LMFDB - Embedded newform 501.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [501,2,Mod(1,501)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(501, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("501.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 501 = 3 \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	501.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:	$4.00050514127$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 8x^{6} + 28x^{5} + 9x^{4} - 64x^{3} + 17x^{2} + 23x + 1 $ x^8 - 3x^7 - 8x^6 + 28x^5 + 9x^4 - 64x^3 + 17x^2 + 23*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.459587$ of defining polynomial
Character	$\chi$	$=$	501.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.459587 q^{2} +1.00000 q^{3} -1.78878 q^{4} -2.63865 q^{5} -0.459587 q^{6} -0.604857 q^{7} +1.74127 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.459587 q^{2} +1.00000 q^{3} -1.78878 q^{4} -2.63865 q^{5} -0.459587 q^{6} -0.604857 q^{7} +1.74127 q^{8} +1.00000 q^{9} +1.21269 q^{10} +4.18757 q^{11} -1.78878 q^{12} -0.588099 q^{13} +0.277984 q^{14} -2.63865 q^{15} +2.77729 q^{16} +3.13576 q^{17} -0.459587 q^{18} +3.33284 q^{19} +4.71996 q^{20} -0.604857 q^{21} -1.92456 q^{22} +2.06079 q^{23} +1.74127 q^{24} +1.96248 q^{25} +0.270283 q^{26} +1.00000 q^{27} +1.08196 q^{28} +10.1474 q^{29} +1.21269 q^{30} -1.00945 q^{31} -4.75896 q^{32} +4.18757 q^{33} -1.44116 q^{34} +1.59601 q^{35} -1.78878 q^{36} -0.963871 q^{37} -1.53173 q^{38} -0.588099 q^{39} -4.59462 q^{40} +10.0988 q^{41} +0.277984 q^{42} -1.46622 q^{43} -7.49065 q^{44} -2.63865 q^{45} -0.947114 q^{46} -3.81359 q^{47} +2.77729 q^{48} -6.63415 q^{49} -0.901929 q^{50} +3.13576 q^{51} +1.05198 q^{52} -2.52878 q^{53} -0.459587 q^{54} -11.0495 q^{55} -1.05322 q^{56} +3.33284 q^{57} -4.66361 q^{58} -3.70087 q^{59} +4.71996 q^{60} +0.962658 q^{61} +0.463931 q^{62} -0.604857 q^{63} -3.36743 q^{64} +1.55179 q^{65} -1.92456 q^{66} -6.12872 q^{67} -5.60919 q^{68} +2.06079 q^{69} -0.733504 q^{70} +4.34451 q^{71} +1.74127 q^{72} +13.8707 q^{73} +0.442983 q^{74} +1.96248 q^{75} -5.96172 q^{76} -2.53288 q^{77} +0.270283 q^{78} +9.16426 q^{79} -7.32830 q^{80} +1.00000 q^{81} -4.64129 q^{82} +15.6712 q^{83} +1.08196 q^{84} -8.27418 q^{85} +0.673854 q^{86} +10.1474 q^{87} +7.29172 q^{88} +5.57911 q^{89} +1.21269 q^{90} +0.355716 q^{91} -3.68630 q^{92} -1.00945 q^{93} +1.75268 q^{94} -8.79421 q^{95} -4.75896 q^{96} -6.60693 q^{97} +3.04897 q^{98} +4.18757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} + 8 q^{3} + 9 q^{4} + 7 q^{5} + 3 q^{6} - 4 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 3 * q^2 + 8 * q^3 + 9 * q^4 + 7 * q^5 + 3 * q^6 - 4 * q^7 + 3 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} + 8 q^{3} + 9 q^{4} + 7 q^{5} + 3 q^{6} - 4 q^{7} + 3 q^{8} + 8 q^{9} - q^{10} + 13 q^{11} + 9 q^{12} + 5 q^{14} + 7 q^{15} + 7 q^{16} + 11 q^{17} + 3 q^{18} + 12 q^{19} + 9 q^{20} - 4 q^{21} - 17 q^{22} + 7 q^{23} + 3 q^{24} - 5 q^{25} + 3 q^{26} + 8 q^{27} - 27 q^{28} + q^{29} - q^{30} - 2 q^{31} + 4 q^{32} + 13 q^{33} - 14 q^{34} - 4 q^{35} + 9 q^{36} - 9 q^{37} - 22 q^{40} + 4 q^{41} + 5 q^{42} + 2 q^{43} + 3 q^{44} + 7 q^{45} - 5 q^{46} + 17 q^{47} + 7 q^{48} - 2 q^{49} - 4 q^{50} + 11 q^{51} - 36 q^{52} + 9 q^{53} + 3 q^{54} + 7 q^{55} + 9 q^{56} + 12 q^{57} - 29 q^{58} + 29 q^{59} + 9 q^{60} - 12 q^{61} - 34 q^{62} - 4 q^{63} - 5 q^{64} + 8 q^{65} - 17 q^{66} + 26 q^{68} + 7 q^{69} + 5 q^{70} + 13 q^{71} + 3 q^{72} - 20 q^{73} - 17 q^{74} - 5 q^{75} + 30 q^{76} - 22 q^{77} + 3 q^{78} + 8 q^{79} - 34 q^{80} + 8 q^{81} + 15 q^{82} + 33 q^{83} - 27 q^{84} - 31 q^{85} + 11 q^{86} + q^{87} - 44 q^{88} + 4 q^{89} - q^{90} + q^{91} - 33 q^{92} - 2 q^{93} - 2 q^{94} + 3 q^{95} + 4 q^{96} - 31 q^{97} - 57 q^{98} + 13 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 8 * q^3 + 9 * q^4 + 7 * q^5 + 3 * q^6 - 4 * q^7 + 3 * q^8 + 8 * q^9 - q^10 + 13 * q^11 + 9 * q^12 + 5 * q^14 + 7 * q^15 + 7 * q^16 + 11 * q^17 + 3 * q^18 + 12 * q^19 + 9 * q^20 - 4 * q^21 - 17 * q^22 + 7 * q^23 + 3 * q^24 - 5 * q^25 + 3 * q^26 + 8 * q^27 - 27 * q^28 + q^29 - q^30 - 2 * q^31 + 4 * q^32 + 13 * q^33 - 14 * q^34 - 4 * q^35 + 9 * q^36 - 9 * q^37 - 22 * q^40 + 4 * q^41 + 5 * q^42 + 2 * q^43 + 3 * q^44 + 7 * q^45 - 5 * q^46 + 17 * q^47 + 7 * q^48 - 2 * q^49 - 4 * q^50 + 11 * q^51 - 36 * q^52 + 9 * q^53 + 3 * q^54 + 7 * q^55 + 9 * q^56 + 12 * q^57 - 29 * q^58 + 29 * q^59 + 9 * q^60 - 12 * q^61 - 34 * q^62 - 4 * q^63 - 5 * q^64 + 8 * q^65 - 17 * q^66 + 26 * q^68 + 7 * q^69 + 5 * q^70 + 13 * q^71 + 3 * q^72 - 20 * q^73 - 17 * q^74 - 5 * q^75 + 30 * q^76 - 22 * q^77 + 3 * q^78 + 8 * q^79 - 34 * q^80 + 8 * q^81 + 15 * q^82 + 33 * q^83 - 27 * q^84 - 31 * q^85 + 11 * q^86 + q^87 - 44 * q^88 + 4 * q^89 - q^90 + q^91 - 33 * q^92 - 2 * q^93 - 2 * q^94 + 3 * q^95 + 4 * q^96 - 31 * q^97 - 57 * 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 $

$2$	−0.459587	−0.324977	−0.162489	−	0.986710i	$-0.551952\pi$
$2$	−0.459587	−0.324977	−0.162489	+	0.986710i	$0.551952\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.78878	−0.894390
$5$	−2.63865	−1.18004	−0.590020	−	0.807388i	$-0.700880\pi$
$5$	−2.63865	−1.18004	−0.590020	+	0.807388i	$0.700880\pi$
$6$	−0.459587	−0.187626
$7$	−0.604857	−0.228614	−0.114307	−	0.993445i	$-0.536465\pi$
$7$	−0.604857	−0.228614	−0.114307	+	0.993445i	$0.536465\pi$
$8$	1.74127	0.615634
$9$	1.00000	0.333333
$10$	1.21269	0.383486
$11$	4.18757	1.26260	0.631301	−	0.775538i	$-0.282521\pi$
$11$	4.18757	1.26260	0.631301	+	0.775538i	$0.282521\pi$
$12$	−1.78878	−0.516376
$13$	−0.588099	−0.163109	−0.0815547	−	0.996669i	$-0.525989\pi$
$13$	−0.588099	−0.163109	−0.0815547	+	0.996669i	$0.525989\pi$
$14$	0.277984	0.0742945
$15$	−2.63865	−0.681297
$16$	2.77729	0.694323
$17$	3.13576	0.760534	0.380267	−	0.924877i	$-0.375832\pi$
$17$	3.13576	0.760534	0.380267	+	0.924877i	$0.375832\pi$
$18$	−0.459587	−0.108326
$19$	3.33284	0.764607	0.382303	−	0.924037i	$-0.375131\pi$
$19$	3.33284	0.764607	0.382303	+	0.924037i	$0.375131\pi$
$20$	4.71996	1.05542
$21$	−0.604857	−0.131991
$22$	−1.92456	−0.410317
$23$	2.06079	0.429705	0.214852	−	0.976647i	$-0.431073\pi$
$23$	2.06079	0.429705	0.214852	+	0.976647i	$0.431073\pi$
$24$	1.74127	0.355436
