LMFDB - Embedded newform 6015.2.a.d.1.20

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:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+1.09145 q^{2} -1.00000 q^{3} -0.808735 q^{4} +1.00000 q^{5} -1.09145 q^{6} +0.212319 q^{7} -3.06560 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.09145 q^{2} -1.00000 q^{3} -0.808735 q^{4} +1.00000 q^{5} -1.09145 q^{6} +0.212319 q^{7} -3.06560 q^{8} +1.00000 q^{9} +1.09145 q^{10} +3.48564 q^{11} +0.808735 q^{12} -3.29790 q^{13} +0.231736 q^{14} -1.00000 q^{15} -1.72848 q^{16} -0.372693 q^{17} +1.09145 q^{18} -3.68869 q^{19} -0.808735 q^{20} -0.212319 q^{21} +3.80440 q^{22} +3.62122 q^{23} +3.06560 q^{24} +1.00000 q^{25} -3.59950 q^{26} -1.00000 q^{27} -0.171710 q^{28} -3.97126 q^{29} -1.09145 q^{30} +1.86735 q^{31} +4.24464 q^{32} -3.48564 q^{33} -0.406776 q^{34} +0.212319 q^{35} -0.808735 q^{36} +6.08964 q^{37} -4.02603 q^{38} +3.29790 q^{39} -3.06560 q^{40} +3.34385 q^{41} -0.231736 q^{42} -7.75720 q^{43} -2.81896 q^{44} +1.00000 q^{45} +3.95239 q^{46} +5.29704 q^{47} +1.72848 q^{48} -6.95492 q^{49} +1.09145 q^{50} +0.372693 q^{51} +2.66713 q^{52} -3.04654 q^{53} -1.09145 q^{54} +3.48564 q^{55} -0.650884 q^{56} +3.68869 q^{57} -4.33443 q^{58} +3.10621 q^{59} +0.808735 q^{60} +5.45729 q^{61} +2.03813 q^{62} +0.212319 q^{63} +8.08978 q^{64} -3.29790 q^{65} -3.80440 q^{66} -11.9444 q^{67} +0.301410 q^{68} -3.62122 q^{69} +0.231736 q^{70} -8.71078 q^{71} -3.06560 q^{72} -12.7858 q^{73} +6.64655 q^{74} -1.00000 q^{75} +2.98318 q^{76} +0.740067 q^{77} +3.59950 q^{78} -14.2726 q^{79} -1.72848 q^{80} +1.00000 q^{81} +3.64964 q^{82} +5.98663 q^{83} +0.171710 q^{84} -0.372693 q^{85} -8.46660 q^{86} +3.97126 q^{87} -10.6856 q^{88} -6.80319 q^{89} +1.09145 q^{90} -0.700207 q^{91} -2.92861 q^{92} -1.86735 q^{93} +5.78146 q^{94} -3.68869 q^{95} -4.24464 q^{96} +8.14205 q^{97} -7.59095 q^{98} +3.48564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	1.09145	0.771772	0.385886	−	0.922546i	$-0.373896\pi$
$2$	1.09145	0.771772	0.385886	+	0.922546i	$0.373896\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.808735	−0.404368
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.09145	−0.445583
$7$	0.212319	0.0802490	0.0401245	−	0.999195i	$-0.487225\pi$
$7$	0.212319	0.0802490	0.0401245	+	0.999195i	$0.487225\pi$
$8$	−3.06560	−1.08385
$9$	1.00000	0.333333
$10$	1.09145	0.345147
$11$	3.48564	1.05096	0.525480	−	0.850806i	$-0.323886\pi$
$11$	3.48564	1.05096	0.525480	+	0.850806i	$0.323886\pi$
$12$	0.808735	0.233462
$13$	−3.29790	−0.914674	−0.457337	−	0.889293i	$-0.651197\pi$
$13$	−3.29790	−0.914674	−0.457337	+	0.889293i	$0.651197\pi$
$14$	0.231736	0.0619339
$15$	−1.00000	−0.258199
$16$	−1.72848	−0.432119
$17$	−0.372693	−0.0903913	−0.0451956	−	0.998978i	$-0.514391\pi$
$17$	−0.372693	−0.0903913	−0.0451956	+	0.998978i	$0.514391\pi$
$18$	1.09145	0.257257
$19$	−3.68869	−0.846245	−0.423122	−	0.906073i	$-0.639066\pi$
$19$	−3.68869	−0.846245	−0.423122	+	0.906073i	$0.639066\pi$
$20$	−0.808735	−0.180839
$21$	−0.212319	−0.0463318
$22$	3.80440	0.811101
$23$	3.62122	0.755077	0.377539	−	0.925994i	$-0.376771\pi$
$23$	3.62122	0.755077	0.377539	+	0.925994i	$0.376771\pi$
$24$	3.06560	0.625762
$25$	1.00000	0.200000
$26$	−3.59950	−0.705920
$27$	−1.00000	−0.192450
$28$	−0.171710	−0.0324501
$29$	−3.97126	−0.737444	−0.368722	−	0.929540i	$-0.620205\pi$
$29$	−3.97126	−0.737444	−0.368722	+	0.929540i	$0.620205\pi$
$30$	−1.09145	−0.199271
$31$	1.86735	0.335387	0.167693	−	0.985839i	$-0.446368\pi$
$31$	1.86735	0.335387	0.167693	+	0.985839i	$0.446368\pi$
$32$	4.24464	0.750354
$33$	−3.48564	−0.606772
$34$	−0.406776	−0.0697615
$35$	0.212319	0.0358884
$36$	−0.808735	−0.134789
$37$	6.08964	1.00113	0.500566	−	0.865699i	$-0.333125\pi$
$37$	6.08964	1.00113	0.500566	+	0.865699i	$0.333125\pi$
$38$	−4.02603	−0.653108
$39$	3.29790	0.528087
$40$	−3.06560	−0.484713
$41$	3.34385	0.522221	0.261110	−	0.965309i	$-0.415911\pi$
$41$	3.34385	0.522221	0.261110	+	0.965309i	$0.415911\pi$
$42$	−0.231736	−0.0357576
$43$	−7.75720	−1.18296	−0.591481	−	0.806319i	$-0.701456\pi$
$43$	−7.75720	−1.18296	−0.591481	+	0.806319i	$0.701456\pi$
$44$	−2.81896	−0.424974
$45$	1.00000	0.149071
$46$	3.95239	0.582748
$47$	5.29704	0.772653	0.386327	−	0.922362i	$-0.373744\pi$
$47$	5.29704	0.772653	0.386327	+	0.922362i	$0.373744\pi$
$48$	1.72848	0.249484
$49$	−6.95492	−0.993560
$50$	1.09145	0.154354
$51$	0.372693	0.0521874
$52$	2.66713	0.369864
$53$	−3.04654	−0.418475	−0.209238	−	0.977865i	$-0.567098\pi$
$53$	−3.04654	−0.418475	−0.209238	+	0.977865i	$0.567098\pi$
$54$	−1.09145	−0.148528
$55$	3.48564	0.470003
$56$	−0.650884	−0.0869780
$57$	3.68869	0.488580
$58$	−4.33443	−0.569139
$59$	3.10621	0.404395	0.202197	−	0.979345i	$-0.435192\pi$
$59$	3.10621	0.404395	0.202197	+	0.979345i	$0.435192\pi$
$60$	0.808735	0.104407
$61$	5.45729	0.698735	0.349367	−	0.936986i	$-0.386396\pi$
$61$	5.45729	0.698735	0.349367	+	0.936986i	$0.386396\pi$
$62$	2.03813	0.258842
$63$	0.212319	0.0267497
$64$	8.08978	1.01122
$65$	−3.29790	−0.409055
$66$	−3.80440	−0.468289
$67$	−11.9444	−1.45924	−0.729620	−	0.683853i	$-0.760303\pi$
$67$	−11.9444	−1.45924	−0.729620	+	0.683853i	$0.760303\pi$
$68$	0.301410	0.0365513
$69$	−3.62122	−0.435944
$70$	0.231736	0.0276977
$71$	−8.71078	−1.03378	−0.516889	−	0.856052i	$-0.672910\pi$
$71$	−8.71078	−1.03378	−0.516889	+	0.856052i	$0.672910\pi$
$72$	−3.06560	−0.361284
$73$	−12.7858	−1.49647	−0.748235	−	0.663434i	$-0.769098\pi$
$73$	−12.7858	−1.49647	−0.748235	+	0.663434i	$0.769098\pi$
$74$	6.64655	0.772645
$75$	−1.00000	−0.115470
