982211i	$-0.560130\pi$
$17$	−1.54849	−0.375564	−0.187782	+	0.982211i	$0.560130\pi$
$18$	1.60756	0.378906
$19$	−1.69205	−0.388183	−0.194091	−	0.980983i	$-0.562176\pi$
$19$	−1.69205	−0.388183	−0.194091	+	0.980983i	$0.562176\pi$
$20$	0.584262	0.130645
$21$	0.859599	0.187580
$22$	−7.64004	−1.62886
$23$	0.956268	0.199396	0.0996979	−	0.995018i	$-0.468212\pi$
$23$	0.956268	0.199396	0.0996979	+	0.995018i	$0.468212\pi$
$24$	−2.27589	−0.464564
$25$	1.00000	0.200000
$26$	0.451798	0.0886049
$27$	1.00000	0.192450
$28$	0.502231	0.0949127
$29$	−7.66583	−1.42351	−0.711754	−	0.702429i	$-0.752099\pi$
$29$	−7.66583	−1.42351	−0.711754	+	0.702429i	$0.752099\pi$
$30$	1.60756	0.293500
$31$	−2.13187	−0.382895	−0.191447	−	0.981503i	$-0.561318\pi$
$31$	−2.13187	−0.382895	−0.191447	+	0.981503i	$0.561318\pi$
$32$	−3.20819	−0.567133
$33$	−4.75256	−0.827314
$34$	−2.48930	−0.426911
$35$	0.859599	0.145299
$36$	0.584262	0.0973769
$37$	−3.76872	−0.619573	−0.309787	−	0.950806i	$-0.600258\pi$
$37$	−3.76872	−0.619573	−0.309787	+	0.950806i	$0.600258\pi$
$38$	−2.72008	−0.441255
$39$	0.281045	0.0450032
$40$	−2.27589	−0.359850
$41$	0.653307	0.102029	0.0510147	−	0.998698i	$-0.483754\pi$
$41$	0.653307	0.102029	0.0510147	+	0.998698i	$0.483754\pi$
$42$	1.38186	0.213226
$43$	4.50506	0.687015	0.343507	−	0.939150i	$-0.388385\pi$
$43$	4.50506	0.687015	0.343507	+	0.939150i	$0.388385\pi$
$44$	−2.77674	−0.418609
$45$	1.00000	0.149071
$46$	1.53726	0.226657
$47$	−5.23238	−0.763221	−0.381611	−	0.924323i	$-0.624630\pi$
$47$	−5.23238	−0.763221	−0.381611	+	0.924323i	$0.624630\pi$
$48$	−4.82716	−0.696741
$49$	−6.26109	−0.894441
$50$	1.60756	0.227344
$51$	−1.54849	−0.216832
$52$	0.164204	0.0227710
$53$	3.80161	0.522192	0.261096	−	0.965313i	$-0.415916\pi$
$53$	3.80161	0.522192	0.261096	+	0.965313i	$0.415916\pi$
$54$	1.60756	0.218762
$55$	−4.75256	−0.640835
$56$	−1.95635	−0.261429
$57$	−1.69205	−0.224118
$58$	−12.3233	−1.61813
$59$	−2.17545	−0.283220	−0.141610	−	0.989923i	$-0.545228\pi$
$59$	−2.17545	−0.283220	−0.141610	+	0.989923i	$0.545228\pi$
$60$	0.584262	0.0754278
$61$	−9.72745	−1.24547	−0.622736	−	0.782432i	$-0.713979\pi$
$61$	−9.72745	−1.24547	−0.622736	+	0.782432i	$0.713979\pi$
$62$	−3.42711	−0.435244
$63$	0.859599	0.108299
$64$	4.49695	0.562119
$65$	0.281045	0.0348594
$66$	−7.64004	−0.940424
$67$	4.08866	0.499509	0.249754	−	0.968309i	$-0.419650\pi$
$67$	4.08866	0.499509	0.249754	+	0.968309i	$0.419650\pi$
$68$	−0.904723	−0.109714
$69$	0.956268	0.115121
$70$	1.38186	0.165164
$71$	3.22877	0.383184	0.191592	−	0.981475i	$-0.438635\pi$
$71$	3.22877	0.383184	0.191592	+	0.981475i	$0.438635\pi$
$72$	−2.27589	−0.268216
$73$	−15.3277	−1.79397	−0.896987	−	0.442057i	$-0.854249\pi$
$73$	−15.3277	−1.79397	−0.896987	+	0.442057i	$0.854249\pi$
$74$	−6.05845	−0.704281
$75$	1.00000	0.115470
$76$	−0.988600	−0.113400
$77$	−4.08529	−0.465562
$78$	0.451798	0.0511560
$79$	11.7326	1.32002	0.660009	−	0.751258i	$-0.270553\pi$
$79$	11.7326	1.32002	0.660009	+	0.751258i	$0.270553\pi$
$80$	−4.82716	−0.539693
$81$	1.00000	0.111111
$82$	1.05023	0.115979
$83$	−13.5950	−1.49224	−0.746122	−	0.665809i	$-0.768086\pi$
$83$	−13.5950	−1.49224	−0.746122	+	0.665809i	$0.768086\pi$
$84$	0.502231	0.0547979
$85$	−1.54849	−0.167957
$86$	7.24217	0.780943
$87$	−7.66583	−0.821863
$88$	10.8163	1.15302
$89$	10.1045	1.07107	0.535537	−	0.844512i	$-0.320109\pi$
$89$	10.1045	1.07107	0.535537	+	0.844512i	$0.320109\pi$
$90$	1.60756	0.169452
$91$	0.241586	0.0253251
$92$	0.558711	0.0582496
$93$	−2.13187	−0.221064
$94$	−8.41139	−0.867568
$95$	−1.69205	−0.173601
$96$	−3.20819	−0.327435
$97$	−7.41676	−0.753058	−0.376529	−	0.926405i	$-0.622882\pi$
$97$	−7.41676	−0.753058	−0.376529	+	0.926405i	$0.622882\pi$
$98$	−10.0651	−1.01673
$99$	−4.75256	−0.477650
$100$	0.584262	0.0584262
$101$	8.05214	0.801218	0.400609	−	0.916249i	$-0.368799\pi$
$101$	8.05214	0.801218	0.400609	+	0.916249i	$0.368799\pi$
$102$	−2.48930	−0.246477
$103$	−11.2293	−1.10646	−0.553228	−	0.833030i	$-0.686604\pi$
$103$	−11.2293	−1.10646	−0.553228	+	0.833030i	$0.686604\pi$
$104$	−0.639628	−0.0627207
$105$	0.859599	0.0838883
$106$	6.11133	0.593585
$107$	−1.93488	−0.187052	−0.0935260	−	0.995617i	$-0.529814\pi$
$107$	−1.93488	−0.187052	−0.0935260	+	0.995617i	$0.529814\pi$
$108$	0.584262	0.0562206
$109$	−17.0694	−1.63496	−0.817478	−	0.575960i	$-0.804629\pi$
$109$	−17.0694	−1.63496	−0.817478	+	0.575960i	$0.804629\pi$
$110$	−7.64004	−0.728449
$111$	−3.76872	−0.357711
$112$	−4.14942	−0.392084
$113$	16.4480	1.54730	0.773649	−	0.633614i	$-0.218429\pi$
$113$	16.4480	1.54730	0.773649	+	0.633614i	$0.218429\pi$
$114$	−2.72008	−0.254759
$115$	0.956268	0.0891725
$116$	−4.47885	−0.415851
$117$	0.281045	0.0259826
$118$	−3.49718	−0.321942
$119$	−1.33108	−0.122020
$120$	−2.27589	−0.207759
$121$	11.5868	1.05335
$122$	−15.6375	−1.41575
$123$	0.653307	0.0589067
$124$	−1.24557	−0.111855
$125$	1.00000	0.0894427
$126$	1.38186	0.123106
$127$	−18.3699	−1.63006	−0.815032	−	0.579416i	$-0.803281\pi$
$127$	−18.3699	−1.63006	−0.815032	+	0.579416i	$0.803281\pi$
$128$	13.6455	1.20610
$129$	4.50506	0.396648
$130$	0.451798	0.0396253
$131$	−14.1050	−1.23236	−0.616178	−	0.787607i	$-0.711320\pi$
$131$	−14.1050	−1.23236	−0.616178	+	0.787607i	$0.711320\pi$