$25$	1.96248	0.392495
$26$	0.270283	0.0530069
$27$	1.00000	0.192450
$28$	1.08196	0.204470
$29$	10.1474	1.88432	0.942162	−	0.335158i	$-0.108790\pi$
$29$	10.1474	1.88432	0.942162	+	0.335158i	$0.108790\pi$
$30$	1.21269	0.221406
$31$	−1.00945	−0.181303	−0.0906515	−	0.995883i	$-0.528895\pi$
$31$	−1.00945	−0.181303	−0.0906515	+	0.995883i	$0.528895\pi$
$32$	−4.75896	−0.841273
$33$	4.18757	0.728963
$34$	−1.44116	−0.247156
$35$	1.59601	0.269774
$36$	−1.78878	−0.298130
$37$	−0.963871	−0.158459	−0.0792297	−	0.996856i	$-0.525246\pi$
$37$	−0.963871	−0.158459	−0.0792297	+	0.996856i	$0.525246\pi$
$38$	−1.53173	−0.248480
$39$	−0.588099	−0.0941713
$40$	−4.59462	−0.726473
$41$	10.0988	1.57717	0.788585	−	0.614926i	$-0.210814\pi$
$41$	10.0988	1.57717	0.788585	+	0.614926i	$0.210814\pi$
$42$	0.277984	0.0428939
$43$	−1.46622	−0.223596	−0.111798	−	0.993731i	$-0.535661\pi$
$43$	−1.46622	−0.223596	−0.111798	+	0.993731i	$0.535661\pi$
$44$	−7.49065	−1.12926
$45$	−2.63865	−0.393347
$46$	−0.947114	−0.139644
$47$	−3.81359	−0.556270	−0.278135	−	0.960542i	$-0.589716\pi$
$47$	−3.81359	−0.556270	−0.278135	+	0.960542i	$0.589716\pi$
$48$	2.77729	0.400867
$49$	−6.63415	−0.947735
$50$	−0.901929	−0.127552
$51$	3.13576	0.439094
$52$	1.05198	0.145883
$53$	−2.52878	−0.347354	−0.173677	−	0.984803i	$-0.555565\pi$
$53$	−2.52878	−0.347354	−0.173677	+	0.984803i	$0.555565\pi$
$54$	−0.459587	−0.0625419
$55$	−11.0495	−1.48992
$56$	−1.05322	−0.140743
$57$	3.33284	0.441446
$58$	−4.66361	−0.612362
$59$	−3.70087	−0.481812	−0.240906	−	0.970548i	$-0.577445\pi$
$59$	−3.70087	−0.481812	−0.240906	+	0.970548i	$0.577445\pi$
$60$	4.71996	0.609345
$61$	0.962658	0.123256	0.0616279	−	0.998099i	$-0.480371\pi$
$61$	0.962658	0.123256	0.0616279	+	0.998099i	$0.480371\pi$
$62$	0.463931	0.0589193
$63$	−0.604857	−0.0762048
$64$	−3.36743	−0.420928
$65$	1.55179	0.192476
$66$	−1.92456	−0.236896
$67$	−6.12872	−0.748742	−0.374371	−	0.927279i	$-0.622141\pi$
$67$	−6.12872	−0.748742	−0.374371	+	0.927279i	$0.622141\pi$
$68$	−5.60919	−0.680214
$69$	2.06079	0.248090
$70$	−0.733504	−0.0876705
$71$	4.34451	0.515599	0.257799	−	0.966198i	$-0.417003\pi$
$71$	4.34451	0.515599	0.257799	+	0.966198i	$0.417003\pi$
$72$	1.74127	0.205211
$73$	13.8707	1.62344	0.811721	−	0.584046i	$-0.198531\pi$
$73$	13.8707	1.62344	0.811721	+	0.584046i	$0.198531\pi$
$74$	0.442983	0.0514957
$75$	1.96248	0.226607
$76$	−5.96172	−0.683857
$77$	−2.53288	−0.288649
$78$	0.270283	0.0306035
$79$	9.16426	1.03106	0.515530	−	0.856872i	$-0.327595\pi$
$79$	9.16426	1.03106	0.515530	+	0.856872i	$0.327595\pi$
$80$	−7.32830	−0.819329
$81$	1.00000	0.111111
$82$	−4.64129	−0.512544
$83$	15.6712	1.72013	0.860067	−	0.510182i	$-0.170422\pi$
$83$	15.6712	1.72013	0.860067	+	0.510182i	$0.170422\pi$
$84$	1.08196	0.118051
$85$	−8.27418	−0.897461
$86$	0.673854	0.0726636
$87$	10.1474	1.08791
$88$	7.29172	0.777300
$89$	5.57911	0.591384	0.295692	−	0.955283i	$-0.404450\pi$
$89$	5.57911	0.591384	0.295692	+	0.955283i	$0.404450\pi$
$90$	1.21269	0.127829
$91$	0.355716	0.0372892
$92$	−3.68630	−0.384324
$93$	−1.00945	−0.104675
$94$	1.75268	0.180775
$95$	−8.79421	−0.902267
$96$	−4.75896	−0.485709
$97$	−6.60693	−0.670832	−0.335416	−	0.942070i	$-0.608877\pi$
$97$	−6.60693	−0.670832	−0.335416	+	0.942070i	$0.608877\pi$
$98$	3.04897	0.307992
$99$	4.18757	0.420867
$100$	−3.51044	−0.351044
$101$	0.212823	0.0211767	0.0105883	−	0.999944i	$-0.496630\pi$
$101$	0.212823	0.0211767	0.0105883	+	0.999944i	$0.496630\pi$
$102$	−1.44116	−0.142696
$103$	−1.50031	−0.147830	−0.0739150	−	0.997265i	$-0.523549\pi$
$103$	−1.50031	−0.147830	−0.0739150	+	0.997265i	$0.523549\pi$
$104$	−1.02404	−0.100416
$105$	1.59601	0.155754
$106$	1.16219	0.112882
$107$	−7.70835	−0.745194	−0.372597	−	0.927993i	$-0.621533\pi$
$107$	−7.70835	−0.745194	−0.372597	+	0.927993i	$0.621533\pi$
$108$	−1.78878	−0.172125
$109$	−19.3144	−1.84998	−0.924991	−	0.379988i	$-0.875928\pi$
$109$	−19.3144	−1.84998	−0.924991	+	0.379988i	$0.875928\pi$
$110$	5.07823	0.484190
$111$	−0.963871	−0.0914866
$112$	−1.67986	−0.158732
$113$	2.91046	0.273793	0.136896	−	0.990585i	$-0.456287\pi$
$113$	2.91046	0.273793	0.136896	+	0.990585i	$0.456287\pi$
$114$	−1.53173	−0.143460
$115$	−5.43771	−0.507069
$116$	−18.1515	−1.68532
$117$	−0.588099	−0.0543698
$118$	1.70087	0.156578
$119$	−1.89669	−0.173869
$120$	−4.59462	−0.419429
$121$	6.53578	0.594162
$122$	−0.442425	−0.0400553
$123$	10.0988	0.910580
$124$	1.80569	0.162156
$125$	8.01496	0.716880
$126$	0.277984	0.0247648
$127$	−11.5989	−1.02923	−0.514617	−	0.857420i	$-0.672066\pi$
$127$	−11.5989	−1.02923	−0.514617	+	0.857420i	$0.672066\pi$
$128$	11.0655	0.978065
$129$	−1.46622	−0.129093
$130$	−0.713182	−0.0625502
$131$	−8.26258	−0.721905	−0.360952	−	0.932584i	$-0.617548\pi$
$131$	−8.26258	−0.721905	−0.360952	+	0.932584i	$0.617548\pi$
$132$	−7.49065	−0.651977
$133$	−2.01589	−0.174800
$134$	2.81668	0.243324
$135$	−2.63865	−0.227099
$136$	5.46022	0.468210
$137$	6.10912	0.521937	0.260969	−	0.965347i	$-0.415958\pi$
$137$	6.10912	0.521937	0.260969	+	0.965347i	$0.415958\pi$
$138$	−0.947114	−0.0806237
$139$	14.8050	1.25574	0.627872	−	0.778317i	$-0.283926\pi$
$139$	14.8050	1.25574	0.627872	+	0.778317i	$0.283926\pi$
$140$	−2.85490	−0.241283
$141$	−3.81359	−0.321163
$142$	−1.99668	−0.167558
$143$	−2.46271	−0.205942
$144$	2.77729	0.231441
$145$	−26.7754	−2.22358
$146$	−6.37479	−0.527582
$147$	−6.63415	−0.547175
$148$	1.72415	0.141725
$149$	7.27551	0.596033	0.298017	−	0.954561i	$-0.403675\pi$
$149$	7.27551	0.596033	0.298017	+	0.954561i	$0.403675\pi$
$150$	−0.901929	−0.0736422
$151$	−6.77287	−0.551168	−0.275584	−	0.961277i	$-0.588871\pi$
$151$	−6.77287	−0.551168	−0.275584	+	0.961277i	$0.588871\pi$
$152$	5.80340	0.470718
$153$	3.13576	0.253511
$154$	1.16408	0.0938043
$155$	2.66359	0.213945
$156$	1.05198	0.0842258
$157$	−13.7559	−1.09784	−0.548919	−	0.835875i	$-0.684961\pi$
$157$	−13.7559	−1.09784	−0.548919	+	0.835875i	$0.684961\pi$
$158$	−4.21178	−0.335071
$159$	−2.52878	−0.200545
$160$	12.5572	0.992736
$161$	−1.24648	−0.0982367
$162$	−0.459587	−0.0361086
$163$	10.7400	0.841222	0.420611	−	0.907241i	$-0.361816\pi$
$163$	10.7400	0.841222	0.420611	+	0.907241i	$0.361816\pi$
$164$	−18.0646	−1.41060
$165$	−11.0495	−0.860206
$166$	−7.20227	−0.559004
$167$	−1.00000	−0.0773823