$76$	2.98318	0.342194
$77$	0.740067	0.0843384
$78$	3.59950	0.407563
$79$	−14.2726	−1.60579	−0.802894	−	0.596121i	$-0.796708\pi$
$79$	−14.2726	−1.60579	−0.802894	+	0.596121i	$0.796708\pi$
$80$	−1.72848	−0.193250
$81$	1.00000	0.111111
$82$	3.64964	0.403036
$83$	5.98663	0.657118	0.328559	−	0.944483i	$-0.393437\pi$
$83$	5.98663	0.657118	0.328559	+	0.944483i	$0.393437\pi$
$84$	0.171710	0.0187351
$85$	−0.372693	−0.0404242
$86$	−8.46660	−0.912977
$87$	3.97126	0.425764
$88$	−10.6856	−1.13908
$89$	−6.80319	−0.721136	−0.360568	−	0.932733i	$-0.617417\pi$
$89$	−6.80319	−0.721136	−0.360568	+	0.932733i	$0.617417\pi$
$90$	1.09145	0.115049
$91$	−0.700207	−0.0734017
$92$	−2.92861	−0.305329
$93$	−1.86735	−0.193636
$94$	5.78146	0.596312
$95$	−3.68869	−0.378452
$96$	−4.24464	−0.433217
$97$	8.14205	0.826699	0.413350	−	0.910572i	$-0.364359\pi$
$97$	8.14205	0.826699	0.413350	+	0.910572i	$0.364359\pi$
$98$	−7.59095	−0.766802
$99$	3.48564	0.350320
$100$	−0.808735	−0.0808735
$101$	3.90365	0.388428	0.194214	−	0.980959i	$-0.437784\pi$
$101$	3.90365	0.388428	0.194214	+	0.980959i	$0.437784\pi$
$102$	0.406776	0.0402768
$103$	9.97657	0.983021	0.491510	−	0.870872i	$-0.336445\pi$
$103$	9.97657	0.983021	0.491510	+	0.870872i	$0.336445\pi$
$104$	10.1100	0.991371
$105$	−0.212319	−0.0207202
$106$	−3.32515	−0.322967
$107$	−9.29854	−0.898923	−0.449462	−	0.893300i	$-0.648384\pi$
$107$	−9.29854	−0.898923	−0.449462	+	0.893300i	$0.648384\pi$
$108$	0.808735	0.0778206
$109$	−5.00170	−0.479076	−0.239538	−	0.970887i	$-0.576996\pi$
$109$	−5.00170	−0.479076	−0.239538	+	0.970887i	$0.576996\pi$
$110$	3.80440	0.362735
$111$	−6.08964	−0.578003
$112$	−0.366988	−0.0346771
$113$	10.5980	0.996979	0.498490	−	0.866896i	$-0.333888\pi$
$113$	10.5980	0.996979	0.498490	+	0.866896i	$0.333888\pi$
$114$	4.02603	0.377072
$115$	3.62122	0.337681
$116$	3.21170	0.298198
$117$	−3.29790	−0.304891
$118$	3.39028	0.312101
$119$	−0.0791297	−0.00725381
$120$	3.06560	0.279849
$121$	1.14967	0.104515
$122$	5.95637	0.539264
$123$	−3.34385	−0.301504
$124$	−1.51019	−0.135620
$125$	1.00000	0.0894427
$126$	0.231736	0.0206446
$127$	−6.06791	−0.538440	−0.269220	−	0.963079i	$-0.586766\pi$
$127$	−6.06791	−0.538440	−0.269220	+	0.963079i	$0.586766\pi$
$128$	0.340303	0.0300788
$129$	7.75720	0.682983
$130$	−3.59950	−0.315697
$131$	7.82715	0.683861	0.341931	−	0.939725i	$-0.388919\pi$
$131$	7.82715	0.683861	0.341931	+	0.939725i	$0.388919\pi$
$132$	2.81896	0.245359
$133$	−0.783179	−0.0679103
$134$	−13.0367	−1.12620
$135$	−1.00000	−0.0860663
$136$	1.14253	0.0979708
$137$	7.37715	0.630273	0.315136	−	0.949046i	$-0.397950\pi$
$137$	7.37715	0.630273	0.315136	+	0.949046i	$0.397950\pi$
$138$	−3.95239	−0.336449
$139$	−20.2092	−1.71412	−0.857060	−	0.515217i	$-0.827711\pi$
$139$	−20.2092	−1.71412	−0.857060	+	0.515217i	$0.827711\pi$
$140$	−0.171710	−0.0145121
$141$	−5.29704	−0.446092
$142$	−9.50738	−0.797842
$143$	−11.4953	−0.961285
$144$	−1.72848	−0.144040
$145$	−3.97126	−0.329795
$146$	−13.9551	−1.15493
$147$	6.95492	0.573632
$148$	−4.92491	−0.404825
$149$	−5.81869	−0.476686	−0.238343	−	0.971181i	$-0.576604\pi$
$149$	−5.81869	−0.476686	−0.238343	+	0.971181i	$0.576604\pi$
$150$	−1.09145	−0.0891166
$151$	1.59846	0.130081	0.0650403	−	0.997883i	$-0.479282\pi$
$151$	1.59846	0.130081	0.0650403	+	0.997883i	$0.479282\pi$
$152$	11.3080	0.917204
$153$	−0.372693	−0.0301304
$154$	0.807746	0.0650900
$155$	1.86735	0.149990
$156$	−2.66713	−0.213541
$157$	−7.89026	−0.629711	−0.314856	−	0.949140i	$-0.601956\pi$
$157$	−7.89026	−0.629711	−0.314856	+	0.949140i	$0.601956\pi$
$158$	−15.5778	−1.23930
$159$	3.04654	0.241607
$160$	4.24464	0.335569
$161$	0.768854	0.0605942
$162$	1.09145	0.0857525
$163$	18.2650	1.43062	0.715312	−	0.698805i	$-0.246284\pi$
$163$	18.2650	1.43062	0.715312	+	0.698805i	$0.246284\pi$
$164$	−2.70428	−0.211169
$165$	−3.48564	−0.271357
$166$	6.53412	0.507146
$167$	−16.4333	−1.27165	−0.635824	−	0.771834i	$-0.719340\pi$
$167$	−16.4333	−1.27165	−0.635824	+	0.771834i	$0.719340\pi$
$168$	0.650884	0.0502168
$169$	−2.12383	−0.163372
$170$	−0.406776	−0.0311983
$171$	−3.68869	−0.282082
$172$	6.27352	0.478351
$173$	14.0752	1.07012	0.535059	−	0.844815i	$-0.320289\pi$
$173$	14.0752	1.07012	0.535059	+	0.844815i	$0.320289\pi$
$174$	4.33443	0.328593
$175$	0.212319	0.0160498
$176$	−6.02484	−0.454140
$177$	−3.10621	−0.233477
$178$	−7.42534	−0.556553
$179$	−9.22698	−0.689657	−0.344828	−	0.938666i	$-0.612063\pi$
$179$	−9.22698	−0.689657	−0.344828	+	0.938666i	$0.612063\pi$
$180$	−0.808735	−0.0602796
$181$	−23.6174	−1.75547	−0.877736	−	0.479145i	$-0.840947\pi$
$181$	−23.6174	−1.75547	−0.877736	+	0.479145i	$0.840947\pi$
$182$	−0.764242	−0.0566494
$183$	−5.45729	−0.403415
$184$	−11.1012	−0.818392
$185$	6.08964	0.447719
$186$	−2.03813	−0.149443
$187$	−1.29907	−0.0949976
$188$	−4.28391	−0.312436
$189$	−0.212319	−0.0154439
$190$	−4.02603	−0.292079
$191$	12.4651	0.901943	0.450971	−	0.892538i	$-0.351078\pi$
$191$	12.4651	0.901943	0.450971	+	0.892538i	$0.351078\pi$
$192$	−8.08978	−0.583829
$193$	−18.6389	−1.34166	−0.670830	−	0.741611i	$-0.734062\pi$
$193$	−18.6389	−1.34166	−0.670830	+	0.741611i	$0.734062\pi$
$194$	8.88664	0.638024
$195$	3.29790	0.236168
$196$	5.62469	0.401763
$197$	−8.29029	−0.590659	−0.295329	−	0.955395i	$-0.595429\pi$
$197$	−8.29029	−0.590659	−0.295329	+	0.955395i	$0.595429\pi$
$198$	3.80440	0.270367
$199$	2.20815	0.156532	0.0782658	−	0.996933i	$-0.475062\pi$
$199$	2.20815	0.156532	0.0782658	+	0.996933i	$0.475062\pi$
$200$	−3.06560	−0.216770
$201$	11.9444	0.842492
$202$	4.26065	0.299778
$203$	−0.843173	−0.0591791