$132$	−2.77674	−0.241684
$133$	−1.45448	−0.126120
$134$	6.57278	0.567801
$135$	1.00000	0.0860663
$136$	3.52419	0.302197
$137$	18.6866	1.59650	0.798251	−	0.602325i	$-0.205759\pi$
$137$	18.6866	1.59650	0.798251	+	0.602325i	$0.205759\pi$
$138$	1.53726	0.130860
$139$	−7.67469	−0.650959	−0.325479	−	0.945549i	$-0.605526\pi$
$139$	−7.67469	−0.650959	−0.325479	+	0.945549i	$0.605526\pi$
$140$	0.502231	0.0424462
$141$	−5.23238	−0.440646
$142$	5.19045	0.435573
$143$	−1.33568	−0.111695
$144$	−4.82716	−0.402263
$145$	−7.66583	−0.636612
$146$	−24.6403	−2.03924
$147$	−6.26109	−0.516406
$148$	−2.20192	−0.180996
$149$	19.0459	1.56030	0.780151	−	0.625591i	$-0.215142\pi$
$149$	19.0459	1.56030	0.780151	+	0.625591i	$0.215142\pi$
$150$	1.60756	0.131257
$151$	11.1638	0.908494	0.454247	−	0.890876i	$-0.349908\pi$
$151$	11.1638	0.908494	0.454247	+	0.890876i	$0.349908\pi$
$152$	3.85092	0.312351
$153$	−1.54849	−0.125188
$154$	−6.56737	−0.529214
$155$	−2.13187	−0.171236
$156$	0.164204	0.0131468
$157$	17.7231	1.41445	0.707227	−	0.706986i	$-0.249946\pi$
$157$	17.7231	1.41445	0.707227	+	0.706986i	$0.249946\pi$
$158$	18.8609	1.50049
$159$	3.80161	0.301487
$160$	−3.20819	−0.253630
$161$	0.822007	0.0647832
$162$	1.60756	0.126302
$163$	11.0765	0.867580	0.433790	−	0.901014i	$-0.357176\pi$
$163$	11.0765	0.867580	0.433790	+	0.901014i	$0.357176\pi$
$164$	0.381702	0.0298059
$165$	−4.75256	−0.369986
$166$	−21.8548	−1.69626
$167$	−18.1681	−1.40589	−0.702944	−	0.711245i	$-0.748132\pi$
$167$	−18.1681	−1.40589	−0.702944	+	0.711245i	$0.748132\pi$
$168$	−1.95635	−0.150936
$169$	−12.9210	−0.993924
$170$	−2.48930	−0.190920
$171$	−1.69205	−0.129394
$172$	2.63213	0.200698
$173$	−14.7639	−1.12248	−0.561240	−	0.827653i	$-0.689676\pi$
$173$	−14.7639	−1.12248	−0.561240	+	0.827653i	$0.689676\pi$
$174$	−12.3233	−0.934228
$175$	0.859599	0.0649796
$176$	22.9414	1.72927
$177$	−2.17545	−0.163517
$178$	16.2436	1.21751
$179$	−9.25607	−0.691831	−0.345916	−	0.938266i	$-0.612432\pi$
$179$	−9.25607	−0.691831	−0.345916	+	0.938266i	$0.612432\pi$
$180$	0.584262	0.0435483
$181$	13.9510	1.03697	0.518487	−	0.855086i	$-0.326496\pi$
$181$	13.9510	1.03697	0.518487	+	0.855086i	$0.326496\pi$
$182$	0.388365	0.0287875
$183$	−9.72745	−0.719074
$184$	−2.17636	−0.160443
$185$	−3.76872	−0.277082
$186$	−3.42711	−0.251288
$187$	7.35929	0.538165
$188$	−3.05708	−0.222960
$189$	0.859599	0.0625266
$190$	−2.72008	−0.197335
$191$	20.8347	1.50755	0.753773	−	0.657135i	$-0.228232\pi$
$191$	20.8347	1.50755	0.753773	+	0.657135i	$0.228232\pi$
$192$	4.49695	0.324540
$193$	−19.8066	−1.42571	−0.712856	−	0.701311i	$-0.752599\pi$
$193$	−19.8066	−1.42571	−0.712856	+	0.701311i	$0.752599\pi$
$194$	−11.9229	−0.856015
$195$	0.281045	0.0201261
$196$	−3.65811	−0.261294
$197$	11.2799	0.803663	0.401832	−	0.915714i	$-0.368374\pi$
$197$	11.2799	0.803663	0.401832	+	0.915714i	$0.368374\pi$
$198$	−7.64004	−0.542954
$199$	−19.3109	−1.36891	−0.684457	−	0.729054i	$-0.739960\pi$
$199$	−19.3109	−1.36891	−0.684457	+	0.729054i	$0.739960\pi$
$200$	−2.27589	−0.160930
$201$	4.08866	0.288392
$202$	12.9443	0.910760
$203$	−6.58954	−0.462495
$204$	−0.904723	−0.0633433
$205$	0.653307	0.0456289
$206$	−18.0518	−1.25773
$207$	0.956268	0.0664652
$208$	−1.35665	−0.0940668
$209$	8.04157	0.556247
$210$	1.38186	0.0953574
$211$	1.90302	0.131010	0.0655048	−	0.997852i	$-0.479134\pi$
$211$	1.90302	0.131010	0.0655048	+	0.997852i	$0.479134\pi$
$212$	2.22114	0.152548
$213$	3.22877	0.221232
$214$	−3.11045	−0.212626
$215$	4.50506	0.307242
$216$	−2.27589	−0.154855
$217$	−1.83255	−0.124402
$218$	−27.4402	−1.85849
$219$	−15.3277	−1.03575
$220$	−2.77674	−0.187208
$221$	−0.435196	−0.0292744
$222$	−6.05845	−0.406617
$223$	−16.6564	−1.11540	−0.557698	−	0.830044i	$-0.688315\pi$
$223$	−16.6564	−1.11540	−0.557698	+	0.830044i	$0.688315\pi$
$224$	−2.75776	−0.184260
$225$	1.00000	0.0666667
$226$	26.4412	1.75884
$227$	15.8587	1.05258	0.526289	−	0.850306i	$-0.323583\pi$
$227$	15.8587	1.05258	0.526289	+	0.850306i	$0.323583\pi$
$228$	−0.988600	−0.0654716
$229$	9.40567	0.621544	0.310772	−	0.950484i	$-0.399412\pi$
$229$	9.40567	0.621544	0.310772	+	0.950484i	$0.399412\pi$
$230$	1.53726	0.101364
$231$	−4.08529	−0.268793
$232$	17.4466	1.14542
$233$	−24.4408	−1.60117	−0.800585	−	0.599219i	$-0.795478\pi$
$233$	−24.4408	−1.60117	−0.800585	+	0.599219i	$0.795478\pi$
$234$	0.451798	0.0295350
$235$	−5.23238	−0.341323
$236$	−1.27103	−0.0827373
$237$	11.7326	0.762112
$238$	−2.13980	−0.138702
$239$	4.97540	0.321832	0.160916	−	0.986968i	$-0.448555\pi$
$239$	4.97540	0.321832	0.160916	+	0.986968i	$0.448555\pi$
$240$	−4.82716	−0.311592
$241$	−15.3886	−0.991267	−0.495633	−	0.868532i	$-0.665064\pi$
$241$	−15.3886	−0.991267	−0.495633	+	0.868532i	$0.665064\pi$
$242$	18.6265	1.19736
$243$	1.00000	0.0641500
$244$	−5.68338	−0.363841
$245$	−6.26109	−0.400006
$246$	1.05023	0.0669604
$247$	−0.475542	−0.0302580
$248$	4.85190	0.308096
$249$	−13.5950	−0.861547
$250$	1.60756	0.101671
$251$	15.3511	0.968953	0.484476	−	0.874804i	$-0.339010\pi$
$251$	15.3511	0.968953	0.484476	+	0.874804i	$0.339010\pi$
$252$	0.502231	0.0316376
$253$	−4.54472	−0.285724
$254$	−29.5308	−1.85292
$255$	−1.54849	−0.0969702
$256$	12.9421	0.808884