$167$	−1.00000	−0.0773823
$168$	−1.05322	−0.0812578
$169$	−12.6541	−0.973395
$170$	3.80271	0.291654
$171$	3.33284	0.254869
$172$	2.62274	0.199982
$173$	1.63924	0.124629	0.0623145	−	0.998057i	$-0.480152\pi$
$173$	1.63924	0.124629	0.0623145	+	0.998057i	$0.480152\pi$
$174$	−4.66361	−0.353548
$175$	−1.18702	−0.0897300
$176$	11.6301	0.876653
$177$	−3.70087	−0.278175
$178$	−2.56409	−0.192186
$179$	−19.0432	−1.42336	−0.711678	−	0.702505i	$-0.752065\pi$
$179$	−19.0432	−1.42336	−0.711678	+	0.702505i	$0.752065\pi$
$180$	4.71996	0.351805
$181$	14.7592	1.09704	0.548520	−	0.836138i	$-0.315192\pi$
$181$	14.7592	1.09704	0.548520	+	0.836138i	$0.315192\pi$
$182$	−0.163482	−0.0121181
$183$	0.962658	0.0711617
$184$	3.58841	0.264541
$185$	2.54332	0.186989
$186$	0.463931	0.0340171
$187$	13.1312	0.960251
$188$	6.82168	0.497522
$189$	−0.604857	−0.0439968
$190$	4.04171	0.293216
$191$	−8.24196	−0.596367	−0.298184	−	0.954508i	$-0.596381\pi$
$191$	−8.24196	−0.596367	−0.298184	+	0.954508i	$0.596381\pi$
$192$	−3.36743	−0.243023
$193$	12.4363	0.895186	0.447593	−	0.894237i	$-0.352281\pi$
$193$	12.4363	0.895186	0.447593	+	0.894237i	$0.352281\pi$
$194$	3.03646	0.218005
$195$	1.55179	0.111126
$196$	11.8670	0.847645
$197$	−18.4826	−1.31683	−0.658415	−	0.752655i	$-0.728773\pi$
$197$	−18.4826	−1.31683	−0.658415	+	0.752655i	$0.728773\pi$
$198$	−1.92456	−0.136772
$199$	4.83561	0.342787	0.171394	−	0.985203i	$-0.445173\pi$
$199$	4.83561	0.342787	0.171394	+	0.985203i	$0.445173\pi$
$200$	3.41721	0.241633
$201$	−6.12872	−0.432287
$202$	−0.0978107	−0.00688193
$203$	−6.13772	−0.430783
$204$	−5.60919	−0.392722
$205$	−26.6472	−1.86112
$206$	0.689523	0.0480414
$207$	2.06079	0.143235
$208$	−1.63332	−0.113251
$209$	13.9565	0.965394
$210$	−0.733504	−0.0506166
$211$	25.4148	1.74963	0.874814	−	0.484459i	$-0.160984\pi$
$211$	25.4148	1.74963	0.874814	+	0.484459i	$0.160984\pi$
$212$	4.52342	0.310670
$213$	4.34451	0.297681
$214$	3.54266	0.242171
$215$	3.86883	0.263852
$216$	1.74127	0.118479
$217$	0.610574	0.0414485
$218$	8.87664	0.601202
$219$	13.8707	0.937294
$220$	19.7652	1.33257
$221$	−1.84414	−0.124050
$222$	0.442983	0.0297311
$223$	13.4950	0.903692	0.451846	−	0.892096i	$-0.350766\pi$
$223$	13.4950	0.903692	0.451846	+	0.892096i	$0.350766\pi$
$224$	2.87849	0.192327
$225$	1.96248	0.130832
$226$	−1.33761	−0.0889765
$227$	22.1793	1.47209	0.736047	−	0.676930i	$-0.236690\pi$
$227$	22.1793	1.47209	0.736047	+	0.676930i	$0.236690\pi$
$228$	−5.96172	−0.394825
$229$	−8.65236	−0.571764	−0.285882	−	0.958265i	$-0.592287\pi$
$229$	−8.65236	−0.571764	−0.285882	+	0.958265i	$0.592287\pi$
$230$	2.49910	0.164786
$231$	−2.53288	−0.166651
$232$	17.6694	1.16005
$233$	−15.2852	−1.00136	−0.500682	−	0.865631i	$-0.666917\pi$
$233$	−15.2852	−1.00136	−0.500682	+	0.865631i	$0.666917\pi$
$234$	0.270283	0.0176690
$235$	10.0627	0.656421
$236$	6.62004	0.430928
$237$	9.16426	0.595282
$238$	0.871693	0.0565035
$239$	−29.8813	−1.93286	−0.966430	−	0.256930i	$-0.917289\pi$
$239$	−29.8813	−1.93286	−0.966430	+	0.256930i	$0.917289\pi$
$240$	−7.32830	−0.473040
$241$	17.5171	1.12837	0.564187	−	0.825647i	$-0.309190\pi$
$241$	17.5171	1.12837	0.564187	+	0.825647i	$0.309190\pi$
$242$	−3.00376	−0.193089
$243$	1.00000	0.0641500
$244$	−1.72198	−0.110239
$245$	17.5052	1.11837
$246$	−4.64129	−0.295918
$247$	−1.96004	−0.124715
$248$	−1.75773	−0.111616
$249$	15.6712	0.993119
$250$	−3.68357	−0.232970
$251$	11.5902	0.731567	0.365784	−	0.930700i	$-0.380801\pi$
$251$	11.5902	0.731567	0.365784	+	0.930700i	$0.380801\pi$
$252$	1.08196	0.0681568
$253$	8.62972	0.542546
$254$	5.33069	0.334477
$255$	−8.27418	−0.518149
$256$	1.64927	0.103079
$257$	−12.3462	−0.770137	−0.385069	−	0.922888i	$-0.625822\pi$
$257$	−12.3462	−0.770137	−0.385069	+	0.922888i	$0.625822\pi$
$258$	0.673854	0.0419523
$259$	0.583004	0.0362261
$260$	−2.77581	−0.172148
$261$	10.1474	0.628108
$262$	3.79738	0.234603
$263$	−10.9134	−0.672948	−0.336474	−	0.941693i	$-0.609234\pi$
$263$	−10.9134	−0.672948	−0.336474	+	0.941693i	$0.609234\pi$
$264$	7.29172	0.448774
$265$	6.67256	0.409892
$266$	0.926479	0.0568061
$267$	5.57911	0.341436
$268$	10.9629	0.669667
$269$	2.64700	0.161391	0.0806953	−	0.996739i	$-0.474286\pi$
$269$	2.64700	0.161391	0.0806953	+	0.996739i	$0.474286\pi$
$270$	1.21269	0.0738020
$271$	15.3534	0.932651	0.466326	−	0.884613i	$-0.345578\pi$
$271$	15.3534	0.932651	0.466326	+	0.884613i	$0.345578\pi$
$272$	8.70892	0.528056
$273$	0.355716	0.0215289
$274$	−2.80767	−0.169618
$275$	8.21802	0.495565
$276$	−3.68630	−0.221889
$277$	18.8696	1.13376	0.566881	−	0.823800i	$-0.308150\pi$
$277$	18.8696	1.13376	0.566881	+	0.823800i	$0.308150\pi$
$278$	−6.80419	−0.408088
$279$	−1.00945	−0.0604343
$280$	2.77908	0.166082
$281$	−2.41769	−0.144227	−0.0721136	−	0.997396i	$-0.522974\pi$
$281$	−2.41769	−0.144227	−0.0721136	+	0.997396i	$0.522974\pi$
$282$	1.75268	0.104371
$283$	−17.2449	−1.02510	−0.512551	−	0.858657i	$-0.671299\pi$
$283$	−17.2449	−1.02510	−0.512551	+	0.858657i	$0.671299\pi$
$284$	−7.77138	−0.461146
$285$	−8.79421	−0.520924
$286$	1.13183	0.0669265
$287$	−6.10834	−0.360564
$288$	−4.75896	−0.280424
$289$	−7.16700	−0.421588
$290$	12.3056	0.722612
$291$	−6.60693	−0.387305
$292$	−24.8116	−1.45199
$293$	−3.14330	−0.183634	−0.0918168	−	0.995776i	$-0.529267\pi$
$293$	−3.14330	−0.183634	−0.0918168	+	0.995776i	$0.529267\pi$
$294$	3.04897	0.177820
$295$	9.76531	0.568558
$296$	−1.67836	−0.0975530
$297$	4.18757	0.242988
$298$	−3.34373	−0.193697
$299$	−1.21195	−0.0700889
$300$	−3.51044	−0.202675
$301$	0.886850	0.0511172
$302$	3.11273	0.179117
$303$	0.212823	0.0122264
$304$	9.25628	0.530884
$305$	−2.54012	−0.145447
$306$	−1.44116	−0.0823854
$307$	27.5662	1.57329	0.786643	−	0.617409i	$-0.211818\pi$
$307$	27.5662	1.57329	0.786643	+	0.617409i	$0.211818\pi$
$308$	4.53077	0.258164
$309$	−1.50031	−0.0853497
$310$	−1.22415	−0.0695272
$311$	3.97921	0.225640	0.112820	−	0.993615i	$-0.464012\pi$
$311$	3.97921	0.225640	0.112820	+	0.993615i	$0.464012\pi$
$312$	−1.02404	−0.0579750
$313$	−15.9773	−0.903090	−0.451545	−	0.892248i	$-0.649127\pi$
$313$	−15.9773	−0.903090	−0.451545	+	0.892248i	$0.649127\pi$
$314$	6.32203	0.356773
$315$	1.59601	0.0899247
$316$	−16.3928	−0.922169
$317$	−25.4618	−1.43008	−0.715038	−	0.699086i	$-0.753590\pi$