$204$	−0.301410	−0.0211029
$205$	3.34385	0.233544
$206$	10.8889	0.758668
$207$	3.62122	0.251692
$208$	5.70035	0.395248
$209$	−12.8575	−0.889369
$210$	−0.231736	−0.0159913
$211$	−5.64443	−0.388579	−0.194289	−	0.980944i	$-0.562240\pi$
$211$	−5.64443	−0.388579	−0.194289	+	0.980944i	$0.562240\pi$
$212$	2.46385	0.169218
$213$	8.71078	0.596853
$214$	−10.1489	−0.693764
$215$	−7.75720	−0.529037
$216$	3.06560	0.208587
$217$	0.396475	0.0269144
$218$	−5.45911	−0.369737
$219$	12.7858	0.863987
$220$	−2.81896	−0.190054
$221$	1.22911	0.0826786
$222$	−6.64655	−0.446087
$223$	5.91710	0.396239	0.198119	−	0.980178i	$-0.436517\pi$
$223$	5.91710	0.396239	0.198119	+	0.980178i	$0.436517\pi$
$224$	0.901218	0.0602152
$225$	1.00000	0.0666667
$226$	11.5672	0.769441
$227$	12.3677	0.820874	0.410437	−	0.911889i	$-0.365376\pi$
$227$	12.3677	0.820874	0.410437	+	0.911889i	$0.365376\pi$
$228$	−2.98318	−0.197566
$229$	6.99246	0.462074	0.231037	−	0.972945i	$-0.425788\pi$
$229$	6.99246	0.462074	0.231037	+	0.972945i	$0.425788\pi$
$230$	3.95239	0.260613
$231$	−0.740067	−0.0486928
$232$	12.1743	0.799280
$233$	−4.89254	−0.320521	−0.160261	−	0.987075i	$-0.551233\pi$
$233$	−4.89254	−0.320521	−0.160261	+	0.987075i	$0.551233\pi$
$234$	−3.59950	−0.235307
$235$	5.29704	0.345541
$236$	−2.51210	−0.163524
$237$	14.2726	0.927103
$238$	−0.0863662	−0.00559829
$239$	−30.0687	−1.94498	−0.972490	−	0.232943i	$-0.925164\pi$
$239$	−30.0687	−1.94498	−0.972490	+	0.232943i	$0.925164\pi$
$240$	1.72848	0.111573
$241$	−29.9369	−1.92841	−0.964204	−	0.265163i	$-0.914574\pi$
$241$	−29.9369	−1.92841	−0.964204	+	0.265163i	$0.914574\pi$
$242$	1.25481	0.0806620
$243$	−1.00000	−0.0641500
$244$	−4.41351	−0.282546
$245$	−6.95492	−0.444334
$246$	−3.64964	−0.232693
$247$	12.1650	0.774038
$248$	−5.72455	−0.363510
$249$	−5.98663	−0.379388
$250$	1.09145	0.0690294
$251$	−23.5335	−1.48542	−0.742709	−	0.669614i	$-0.766460\pi$
$251$	−23.5335	−1.48542	−0.742709	+	0.669614i	$0.766460\pi$
$252$	−0.171710	−0.0108167
$253$	12.6223	0.793555
$254$	−6.62282	−0.415553
$255$	0.372693	0.0233389
$256$	−15.8081	−0.988008
$257$	10.0538	0.627139	0.313570	−	0.949565i	$-0.398475\pi$
$257$	10.0538	0.627139	0.313570	+	0.949565i	$0.398475\pi$
$258$	8.46660	0.527107
$259$	1.29295	0.0803397
$260$	2.66713	0.165408
$261$	−3.97126	−0.245815
$262$	8.54295	0.527785
$263$	−19.6548	−1.21197	−0.605983	−	0.795477i	$-0.707220\pi$
$263$	−19.6548	−1.21197	−0.605983	+	0.795477i	$0.707220\pi$
$264$	10.6856	0.657651
$265$	−3.04654	−0.187148
$266$	−0.854802	−0.0524113
$267$	6.80319	0.416348
$268$	9.65985	0.590069
$269$	6.07640	0.370485	0.185242	−	0.982693i	$-0.440693\pi$
$269$	6.07640	0.370485	0.185242	+	0.982693i	$0.440693\pi$
$270$	−1.09145	−0.0664236
$271$	−28.6134	−1.73814	−0.869069	−	0.494691i	$-0.835281\pi$
$271$	−28.6134	−1.73814	−0.869069	+	0.494691i	$0.835281\pi$
$272$	0.644191	0.0390598
$273$	0.700207	0.0423785
$274$	8.05180	0.486427
$275$	3.48564	0.210192
$276$	2.92861	0.176282
$277$	−6.39683	−0.384348	−0.192174	−	0.981361i	$-0.561554\pi$
$277$	−6.39683	−0.384348	−0.192174	+	0.981361i	$0.561554\pi$
$278$	−22.0573	−1.32291
$279$	1.86735	0.111796
$280$	−0.650884	−0.0388978
$281$	8.08508	0.482316	0.241158	−	0.970486i	$-0.422473\pi$
$281$	8.08508	0.482316	0.241158	+	0.970486i	$0.422473\pi$
$282$	−5.78146	−0.344281
$283$	−9.02654	−0.536572	−0.268286	−	0.963339i	$-0.586457\pi$
$283$	−9.02654	−0.536572	−0.268286	+	0.963339i	$0.586457\pi$
$284$	7.04471	0.418027
$285$	3.68869	0.218499
$286$	−12.5466	−0.741893
$287$	0.709961	0.0419077
$288$	4.24464	0.250118
$289$	−16.8611	−0.991829
$290$	−4.33443	−0.254527
$291$	−8.14205	−0.477295
$292$	10.3404	0.605124
$293$	−15.0151	−0.877190	−0.438595	−	0.898685i	$-0.644524\pi$
$293$	−15.0151	−0.877190	−0.438595	+	0.898685i	$0.644524\pi$
$294$	7.59095	0.442713
$295$	3.10621	0.180851
$296$	−18.6684	−1.08508
$297$	−3.48564	−0.202257
$298$	−6.35082	−0.367893
$299$	−11.9424	−0.690649
$300$	0.808735	0.0466923
$301$	−1.64700	−0.0949315
$302$	1.74464	0.100393
$303$	−3.90365	−0.224259
$304$	6.37582	0.365679
$305$	5.45729	0.312484
$306$	−0.406776	−0.0232538
$307$	−2.28299	−0.130297	−0.0651486	−	0.997876i	$-0.520752\pi$
$307$	−2.28299	−0.130297	−0.0651486	+	0.997876i	$0.520752\pi$
$308$	−0.598518	−0.0341037
$309$	−9.97657	−0.567547
$310$	2.03813	0.115758
$311$	−12.5134	−0.709569	−0.354785	−	0.934948i	$-0.615446\pi$
$311$	−12.5134	−0.709569	−0.354785	+	0.934948i	$0.615446\pi$
$312$	−10.1100	−0.572368
$313$	−22.1924	−1.25439	−0.627194	−	0.778863i	$-0.715797\pi$
$313$	−22.1924	−1.25439	−0.627194	+	0.778863i	$0.715797\pi$
$314$	−8.61183	−0.485994
$315$	0.212319	0.0119628
$316$	11.5427	0.649329
$317$	21.2329	1.19256	0.596279	−	0.802777i	$-0.296645\pi$
$317$	21.2329	1.19256	0.596279	+	0.802777i	$0.296645\pi$
$318$	3.32515	0.186465
$319$	−13.8424	−0.775024
$320$	8.08978	0.452232
$321$	9.29854	0.518994
$322$	0.839166	0.0467649
$323$	1.37475	0.0764931
$324$	−0.808735	−0.0449297
$325$	−3.29790	−0.182935
$326$	19.9353	1.10412
$327$	5.00170	0.276594
$328$	−10.2509	−0.566010
$329$	1.12466	0.0620046
$330$	−3.80440	−0.209425
$331$	28.0110	1.53962	0.769811	−	0.638272i	$-0.220351\pi$
$331$	28.0110	1.53962	0.769811	+	0.638272i	$0.220351\pi$
$332$	−4.84160	−0.265717
$333$	6.08964	0.333710
$334$	−17.9362	−0.981423
$335$	−11.9444	−0.652592
$336$	0.366988	0.0200209
$337$	18.6476	1.01580	0.507900	−	0.861416i	$-0.330422\pi$
$337$	18.6476	1.01580	0.507900	+	0.861416i	$0.330422\pi$
$338$	−2.31806	−0.126086
$339$	−10.5980	−0.575606
$340$	0.301410	0.0163462
$341$	6.50892	0.352478
$342$	−4.02603	−0.217703
$343$	−2.96289	−0.159981