$257$	26.1593	1.63177	0.815887	−	0.578211i	$-0.196249\pi$
$257$	26.1593	1.63177	0.815887	+	0.578211i	$0.196249\pi$
$258$	7.24217	0.450878
$259$	−3.23959	−0.201298
$260$	0.164204	0.0101835
$261$	−7.66583	−0.474503
$262$	−22.6746	−1.40084
$263$	10.1163	0.623800	0.311900	−	0.950115i	$-0.399035\pi$
$263$	10.1163	0.623800	0.311900	+	0.950115i	$0.399035\pi$
$264$	10.8163	0.665697
$265$	3.80161	0.233531
$266$	−2.33818	−0.143363
$267$	10.1045	0.618384
$268$	2.38884	0.145922
$269$	18.3156	1.11672	0.558361	−	0.829598i	$-0.311430\pi$
$269$	18.3156	1.11672	0.558361	+	0.829598i	$0.311430\pi$
$270$	1.60756	0.0978332
$271$	16.1522	0.981176	0.490588	−	0.871392i	$-0.336782\pi$
$271$	16.1522	0.981176	0.490588	+	0.871392i	$0.336782\pi$
$272$	7.47481	0.453227
$273$	0.241586	0.0146215
$274$	30.0399	1.81477
$275$	−4.75256	−0.286590
$276$	0.558711	0.0336304
$277$	−31.0262	−1.86418	−0.932092	−	0.362222i	$-0.882018\pi$
$277$	−31.0262	−1.86418	−0.932092	+	0.362222i	$0.882018\pi$
$278$	−12.3376	−0.739957
$279$	−2.13187	−0.127632
$280$	−1.95635	−0.116914
$281$	−3.04710	−0.181774	−0.0908872	−	0.995861i	$-0.528970\pi$
$281$	−3.04710	−0.181774	−0.0908872	+	0.995861i	$0.528970\pi$
$282$	−8.41139	−0.500891
$283$	28.3725	1.68657	0.843284	−	0.537468i	$-0.180619\pi$
$283$	28.3725	1.68657	0.843284	+	0.537468i	$0.180619\pi$
$284$	1.88645	0.111940
$285$	−1.69205	−0.100228
$286$	−2.14720	−0.126966
$287$	0.561582	0.0331491
$288$	−3.20819	−0.189044
$289$	−14.6022	−0.858952
$290$	−12.3233	−0.723650
$291$	−7.41676	−0.434778
$292$	−8.95540	−0.524075
$293$	3.63724	0.212490	0.106245	−	0.994340i	$-0.466117\pi$
$293$	3.63724	0.212490	0.106245	+	0.994340i	$0.466117\pi$
$294$	−10.0651	−0.587009
$295$	−2.17545	−0.126660
$296$	8.57719	0.498539
$297$	−4.75256	−0.275771
$298$	30.6175	1.77363
$299$	0.268755	0.0155425
$300$	0.584262	0.0337324
$301$	3.87254	0.223210
$302$	17.9465	1.03270
$303$	8.05214	0.462583
$304$	8.16780	0.468455
$305$	−9.72745	−0.556992
$306$	−2.48930	−0.142304
$307$	−5.58371	−0.318679	−0.159340	−	0.987224i	$-0.550936\pi$
$307$	−5.58371	−0.318679	−0.159340	+	0.987224i	$0.550936\pi$
$308$	−2.38688	−0.136005
$309$	−11.2293	−0.638812
$310$	−3.42711	−0.194647
$311$	17.2785	0.979774	0.489887	−	0.871786i	$-0.337038\pi$
$311$	17.2785	0.979774	0.489887	+	0.871786i	$0.337038\pi$
$312$	−0.639628	−0.0362118
$313$	0.287359	0.0162425	0.00812126	−	0.999967i	$-0.497415\pi$
$313$	0.287359	0.0162425	0.00812126	+	0.999967i	$0.497415\pi$
$314$	28.4910	1.60784
$315$	0.859599	0.0484329
$316$	6.85489	0.385618
$317$	−27.6908	−1.55527	−0.777637	−	0.628714i	$-0.783582\pi$
$317$	−27.6908	−1.55527	−0.777637	+	0.628714i	$0.783582\pi$
$318$	6.11133	0.342707
$319$	36.4323	2.03982
$320$	4.49695	0.251387
$321$	−1.93488	−0.107995
$322$	1.32143	0.0736404
$323$	2.62012	0.145788
$324$	0.584262	0.0324590
$325$	0.281045	0.0155896
$326$	17.8062	0.986195
$327$	−17.0694	−0.943943
$328$	−1.48685	−0.0820978
$329$	−4.49775	−0.247969
$330$	−7.64004	−0.420570
$331$	−7.02599	−0.386183	−0.193092	−	0.981181i	$-0.561851\pi$
$331$	−7.02599	−0.386183	−0.193092	+	0.981181i	$0.561851\pi$
$332$	−7.94303	−0.435930
$333$	−3.76872	−0.206524
$334$	−29.2064	−1.59810
$335$	4.08866	0.223387
$336$	−4.14942	−0.226370
$337$	−1.40163	−0.0763519	−0.0381760	−	0.999271i	$-0.512155\pi$
$337$	−1.40163	−0.0763519	−0.0381760	+	0.999271i	$0.512155\pi$
$338$	−20.7714	−1.12981
$339$	16.4480	0.893333
$340$	−0.904723	−0.0490655
$341$	10.1318	0.548669
$342$	−2.72008	−0.147085
$343$	−11.3992	−0.615500
$344$	−10.2530	−0.552806
$345$	0.956268	0.0514838
$346$	−23.7340	−1.27595
$347$	−1.98999	−0.106829	−0.0534143	−	0.998572i	$-0.517010\pi$
$347$	−1.98999	−0.106829	−0.0534143	+	0.998572i	$0.517010\pi$
$348$	−4.47885	−0.240091
$349$	5.71992	0.306180	0.153090	−	0.988212i	$-0.451077\pi$
$349$	5.71992	0.306180	0.153090	+	0.988212i	$0.451077\pi$
$350$	1.38186	0.0738635
$351$	0.281045	0.0150011
$352$	15.2471	0.812674
$353$	−3.72040	−0.198017	−0.0990086	−	0.995087i	$-0.531567\pi$
$353$	−3.72040	−0.198017	−0.0990086	+	0.995087i	$0.531567\pi$
$354$	−3.49718	−0.185873
$355$	3.22877	0.171365
$356$	5.90366	0.312893
$357$	−1.33108	−0.0704483
$358$	−14.8797	−0.786418
$359$	16.7256	0.882746	0.441373	−	0.897324i	$-0.354492\pi$
$359$	16.7256	0.882746	0.441373	+	0.897324i	$0.354492\pi$
$360$	−2.27589	−0.119950
$361$	−16.1370	−0.849314
$362$	22.4272	1.17875
$363$	11.5868	0.608150
$364$	0.141149	0.00739824
$365$	−15.3277	−0.802290
$366$	−15.6375	−0.817385
$367$	23.6055	1.23220	0.616098	−	0.787669i	$-0.288712\pi$
$367$	23.6055	1.23220	0.616098	+	0.787669i	$0.288712\pi$
$368$	−4.61606	−0.240629
$369$	0.653307	0.0340098
$370$	−6.05845	−0.314964
$371$	3.26786	0.169659
$372$	−1.24557	−0.0645797
$373$	2.02732	0.104971	0.0524854	−	0.998622i	$-0.483286\pi$
$373$	2.02732	0.104971	0.0524854	+	0.998622i	$0.483286\pi$
$374$	11.8305	0.611742
$375$	1.00000	0.0516398
$376$	11.9083	0.614125
$377$	−2.15444	−0.110959
$378$	1.38186	0.0710752
$379$	20.0390	1.02933	0.514667	−	0.857390i	$-0.327916\pi$
$379$	20.0390	1.02933	0.514667	+	0.857390i	$0.327916\pi$
$380$	−0.988600	−0.0507141
$381$	−18.3699	−0.941118
$382$	33.4931	1.71366
$383$	−25.9400	−1.32547	−0.662736	−	0.748853i	$-0.730605\pi$