$317$	−25.4618	−1.43008	−0.715038	+	0.699086i	$0.753590\pi$
$318$	1.16219	0.0651726
$319$	42.4930	2.37915
$320$	8.88546	0.496712
$321$	−7.70835	−0.430238
$322$	0.572868	0.0319247
$323$	10.4510	0.581509
$324$	−1.78878	−0.0993766
$325$	−1.15413	−0.0640197
$326$	−4.93597	−0.273378
$327$	−19.3144	−1.06809
$328$	17.5848	0.970959
$329$	2.30668	0.127171
$330$	5.07823	0.279547
$331$	−24.0840	−1.32378	−0.661889	−	0.749602i	$-0.730245\pi$
$331$	−24.0840	−1.32378	−0.661889	+	0.749602i	$0.730245\pi$
$332$	−28.0323	−1.53847
$333$	−0.963871	−0.0528198
$334$	0.459587	0.0251475
$335$	16.1715	0.883546
$336$	−1.67986	−0.0916441
$337$	−7.35478	−0.400641	−0.200320	−	0.979730i	$-0.564198\pi$
$337$	−7.35478	−0.400641	−0.200320	+	0.979730i	$0.564198\pi$
$338$	5.81568	0.316331
$339$	2.91046	0.158074
$340$	14.8007	0.802680
$341$	−4.22716	−0.228913
$342$	−1.53173	−0.0828266
$343$	8.24671	0.445280
$344$	−2.55308	−0.137653
$345$	−5.43771	−0.292756
$346$	−0.753373	−0.0405016
$347$	20.8836	1.12109	0.560544	−	0.828125i	$-0.310592\pi$
$347$	20.8836	1.12109	0.560544	+	0.828125i	$0.310592\pi$
$348$	−18.1515	−0.973020
$349$	−26.6111	−1.42446	−0.712229	−	0.701947i	$-0.752314\pi$
$349$	−26.6111	−1.42446	−0.712229	+	0.701947i	$0.752314\pi$
$350$	0.545538	0.0291602
$351$	−0.588099	−0.0313904
$352$	−19.9285	−1.06219
$353$	2.13148	0.113447	0.0567237	−	0.998390i	$-0.481935\pi$
$353$	2.13148	0.113447	0.0567237	+	0.998390i	$0.481935\pi$
$354$	1.70087	0.0904004
$355$	−11.4637	−0.608428
$356$	−9.97979	−0.528928
$357$	−1.89669	−0.100383
$358$	8.75202	0.462559
$359$	12.5447	0.662082	0.331041	−	0.943616i	$-0.392600\pi$
$359$	12.5447	0.662082	0.331041	+	0.943616i	$0.392600\pi$
$360$	−4.59462	−0.242158
$361$	−7.89215	−0.415376
$362$	−6.78312	−0.356513
$363$	6.53578	0.343040
$364$	−0.636297	−0.0333510
$365$	−36.5999	−1.91573
$366$	−0.442425	−0.0231259
$367$	−18.2125	−0.950686	−0.475343	−	0.879800i	$-0.657676\pi$
$367$	−18.2125	−0.950686	−0.475343	+	0.879800i	$0.657676\pi$
$368$	5.72342	0.298354
$369$	10.0988	0.525723
$370$	−1.16888	−0.0607670
$371$	1.52955	0.0794102
$372$	1.80569	0.0936205
$373$	24.0633	1.24595	0.622976	−	0.782241i	$-0.285923\pi$
$373$	24.0633	1.24595	0.622976	+	0.782241i	$0.285923\pi$
$374$	−6.03495	−0.312060
$375$	8.01496	0.413891
$376$	−6.64052	−0.342458
$377$	−5.96768	−0.307351
$378$	0.277984	0.0142980
$379$	18.1878	0.934243	0.467122	−	0.884193i	$-0.345291\pi$
$379$	18.1878	0.934243	0.467122	+	0.884193i	$0.345291\pi$
$380$	15.7309	0.806978
$381$	−11.5989	−0.594228
$382$	3.78790	0.193806
$383$	−21.9159	−1.11985	−0.559926	−	0.828542i	$-0.689171\pi$
$383$	−21.9159	−1.11985	−0.559926	+	0.828542i	$0.689171\pi$
$384$	11.0655	0.564686
$385$	6.68339	0.340617
$386$	−5.71558	−0.290915
$387$	−1.46622	−0.0745319
$388$	11.8183	0.599986
$389$	6.79088	0.344311	0.172156	−	0.985070i	$-0.444927\pi$
$389$	6.79088	0.344311	0.172156	+	0.985070i	$0.444927\pi$
$390$	−0.713182	−0.0361134
$391$	6.46215	0.326805
$392$	−11.5519	−0.583458
$393$	−8.26258	−0.416792
$394$	8.49436	0.427940
$395$	−24.1813	−1.21669
$396$	−7.49065	−0.376419
$397$	−36.3338	−1.82354	−0.911770	−	0.410701i	$-0.865284\pi$
$397$	−36.3338	−1.82354	−0.911770	+	0.410701i	$0.865284\pi$
$398$	−2.22238	−0.111398
$399$	−2.01589	−0.100921
$400$	5.45037	0.272518
$401$	−26.5238	−1.32453	−0.662267	−	0.749268i	$-0.730405\pi$
$401$	−26.5238	−1.32453	−0.662267	+	0.749268i	$0.730405\pi$
$402$	2.81668	0.140483
$403$	0.593658	0.0295722
$404$	−0.380693	−0.0189402
$405$	−2.63865	−0.131116
$406$	2.82082	0.139995
$407$	−4.03628	−0.200071
$408$	5.46022	0.270321
$409$	11.5743	0.572313	0.286157	−	0.958183i	$-0.407622\pi$
$409$	11.5743	0.572313	0.286157	+	0.958183i	$0.407622\pi$
$410$	12.2467	0.604823
$411$	6.10912	0.301341
$412$	2.68372	0.132218
$413$	2.23850	0.110149
$414$	−0.947114	−0.0465481
$415$	−41.3507	−2.02983
$416$	2.79874	0.137220
$417$	14.8050	0.725004
$418$	−6.41424	−0.313731
$419$	28.7087	1.40251	0.701256	−	0.712909i	$-0.252623\pi$
$419$	28.7087	1.40251	0.701256	+	0.712909i	$0.252623\pi$
$420$	−2.85490	−0.139305
$421$	−31.6417	−1.54212	−0.771061	−	0.636762i	$-0.780274\pi$
$421$	−31.6417	−1.54212	−0.771061	+	0.636762i	$0.780274\pi$
$422$	−11.6803	−0.568589
$423$	−3.81359	−0.185423
$424$	−4.40330	−0.213843
$425$	6.15386	0.298506
$426$	−1.99668	−0.0967396
$427$	−0.582270	−0.0281780
$428$	13.7885	0.666494
$429$	−2.46271	−0.118901
$430$	−1.77807	−0.0857459
$431$	27.0921	1.30498	0.652490	−	0.757798i	$-0.273725\pi$
$431$	27.0921	1.30498	0.652490	+	0.757798i	$0.273725\pi$
$432$	2.77729	0.133622
$433$	−37.9931	−1.82583	−0.912915	−	0.408150i	$-0.866174\pi$
$433$	−37.9931	−1.82583	−0.912915	+	0.408150i	$0.866174\pi$
$434$	−0.280612	−0.0134698
$435$	−26.7754	−1.28378
$436$	34.5492	1.65461
$437$	6.86830	0.328555
$438$	−6.37479	−0.304599
$439$	−27.8044	−1.32703	−0.663516	−	0.748162i	$-0.730937\pi$
$439$	−27.8044	−1.32703	−0.663516	+	0.748162i	$0.730937\pi$
$440$	−19.2403	−0.917245
$441$	−6.63415	−0.315912
$442$	0.847543	0.0403135
$443$	−7.02886	−0.333951	−0.166976	−	0.985961i	$-0.553400\pi$
$443$	−7.02886	−0.333951	−0.166976	+	0.985961i	$0.553400\pi$
$444$	1.72415	0.0818247
$445$	−14.7213	−0.697857
$446$	−6.20213	−0.293679
$447$	7.27551	0.344120
$448$	2.03681	0.0962303
$449$	6.19816	0.292509	0.146255	−	0.989247i	$-0.453278\pi$
$449$	6.19816	0.292509	0.146255	+	0.989247i	$0.453278\pi$
$450$	−0.901929	−0.0425173
$451$	42.2895	1.99134
$452$	−5.20617	−0.244878
$453$	−6.77287	−0.318217
$454$	−10.1933	−0.478397
$455$	−0.938610	−0.0440027
$456$	5.80340	0.271769
$457$	−24.9646	−1.16779	−0.583897	−	0.811828i	$-0.698473\pi$
$457$	−24.9646	−1.16779	−0.583897	+	0.811828i	$0.698473\pi$
$458$	3.97651	0.185810
$459$	3.13576	0.146365
$460$	9.72687	0.453517
$461$	33.7554	1.57215	0.786073	−	0.618134i	$-0.212111\pi$
$461$	33.7554	1.57215	0.786073	+	0.618134i	$0.212111\pi$
$462$	1.16408	0.0541579
$463$	17.1602	0.797502	0.398751	−	0.917059i	$-0.369444\pi$
$463$	17.1602	0.797502	0.398751	+	0.917059i	$0.369444\pi$
$464$	28.1823	1.30833
$465$	2.66359	0.123521
$466$	7.02486	0.325420
$467$	23.4137	1.08346	0.541728	−	0.840554i	$-0.317770\pi$
$467$	23.4137	1.08346	0.541728	+	0.840554i	$0.317770\pi$
$468$	1.05198	0.0486278
$469$	3.70700	0.171173
$470$	−4.62471	−0.213322
$471$	−13.7559	−0.633838
$472$	−6.44423	−0.296620