$344$	23.7804	1.28216
$345$	−3.62122	−0.194960
$346$	15.3624	0.825888
$347$	−31.9778	−1.71666	−0.858328	−	0.513101i	$-0.828496\pi$
$347$	−31.9778	−1.71666	−0.858328	+	0.513101i	$0.828496\pi$
$348$	−3.21170	−0.172165
$349$	11.9019	0.637095	0.318547	−	0.947907i	$-0.396805\pi$
$349$	11.9019	0.637095	0.318547	+	0.947907i	$0.396805\pi$
$350$	0.231736	0.0123868
$351$	3.29790	0.176029
$352$	14.7953	0.788592
$353$	−30.9375	−1.64664	−0.823318	−	0.567581i	$-0.807879\pi$
$353$	−30.9375	−1.64664	−0.823318	+	0.567581i	$0.807879\pi$
$354$	−3.39028	−0.180191
$355$	−8.71078	−0.462320
$356$	5.50198	0.291604
$357$	0.0791297	0.00418799
$358$	−10.0708	−0.532258
$359$	−21.0161	−1.10919	−0.554594	−	0.832121i	$-0.687126\pi$
$359$	−21.0161	−1.10919	−0.554594	+	0.832121i	$0.687126\pi$
$360$	−3.06560	−0.161571
$361$	−5.39353	−0.283870
$362$	−25.7773	−1.35482
$363$	−1.14967	−0.0603419
$364$	0.566282	0.0296812
$365$	−12.7858	−0.669242
$366$	−5.95637	−0.311344
$367$	−3.63168	−0.189572	−0.0947861	−	0.995498i	$-0.530217\pi$
$367$	−3.63168	−0.189572	−0.0947861	+	0.995498i	$0.530217\pi$
$368$	−6.25920	−0.326283
$369$	3.34385	0.174074
$370$	6.64655	0.345537
$371$	−0.646839	−0.0335822
$372$	1.51019	0.0783000
$373$	2.57946	0.133559	0.0667796	−	0.997768i	$-0.478728\pi$
$373$	2.57946	0.133559	0.0667796	+	0.997768i	$0.478728\pi$
$374$	−1.41787	−0.0733165
$375$	−1.00000	−0.0516398
$376$	−16.2386	−0.837442
$377$	13.0968	0.674521
$378$	−0.231736	−0.0119192
$379$	36.6168	1.88088	0.940440	−	0.339959i	$-0.110413\pi$
$379$	36.6168	1.88088	0.940440	+	0.339959i	$0.110413\pi$
$380$	2.98318	0.153034
$381$	6.06791	0.310868
$382$	13.6050	0.696094
$383$	2.72772	0.139380	0.0696899	−	0.997569i	$-0.477799\pi$
$383$	2.72772	0.139380	0.0696899	+	0.997569i	$0.477799\pi$
$384$	−0.340303	−0.0173660
$385$	0.740067	0.0377173
$386$	−20.3435	−1.03546
$387$	−7.75720	−0.394321
$388$	−6.58476	−0.334290
$389$	−15.4226	−0.781955	−0.390978	−	0.920400i	$-0.627863\pi$
$389$	−15.4226	−0.781955	−0.390978	+	0.920400i	$0.627863\pi$
$390$	3.59950	0.182268
$391$	−1.34960	−0.0682524
$392$	21.3210	1.07687
$393$	−7.82715	−0.394827
$394$	−9.04845	−0.455854
$395$	−14.2726	−0.718131
$396$	−2.81896	−0.141658
$397$	−15.2841	−0.767085	−0.383543	−	0.923523i	$-0.625296\pi$
$397$	−15.2841	−0.767085	−0.383543	+	0.923523i	$0.625296\pi$
$398$	2.41009	0.120807
$399$	0.783179	0.0392080
$400$	−1.72848	−0.0864239
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	13.0367	0.650212
$403$	−6.15835	−0.306770
$404$	−3.15702	−0.157068
$405$	1.00000	0.0496904
$406$	−0.920282	−0.0456728
$407$	21.2263	1.05215
$408$	−1.14253	−0.0565635
$409$	−34.0282	−1.68259	−0.841293	−	0.540579i	$-0.818205\pi$
$409$	−34.0282	−1.68259	−0.841293	+	0.540579i	$0.818205\pi$
$410$	3.64964	0.180243
$411$	−7.37715	−0.363888
$412$	−8.06840	−0.397502
$413$	0.659508	0.0324523
$414$	3.95239	0.194249
$415$	5.98663	0.293872
$416$	−13.9984	−0.686329
$417$	20.2092	0.989647
$418$	−14.0333	−0.686390
$419$	31.6352	1.54548	0.772740	−	0.634722i	$-0.218885\pi$
$419$	31.6352	1.54548	0.772740	+	0.634722i	$0.218885\pi$
$420$	0.171710	0.00837858
$421$	−26.3251	−1.28301	−0.641503	−	0.767120i	$-0.721689\pi$
$421$	−26.3251	−1.28301	−0.641503	+	0.767120i	$0.721689\pi$
$422$	−6.16062	−0.299894
$423$	5.29704	0.257551
$424$	9.33948	0.453565
$425$	−0.372693	−0.0180783
$426$	9.50738	0.460634
$427$	1.15869	0.0560728
$428$	7.52005	0.363495
$429$	11.4953	0.554998
$430$	−8.46660	−0.408296
$431$	3.14130	0.151311	0.0756555	−	0.997134i	$-0.475895\pi$
$431$	3.14130	0.151311	0.0756555	+	0.997134i	$0.475895\pi$
$432$	1.72848	0.0831614
$433$	−20.3558	−0.978237	−0.489118	−	0.872217i	$-0.662681\pi$
$433$	−20.3558	−0.978237	−0.489118	+	0.872217i	$0.662681\pi$
$434$	0.432732	0.0207718
$435$	3.97126	0.190407
$436$	4.04505	0.193723
$437$	−13.3576	−0.638980
$438$	13.9551	0.666801
$439$	−3.59017	−0.171349	−0.0856747	−	0.996323i	$-0.527305\pi$
$439$	−3.59017	−0.171349	−0.0856747	+	0.996323i	$0.527305\pi$
$440$	−10.6856	−0.509414
$441$	−6.95492	−0.331187
$442$	1.34151	0.0638090
$443$	39.9856	1.89977	0.949887	−	0.312592i	$-0.101197\pi$
$443$	39.9856	1.89977	0.949887	+	0.312592i	$0.101197\pi$
$444$	4.92491	0.233726
$445$	−6.80319	−0.322502
$446$	6.45823	0.305806
$447$	5.81869	0.275215
$448$	1.71761	0.0811495
$449$	34.1369	1.61102	0.805510	−	0.592583i	$-0.201892\pi$
$449$	34.1369	1.61102	0.805510	+	0.592583i	$0.201892\pi$
$450$	1.09145	0.0514515
$451$	11.6554	0.548833
$452$	−8.57100	−0.403146
$453$	−1.59846	−0.0751021
$454$	13.4987	0.633528
$455$	−0.700207	−0.0328262
$456$	−11.3080	−0.529548
$457$	36.3528	1.70051	0.850257	−	0.526368i	$-0.176447\pi$
$457$	36.3528	1.70051	0.850257	+	0.526368i	$0.176447\pi$
$458$	7.63192	0.356616
$459$	0.372693	0.0173958
$460$	−2.92861	−0.136547
$461$	−3.94512	−0.183742	−0.0918712	−	0.995771i	$-0.529285\pi$
$461$	−3.94512	−0.183742	−0.0918712	+	0.995771i	$0.529285\pi$
$462$	−0.807746	−0.0375798
$463$	34.1585	1.58748	0.793740	−	0.608258i	$-0.208131\pi$
$463$	34.1585	1.58748	0.793740	+	0.608258i	$0.208131\pi$
$464$	6.86423	0.318664
$465$	−1.86735	−0.0865965
$466$	−5.33997	−0.247369
$467$	41.4550	1.91831	0.959155	−	0.282880i	$-0.0912898\pi$
$467$	41.4550	1.91831	0.959155	+	0.282880i	$0.0912898\pi$
$468$	2.66713	0.123288
$469$	−2.53602	−0.117102
$470$	5.78146	0.266679
$471$	7.89026	0.363564
$472$	−9.52240	−0.438304
$473$	−27.0388	−1.24324
$474$	15.5778	0.715512
$475$	−3.68869	−0.169249
$476$	0.0639950	0.00293321
$477$	−3.04654	−0.139492
$478$	−32.8185	−1.50108
$479$	−22.2540	−1.01681	−0.508405	−	0.861118i	$-0.669765\pi$