$383$	−25.9400	−1.32547	−0.662736	+	0.748853i	$0.730605\pi$
$384$	13.6455	0.696345
$385$	−4.08529	−0.208206
$386$	−31.8404	−1.62063
$387$	4.50506	0.229005
$388$	−4.33333	−0.219991
$389$	−21.5939	−1.09485	−0.547426	−	0.836854i	$-0.684392\pi$
$389$	−21.5939	−1.09485	−0.547426	+	0.836854i	$0.684392\pi$
$390$	0.451798	0.0228777
$391$	−1.48077	−0.0748859
$392$	14.2496	0.719711
$393$	−14.1050	−0.711502
$394$	18.1332	0.913539
$395$	11.7326	0.590330
$396$	−2.77674	−0.139536
$397$	9.06265	0.454841	0.227421	−	0.973797i	$-0.426971\pi$
$397$	9.06265	0.454841	0.227421	+	0.973797i	$0.426971\pi$
$398$	−31.0435	−1.55607
$399$	−1.45448	−0.0728153
$400$	−4.82716	−0.241358
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	6.57278	0.327820
$403$	−0.599151	−0.0298458
$404$	4.70455	0.234060
$405$	1.00000	0.0496904
$406$	−10.5931	−0.525727
$407$	17.9110	0.887818
$408$	3.52419	0.174474
$409$	15.3651	0.759753	0.379877	−	0.925037i	$-0.375966\pi$
$409$	15.3651	0.759753	0.379877	+	0.925037i	$0.375966\pi$
$410$	1.05023	0.0518673
$411$	18.6866	0.921741
$412$	−6.56084	−0.323230
$413$	−1.87002	−0.0920176
$414$	1.53726	0.0755523
$415$	−13.5950	−0.667352
$416$	−0.901646	−0.0442068
$417$	−7.67469	−0.375831
$418$	12.9273	0.632296
$419$	−17.1604	−0.838342	−0.419171	−	0.907907i	$-0.637679\pi$
$419$	−17.1604	−0.838342	−0.419171	+	0.907907i	$0.637679\pi$
$420$	0.502231	0.0245063
$421$	31.0148	1.51157	0.755785	−	0.654820i	$-0.227256\pi$
$421$	31.0148	1.51157	0.755785	+	0.654820i	$0.227256\pi$
$422$	3.05923	0.148921
$423$	−5.23238	−0.254407
$424$	−8.65205	−0.420181
$425$	−1.54849	−0.0751128
$426$	5.19045	0.251478
$427$	−8.36171	−0.404651
$428$	−1.13048	−0.0546437
$429$	−1.33568	−0.0644874
$430$	7.24217	0.349248
$431$	−33.7613	−1.62622	−0.813112	−	0.582107i	$-0.802228\pi$
$431$	−33.7613	−1.62622	−0.813112	+	0.582107i	$0.802228\pi$
$432$	−4.82716	−0.232247
$433$	4.05692	0.194963	0.0974815	−	0.995237i	$-0.468921\pi$
$433$	4.05692	0.194963	0.0974815	+	0.995237i	$0.468921\pi$
$434$	−2.94594	−0.141410
$435$	−7.66583	−0.367548
$436$	−9.97302	−0.477621
$437$	−1.61805	−0.0774020
$438$	−24.6403	−1.17736
$439$	−19.6114	−0.936002	−0.468001	−	0.883728i	$-0.655026\pi$
$439$	−19.6114	−0.936002	−0.468001	+	0.883728i	$0.655026\pi$
$440$	10.8163	0.515647
$441$	−6.26109	−0.298147
$442$	−0.699605	−0.0332768
$443$	−4.05751	−0.192778	−0.0963890	−	0.995344i	$-0.530729\pi$
$443$	−4.05751	−0.192778	−0.0963890	+	0.995344i	$0.530729\pi$
$444$	−2.20192	−0.104498
$445$	10.1045	0.478999
$446$	−26.7763	−1.26789
$447$	19.0459	0.900841
$448$	3.86558	0.182631
$449$	3.94257	0.186061	0.0930306	−	0.995663i	$-0.470345\pi$
$449$	3.94257	0.186061	0.0930306	+	0.995663i	$0.470345\pi$
$450$	1.60756	0.0757813
$451$	−3.10488	−0.146203
$452$	9.60994	0.452013
$453$	11.1638	0.524520
$454$	25.4938	1.19649
$455$	0.241586	0.0113257
$456$	3.85092	0.180336
$457$	19.8969	0.930738	0.465369	−	0.885117i	$-0.345922\pi$
$457$	19.8969	0.930738	0.465369	+	0.885117i	$0.345922\pi$
$458$	15.1202	0.706521
$459$	−1.54849	−0.0722773
$460$	0.558711	0.0260500
$461$	−41.5350	−1.93448	−0.967238	−	0.253871i	$-0.918296\pi$
$461$	−41.5350	−1.93448	−0.967238	+	0.253871i	$0.918296\pi$
$462$	−6.56737	−0.305542
$463$	36.1265	1.67894	0.839471	−	0.543404i	$-0.182865\pi$
$463$	36.1265	1.67894	0.839471	+	0.543404i	$0.182865\pi$
$464$	37.0042	1.71788
$465$	−2.13187	−0.0988630
$466$	−39.2901	−1.82008
$467$	35.5653	1.64577	0.822883	−	0.568211i	$-0.192364\pi$
$467$	35.5653	1.64577	0.822883	+	0.568211i	$0.192364\pi$
$468$	0.164204	0.00759033
$469$	3.51460	0.162289
$470$	−8.41139	−0.387988
$471$	17.7231	0.816636
$472$	4.95109	0.227893
$473$	−21.4105	−0.984458
$474$	18.8609	0.866308
$475$	−1.69205	−0.0776366
$476$	−0.777699	−0.0356458
$477$	3.80161	0.174064
$478$	7.99828	0.365833
$479$	18.8192	0.859869	0.429935	−	0.902860i	$-0.358537\pi$
$479$	18.8192	0.859869	0.429935	+	0.902860i	$0.358537\pi$
$480$	−3.20819	−0.146433
$481$	−1.05918	−0.0482944
$482$	−24.7381	−1.12679
$483$	0.822007	0.0374026
$484$	6.76973	0.307715
$485$	−7.41676	−0.336778
$486$	1.60756	0.0729206
$487$	−6.51640	−0.295286	−0.147643	−	0.989041i	$-0.547169\pi$
$487$	−6.51640	−0.295286	−0.147643	+	0.989041i	$0.547169\pi$
$488$	22.1386	1.00217
$489$	11.0765	0.500898
$490$	−10.0651	−0.454695
$491$	−5.56069	−0.250951	−0.125475	−	0.992097i	$-0.540046\pi$
$491$	−5.56069	−0.250951	−0.125475	+	0.992097i	$0.540046\pi$
$492$	0.381702	0.0172085
$493$	11.8705	0.534619
$494$	−0.764465	−0.0343949
$495$	−4.75256	−0.213612
$496$	10.2909	0.462074
$497$	2.77545	0.124496
$498$	−21.8548	−0.979338
$499$	−16.1645	−0.723621	−0.361811	−	0.932252i	$-0.617841\pi$
$499$	−16.1645	−0.723621	−0.361811	+	0.932252i	$0.617841\pi$
$500$	0.584262	0.0261290
$501$	−18.1681	−0.811690
$502$	24.6779	1.10143
$503$	−42.1248	−1.87825	−0.939125	−	0.343576i	$-0.888362\pi$
$503$	−42.1248	−1.87825	−0.939125	+	0.343576i	$0.888362\pi$
$504$	−1.95635	−0.0871429
$505$	8.05214	0.358315
$506$	−7.30593	−0.324788
$507$	−12.9210	−0.573842
$508$	−10.7328	−0.476192
$509$	35.4368	1.57071	0.785354	−	0.619047i	$-0.212481\pi$
$509$	35.4368	1.57071	0.785354	+	0.619047i	$0.212481\pi$
$510$	−2.48930	−0.110228
$511$	−13.1757	−0.582858
$512$	−6.48572	−0.286631
$513$	−1.69205	−0.0747058