$473$	−6.13989	−0.282312
$474$	−4.21178	−0.193453
$475$	6.54063	0.300105
$476$	3.39275	0.155507
$477$	−2.52878	−0.115785
$478$	13.7331	0.628135
$479$	12.8820	0.588594	0.294297	−	0.955714i	$-0.404914\pi$
$479$	12.8820	0.588594	0.294297	+	0.955714i	$0.404914\pi$
$480$	12.5572	0.573156
$481$	0.566852	0.0258462
$482$	−8.05062	−0.366696
$483$	−1.24648	−0.0567170
$484$	−11.6911	−0.531412
$485$	17.4334	0.791609
$486$	−0.459587	−0.0208473
$487$	−37.7019	−1.70844	−0.854218	−	0.519915i	$-0.825963\pi$
$487$	−37.7019	−1.70844	−0.854218	+	0.519915i	$0.825963\pi$
$488$	1.67625	0.0758804
$489$	10.7400	0.485680
$490$	−8.04517	−0.363444
$491$	−12.3330	−0.556581	−0.278290	−	0.960497i	$-0.589768\pi$
$491$	−12.3330	−0.556581	−0.278290	+	0.960497i	$0.589768\pi$
$492$	−18.0646	−0.814413
$493$	31.8198	1.43309
$494$	0.900811	0.0405294
$495$	−11.0495	−0.496640
$496$	−2.80354	−0.125883
$497$	−2.62781	−0.117873
$498$	−7.20227	−0.322741
$499$	11.1753	0.500274	0.250137	−	0.968210i	$-0.419524\pi$
$499$	11.1753	0.500274	0.250137	+	0.968210i	$0.419524\pi$
$500$	−14.3370	−0.641170
$501$	−1.00000	−0.0446767
$502$	−5.32671	−0.237743
$503$	−27.2408	−1.21461	−0.607303	−	0.794470i	$-0.707748\pi$
$503$	−27.2408	−1.21461	−0.607303	+	0.794470i	$0.707748\pi$
$504$	−1.05322	−0.0469142
$505$	−0.561565	−0.0249893
$506$	−3.96611	−0.176315
$507$	−12.6541	−0.561990
$508$	20.7478	0.920536
$509$	8.83882	0.391774	0.195887	−	0.980627i	$-0.437241\pi$
$509$	8.83882	0.391774	0.195887	+	0.980627i	$0.437241\pi$
$510$	3.80271	0.168387
$511$	−8.38978	−0.371142
$512$	−22.8891	−1.01156
$513$	3.33284	0.147149
$514$	5.67417	0.250277
$515$	3.95879	0.174445
$516$	2.62274	0.115460
$517$	−15.9697	−0.702347
$518$	−0.267941	−0.0117727
$519$	1.63924	0.0719545
$520$	2.70209	0.118495
$521$	−35.2225	−1.54312	−0.771562	−	0.636154i	$-0.780524\pi$
$521$	−35.2225	−1.54312	−0.771562	+	0.636154i	$0.780524\pi$
$522$	−4.66361	−0.204121
$523$	0.251562	0.0110000	0.00550001	−	0.999985i	$-0.498249\pi$
$523$	0.251562	0.0110000	0.00550001	+	0.999985i	$0.498249\pi$
$524$	14.7799	0.645664
$525$	−1.18702	−0.0518057
$526$	5.01565	0.218693
$527$	−3.16540	−0.137887
$528$	11.6301	0.506136
$529$	−18.7531	−0.815354
$530$	−3.06662	−0.133206
$531$	−3.70087	−0.160604
$532$	3.60599	0.156339
$533$	−5.93911	−0.257251
$534$	−2.56409	−0.110959
$535$	20.3396	0.879359
$536$	−10.6718	−0.460951
$537$	−19.0432	−0.821775
$538$	−1.21653	−0.0524483
$539$	−27.7810	−1.19661
$540$	4.71996	0.203115
$541$	30.5799	1.31473	0.657366	−	0.753572i	$-0.271671\pi$
$541$	30.5799	1.31473	0.657366	+	0.753572i	$0.271671\pi$
$542$	−7.05622	−0.303090
$543$	14.7592	0.633376
$544$	−14.9230	−0.639816
$545$	50.9639	2.18305
$546$	−0.163482	−0.00699640
$547$	20.4268	0.873388	0.436694	−	0.899610i	$-0.356149\pi$
$547$	20.4268	0.873388	0.436694	+	0.899610i	$0.356149\pi$
$548$	−10.9279	−0.466815
$549$	0.962658	0.0410853
$550$	−3.77690	−0.161047
$551$	33.8197	1.44077
$552$	3.58841	0.152733
$553$	−5.54306	−0.235715
$554$	−8.67221	−0.368447
$555$	2.54332	0.107958
$556$	−26.4829	−1.12312
$557$	−4.28570	−0.181591	−0.0907956	−	0.995870i	$-0.528941\pi$
$557$	−4.28570	−0.181591	−0.0907956	+	0.995870i	$0.528941\pi$
$558$	0.463931	0.0196398
$559$	0.862281	0.0364706
$560$	4.43257	0.187310
$561$	13.1312	0.554401
$562$	1.11114	0.0468706
$563$	−34.7819	−1.46588	−0.732942	−	0.680292i	$-0.761853\pi$
$563$	−34.7819	−1.46588	−0.732942	+	0.680292i	$0.761853\pi$
$564$	6.82168	0.287245
$565$	−7.67968	−0.323087
$566$	7.92552	0.333135
$567$	−0.604857	−0.0254016
$568$	7.56499	0.317420
$569$	1.01037	0.0423571	0.0211785	−	0.999776i	$-0.493258\pi$
$569$	1.01037	0.0423571	0.0211785	+	0.999776i	$0.493258\pi$
$570$	4.04171	0.169288
$571$	4.17041	0.174526	0.0872632	−	0.996185i	$-0.472188\pi$
$571$	4.17041	0.174526	0.0872632	+	0.996185i	$0.472188\pi$
$572$	4.40525	0.184193
$573$	−8.24196	−0.344313
$574$	2.80731	0.117175
$575$	4.04426	0.168657
$576$	−3.36743	−0.140309
$577$	−22.0426	−0.917647	−0.458824	−	0.888527i	$-0.651729\pi$
$577$	−22.0426	−0.917647	−0.458824	+	0.888527i	$0.651729\pi$
$578$	3.29386	0.137007
$579$	12.4363	0.516836
$580$	47.8953	1.98875
$581$	−9.47881	−0.393247
$582$	3.03646	0.125865
$583$	−10.5894	−0.438570
$584$	24.1527	0.999445
$585$	1.55179	0.0641586
$586$	1.44462	0.0596767
$587$	2.82344	0.116536	0.0582678	−	0.998301i	$-0.481442\pi$
$587$	2.82344	0.116536	0.0582678	+	0.998301i	$0.481442\pi$
$588$	11.8670	0.489388
$589$	−3.36435	−0.138626
$590$	−4.48801	−0.184768
$591$	−18.4826	−0.760272
$592$	−2.67695	−0.110022
$593$	−45.6709	−1.87548	−0.937740	−	0.347339i	$-0.887085\pi$
$593$	−45.6709	−1.87548	−0.937740	+	0.347339i	$0.887085\pi$
$594$	−1.92456	−0.0789655
$595$	5.00469	0.205172
$596$	−13.0143	−0.533086
$597$	4.83561	0.197908
$598$	0.556997	0.0227773
$599$	37.8313	1.54575	0.772873	−	0.634561i	$-0.218819\pi$
$599$	37.8313	1.54575	0.772873	+	0.634561i	$0.218819\pi$
$600$	3.41721	0.139507
$601$	−6.83325	−0.278734	−0.139367	−	0.990241i	$-0.544507\pi$
$601$	−6.83325	−0.278734	−0.139367	+	0.990241i	$0.544507\pi$
$602$	−0.407585	−0.0166119
$603$	−6.12872	−0.249581
$604$	12.1152	0.492959
$605$	−17.2456	−0.701135
$606$	−0.0978107	−0.00397329
$607$	−22.9026	−0.929587	−0.464794	−	0.885419i	$-0.653872\pi$
$607$	−22.9026	−0.929587	−0.464794	+	0.885419i	$0.653872\pi$
$608$	−15.8609	−0.643243
$609$	−6.13772	−0.248713
$610$	1.16741	0.0472669
$611$	2.24277	0.0907329
$612$	−5.60919	−0.226738
$613$	−5.01302	−0.202474	−0.101237	−	0.994862i	$-0.532280\pi$
$613$	−5.01302	−0.202474	−0.101237	+	0.994862i	$0.532280\pi$
$614$	−12.6691	−0.511282
$615$	−26.6472	−1.07452
$616$	−4.41044	−0.177702
$617$	−21.2112	−0.853931	−0.426966	−	0.904268i	$-0.640417\pi$
$617$	−21.2112	−0.853931	−0.426966	+	0.904268i	$0.640417\pi$
$618$	0.689523	0.0277367
$619$	12.4720	0.501290	0.250645	−	0.968079i	$-0.419357\pi$
$619$	12.4720	0.501290	0.250645	+	0.968079i	$0.419357\pi$
$620$	−4.76458	−0.191350
$621$	2.06079	0.0826967
$622$	−1.82880	−0.0733280
$623$	−3.37456	−0.135199
$624$	−1.63332	−0.0653853
$625$	−30.9611	−1.23844
$626$	7.34296	0.293484
$627$	13.9565	0.557370
$628$	24.6062	0.981896
$629$	−3.02247	−0.120514
$630$	−0.733504	−0.0292235
$631$	43.7516	1.74172	0.870862	−	0.491528i	$-0.163561\pi$
$631$	43.7516	1.74172	0.870862	+	0.491528i	$0.163561\pi$
$632$	15.9575	0.634755