$479$	−22.2540	−1.01681	−0.508405	+	0.861118i	$0.669765\pi$
$480$	−4.24464	−0.193741
$481$	−20.0831	−0.915709
$482$	−32.6747	−1.48829
$483$	−0.768854	−0.0349841
$484$	−0.929777	−0.0422626
$485$	8.14205	0.369711
$486$	−1.09145	−0.0495092
$487$	10.1133	0.458279	0.229139	−	0.973394i	$-0.426409\pi$
$487$	10.1133	0.458279	0.229139	+	0.973394i	$0.426409\pi$
$488$	−16.7299	−0.757325
$489$	−18.2650	−0.825972
$490$	−7.59095	−0.342924
$491$	21.6694	0.977924	0.488962	−	0.872305i	$-0.337376\pi$
$491$	21.6694	0.977924	0.488962	+	0.872305i	$0.337376\pi$
$492$	2.70428	0.121919
$493$	1.48006	0.0666585
$494$	13.2775	0.597381
$495$	3.48564	0.156668
$496$	−3.22768	−0.144927
$497$	−1.84946	−0.0829597
$498$	−6.53412	−0.292801
$499$	−0.587417	−0.0262964	−0.0131482	−	0.999914i	$-0.504185\pi$
$499$	−0.587417	−0.0262964	−0.0131482	+	0.999914i	$0.504185\pi$
$500$	−0.808735	−0.0361677
$501$	16.4333	0.734186
$502$	−25.6856	−1.14640
$503$	−24.4198	−1.08883	−0.544413	−	0.838818i	$-0.683247\pi$
$503$	−24.4198	−1.08883	−0.544413	+	0.838818i	$0.683247\pi$
$504$	−0.650884	−0.0289927
$505$	3.90365	0.173710
$506$	13.7766	0.612444
$507$	2.12383	0.0943226
$508$	4.90733	0.217728
$509$	−36.0465	−1.59773	−0.798867	−	0.601507i	$-0.794567\pi$
$509$	−36.0465	−1.59773	−0.798867	+	0.601507i	$0.794567\pi$
$510$	0.406776	0.0180123
$511$	−2.71468	−0.120090
$512$	−17.9344	−0.792596
$513$	3.68869	0.162860
$514$	10.9732	0.484009
$515$	9.97657	0.439620
$516$	−6.27352	−0.276176
$517$	18.4636	0.812027
$518$	1.41119	0.0620040
$519$	−14.0752	−0.617833
$520$	10.1100	0.443355
$521$	10.0706	0.441199	0.220600	−	0.975364i	$-0.429199\pi$
$521$	10.0706	0.441199	0.220600	+	0.975364i	$0.429199\pi$
$522$	−4.33443	−0.189713
$523$	18.4419	0.806409	0.403205	−	0.915110i	$-0.367896\pi$
$523$	18.4419	0.806409	0.403205	+	0.915110i	$0.367896\pi$
$524$	−6.33009	−0.276531
$525$	−0.212319	−0.00926635
$526$	−21.4522	−0.935362
$527$	−0.695950	−0.0303160
$528$	6.02484	0.262198
$529$	−9.88675	−0.429858
$530$	−3.32515	−0.144435
$531$	3.10621	0.134798
$532$	0.633385	0.0274607
$533$	−11.0277	−0.477662
$534$	7.42534	0.321326
$535$	−9.29854	−0.402011
$536$	36.6167	1.58160
$537$	9.22698	0.398173
$538$	6.63210	0.285930
$539$	−24.2423	−1.04419
$540$	0.808735	0.0348024
$541$	30.1876	1.29787	0.648934	−	0.760845i	$-0.275215\pi$
$541$	30.1876	1.29787	0.648934	+	0.760845i	$0.275215\pi$
$542$	−31.2301	−1.34145
$543$	23.6174	1.01352
$544$	−1.58195	−0.0678255
$545$	−5.00170	−0.214249
$546$	0.764242	0.0327065
$547$	−20.9254	−0.894707	−0.447354	−	0.894357i	$-0.647633\pi$
$547$	−20.9254	−0.894707	−0.447354	+	0.894357i	$0.647633\pi$
$548$	−5.96616	−0.254862
$549$	5.45729	0.232912
$550$	3.80440	0.162220
$551$	14.6488	0.624058
$552$	11.1012	0.472499
$553$	−3.03033	−0.128863
$554$	−6.98182	−0.296629
$555$	−6.08964	−0.258491
$556$	16.3439	0.693134
$557$	−8.67959	−0.367766	−0.183883	−	0.982948i	$-0.558867\pi$
$557$	−8.67959	−0.367766	−0.183883	+	0.982948i	$0.558867\pi$
$558$	2.03813	0.0862807
$559$	25.5825	1.08202
$560$	−0.366988	−0.0155081
$561$	1.29907	0.0548469
$562$	8.82447	0.372238
$563$	17.7634	0.748639	0.374319	−	0.927300i	$-0.377876\pi$
$563$	17.7634	0.748639	0.374319	+	0.927300i	$0.377876\pi$
$564$	4.28391	0.180385
$565$	10.5980	0.445863
$566$	−9.85203	−0.414112
$567$	0.212319	0.00891655
$568$	26.7037	1.12046
$569$	28.2757	1.18538	0.592688	−	0.805432i	$-0.298067\pi$
$569$	28.2757	1.18538	0.592688	+	0.805432i	$0.298067\pi$
$570$	4.02603	0.168632
$571$	43.2531	1.81009	0.905044	−	0.425318i	$-0.139838\pi$
$571$	43.2531	1.81009	0.905044	+	0.425318i	$0.139838\pi$
$572$	9.29665	0.388712
$573$	−12.4651	−0.520737
$574$	0.774888	0.0323432
$575$	3.62122	0.151015
$576$	8.08978	0.337074
$577$	5.32244	0.221576	0.110788	−	0.993844i	$-0.464663\pi$
$577$	5.32244	0.221576	0.110788	+	0.993844i	$0.464663\pi$
$578$	−18.4031	−0.765466
$579$	18.6389	0.774608
$580$	3.21170	0.133358
$581$	1.27108	0.0527331
$582$	−8.88664	−0.368363
$583$	−10.6192	−0.439800
$584$	39.1962	1.62195
$585$	−3.29790	−0.136352
$586$	−16.3882	−0.676991
$587$	−17.8620	−0.737242	−0.368621	−	0.929580i	$-0.620170\pi$
$587$	−17.8620	−0.737242	−0.368621	+	0.929580i	$0.620170\pi$
$588$	−5.62469	−0.231958
$589$	−6.88810	−0.283819
$590$	3.39028	0.139576
$591$	8.29029	0.341017
$592$	−10.5258	−0.432608
$593$	43.5104	1.78676	0.893379	−	0.449304i	$-0.148328\pi$
$593$	43.5104	1.78676	0.893379	+	0.449304i	$0.148328\pi$
$594$	−3.80440	−0.156096
$595$	−0.0791297	−0.00324400
$596$	4.70578	0.192756
$597$	−2.20815	−0.0903736
$598$	−13.0346	−0.533024
$599$	36.7418	1.50123	0.750615	−	0.660740i	$-0.229757\pi$
$599$	36.7418	1.50123	0.750615	+	0.660740i	$0.229757\pi$
$600$	3.06560	0.125152
$601$	26.5887	1.08458	0.542289	−	0.840192i	$-0.317558\pi$
$601$	26.5887	1.08458	0.542289	+	0.840192i	$0.317558\pi$
$602$	−1.79762	−0.0732655
$603$	−11.9444	−0.486413
$604$	−1.29273	−0.0526004
$605$	1.14967	0.0467406
$606$	−4.26065	−0.173077
$607$	−20.9380	−0.849848	−0.424924	−	0.905229i	$-0.639699\pi$
$607$	−20.9380	−0.849848	−0.424924	+	0.905229i	$0.639699\pi$
$608$	−15.6572	−0.634983
$609$	0.843173	0.0341671
$610$	5.95637	0.241166
$611$	−17.4691	−0.706726
$612$	0.301410	0.0121838
$613$	−42.5198	−1.71736	−0.858679	−	0.512513i	$-0.828715\pi$
$613$	−42.5198	−1.71736	−0.858679	+	0.512513i	$0.828715\pi$
$614$	−2.49177	−0.100560
$615$	−3.34385	−0.134837
$616$	−2.26875	−0.0914103
$617$	32.3109	1.30079	0.650393	−	0.759598i	$-0.274604\pi$
$617$	32.3109	1.30079	0.650393	+	0.759598i	$0.274604\pi$
$618$	−10.8889	−0.438017
$619$	24.1664	0.971328	0.485664	−	0.874145i	$-0.338578\pi$