$514$	42.0528	1.85487
$515$	−11.2293	−0.494822
$516$	2.63213	0.115873
$517$	24.8672	1.09366
$518$	−5.20784	−0.228819
$519$	−14.7639	−0.648064
$520$	−0.639628	−0.0280495
$521$	−36.9104	−1.61707	−0.808537	−	0.588445i	$-0.799740\pi$
$521$	−36.9104	−1.61707	−0.808537	+	0.588445i	$0.799740\pi$
$522$	−12.3233	−0.539377
$523$	12.7795	0.558809	0.279404	−	0.960174i	$-0.409863\pi$
$523$	12.7795	0.558809	0.279404	+	0.960174i	$0.409863\pi$
$524$	−8.24099	−0.360009
$525$	0.859599	0.0375160
$526$	16.2627	0.709086
$527$	3.30118	0.143802
$528$	22.9414	0.998395
$529$	−22.0856	−0.960241
$530$	6.11133	0.265459
$531$	−2.17545	−0.0944067
$532$	−0.849799	−0.0368435
$533$	0.183609	0.00795298
$534$	16.2436	0.702930
$535$	−1.93488	−0.0836522
$536$	−9.30533	−0.401929
$537$	−9.25607	−0.399429
$538$	29.4435	1.26940
$539$	29.7562	1.28169
$540$	0.584262	0.0251426
$541$	−34.4355	−1.48050	−0.740250	−	0.672332i	$-0.765293\pi$
$541$	−34.4355	−1.48050	−0.740250	+	0.672332i	$0.765293\pi$
$542$	25.9657	1.11532
$543$	13.9510	0.598697
$544$	4.96785	0.212995
$545$	−17.0694	−0.731175
$546$	0.388365	0.0166205
$547$	26.2898	1.12407	0.562036	−	0.827113i	$-0.310018\pi$
$547$	26.2898	1.12407	0.562036	+	0.827113i	$0.310018\pi$
$548$	10.9178	0.466387
$549$	−9.72745	−0.415158
$550$	−7.64004	−0.325772
$551$	12.9710	0.552582
$552$	−2.17636	−0.0926321
$553$	10.0853	0.428871
$554$	−49.8766	−2.11905
$555$	−3.76872	−0.159973
$556$	−4.48403	−0.190165
$557$	−27.4995	−1.16519	−0.582596	−	0.812762i	$-0.697963\pi$
$557$	−27.4995	−1.16519	−0.582596	+	0.812762i	$0.697963\pi$
$558$	−3.42711	−0.145081
$559$	1.26612	0.0535514
$560$	−4.14942	−0.175345
$561$	7.35929	0.310709
$562$	−4.89840	−0.206627
$563$	−36.1031	−1.52156	−0.760782	−	0.649008i	$-0.775184\pi$
$563$	−36.1031	−1.52156	−0.760782	+	0.649008i	$0.775184\pi$
$564$	−3.05708	−0.128726
$565$	16.4480	0.691973
$566$	45.6105	1.91715
$567$	0.859599	0.0360998
$568$	−7.34832	−0.308329
$569$	19.9095	0.834648	0.417324	−	0.908758i	$-0.362968\pi$
$569$	19.9095	0.834648	0.417324	+	0.908758i	$0.362968\pi$
$570$	−2.72008	−0.113932
$571$	30.7787	1.28805	0.644024	−	0.765005i	$-0.277264\pi$
$571$	30.7787	1.28805	0.644024	+	0.765005i	$0.277264\pi$
$572$	−0.780388	−0.0326297
$573$	20.8347	0.870382
$574$	0.902779	0.0376813
$575$	0.956268	0.0398791
$576$	4.49695	0.187373
$577$	−2.82656	−0.117671	−0.0588356	−	0.998268i	$-0.518739\pi$
$577$	−2.82656	−0.117671	−0.0588356	+	0.998268i	$0.518739\pi$
$578$	−23.4739	−0.976387
$579$	−19.8066	−0.823135
$580$	−4.47885	−0.185974
$581$	−11.6862	−0.484827
$582$	−11.9229	−0.494221
$583$	−18.0674	−0.748275
$584$	34.8842	1.44352
$585$	0.281045	0.0116198
$586$	5.84710	0.241541
$587$	26.1117	1.07775	0.538873	−	0.842387i	$-0.318850\pi$
$587$	26.1117	1.07775	0.538873	+	0.842387i	$0.318850\pi$
$588$	−3.65811	−0.150858
$589$	3.60723	0.148633
$590$	−3.49718	−0.143977
$591$	11.2799	0.463995
$592$	18.1922	0.747695
$593$	13.0726	0.536827	0.268414	−	0.963304i	$-0.413501\pi$
$593$	13.0726	0.536827	0.268414	+	0.963304i	$0.413501\pi$
$594$	−7.64004	−0.313475
$595$	−1.33108	−0.0545690
$596$	11.1278	0.455812
$597$	−19.3109	−0.790342
$598$	0.432040	0.0176674
$599$	19.1760	0.783509	0.391755	−	0.920070i	$-0.371868\pi$
$599$	19.1760	0.783509	0.391755	+	0.920070i	$0.371868\pi$
$600$	−2.27589	−0.0929128
$601$	−17.4982	−0.713767	−0.356883	−	0.934149i	$-0.616161\pi$
$601$	−17.4982	−0.713767	−0.356883	+	0.934149i	$0.616161\pi$
$602$	6.22536	0.253727
$603$	4.08866	0.166503
$604$	6.52256	0.265399
$605$	11.5868	0.471071
$606$	12.9443	0.525827
$607$	−36.1771	−1.46838	−0.734191	−	0.678943i	$-0.762438\pi$
$607$	−36.1771	−1.46838	−0.734191	+	0.678943i	$0.762438\pi$
$608$	5.42842	0.220151
$609$	−6.58954	−0.267022
$610$	−15.6375	−0.633144
$611$	−1.47054	−0.0594915
$612$	−0.904723	−0.0365713
$613$	−37.6859	−1.52212	−0.761059	−	0.648683i	$-0.775320\pi$
$613$	−37.6859	−1.52212	−0.761059	+	0.648683i	$0.775320\pi$
$614$	−8.97617	−0.362249
$615$	0.653307	0.0263439
$616$	9.29768	0.374614
$617$	37.1571	1.49589	0.747944	−	0.663762i	$-0.231041\pi$
$617$	37.1571	1.49589	0.747944	+	0.663762i	$0.231041\pi$
$618$	−18.0518	−0.726150
$619$	−4.51317	−0.181399	−0.0906997	−	0.995878i	$-0.528910\pi$
$619$	−4.51317	−0.181399	−0.0906997	+	0.995878i	$0.528910\pi$
$620$	−1.24557	−0.0500232
$621$	0.956268	0.0383737
$622$	27.7763	1.11373
$623$	8.68581	0.347989
$624$	−1.35665	−0.0543095
$625$	1.00000	0.0400000
$626$	0.461949	0.0184632
$627$	8.04157	0.321149
$628$	10.3549	0.413206
$629$	5.83582	0.232690
$630$	1.38186	0.0550546
$631$	43.8744	1.74661	0.873305	−	0.487173i	$-0.161972\pi$
$631$	43.8744	1.74661	0.873305	+	0.487173i	$0.161972\pi$
$632$	−26.7020	−1.06215
$633$	1.90302	0.0756384
$634$	−44.5148	−1.76791
$635$	−18.3699	−0.728987
$636$	2.22114	0.0880738
$637$	−1.75965	−0.0697198
$638$	58.5672	2.31870
$639$	3.22877	0.127728
$640$	13.6455	0.539386
$641$	−0.698827	−0.0276020	−0.0138010	−	0.999905i	$-0.504393\pi$
$641$	−0.698827	−0.0276020	−0.0138010	+	0.999905i	$0.504393\pi$
$642$	−3.11045	−0.122760
$643$	−25.2728	−0.996663	−0.498332	−	0.866987i	$-0.666054\pi$
$643$	−25.2728	−0.996663	−0.498332	+	0.866987i	$0.666054\pi$
$644$	0.480267	0.0189252
$645$	4.50506	0.177386
$646$	4.21202	0.165720