$633$	25.4148	1.01015
$634$	11.7019	0.464742
$635$	30.6054	1.21454
$636$	4.52342	0.179365
$637$	3.90154	0.154585
$638$	−19.5292	−0.773170
$639$	4.34451	0.171866
$640$	−29.1981	−1.15416
$641$	14.2570	0.563116	0.281558	−	0.959544i	$-0.409149\pi$
$641$	14.2570	0.563116	0.281558	+	0.959544i	$0.409149\pi$
$642$	3.54266	0.139818
$643$	−32.7973	−1.29340	−0.646699	−	0.762745i	$-0.723851\pi$
$643$	−32.7973	−1.29340	−0.646699	+	0.762745i	$0.723851\pi$
$644$	2.22968	0.0878619
$645$	3.86883	0.152335
$646$	−4.80315	−0.188977
$647$	−2.71497	−0.106736	−0.0533682	−	0.998575i	$-0.516996\pi$
$647$	−2.71497	−0.106736	−0.0533682	+	0.998575i	$0.516996\pi$
$648$	1.74127	0.0684037
$649$	−15.4977	−0.608337
$650$	0.530424	0.0208049
$651$	0.610574	0.0239303
$652$	−19.2115	−0.752381
$653$	0.282536	0.0110565	0.00552825	−	0.999985i	$-0.498240\pi$
$653$	0.282536	0.0110565	0.00552825	+	0.999985i	$0.498240\pi$
$654$	8.87664	0.347104
$655$	21.8021	0.851877
$656$	28.0474	1.09507
$657$	13.8707	0.541147
$658$	−1.06012	−0.0413278
$659$	2.66474	0.103804	0.0519018	−	0.998652i	$-0.483472\pi$
$659$	2.66474	0.103804	0.0519018	+	0.998652i	$0.483472\pi$
$660$	19.7652	0.769359
$661$	22.1445	0.861321	0.430660	−	0.902514i	$-0.358281\pi$
$661$	22.1445	0.861321	0.430660	+	0.902514i	$0.358281\pi$
$662$	11.0687	0.430198
$663$	−1.84414	−0.0716204
$664$	27.2878	1.05897
$665$	5.31924	0.206271
$666$	0.442983	0.0171652
$667$	20.9117	0.809703
$668$	1.78878	0.0692100
$669$	13.4950	0.521747
$670$	−7.43224	−0.287132
$671$	4.03120	0.155623
$672$	2.87849	0.111040
$673$	−13.6686	−0.526886	−0.263443	−	0.964675i	$-0.584858\pi$
$673$	−13.6686	−0.526886	−0.263443	+	0.964675i	$0.584858\pi$
$674$	3.38016	0.130199
$675$	1.96248	0.0755358
$676$	22.6355	0.870595
$677$	−5.36889	−0.206343	−0.103172	−	0.994664i	$-0.532899\pi$
$677$	−5.36889	−0.206343	−0.103172	+	0.994664i	$0.532899\pi$
$678$	−1.33761	−0.0513706
$679$	3.99625	0.153362
$680$	−14.4076	−0.552507
$681$	22.1793	0.849914
$682$	1.94275	0.0743916
$683$	−35.4099	−1.35492	−0.677460	−	0.735559i	$-0.736919\pi$
$683$	−35.4099	−1.35492	−0.677460	+	0.735559i	$0.736919\pi$
$684$	−5.96172	−0.227952
$685$	−16.1198	−0.615907
$686$	−3.79008	−0.144706
$687$	−8.65236	−0.330108
$688$	−4.07211	−0.155248
$689$	1.48717	0.0566567
$690$	2.49910	0.0951392
$691$	2.30779	0.0877924	0.0438962	−	0.999036i	$-0.486023\pi$
$691$	2.30779	0.0877924	0.0438962	+	0.999036i	$0.486023\pi$
$692$	−2.93223	−0.111467
$693$	−2.53288	−0.0962163
$694$	−9.59782	−0.364328
$695$	−39.0652	−1.48183
$696$	17.6694	0.669757
$697$	31.6675	1.19949
$698$	12.2301	0.462916
$699$	−15.2852	−0.578138
$700$	2.12331	0.0802536
$701$	−18.6519	−0.704474	−0.352237	−	0.935911i	$-0.614579\pi$
$701$	−18.6519	−0.704474	−0.352237	+	0.935911i	$0.614579\pi$
$702$	0.270283	0.0102012
$703$	−3.21243	−0.121159
$704$	−14.1014	−0.531465
$705$	10.0627	0.378985
$706$	−0.979602	−0.0368678
$707$	−0.128727	−0.00484129
$708$	6.62004	0.248796
$709$	−8.83611	−0.331847	−0.165924	−	0.986139i	$-0.553061\pi$
$709$	−8.83611	−0.331847	−0.165924	+	0.986139i	$0.553061\pi$
$710$	5.26855	0.197725
$711$	9.16426	0.343686
$712$	9.71476	0.364076
$713$	−2.08027	−0.0779068
$714$	0.871693	0.0326223
$715$	6.49823	0.243020
$716$	34.0641	1.27304
$717$	−29.8813	−1.11594
$718$	−5.76537	−0.215162
$719$	17.8566	0.665940	0.332970	−	0.942937i	$-0.391949\pi$
$719$	17.8566	0.665940	0.332970	+	0.942937i	$0.391949\pi$
$720$	−7.32830	−0.273110
$721$	0.907473	0.0337960
$722$	3.62713	0.134988
$723$	17.5171	0.651466
$724$	−26.4009	−0.981181
$725$	19.9140	0.739588
$726$	−3.00376	−0.111480
$727$	−20.2602	−0.751409	−0.375704	−	0.926740i	$-0.622599\pi$
$727$	−20.2602	−0.751409	−0.375704	+	0.926740i	$0.622599\pi$
$728$	0.619399	0.0229565
$729$	1.00000	0.0370370
$730$	16.8208	0.622567
$731$	−4.59770	−0.170052
$732$	−1.72198	−0.0636463
$733$	−16.9048	−0.624394	−0.312197	−	0.950017i	$-0.601065\pi$
$733$	−16.9048	−0.624394	−0.312197	+	0.950017i	$0.601065\pi$
$734$	8.37025	0.308951
$735$	17.5052	0.645689
$736$	−9.80722	−0.361499
$737$	−25.6645	−0.945363
$738$	−4.64129	−0.170848
$739$	−35.1818	−1.29418	−0.647092	−	0.762412i	$-0.724015\pi$
$739$	−35.1818	−1.29418	−0.647092	+	0.762412i	$0.724015\pi$
$740$	−4.54944	−0.167241
$741$	−1.96004	−0.0720040
$742$	−0.702961	−0.0258065
$743$	29.8016	1.09331	0.546657	−	0.837356i	$-0.315900\pi$
$743$	29.8016	1.09331	0.546657	+	0.837356i	$0.315900\pi$
$744$	−1.75773	−0.0644417
$745$	−19.1975	−0.703343
$746$	−11.0592	−0.404906
$747$	15.6712	0.573378
$748$	−23.4889	−0.858839
$749$	4.66245	0.170362
$750$	−3.68357	−0.134505
$751$	−41.8463	−1.52699	−0.763497	−	0.645812i	$-0.776519\pi$
$751$	−41.8463	−1.52699	−0.763497	+	0.645812i	$0.776519\pi$
$752$	−10.5915	−0.386231
$753$	11.5902	0.422371
$754$	2.74267	0.0998821
$755$	17.8712	0.650401
$756$	1.08196	0.0393503
$757$	20.1667	0.732973	0.366486	−	0.930423i	$-0.380561\pi$
$757$	20.1667	0.732973	0.366486	+	0.930423i	$0.380561\pi$
$758$	−8.35887	−0.303608
$759$	8.62972	0.313239
$760$	−15.3131	−0.555466
$761$	−47.8942	−1.73616	−0.868082	−	0.496421i	$-0.834647\pi$
$761$	−47.8942	−1.73616	−0.868082	+	0.496421i	$0.834647\pi$
$762$	5.33069	0.193111
$763$	11.6824	0.422933
$764$	14.7431	0.533385
$765$	−8.27418	−0.299154
$766$	10.0723	0.363927
$767$	2.17648	0.0785881
$768$	1.64927	0.0595130
$769$	12.1859	0.439433	0.219717	−	0.975564i	$-0.429487\pi$
$769$	12.1859	0.439433	0.219717	+	0.975564i	$0.429487\pi$
$770$	−3.07160	−0.110693
$771$	−12.3462	−0.444639
$772$	−22.2458	−0.800646
$773$	47.6169	1.71266	0.856331	−	0.516427i	$-0.172738\pi$
$773$	47.6169	1.71266	0.856331	+	0.516427i	$0.172738\pi$
$774$	0.673854	0.0242212
$775$	−1.98103	−0.0711606
$776$	−11.5045	−0.412987
$777$	0.583004	0.0209151
$778$	−3.12100	−0.111893
$779$	33.6578	1.20592
$780$	−2.77581	−0.0993899
$781$	18.1930	0.650996
$782$	−2.96992	−0.106204
$783$	10.1474	0.362638
$784$	−18.4250	−0.658034
$785$	36.2970	1.29549
$786$	3.79738	0.135448
$787$	−25.4329	−0.906586	−0.453293	−	0.891361i	$-0.649751\pi$
$787$	−25.4329	−0.906586	−0.453293	+	0.891361i	$0.649751\pi$
$788$	33.0613	1.17776
$789$	−10.9134	−0.388527
$790$	11.1134	0.395397
$791$	−1.76041	−0.0625930
$792$	7.29172	0.259100
$793$	−0.566139	−0.0201042
$794$	16.6985	0.592609
$795$	6.67256	0.236651
$796$	−8.64984	−0.306585