$619$	24.1664	0.971328	0.485664	+	0.874145i	$0.338578\pi$
$620$	−1.51019	−0.0606509
$621$	−3.62122	−0.145315
$622$	−13.6577	−0.547626
$623$	−1.44444	−0.0578705
$624$	−5.70035	−0.228197
$625$	1.00000	0.0400000
$626$	−24.2219	−0.968102
$627$	12.8575	0.513477
$628$	6.38113	0.254635
$629$	−2.26957	−0.0904935
$630$	0.231736	0.00923257
$631$	−28.4199	−1.13138	−0.565690	−	0.824618i	$-0.691390\pi$
$631$	−28.4199	−1.13138	−0.565690	+	0.824618i	$0.691390\pi$
$632$	43.7539	1.74044
$633$	5.64443	0.224346
$634$	23.1747	0.920383
$635$	−6.06791	−0.240798
$636$	−2.46385	−0.0976979
$637$	22.9367	0.908784
$638$	−15.1083	−0.598142
$639$	−8.71078	−0.344593
$640$	0.340303	0.0134516
$641$	18.6817	0.737883	0.368942	−	0.929453i	$-0.379720\pi$
$641$	18.6817	0.737883	0.368942	+	0.929453i	$0.379720\pi$
$642$	10.1489	0.400545
$643$	19.8363	0.782266	0.391133	−	0.920334i	$-0.372083\pi$
$643$	19.8363	0.782266	0.391133	+	0.920334i	$0.372083\pi$
$644$	−0.621799	−0.0245023
$645$	7.75720	0.305439
$646$	1.50047	0.0590353
$647$	4.77555	0.187746	0.0938730	−	0.995584i	$-0.470075\pi$
$647$	4.77555	0.187746	0.0938730	+	0.995584i	$0.470075\pi$
$648$	−3.06560	−0.120428
$649$	10.8271	0.425002
$650$	−3.59950	−0.141184
$651$	−0.396475	−0.0155391
$652$	−14.7715	−0.578498
$653$	45.3660	1.77531	0.887654	−	0.460510i	$-0.152334\pi$
$653$	45.3660	1.77531	0.887654	+	0.460510i	$0.152334\pi$
$654$	5.45911	0.213468
$655$	7.82715	0.305832
$656$	−5.77976	−0.225662
$657$	−12.7858	−0.498823
$658$	1.22751	0.0478535
$659$	11.4648	0.446607	0.223303	−	0.974749i	$-0.428316\pi$
$659$	11.4648	0.446607	0.223303	+	0.974749i	$0.428316\pi$
$660$	2.81896	0.109728
$661$	26.5936	1.03437	0.517186	−	0.855873i	$-0.326980\pi$
$661$	26.5936	1.03437	0.517186	+	0.855873i	$0.326980\pi$
$662$	30.5726	1.18824
$663$	−1.22911	−0.0477345
$664$	−18.3526	−0.712219
$665$	−0.783179	−0.0303704
$666$	6.64655	0.257548
$667$	−14.3808	−0.556827
$668$	13.2902	0.514213
$669$	−5.91710	−0.228768
$670$	−13.0367	−0.503652
$671$	19.0221	0.734342
$672$	−0.901218	−0.0347652
$673$	−15.5139	−0.598015	−0.299008	−	0.954251i	$-0.596656\pi$
$673$	−15.5139	−0.598015	−0.299008	+	0.954251i	$0.596656\pi$
$674$	20.3530	0.783967
$675$	−1.00000	−0.0384900
$676$	1.71762	0.0660621
$677$	−29.4259	−1.13093	−0.565464	−	0.824773i	$-0.691303\pi$
$677$	−29.4259	−1.13093	−0.565464	+	0.824773i	$0.691303\pi$
$678$	−11.5672	−0.444237
$679$	1.72871	0.0663418
$680$	1.14253	0.0438139
$681$	−12.3677	−0.473932
$682$	7.10417	0.272033
$683$	−3.91763	−0.149904	−0.0749521	−	0.997187i	$-0.523880\pi$
$683$	−3.91763	−0.149904	−0.0749521	+	0.997187i	$0.523880\pi$
$684$	2.98318	0.114065
$685$	7.37715	0.281867
$686$	−3.23385	−0.123469
$687$	−6.99246	−0.266779
$688$	13.4081	0.511181
$689$	10.0472	0.382768
$690$	−3.95239	−0.150465
$691$	−8.09089	−0.307792	−0.153896	−	0.988087i	$-0.549182\pi$
$691$	−8.09089	−0.307792	−0.153896	+	0.988087i	$0.549182\pi$
$692$	−11.3831	−0.432721
$693$	0.740067	0.0281128
$694$	−34.9022	−1.32487
$695$	−20.2092	−0.766578
$696$	−12.1743	−0.461465
$697$	−1.24623	−0.0472042
$698$	12.9904	0.491692
$699$	4.89254	0.185053
$700$	−0.171710	−0.00649002
$701$	−37.4790	−1.41556	−0.707780	−	0.706433i	$-0.750303\pi$
$701$	−37.4790	−1.41556	−0.707780	+	0.706433i	$0.750303\pi$
$702$	3.59950	0.135854
$703$	−22.4628	−0.847202
$704$	28.1980	1.06275
$705$	−5.29704	−0.199498
$706$	−33.7667	−1.27083
$707$	0.828819	0.0311710
$708$	2.51210	0.0944107
$709$	16.6358	0.624770	0.312385	−	0.949956i	$-0.398872\pi$
$709$	16.6358	0.624770	0.312385	+	0.949956i	$0.398872\pi$
$710$	−9.50738	−0.356806
$711$	−14.2726	−0.535263
$712$	20.8558	0.781605
$713$	6.76211	0.253243
$714$	0.0863662	0.00323217
$715$	−11.4953	−0.429900
$716$	7.46218	0.278875
$717$	30.0687	1.12294
$718$	−22.9380	−0.856040
$719$	−9.81846	−0.366167	−0.183083	−	0.983097i	$-0.558608\pi$
$719$	−9.81846	−0.366167	−0.183083	+	0.983097i	$0.558608\pi$
$720$	−1.72848	−0.0644165
$721$	2.11821	0.0788864
$722$	−5.88677	−0.219083
$723$	29.9369	1.11337
$724$	19.1003	0.709856
$725$	−3.97126	−0.147489
$726$	−1.25481	−0.0465702
$727$	−11.5182	−0.427188	−0.213594	−	0.976923i	$-0.568517\pi$
$727$	−11.5182	−0.427188	−0.213594	+	0.976923i	$0.568517\pi$
$728$	2.14655	0.0795565
$729$	1.00000	0.0370370
$730$	−13.9551	−0.516502
$731$	2.89105	0.106929
$732$	4.41351	0.163128
$733$	−22.1880	−0.819532	−0.409766	−	0.912191i	$-0.634390\pi$
$733$	−22.1880	−0.819532	−0.409766	+	0.912191i	$0.634390\pi$
$734$	−3.96380	−0.146307
$735$	6.95492	0.256536
$736$	15.3708	0.566575
$737$	−41.6338	−1.53360
$738$	3.64964	0.134345
$739$	0.282600	0.0103956	0.00519781	−	0.999986i	$-0.498345\pi$
$739$	0.282600	0.0103956	0.00519781	+	0.999986i	$0.498345\pi$
$740$	−4.92491	−0.181043
$741$	−12.1650	−0.446891
$742$	−0.705993	−0.0259178
$743$	39.9120	1.46423	0.732115	−	0.681181i	$-0.238533\pi$
$743$	39.9120	1.46423	0.732115	+	0.681181i	$0.238533\pi$
$744$	5.72455	0.209872
$745$	−5.81869	−0.213180
$746$	2.81535	0.103077
$747$	5.98663	0.219039
$748$	1.05061	0.0384139
$749$	−1.97425	−0.0721377
$750$	−1.09145	−0.0398541
$751$	19.2066	0.700858	0.350429	−	0.936589i	$-0.386036\pi$
$751$	19.2066	0.700858	0.350429	+	0.936589i	$0.386036\pi$
$752$	−9.15582	−0.333878
$753$	23.5335	0.857607
$754$	14.2945	0.520577
$755$	1.59846	0.0581738
$756$	0.171710	0.00624502
$757$	−36.8709	−1.34010	−0.670048	−	0.742318i	$-0.733726\pi$
$757$	−36.8709	−1.34010	−0.670048	+	0.742318i	$0.733726\pi$
$758$	39.9655	1.45161
$759$	−12.6223	−0.458159
$760$	11.3080	0.410186
$761$	1.35041	0.0489524	0.0244762	−	0.999700i	$-0.492208\pi$
$761$	1.35041	0.0489524	0.0244762	+	0.999700i	$0.492208\pi$