$647$	−5.31994	−0.209148	−0.104574	−	0.994517i	$-0.533348\pi$
$647$	−5.31994	−0.209148	−0.104574	+	0.994517i	$0.533348\pi$
$648$	−2.27589	−0.0894054
$649$	10.3390	0.405840
$650$	0.451798	0.0177210
$651$	−1.83255	−0.0718234
$652$	6.47159	0.253447
$653$	−13.4992	−0.528264	−0.264132	−	0.964487i	$-0.585085\pi$
$653$	−13.4992	−0.528264	−0.264132	+	0.964487i	$0.585085\pi$
$654$	−27.4402	−1.07300
$655$	−14.1050	−0.551127
$656$	−3.15362	−0.123128
$657$	−15.3277	−0.597991
$658$	−7.23042	−0.281871
$659$	1.16466	0.0453687	0.0226844	−	0.999743i	$-0.492779\pi$
$659$	1.16466	0.0453687	0.0226844	+	0.999743i	$0.492779\pi$
$660$	−2.77674	−0.108084
$661$	−22.5322	−0.876399	−0.438200	−	0.898878i	$-0.644384\pi$
$661$	−22.5322	−0.876399	−0.438200	+	0.898878i	$0.644384\pi$
$662$	−11.2947	−0.438982
$663$	−0.435196	−0.0169016
$664$	30.9407	1.20073
$665$	−1.45448	−0.0564025
$666$	−6.05845	−0.234760
$667$	−7.33059	−0.283842
$668$	−10.6149	−0.410703
$669$	−16.6564	−0.643974
$670$	6.57278	0.253928
$671$	46.2303	1.78470
$672$	−2.75776	−0.106383
$673$	−42.2560	−1.62885	−0.814425	−	0.580269i	$-0.802947\pi$
$673$	−42.2560	−1.62885	−0.814425	+	0.580269i	$0.802947\pi$
$674$	−2.25322	−0.0867907
$675$	1.00000	0.0384900
$676$	−7.54925	−0.290356
$677$	36.3535	1.39718	0.698589	−	0.715523i	$-0.253811\pi$
$677$	36.3535	1.39718	0.698589	+	0.715523i	$0.253811\pi$
$678$	26.4412	1.01547
$679$	−6.37544	−0.244667
$680$	3.52419	0.135147
$681$	15.8587	0.607706
$682$	16.2876	0.623683
$683$	25.9454	0.992773	0.496387	−	0.868102i	$-0.334660\pi$
$683$	25.9454	0.992773	0.496387	+	0.868102i	$0.334660\pi$
$684$	−0.988600	−0.0378001
$685$	18.6866	0.713977
$686$	−18.3250	−0.699651
$687$	9.40567	0.358849
$688$	−21.7466	−0.829083
$689$	1.06842	0.0407037
$690$	1.53726	0.0585226
$691$	−48.8951	−1.86006	−0.930029	−	0.367486i	$-0.880219\pi$
$691$	−48.8951	−1.86006	−0.930029	+	0.367486i	$0.880219\pi$
$692$	−8.62599	−0.327911
$693$	−4.08529	−0.155187
$694$	−3.19904	−0.121434
$695$	−7.67469	−0.291118
$696$	17.4466	0.661311
$697$	−1.01164	−0.0383186
$698$	9.19514	0.348041
$699$	−24.4408	−0.924436
$700$	0.502231	0.0189825
$701$	−30.0014	−1.13314	−0.566568	−	0.824015i	$-0.691729\pi$
$701$	−30.0014	−1.13314	−0.566568	+	0.824015i	$0.691729\pi$
$702$	0.451798	0.0170520
$703$	6.37686	0.240508
$704$	−21.3720	−0.805488
$705$	−5.23238	−0.197063
$706$	−5.98079	−0.225090
$707$	6.92161	0.260314
$708$	−1.27103	−0.0477684
$709$	31.1618	1.17030	0.585152	−	0.810923i	$-0.301035\pi$
$709$	31.1618	1.17030	0.585152	+	0.810923i	$0.301035\pi$
$710$	5.19045	0.194794
$711$	11.7326	0.440006
$712$	−22.9967	−0.861838
$713$	−2.03864	−0.0763476
$714$	−2.13980	−0.0800799
$715$	−1.33568	−0.0499517
$716$	−5.40797	−0.202105
$717$	4.97540	0.185810
$718$	26.8875	1.00343
$719$	24.2313	0.903675	0.451838	−	0.892100i	$-0.350769\pi$
$719$	24.2313	0.903675	0.451838	+	0.892100i	$0.350769\pi$
$720$	−4.82716	−0.179898
$721$	−9.65269	−0.359485
$722$	−25.9412	−0.965432
$723$	−15.3886	−0.572308
$724$	8.15106	0.302932
$725$	−7.66583	−0.284702
$726$	18.6265	0.691295
$727$	−37.3571	−1.38550	−0.692750	−	0.721178i	$-0.743601\pi$
$727$	−37.3571	−1.38550	−0.692750	+	0.721178i	$0.743601\pi$
$728$	−0.549823	−0.0203778
$729$	1.00000	0.0370370
$730$	−24.6403	−0.911978
$731$	−6.97604	−0.258018
$732$	−5.68338	−0.210064
$733$	24.4147	0.901776	0.450888	−	0.892581i	$-0.351107\pi$
$733$	24.4147	0.901776	0.450888	+	0.892581i	$0.351107\pi$
$734$	37.9473	1.40066
$735$	−6.26109	−0.230944
$736$	−3.06789	−0.113084
$737$	−19.4316	−0.715771
$738$	1.05023	0.0386596
$739$	3.47803	0.127941	0.0639706	−	0.997952i	$-0.479624\pi$
$739$	3.47803	0.127941	0.0639706	+	0.997952i	$0.479624\pi$
$740$	−2.20192	−0.0809441
$741$	−0.475542	−0.0174695
$742$	5.25330	0.192855
$743$	−7.75564	−0.284527	−0.142263	−	0.989829i	$-0.545438\pi$
$743$	−7.75564	−0.284527	−0.142263	+	0.989829i	$0.545438\pi$
$744$	4.85190	0.177879
$745$	19.0459	0.697788
$746$	3.25905	0.119322
$747$	−13.5950	−0.497415
$748$	4.29975	0.157214
$749$	−1.66322	−0.0607728
$750$	1.60756	0.0586999
$751$	−36.0326	−1.31485	−0.657424	−	0.753520i	$-0.728354\pi$
$751$	−36.0326	−1.31485	−0.657424	+	0.753520i	$0.728354\pi$
$752$	25.2576	0.921048
$753$	15.3511	0.559425
$754$	−3.46341	−0.126130
$755$	11.1638	0.406291
$756$	0.502231	0.0182660
$757$	−2.76238	−0.100400	−0.0502002	−	0.998739i	$-0.515986\pi$
$757$	−2.76238	−0.100400	−0.0502002	+	0.998739i	$0.515986\pi$
$758$	32.2139	1.17006
$759$	−4.54472	−0.164963
$760$	3.85092	0.139688
$761$	−24.7389	−0.896783	−0.448392	−	0.893837i	$-0.648003\pi$
$761$	−24.7389	−0.896783	−0.448392	+	0.893837i	$0.648003\pi$
$762$	−29.5308	−1.06979
$763$	−14.6729	−0.531194
$764$	12.1729	0.440401
$765$	−1.54849	−0.0559858
$766$	−41.7002	−1.50669
$767$	−0.611401	−0.0220764
$768$	12.9421	0.467009
$769$	25.5146	0.920080	0.460040	−	0.887898i	$-0.347835\pi$
$769$	25.5146	0.920080	0.460040	+	0.887898i	$0.347835\pi$
$770$	−6.56737	−0.236672
$771$	26.1593	0.942105
$772$	−11.5722	−0.416494
$773$	−15.3958	−0.553750	−0.276875	−	0.960906i	$-0.589299\pi$
$773$	−15.3958	−0.553750	−0.276875	+	0.960906i	$0.589299\pi$
$774$	7.24217	0.260314
$775$	−2.13187	−0.0765790
$776$	16.8797	0.605947
$777$	−3.23959	−0.116219
$778$	−34.7135	−1.24454
$779$	−1.10543	−0.0396061