$797$	13.4752	0.477315	0.238658	−	0.971104i	$-0.423293\pi$
$797$	13.4752	0.477315	0.238658	+	0.971104i	$0.423293\pi$
$798$	0.926479	0.0327970
$799$	−11.9585	−0.423062
$800$	−9.33934	−0.330196
$801$	5.57911	0.197128
$802$	12.1900	0.430443
$803$	58.0845	2.04976
$804$	10.9629	0.386633
$805$	3.28904	0.115923
$806$	−0.272838	−0.00961030
$807$	2.64700	0.0931789
$808$	0.370583	0.0130371
$809$	−17.0866	−0.600732	−0.300366	−	0.953824i	$-0.597109\pi$
$809$	−17.0866	−0.600732	−0.300366	+	0.953824i	$0.597109\pi$
$810$	1.21269	0.0426096
$811$	18.7124	0.657080	0.328540	−	0.944490i	$-0.393443\pi$
$811$	18.7124	0.657080	0.328540	+	0.944490i	$0.393443\pi$
$812$	10.9790	0.385288
$813$	15.3534	0.538466
$814$	1.85502	0.0650186
$815$	−28.3391	−0.992676
$816$	8.70892	0.304873
$817$	−4.88667	−0.170963
$818$	−5.31941	−0.185989
$819$	0.355716	0.0124297
$820$	47.6660	1.66457
$821$	43.7257	1.52604	0.763019	−	0.646377i	$-0.223716\pi$
$821$	43.7257	1.52604	0.763019	+	0.646377i	$0.223716\pi$
$822$	−2.80767	−0.0979288
$823$	−20.6687	−0.720466	−0.360233	−	0.932862i	$-0.617303\pi$
$823$	−20.6687	−0.720466	−0.360233	+	0.932862i	$0.617303\pi$
$824$	−2.61245	−0.0910091
$825$	8.21802	0.286115
$826$	−1.02878	−0.0357960
$827$	53.5678	1.86274	0.931368	−	0.364080i	$-0.118617\pi$
$827$	53.5678	1.86274	0.931368	+	0.364080i	$0.118617\pi$
$828$	−3.68630	−0.128108
$829$	8.09767	0.281244	0.140622	−	0.990063i	$-0.455090\pi$
$829$	8.09767	0.281244	0.140622	+	0.990063i	$0.455090\pi$
$830$	19.0043	0.659648
$831$	18.8696	0.654578
$832$	1.98038	0.0686574
$833$	−20.8031	−0.720785
$834$	−6.80419	−0.235610
$835$	2.63865	0.0913143
$836$	−24.9652	−0.863438
$837$	−1.00945	−0.0348918
$838$	−13.1942	−0.455785
$839$	35.9455	1.24098	0.620489	−	0.784215i	$-0.286934\pi$
$839$	35.9455	1.24098	0.620489	+	0.784215i	$0.286934\pi$
$840$	2.77908	0.0958875
$841$	73.9696	2.55068
$842$	14.5421	0.501154
$843$	−2.41769	−0.0832696
$844$	−45.4615	−1.56485
$845$	33.3899	1.14865
$846$	1.75268	0.0602584
$847$	−3.95321	−0.135834
$848$	−7.02315	−0.241176
$849$	−17.2449	−0.591842
$850$	−2.82823	−0.0970076
$851$	−1.98634	−0.0680908
$852$	−7.77138	−0.266243
$853$	−43.1857	−1.47865	−0.739325	−	0.673348i	$-0.764855\pi$
$853$	−43.1857	−1.47865	−0.739325	+	0.673348i	$0.764855\pi$
$854$	0.267604	0.00915722
$855$	−8.79421	−0.300756
$856$	−13.4224	−0.458767
$857$	26.1566	0.893491	0.446746	−	0.894661i	$-0.352583\pi$
$857$	26.1566	0.893491	0.446746	+	0.894661i	$0.352583\pi$
$858$	1.13183	0.0386400
$859$	15.1284	0.516174	0.258087	−	0.966122i	$-0.416908\pi$
$859$	15.1284	0.516174	0.258087	+	0.966122i	$0.416908\pi$
$860$	−6.92049	−0.235987
$861$	−6.10834	−0.208172
$862$	−12.4512	−0.424089
$863$	15.0990	0.513977	0.256989	−	0.966414i	$-0.417270\pi$
$863$	15.0990	0.513977	0.256989	+	0.966414i	$0.417270\pi$
$864$	−4.75896	−0.161903
$865$	−4.32538	−0.147067
$866$	17.4611	0.593353
$867$	−7.16700	−0.243404
$868$	−1.09218	−0.0370711
$869$	38.3760	1.30182
$870$	12.3056	0.417200
$871$	3.60430	0.122127
$872$	−33.6317	−1.13891
$873$	−6.60693	−0.223611
$874$	−3.15658	−0.106773
$875$	−4.84790	−0.163889
$876$	−24.8116	−0.838306
$877$	−43.4986	−1.46884	−0.734422	−	0.678693i	$-0.762547\pi$
$877$	−43.4986	−1.46884	−0.734422	+	0.678693i	$0.762547\pi$
$878$	12.7786	0.431255
$879$	−3.14330	−0.106021
$880$	−30.6878	−1.03449
$881$	13.7969	0.464828	0.232414	−	0.972617i	$-0.425338\pi$
$881$	13.7969	0.464828	0.232414	+	0.972617i	$0.425338\pi$
$882$	3.04897	0.102664
$883$	2.77424	0.0933607	0.0466804	−	0.998910i	$-0.485136\pi$
$883$	2.77424	0.0933607	0.0466804	+	0.998910i	$0.485136\pi$
$884$	3.29876	0.110949
$885$	9.76531	0.328257
$886$	3.23038	0.108527
$887$	42.3348	1.42146	0.710732	−	0.703462i	$-0.248364\pi$
$887$	42.3348	1.42146	0.710732	+	0.703462i	$0.248364\pi$
$888$	−1.67836	−0.0563222
$889$	7.01565	0.235298
$890$	6.76573	0.226788
$891$	4.18757	0.140289
$892$	−24.1396	−0.808253
$893$	−12.7101	−0.425328
$894$	−3.34373	−0.111831
$895$	50.2484	1.67962
$896$	−6.69307	−0.223600
$897$	−1.21195	−0.0404659
$898$	−2.84859	−0.0950588
$899$	−10.2433	−0.341634
$900$	−3.51044	−0.117015
$901$	−7.92964	−0.264175
$902$	−19.4357	−0.647139
$903$	0.886850	0.0295125
$904$	5.06791	0.168556
$905$	−38.9443	−1.29455
$906$	3.11273	0.103413
$907$	−7.94687	−0.263871	−0.131936	−	0.991258i	$-0.542119\pi$
$907$	−7.94687	−0.263871	−0.131936	+	0.991258i	$0.542119\pi$
$908$	−39.6739	−1.31663
$909$	0.212823	0.00705889
$910$	0.431373	0.0142999
$911$	−58.6923	−1.94456	−0.972281	−	0.233814i	$-0.924879\pi$
$911$	−58.6923	−1.94456	−0.972281	+	0.233814i	$0.924879\pi$
$912$	9.25628	0.306506
$913$	65.6242	2.17184
$914$	11.4734	0.379506
$915$	−2.54012	−0.0839737
$916$	15.4772	0.511380
$917$	4.99768	0.165038
$918$	−1.44116	−0.0475652
$919$	38.5200	1.27066	0.635328	−	0.772242i	$-0.280865\pi$
$919$	38.5200	1.27066	0.635328	+	0.772242i	$0.280865\pi$
$920$	−9.46855	−0.312169
$921$	27.5662	0.908337
$922$	−15.5136	−0.510912
$923$	−2.55501	−0.0840990
$924$	4.53077	0.149051
$925$	−1.89157	−0.0621946
$926$	−7.88661	−0.259170
$927$	−1.50031	−0.0492767
$928$	−48.2910	−1.58523
$929$	38.6862	1.26925	0.634627	−	0.772818i	$-0.281154\pi$
$929$	38.6862	1.26925	0.634627	+	0.772818i	$0.281154\pi$
$930$	−1.22415	−0.0401416
$931$	−22.1106	−0.724645
$932$	27.3418	0.895609
$933$	3.97921	0.130274
$934$	−10.7606	−0.352098
$935$	−34.6487	−1.13313
$936$	−1.02404	−0.0334719
$937$	−50.9642	−1.66493	−0.832463	−	0.554080i	$-0.813070\pi$
$937$	−50.9642	−1.66493	−0.832463	+	0.554080i	$0.813070\pi$
$938$	−1.70369	−0.0556274
$939$	−15.9773	−0.521399
$940$	−18.0000	−0.587096
$941$	−44.6968	−1.45708	−0.728538	−	0.685006i	$-0.759800\pi$
$941$	−44.6968	−1.45708	−0.728538	+	0.685006i	$0.759800\pi$
$942$	6.32203	0.205983
$943$	20.8116	0.677718
$944$	−10.2784	−0.334533
$945$	1.59601	0.0519181
$946$	2.82181	0.0917451
$947$	−9.32767	−0.303109	−0.151554	−	0.988449i	$-0.548428\pi$
$947$	−9.32767	−0.303109	−0.151554	+	0.988449i	$0.548428\pi$
$948$	−16.3928	−0.532415
$949$	−8.15734	−0.264799
$950$	−3.00599	−0.0975272
$951$	−25.4618	−0.825654
$952$	−3.30265	−0.107040
$953$	−4.95569	−0.160530	−0.0802652	−	0.996774i	$-0.525577\pi$
$953$	−4.95569	−0.160530	−0.0802652	+	0.996774i	$0.525577\pi$
$954$	1.16219	0.0376274
$955$	21.7477	0.703738
$956$	53.4510	1.72873
$957$	42.4930	1.37360