$762$	6.62282	0.239920
$763$	−1.06195	−0.0384453
$764$	−10.0810	−0.364716
$765$	−0.372693	−0.0134747
$766$	2.97717	0.107569
$767$	−10.2440	−0.369889
$768$	15.8081	0.570427
$769$	14.5117	0.523306	0.261653	−	0.965162i	$-0.415732\pi$
$769$	14.5117	0.523306	0.261653	+	0.965162i	$0.415732\pi$
$770$	0.807746	0.0291092
$771$	−10.0538	−0.362079
$772$	15.0740	0.542524
$773$	0.345183	0.0124154	0.00620769	−	0.999981i	$-0.498024\pi$
$773$	0.345183	0.0124154	0.00620769	+	0.999981i	$0.498024\pi$
$774$	−8.46660	−0.304326
$775$	1.86735	0.0670773
$776$	−24.9602	−0.896020
$777$	−1.29295	−0.0463842
$778$	−16.8330	−0.603491
$779$	−12.3344	−0.441927
$780$	−2.66713	−0.0954986
$781$	−30.3626	−1.08646
$782$	−1.47303	−0.0526753
$783$	3.97126	0.141921
$784$	12.0214	0.429337
$785$	−7.89026	−0.281615
$786$	−8.54295	−0.304717
$787$	8.57566	0.305689	0.152845	−	0.988250i	$-0.451157\pi$
$787$	8.57566	0.305689	0.152845	+	0.988250i	$0.451157\pi$
$788$	6.70465	0.238843
$789$	19.6548	0.699729
$790$	−15.5778	−0.554233
$791$	2.25016	0.0800066
$792$	−10.6856	−0.379695
$793$	−17.9976	−0.639115
$794$	−16.6818	−0.592015
$795$	3.04654	0.108050
$796$	−1.78581	−0.0632963
$797$	−13.4359	−0.475924	−0.237962	−	0.971274i	$-0.576479\pi$
$797$	−13.4359	−0.475924	−0.237962	+	0.971274i	$0.576479\pi$
$798$	0.854802	0.0302597
$799$	−1.97417	−0.0698411
$800$	4.24464	0.150071
$801$	−6.80319	−0.240379
$802$	1.09145	0.0385405
$803$	−44.5668	−1.57273
$804$	−9.65985	−0.340677
$805$	0.768854	0.0270985
$806$	−6.72154	−0.236756
$807$	−6.07640	−0.213900
$808$	−11.9670	−0.420999
$809$	−14.6650	−0.515593	−0.257796	−	0.966199i	$-0.582996\pi$
$809$	−14.6650	−0.515593	−0.257796	+	0.966199i	$0.582996\pi$
$810$	1.09145	0.0383497
$811$	−3.24677	−0.114010	−0.0570048	−	0.998374i	$-0.518155\pi$
$811$	−3.24677	−0.114010	−0.0570048	+	0.998374i	$0.518155\pi$
$812$	0.681904	0.0239301
$813$	28.6134	1.00351
$814$	23.1674	0.812019
$815$	18.2650	0.639795
$816$	−0.644191	−0.0225512
$817$	28.6139	1.00107
$818$	−37.1401	−1.29857
$819$	−0.700207	−0.0244672
$820$	−2.70428	−0.0944377
$821$	4.20346	0.146702	0.0733509	−	0.997306i	$-0.476631\pi$
$821$	4.20346	0.146702	0.0733509	+	0.997306i	$0.476631\pi$
$822$	−8.05180	−0.280839
$823$	−6.59971	−0.230051	−0.115026	−	0.993363i	$-0.536695\pi$
$823$	−6.59971	−0.230051	−0.115026	+	0.993363i	$0.536695\pi$
$824$	−30.5841	−1.06545
$825$	−3.48564	−0.121354
$826$	0.719820	0.0250457
$827$	−11.3932	−0.396179	−0.198089	−	0.980184i	$-0.563474\pi$
$827$	−11.3932	−0.396179	−0.198089	+	0.980184i	$0.563474\pi$
$828$	−2.92861	−0.101776
$829$	−6.52787	−0.226722	−0.113361	−	0.993554i	$-0.536162\pi$
$829$	−6.52787	−0.226722	−0.113361	+	0.993554i	$0.536162\pi$
$830$	6.53412	0.226803
$831$	6.39683	0.221903
$832$	−26.6793	−0.924938
$833$	2.59205	0.0898092
$834$	22.0573	0.763782
$835$	−16.4333	−0.568698
$836$	10.3983	0.359632
$837$	−1.86735	−0.0645452
$838$	34.5283	1.19276
$839$	−13.8468	−0.478044	−0.239022	−	0.971014i	$-0.576827\pi$
$839$	−13.8468	−0.478044	−0.239022	+	0.971014i	$0.576827\pi$
$840$	0.650884	0.0224576
$841$	−13.2291	−0.456176
$842$	−28.7325	−0.990189
$843$	−8.08508	−0.278465
$844$	4.56485	0.157129
$845$	−2.12383	−0.0730620
$846$	5.78146	0.198771
$847$	0.244096	0.00838724
$848$	5.26588	0.180831
$849$	9.02654	0.309790
$850$	−0.406776	−0.0139523
$851$	22.0520	0.755931
$852$	−7.04471	−0.241348
$853$	−15.5568	−0.532653	−0.266326	−	0.963883i	$-0.585810\pi$
$853$	−15.5568	−0.532653	−0.266326	+	0.963883i	$0.585810\pi$
$854$	1.26465	0.0432754
$855$	−3.68869	−0.126151
$856$	28.5056	0.974300
$857$	−42.5314	−1.45285	−0.726423	−	0.687248i	$-0.758819\pi$
$857$	−42.5314	−1.45285	−0.726423	+	0.687248i	$0.758819\pi$
$858$	12.5466	0.428332
$859$	28.8567	0.984578	0.492289	−	0.870432i	$-0.336160\pi$
$859$	28.8567	0.984578	0.492289	+	0.870432i	$0.336160\pi$
$860$	6.27352	0.213925
$861$	−0.709961	−0.0241954
$862$	3.42857	0.116778
$863$	−17.6596	−0.601141	−0.300571	−	0.953760i	$-0.597177\pi$
$863$	−17.6596	−0.601141	−0.300571	+	0.953760i	$0.597177\pi$
$864$	−4.24464	−0.144406
$865$	14.0752	0.478571
$866$	−22.2173	−0.754976
$867$	16.8611	0.572633
$868$	−0.320643	−0.0108833
$869$	−49.7490	−1.68762
$870$	4.33443	0.146951
$871$	39.3915	1.33473
$872$	15.3332	0.519247
$873$	8.14205	0.275566
$874$	−14.5791	−0.493147
$875$	0.212319	0.00717769
$876$	−10.3404	−0.349368
$877$	36.8602	1.24468	0.622341	−	0.782747i	$-0.286182\pi$
$877$	36.8602	1.24468	0.622341	+	0.782747i	$0.286182\pi$
$878$	−3.91849	−0.132243
$879$	15.0151	0.506446
$880$	−6.02484	−0.203097
$881$	−25.5980	−0.862418	−0.431209	−	0.902252i	$-0.641913\pi$
$881$	−25.5980	−0.862418	−0.431209	+	0.902252i	$0.641913\pi$
$882$	−7.59095	−0.255601
$883$	−9.20196	−0.309670	−0.154835	−	0.987940i	$-0.549485\pi$
$883$	−9.20196	−0.309670	−0.154835	+	0.987940i	$0.549485\pi$
$884$	−0.994021	−0.0334325
$885$	−3.10621	−0.104414
$886$	43.6424	1.46619
$887$	10.3702	0.348196	0.174098	−	0.984728i	$-0.444299\pi$
$887$	10.3702	0.348196	0.174098	+	0.984728i	$0.444299\pi$
$888$	18.6684	0.626470
$889$	−1.28833	−0.0432093
$890$	−7.42534	−0.248898
$891$	3.48564	0.116773
$892$	−4.78537	−0.160226
$893$	−19.5392	−0.653854
$894$	6.35082	0.212403
$895$	−9.22698	−0.308424
$896$	0.0722527	0.00241379
$897$	11.9424	0.398747
$898$	37.2587	1.24334
$899$	−7.41575	−0.247329
$900$	−0.808735	−0.0269578
$901$	1.13543	0.0378265
$902$	12.7213	0.423574
$903$	1.64700	0.0548087
$904$	−32.4893	−1.08058
$905$	−23.6174	−0.785071
$906$	−1.74464	−0.0579617
$907$	55.3978	1.83945	0.919727	−	0.392558i	$-0.128410\pi$
$907$	55.3978	1.83945	0.919727	+	0.392558i	$0.128410\pi$