$780$	0.164204	0.00587944
$781$	−15.3449	−0.549084
$782$	−2.38044	−0.0851242
$783$	−7.66583	−0.273954
$784$	30.2233	1.07940
$785$	17.7231	0.632563
$786$	−22.6746	−0.808778
$787$	45.2596	1.61333	0.806665	−	0.591009i	$-0.201270\pi$
$787$	45.2596	1.61333	0.806665	+	0.591009i	$0.201270\pi$
$788$	6.59044	0.234775
$789$	10.1163	0.360151
$790$	18.8609	0.671039
$791$	14.1387	0.502714
$792$	10.8163	0.384340
$793$	−2.73385	−0.0970820
$794$	14.5688	0.517027
$795$	3.80161	0.134829
$796$	−11.2826	−0.399902
$797$	18.3561	0.650207	0.325103	−	0.945679i	$-0.394601\pi$
$797$	18.3561	0.650207	0.325103	+	0.945679i	$0.394601\pi$
$798$	−2.33818	−0.0827706
$799$	8.10229	0.286639
$800$	−3.20819	−0.113427
$801$	10.1045	0.357024
$802$	−1.60756	−0.0567651
$803$	72.8459	2.57068
$804$	2.38884	0.0842480
$805$	0.822007	0.0289719
$806$	−0.963174	−0.0339264
$807$	18.3156	0.644740
$808$	−18.3258	−0.644699
$809$	35.0707	1.23302	0.616511	−	0.787346i	$-0.288546\pi$
$809$	35.0707	1.23302	0.616511	+	0.787346i	$0.288546\pi$
$810$	1.60756	0.0564840
$811$	37.1352	1.30399	0.651996	−	0.758222i	$-0.273932\pi$
$811$	37.1352	1.30399	0.651996	+	0.758222i	$0.273932\pi$
$812$	−3.85001	−0.135109
$813$	16.1522	0.566482
$814$	28.7932	1.00920
$815$	11.0765	0.387994
$816$	7.47481	0.261671
$817$	−7.62278	−0.266687
$818$	24.7003	0.863626
$819$	0.241586	0.00844170
$820$	0.381702	0.0133296
$821$	33.2672	1.16103	0.580517	−	0.814248i	$-0.302851\pi$
$821$	33.2672	1.16103	0.580517	+	0.814248i	$0.302851\pi$
$822$	30.0399	1.04776
$823$	−16.0839	−0.560651	−0.280325	−	0.959905i	$-0.590442\pi$
$823$	−16.0839	−0.560651	−0.280325	+	0.959905i	$0.590442\pi$
$824$	25.5566	0.890308
$825$	−4.75256	−0.165463
$826$	−3.00617	−0.104598
$827$	−40.0149	−1.39145	−0.695727	−	0.718307i	$-0.744917\pi$
$827$	−40.0149	−1.39145	−0.695727	+	0.718307i	$0.744917\pi$
$828$	0.558711	0.0194165
$829$	−2.00299	−0.0695668	−0.0347834	−	0.999395i	$-0.511074\pi$
$829$	−2.00299	−0.0695668	−0.0347834	+	0.999395i	$0.511074\pi$
$830$	−21.8548	−0.758592
$831$	−31.0262	−1.07629
$832$	1.26385	0.0438160
$833$	9.69524	0.335920
$834$	−12.3376	−0.427215
$835$	−18.1681	−0.628733
$836$	4.69838	0.162497
$837$	−2.13187	−0.0736882
$838$	−27.5865	−0.952960
$839$	−3.95552	−0.136560	−0.0682799	−	0.997666i	$-0.521751\pi$
$839$	−3.95552	−0.136560	−0.0682799	+	0.997666i	$0.521751\pi$
$840$	−1.95635	−0.0675006
$841$	29.7649	1.02638
$842$	49.8583	1.71823
$843$	−3.04710	−0.104948
$844$	1.11186	0.0382719
$845$	−12.9210	−0.444496
$846$	−8.41139	−0.289189
$847$	9.96001	0.342230
$848$	−18.3510	−0.630176
$849$	28.3725	0.973740
$850$	−2.48930	−0.0853822
$851$	−3.60391	−0.123540
$852$	1.88645	0.0646286
$853$	−8.80033	−0.301317	−0.150659	−	0.988586i	$-0.548139\pi$
$853$	−8.80033	−0.301317	−0.150659	+	0.988586i	$0.548139\pi$
$854$	−13.4420	−0.459975
$855$	−1.69205	−0.0578669
$856$	4.40358	0.150511
$857$	4.53178	0.154803	0.0774013	−	0.997000i	$-0.475338\pi$
$857$	4.53178	0.154803	0.0774013	+	0.997000i	$0.475338\pi$
$858$	−2.14720	−0.0733041
$859$	13.4173	0.457793	0.228896	−	0.973451i	$-0.426488\pi$
$859$	13.4173	0.457793	0.228896	+	0.973451i	$0.426488\pi$
$860$	2.63213	0.0897550
$861$	0.561582	0.0191387
$862$	−54.2734	−1.84856
$863$	3.62282	0.123322	0.0616611	−	0.998097i	$-0.480360\pi$
$863$	3.62282	0.123322	0.0616611	+	0.998097i	$0.480360\pi$
$864$	−3.20819	−0.109145
$865$	−14.7639	−0.501989
$866$	6.52175	0.221618
$867$	−14.6022	−0.495916
$868$	−1.07069	−0.0363416
$869$	−55.7597	−1.89152
$870$	−12.3233	−0.417799
$871$	1.14910	0.0389357
$872$	38.8482	1.31557
$873$	−7.41676	−0.251019
$874$	−2.60112	−0.0879844
$875$	0.859599	0.0290597
$876$	−8.95540	−0.302575
$877$	17.7892	0.600697	0.300349	−	0.953829i	$-0.402897\pi$
$877$	17.7892	0.600697	0.300349	+	0.953829i	$0.402897\pi$
$878$	−31.5266	−1.06397
$879$	3.63724	0.122681
$880$	22.9414	0.773353
$881$	29.8475	1.00559	0.502794	−	0.864406i	$-0.332305\pi$
$881$	29.8475	1.00559	0.502794	+	0.864406i	$0.332305\pi$
$882$	−10.0651	−0.338910
$883$	−3.19126	−0.107394	−0.0536972	−	0.998557i	$-0.517101\pi$
$883$	−3.19126	−0.107394	−0.0536972	+	0.998557i	$0.517101\pi$
$884$	−0.254268	−0.00855196
$885$	−2.17545	−0.0731271
$886$	−6.52270	−0.219134
$887$	−38.5400	−1.29405	−0.647023	−	0.762470i	$-0.723986\pi$
$887$	−38.5400	−1.29405	−0.647023	+	0.762470i	$0.723986\pi$
$888$	8.57719	0.287832
$889$	−15.7907	−0.529604
$890$	16.2436	0.544487
$891$	−4.75256	−0.159217
$892$	−9.73171	−0.325842
$893$	8.85345	0.296269
$894$	30.6175	1.02400
$895$	−9.25607	−0.309396
$896$	11.7297	0.391861
$897$	0.268755	0.00897345
$898$	6.33793	0.211499
$899$	16.3425	0.545054
$900$	0.584262	0.0194754
$901$	−5.88676	−0.196116
$902$	−4.99129	−0.166192
$903$	3.87254	0.128870
$904$	−37.4338	−1.24503
$905$	13.9510	0.463749
$906$	17.9465	0.596231
$907$	10.0603	0.334048	0.167024	−	0.985953i	$-0.446584\pi$
$907$	10.0603	0.334048	0.167024	+	0.985953i	$0.446584\pi$
$908$	9.26562	0.307490
$909$	8.05214	0.267073
$910$	0.388365	0.0128742
$911$	−24.3891	−0.808048	−0.404024	−	0.914748i	$-0.632389\pi$
$911$	−24.3891	−0.808048	−0.404024	+	0.914748i	$0.632389\pi$
$912$	8.16780	0.270463
$913$	64.6110	2.13831
$914$	31.9856	1.05799
$915$	−9.72745	−0.321580
$916$	5.49537	0.181572