$958$	−5.92041	−0.191280
$959$	−3.69514	−0.119322
$960$	8.88546	0.286777
$961$	−29.9810	−0.967129
$962$	−0.260518	−0.00839944
$963$	−7.70835	−0.248398
$964$	−31.3342	−1.00921
$965$	−32.8151	−1.05636
$966$	0.572868	0.0184317
$967$	−31.4033	−1.00986	−0.504931	−	0.863159i	$-0.668482\pi$
$967$	−31.4033	−1.00986	−0.504931	+	0.863159i	$0.668482\pi$
$968$	11.3806	0.365786
$969$	10.4510	0.335735
$970$	−8.01216	−0.257255
$971$	−38.8079	−1.24540	−0.622702	−	0.782459i	$-0.713965\pi$
$971$	−38.8079	−1.24540	−0.622702	+	0.782459i	$0.713965\pi$
$972$	−1.78878	−0.0573751
$973$	−8.95490	−0.287081
$974$	17.3273	0.555203
$975$	−1.15413	−0.0369618
$976$	2.67358	0.0855793
$977$	36.8665	1.17946	0.589732	−	0.807599i	$-0.299233\pi$
$977$	36.8665	1.17946	0.589732	+	0.807599i	$0.299233\pi$
$978$	−4.93597	−0.157835
$979$	23.3629	0.746682
$980$	−31.3129	−1.00026
$981$	−19.3144	−0.616661
$982$	5.66809	0.180876
$983$	−14.6521	−0.467330	−0.233665	−	0.972317i	$-0.575072\pi$
$983$	−14.6521	−0.467330	−0.233665	+	0.972317i	$0.575072\pi$
$984$	17.5848	0.560583
$985$	48.7691	1.55391
$986$	−14.6240	−0.465722
$987$	2.30668	0.0734224
$988$	3.50609	0.111543
$989$	−3.02157	−0.0960802
$990$	5.07823	0.161397
$991$	−22.2752	−0.707595	−0.353797	−	0.935322i	$-0.615110\pi$
$991$	−22.2752	−0.707595	−0.353797	+	0.935322i	$0.615110\pi$
$992$	4.80394	0.152525
$993$	−24.0840	−0.764283
$994$	1.20771	0.0383061
$995$	−12.7595	−0.404503
$996$	−28.0323	−0.888236
$997$	6.53346	0.206917	0.103458	−	0.994634i	$-0.467009\pi$
$997$	6.53346	0.206917	0.103458	+	0.994634i	$0.467009\pi$
$998$	−5.13601	−0.162578
$999$	−0.963871	−0.0304955

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	501.2.a.e.1.3	✓	8
3.2	odd	2		1503.2.a.e.1.6		8
4.3	odd	2		8016.2.a.x.1.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
501.2.a.e.1.3	✓	8	1.1	even	1	trivial
1503.2.a.e.1.6		8	3.2	odd	2
8016.2.a.x.1.1		8	4.3	odd	2

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:	\( N \)	\(=\)	\( 501 = 3 \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	501.a (trivial)

\(f(q)\)	\(=\)	\(q-0.459587 q^{2} +1.00000 q^{3} -1.78878 q^{4} -2.63865 q^{5} -0.459587 q^{6} -0.604857 q^{7} +1.74127 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.459587 q^{2} +1.00000 q^{3} -1.78878 q^{4} -2.63865 q^{5} -0.459587 q^{6} -0.604857 q^{7} +1.74127 q^{8} +1.00000 q^{9} +1.21269 q^{10} +4.18757 q^{11} -1.78878 q^{12} -0.588099 q^{13} +0.277984 q^{14} -2.63865 q^{15} +2.77729 q^{16} +3.13576 q^{17} -0.459587 q^{18} +3.33284 q^{19} +4.71996 q^{20} -0.604857 q^{21} -1.92456 q^{22} +2.06079 q^{23} +1.74127 q^{24} +1.96248 q^{25} +0.270283 q^{26} +1.00000 q^{27} +1.08196 q^{28} +10.1474 q^{29} +1.21269 q^{30} -1.00945 q^{31} -4.75896 q^{32} +4.18757 q^{33} -1.44116 q^{34} +1.59601 q^{35} -1.78878 q^{36} -0.963871 q^{37} -1.53173 q^{38} -0.588099 q^{39} -4.59462 q^{40} +10.0988 q^{41} +0.277984 q^{42} -1.46622 q^{43} -7.49065 q^{44} -2.63865 q^{45} -0.947114 q^{46} -3.81359 q^{47} +2.77729 q^{48} -6.63415 q^{49} -0.901929 q^{50} +3.13576 q^{51} +1.05198 q^{52} -2.52878 q^{53} -0.459587 q^{54} -11.0495 q^{55} -1.05322 q^{56} +3.33284 q^{57} -4.66361 q^{58} -3.70087 q^{59} +4.71996 q^{60} +0.962658 q^{61} +0.463931 q^{62} -0.604857 q^{63} -3.36743 q^{64} +1.55179 q^{65} -1.92456 q^{66} -6.12872 q^{67} -5.60919 q^{68} +2.06079 q^{69} -0.733504 q^{70} +4.34451 q^{71} +1.74127 q^{72} +13.8707 q^{73} +0.442983 q^{74} +1.96248 q^{75} -5.96172 q^{76} -2.53288 q^{77} +0.270283 q^{78} +9.16426 q^{79} -7.32830 q^{80} +1.00000 q^{81} -4.64129 q^{82} +15.6712 q^{83} +1.08196 q^{84} -8.27418 q^{85} +0.673854 q^{86} +10.1474 q^{87} +7.29172 q^{88} +5.57911 q^{89} +1.21269 q^{90} +0.355716 q^{91} -3.68630 q^{92} -1.00945 q^{93} +1.75268 q^{94} -8.79421 q^{95} -4.75896 q^{96} -6.60693 q^{97} +3.04897 q^{98} +4.18757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} + 8 q^{3} + 9 q^{4} + 7 q^{5} + 3 q^{6} - 4 q^{7} + 3 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 3 * q^2 + 8 * q^3 + 9 * q^4 + 7 * q^5 + 3 * q^6 - 4 * q^7 + 3 * q^8 + 8 * q^9	\( 8 q + 3 q^{2} + 8 q^{3} + 9 q^{4} + 7 q^{5} + 3 q^{6} - 4 q^{7} + 3 q^{8} + 8 q^{9} - q^{10} + 13 q^{11} + 9 q^{12} + 5 q^{14} + 7 q^{15} + 7 q^{16} + 11 q^{17} + 3 q^{18} + 12 q^{19} + 9 q^{20} - 4 q^{21} - 17 q^{22} + 7 q^{23} + 3 q^{24} - 5 q^{25} + 3 q^{26} + 8 q^{27} - 27 q^{28} + q^{29} - q^{30} - 2 q^{31} + 4 q^{32} + 13 q^{33} - 14 q^{34} - 4 q^{35} + 9 q^{36} - 9 q^{37} - 22 q^{40} + 4 q^{41} + 5 q^{42} + 2 q^{43} + 3 q^{44} + 7 q^{45} - 5 q^{46} + 17 q^{47} + 7 q^{48} - 2 q^{49} - 4 q^{50} + 11 q^{51} - 36 q^{52} + 9 q^{53} + 3 q^{54} + 7 q^{55} + 9 q^{56} + 12 q^{57} - 29 q^{58} + 29 q^{59} + 9 q^{60} - 12 q^{61} - 34 q^{62} - 4 q^{63} - 5 q^{64} + 8 q^{65} - 17 q^{66} + 26 q^{68} + 7 q^{69} + 5 q^{70} + 13 q^{71} + 3 q^{72} - 20 q^{73} - 17 q^{74} - 5 q^{75} + 30 q^{76} - 22 q^{77} + 3 q^{78} + 8 q^{79} - 34 q^{80} + 8 q^{81} + 15 q^{82} + 33 q^{83} - 27 q^{84} - 31 q^{85} + 11 q^{86} + q^{87} - 44 q^{88} + 4 q^{89} - q^{90} + q^{91} - 33 q^{92} - 2 q^{93} - 2 q^{94} + 3 q^{95} + 4 q^{96} - 31 q^{97} - 57 q^{98} + 13 q^{99}+O(q^{100}) \) 8 * q + 3 * q^2 + 8 * q^3 + 9 * q^4 + 7 * q^5 + 3 * q^6 - 4 * q^7 + 3 * q^8 + 8 * q^9 - q^10 + 13 * q^11 + 9 * q^12 + 5 * q^14 + 7 * q^15 + 7 * q^16 + 11 * q^17 + 3 * q^18 + 12 * q^19 + 9 * q^20 - 4 * q^21 - 17 * q^22 + 7 * q^23 + 3 * q^24 - 5 * q^25 + 3 * q^26 + 8 * q^27 - 27 * q^28 + q^29 - q^30 - 2 * q^31 + 4 * q^32 + 13 * q^33 - 14 * q^34 - 4 * q^35 + 9 * q^36 - 9 * q^37 - 22 * q^40 + 4 * q^41 + 5 * q^42 + 2 * q^43 + 3 * q^44 + 7 * q^45 - 5 * q^46 + 17 * q^47 + 7 * q^48 - 2 * q^49 - 4 * q^50 + 11 * q^51 - 36 * q^52 + 9 * q^53 + 3 * q^54 + 7 * q^55 + 9 * q^56 + 12 * q^57 - 29 * q^58 + 29 * q^59 + 9 * q^60 - 12 * q^61 - 34 * q^62 - 4 * q^63 - 5 * q^64 + 8 * q^65 - 17 * q^66 + 26 * q^68 + 7 * q^69 + 5 * q^70 + 13 * q^71 + 3 * q^72 - 20 * q^73 - 17 * q^74 - 5 * q^75 + 30 * q^76 - 22 * q^77 + 3 * q^78 + 8 * q^79 - 34 * q^80 + 8 * q^81 + 15 * q^82 + 33 * q^83 - 27 * q^84 - 31 * q^85 + 11 * q^86 + q^87 - 44 * q^88 + 4 * q^89 - q^90 + q^91 - 33 * q^92 - 2 * q^93 - 2 * q^94 + 3 * q^95 + 4 * q^96 - 31 * q^97 - 57 * q^98 + 13 * q^99

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