$908$	−10.0022	−0.331935
$909$	3.90365	0.129476
$910$	−0.764242	−0.0253344
$911$	−54.8477	−1.81719	−0.908593	−	0.417682i	$-0.862843\pi$
$911$	−54.8477	−1.81719	−0.908593	+	0.417682i	$0.862843\pi$
$912$	−6.37582	−0.211125
$913$	20.8672	0.690605
$914$	39.6773	1.31241
$915$	−5.45729	−0.180413
$916$	−5.65504	−0.186848
$917$	1.66185	0.0548792
$918$	0.406776	0.0134256
$919$	59.0292	1.94719	0.973596	−	0.228277i	$-0.0733092\pi$
$919$	59.0292	1.94719	0.973596	+	0.228277i	$0.0733092\pi$
$920$	−11.1012	−0.365996
$921$	2.28299	0.0752272
$922$	−4.30590	−0.141807
$923$	28.7273	0.945571
$924$	0.598518	0.0196898
$925$	6.08964	0.200226
$926$	37.2823	1.22517
$927$	9.97657	0.327674
$928$	−16.8566	−0.553344
$929$	−0.901817	−0.0295877	−0.0147938	−	0.999891i	$-0.504709\pi$
$929$	−0.901817	−0.0295877	−0.0147938	+	0.999891i	$0.504709\pi$
$930$	−2.03813	−0.0668328
$931$	25.6546	0.840795
$932$	3.95677	0.129608
$933$	12.5134	0.409670
$934$	45.2461	1.48050
$935$	−1.29907	−0.0424842
$936$	10.1100	0.330457
$937$	−7.89840	−0.258029	−0.129015	−	0.991643i	$-0.541181\pi$
$937$	−7.89840	−0.258029	−0.129015	+	0.991643i	$0.541181\pi$
$938$	−2.76794	−0.0903765
$939$	22.1924	0.724221
$940$	−4.28391	−0.139726
$941$	51.1902	1.66875	0.834377	−	0.551195i	$-0.185828\pi$
$941$	51.1902	1.66875	0.834377	+	0.551195i	$0.185828\pi$
$942$	8.61183	0.280589
$943$	12.1088	0.394317
$944$	−5.36902	−0.174747
$945$	−0.212319	−0.00690673
$946$	−29.5115	−0.959502
$947$	19.8623	0.645438	0.322719	−	0.946495i	$-0.395403\pi$
$947$	19.8623	0.645438	0.322719	+	0.946495i	$0.395403\pi$
$948$	−11.5427	−0.374890
$949$	42.1665	1.36878
$950$	−4.02603	−0.130622
$951$	−21.2329	−0.688524
$952$	0.242580	0.00786206
$953$	7.77587	0.251885	0.125943	−	0.992038i	$-0.459804\pi$
$953$	7.77587	0.251885	0.125943	+	0.992038i	$0.459804\pi$
$954$	−3.32515	−0.107656
$955$	12.4651	0.403361
$956$	24.3176	0.786487
$957$	13.8424	0.447460
$958$	−24.2891	−0.784745
$959$	1.56631	0.0505788
$960$	−8.08978	−0.261096
$961$	−27.5130	−0.887516
$962$	−21.9197	−0.706718
$963$	−9.29854	−0.299641
$964$	24.2110	0.779785
$965$	−18.6389	−0.600009
$966$	−0.839166	−0.0269997
$967$	24.2449	0.779663	0.389831	−	0.920886i	$-0.372533\pi$
$967$	24.2449	0.779663	0.389831	+	0.920886i	$0.372533\pi$
$968$	−3.52442	−0.113279
$969$	−1.37475	−0.0441633
$970$	8.88664	0.285333
$971$	3.80032	0.121958	0.0609790	−	0.998139i	$-0.480578\pi$
$971$	3.80032	0.121958	0.0609790	+	0.998139i	$0.480578\pi$
$972$	0.808735	0.0259402
$973$	−4.29079	−0.137556
$974$	11.0382	0.353687
$975$	3.29790	0.105617
$976$	−9.43281	−0.301937
$977$	2.93362	0.0938547	0.0469274	−	0.998898i	$-0.485057\pi$
$977$	2.93362	0.0938547	0.0469274	+	0.998898i	$0.485057\pi$
$978$	−19.9353	−0.637462
$979$	−23.7134	−0.757885
$980$	5.62469	0.179674
$981$	−5.00170	−0.159692
$982$	23.6510	0.754735
$983$	8.93196	0.284885	0.142443	−	0.989803i	$-0.454504\pi$
$983$	8.93196	0.284885	0.142443	+	0.989803i	$0.454504\pi$
$984$	10.2509	0.326786
$985$	−8.29029	−0.264151
$986$	1.61541	0.0514452
$987$	−1.12466	−0.0357984
$988$	−9.83823	−0.312996
$989$	−28.0905	−0.893227
$990$	3.80440	0.120912
$991$	−7.60282	−0.241512	−0.120756	−	0.992682i	$-0.538532\pi$
$991$	−7.60282	−0.241512	−0.120756	+	0.992682i	$0.538532\pi$
$992$	7.92626	0.251659
$993$	−28.0110	−0.888901
$994$	−2.01860	−0.0640260
$995$	2.20815	0.0700031
$996$	4.84160	0.153412
$997$	55.2466	1.74968	0.874839	−	0.484414i	$-0.160967\pi$
$997$	55.2466	1.74968	0.874839	+	0.484414i	$0.160967\pi$
$998$	−0.641137	−0.0202948
$999$	−6.08964	−0.192668

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.20	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.20	✓	29	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)

\(f(q)\)	\(=\)	\(q+1.09145 q^{2} -1.00000 q^{3} -0.808735 q^{4} +1.00000 q^{5} -1.09145 q^{6} +0.212319 q^{7} -3.06560 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.09145 q^{2} -1.00000 q^{3} -0.808735 q^{4} +1.00000 q^{5} -1.09145 q^{6} +0.212319 q^{7} -3.06560 q^{8} +1.00000 q^{9} +1.09145 q^{10} +3.48564 q^{11} +0.808735 q^{12} -3.29790 q^{13} +0.231736 q^{14} -1.00000 q^{15} -1.72848 q^{16} -0.372693 q^{17} +1.09145 q^{18} -3.68869 q^{19} -0.808735 q^{20} -0.212319 q^{21} +3.80440 q^{22} +3.62122 q^{23} +3.06560 q^{24} +1.00000 q^{25} -3.59950 q^{26} -1.00000 q^{27} -0.171710 q^{28} -3.97126 q^{29} -1.09145 q^{30} +1.86735 q^{31} +4.24464 q^{32} -3.48564 q^{33} -0.406776 q^{34} +0.212319 q^{35} -0.808735 q^{36} +6.08964 q^{37} -4.02603 q^{38} +3.29790 q^{39} -3.06560 q^{40} +3.34385 q^{41} -0.231736 q^{42} -7.75720 q^{43} -2.81896 q^{44} +1.00000 q^{45} +3.95239 q^{46} +5.29704 q^{47} +1.72848 q^{48} -6.95492 q^{49} +1.09145 q^{50} +0.372693 q^{51} +2.66713 q^{52} -3.04654 q^{53} -1.09145 q^{54} +3.48564 q^{55} -0.650884 q^{56} +3.68869 q^{57} -4.33443 q^{58} +3.10621 q^{59} +0.808735 q^{60} +5.45729 q^{61} +2.03813 q^{62} +0.212319 q^{63} +8.08978 q^{64} -3.29790 q^{65} -3.80440 q^{66} -11.9444 q^{67} +0.301410 q^{68} -3.62122 q^{69} +0.231736 q^{70} -8.71078 q^{71} -3.06560 q^{72} -12.7858 q^{73} +6.64655 q^{74} -1.00000 q^{75} +2.98318 q^{76} +0.740067 q^{77} +3.59950 q^{78} -14.2726 q^{79} -1.72848 q^{80} +1.00000 q^{81} +3.64964 q^{82} +5.98663 q^{83} +0.171710 q^{84} -0.372693 q^{85} -8.46660 q^{86} +3.97126 q^{87} -10.6856 q^{88} -6.80319 q^{89} +1.09145 q^{90} -0.700207 q^{91} -2.92861 q^{92} -1.86735 q^{93} +5.78146 q^{94} -3.68869 q^{95} -4.24464 q^{96} +8.14205 q^{97} -7.59095 q^{98} +3.48564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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