$917$	−12.1246	−0.400390
$918$	−2.48930	−0.0821590
$919$	31.9458	1.05380	0.526898	−	0.849929i	$-0.323355\pi$
$919$	31.9458	1.05380	0.526898	+	0.849929i	$0.323355\pi$
$920$	−2.17636	−0.0717525
$921$	−5.58371	−0.183989
$922$	−66.7701	−2.19896
$923$	0.907430	0.0298684
$924$	−2.38688	−0.0785226
$925$	−3.76872	−0.123915
$926$	58.0757	1.90849
$927$	−11.2293	−0.368818
$928$	24.5934	0.807319
$929$	10.3271	0.338823	0.169411	−	0.985545i	$-0.445813\pi$
$929$	10.3271	0.338823	0.169411	+	0.985545i	$0.445813\pi$
$930$	−3.42711	−0.112380
$931$	10.5941	0.347207
$932$	−14.2798	−0.467751
$933$	17.2785	0.565673
$934$	57.1735	1.87077
$935$	7.35929	0.240675
$936$	−0.639628	−0.0209069
$937$	31.1943	1.01907	0.509536	−	0.860449i	$-0.329817\pi$
$937$	31.1943	1.01907	0.509536	+	0.860449i	$0.329817\pi$
$938$	5.64995	0.184477
$939$	0.287359	0.00937762
$940$	−3.05708	−0.0997109
$941$	−25.1019	−0.818298	−0.409149	−	0.912467i	$-0.634174\pi$
$941$	−25.1019	−0.818298	−0.409149	+	0.912467i	$0.634174\pi$
$942$	28.4910	0.928286
$943$	0.624737	0.0203442
$944$	10.5013	0.341787
$945$	0.859599	0.0279628
$946$	−34.4188	−1.11905
$947$	60.1409	1.95432	0.977158	−	0.212516i	$-0.0681658\pi$
$947$	60.1409	1.95432	0.977158	+	0.212516i	$0.0681658\pi$
$948$	6.85489	0.222637
$949$	−4.30778	−0.139836
$950$	−2.72008	−0.0882510
$951$	−27.6908	−0.897937
$952$	3.02939	0.0981832
$953$	−53.1332	−1.72115	−0.860576	−	0.509321i	$-0.829897\pi$
$953$	−53.1332	−1.72115	−0.860576	+	0.509321i	$0.829897\pi$
$954$	6.11133	0.197862
$955$	20.8347	0.674195
$956$	2.90694	0.0940171
$957$	36.4323	1.17769
$958$	30.2530	0.977430
$959$	16.0630	0.518700
$960$	4.49695	0.145139
$961$	−26.4551	−0.853392
$962$	−1.70270	−0.0548972
$963$	−1.93488	−0.0623507
$964$	−8.99096	−0.289579
$965$	−19.8066	−0.637598
$966$	1.32143	0.0425163
$967$	−34.8921	−1.12205	−0.561027	−	0.827798i	$-0.689594\pi$
$967$	−34.8921	−1.12205	−0.561027	+	0.827798i	$0.689594\pi$
$968$	−26.3703	−0.847573
$969$	2.62012	0.0841705
$970$	−11.9229	−0.382822
$971$	13.3261	0.427654	0.213827	−	0.976872i	$-0.431407\pi$
$971$	13.3261	0.427654	0.213827	+	0.976872i	$0.431407\pi$
$972$	0.584262	0.0187402
$973$	−6.59716	−0.211495
$974$	−10.4755	−0.335658
$975$	0.281045	0.00900065
$976$	46.9560	1.50302
$977$	39.1757	1.25334	0.626671	−	0.779284i	$-0.284417\pi$
$977$	39.1757	1.25334	0.626671	+	0.779284i	$0.284417\pi$
$978$	17.8062	0.569380
$979$	−48.0222	−1.53479
$980$	−3.65811	−0.116854
$981$	−17.0694	−0.544985
$982$	−8.93917	−0.285260
$983$	−43.1717	−1.37696	−0.688482	−	0.725254i	$-0.741722\pi$
$983$	−43.1717	−1.37696	−0.688482	+	0.725254i	$0.741722\pi$
$984$	−1.48685	−0.0473992
$985$	11.2799	0.359409
$986$	19.0825	0.607711
$987$	−4.49775	−0.143165
$988$	−0.277841	−0.00883930
$989$	4.30804	0.136988
$990$	−7.64004	−0.242816
$991$	50.5355	1.60531	0.802656	−	0.596442i	$-0.203420\pi$
$991$	50.5355	1.60531	0.802656	+	0.596442i	$0.203420\pi$
$992$	6.83944	0.217152
$993$	−7.02599	−0.222963
$994$	4.46171	0.141517
$995$	−19.3109	−0.612197
$996$	−7.94303	−0.251685
$997$	48.2453	1.52794	0.763971	−	0.645250i	$-0.223247\pi$
$997$	48.2453	1.52794	0.763971	+	0.645250i	$0.223247\pi$
$998$	−25.9854	−0.822554
$999$	−3.76872	−0.119237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.19	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.19	✓	23	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.60756 q^{2} +1.00000 q^{3} +0.584262 q^{4} +1.00000 q^{5} +1.60756 q^{6} +0.859599 q^{7} -2.27589 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.60756 q^{2} +1.00000 q^{3} +0.584262 q^{4} +1.00000 q^{5} +1.60756 q^{6} +0.859599 q^{7} -2.27589 q^{8} +1.00000 q^{9} +1.60756 q^{10} -4.75256 q^{11} +0.584262 q^{12} +0.281045 q^{13} +1.38186 q^{14} +1.00000 q^{15} -4.82716 q^{16} -1.54849 q^{17} +1.60756 q^{18} -1.69205 q^{19} +0.584262 q^{20} +0.859599 q^{21} -7.64004 q^{22} +0.956268 q^{23} -2.27589 q^{24} +1.00000 q^{25} +0.451798 q^{26} +1.00000 q^{27} +0.502231 q^{28} -7.66583 q^{29} +1.60756 q^{30} -2.13187 q^{31} -3.20819 q^{32} -4.75256 q^{33} -2.48930 q^{34} +0.859599 q^{35} +0.584262 q^{36} -3.76872 q^{37} -2.72008 q^{38} +0.281045 q^{39} -2.27589 q^{40} +0.653307 q^{41} +1.38186 q^{42} +4.50506 q^{43} -2.77674 q^{44} +1.00000 q^{45} +1.53726 q^{46} -5.23238 q^{47} -4.82716 q^{48} -6.26109 q^{49} +1.60756 q^{50} -1.54849 q^{51} +0.164204 q^{52} +3.80161 q^{53} +1.60756 q^{54} -4.75256 q^{55} -1.95635 q^{56} -1.69205 q^{57} -12.3233 q^{58} -2.17545 q^{59} +0.584262 q^{60} -9.72745 q^{61} -3.42711 q^{62} +0.859599 q^{63} +4.49695 q^{64} +0.281045 q^{65} -7.64004 q^{66} +4.08866 q^{67} -0.904723 q^{68} +0.956268 q^{69} +1.38186 q^{70} +3.22877 q^{71} -2.27589 q^{72} -15.3277 q^{73} -6.05845 q^{74} +1.00000 q^{75} -0.988600 q^{76} -4.08529 q^{77} +0.451798 q^{78} +11.7326 q^{79} -4.82716 q^{80} +1.00000 q^{81} +1.05023 q^{82} -13.5950 q^{83} +0.502231 q^{84} -1.54849 q^{85} +7.24217 q^{86} -7.66583 q^{87} +10.8163 q^{88} +10.1045 q^{89} +1.60756 q^{90} +0.241586 q^{91} +0.558711 q^{92} -2.13187 q^{93} -8.41139 q^{94} -1.69205 q^{95} -3.20819 q^{96} -7.41676 q^{97} -10.0651 q^{98} -4.75256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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