LMFDB - Embedded newform 4011.2.a.l.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.482188 q^{2} -1.00000 q^{3} -1.76749 q^{4} -4.13435 q^{5} +0.482188 q^{6} +1.00000 q^{7} +1.81664 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.482188 q^{2} -1.00000 q^{3} -1.76749 q^{4} -4.13435 q^{5} +0.482188 q^{6} +1.00000 q^{7} +1.81664 q^{8} +1.00000 q^{9} +1.99354 q^{10} +0.997504 q^{11} +1.76749 q^{12} +0.702717 q^{13} -0.482188 q^{14} +4.13435 q^{15} +2.65903 q^{16} -2.33904 q^{17} -0.482188 q^{18} -1.46177 q^{19} +7.30745 q^{20} -1.00000 q^{21} -0.480984 q^{22} -6.00006 q^{23} -1.81664 q^{24} +12.0929 q^{25} -0.338842 q^{26} -1.00000 q^{27} -1.76749 q^{28} -3.91669 q^{29} -1.99354 q^{30} +9.76370 q^{31} -4.91543 q^{32} -0.997504 q^{33} +1.12786 q^{34} -4.13435 q^{35} -1.76749 q^{36} -7.34101 q^{37} +0.704847 q^{38} -0.702717 q^{39} -7.51064 q^{40} -2.43757 q^{41} +0.482188 q^{42} -9.17914 q^{43} -1.76308 q^{44} -4.13435 q^{45} +2.89316 q^{46} -11.9268 q^{47} -2.65903 q^{48} +1.00000 q^{49} -5.83105 q^{50} +2.33904 q^{51} -1.24205 q^{52} -0.531897 q^{53} +0.482188 q^{54} -4.12403 q^{55} +1.81664 q^{56} +1.46177 q^{57} +1.88858 q^{58} +9.50800 q^{59} -7.30745 q^{60} +0.836502 q^{61} -4.70794 q^{62} +1.00000 q^{63} -2.94789 q^{64} -2.90528 q^{65} +0.480984 q^{66} -6.93613 q^{67} +4.13423 q^{68} +6.00006 q^{69} +1.99354 q^{70} -11.0801 q^{71} +1.81664 q^{72} -8.28151 q^{73} +3.53975 q^{74} -12.0929 q^{75} +2.58367 q^{76} +0.997504 q^{77} +0.338842 q^{78} +1.46338 q^{79} -10.9934 q^{80} +1.00000 q^{81} +1.17536 q^{82} +11.2131 q^{83} +1.76749 q^{84} +9.67040 q^{85} +4.42607 q^{86} +3.91669 q^{87} +1.81211 q^{88} +7.66990 q^{89} +1.99354 q^{90} +0.702717 q^{91} +10.6051 q^{92} -9.76370 q^{93} +5.75096 q^{94} +6.04347 q^{95} +4.91543 q^{96} -15.7928 q^{97} -0.482188 q^{98} +0.997504 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) $ 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * 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 $

$2$	−0.482188	−0.340958	−0.170479	−	0.985361i	$-0.554532\pi$
$2$	−0.482188	−0.340958	−0.170479	+	0.985361i	$0.554532\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.76749	−0.883747
$5$	−4.13435	−1.84894	−0.924470	−	0.381255i	$-0.875492\pi$
$5$	−4.13435	−1.84894	−0.924470	+	0.381255i	$0.875492\pi$
$6$	0.482188	0.196852
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.81664	0.642279
$9$	1.00000	0.333333
$10$	1.99354	0.630412
$11$	0.997504	0.300759	0.150379	−	0.988628i	$-0.451950\pi$
$11$	0.997504	0.300759	0.150379	+	0.988628i	$0.451950\pi$
$12$	1.76749	0.510232
$13$	0.702717	0.194899	0.0974494	−	0.995240i	$-0.468932\pi$
$13$	0.702717	0.194899	0.0974494	+	0.995240i	$0.468932\pi$
$14$	−0.482188	−0.128870
$15$	4.13435	1.06749
$16$	2.65903	0.664757
$17$	−2.33904	−0.567300	−0.283650	−	0.958928i	$-0.591545\pi$
$17$	−2.33904	−0.567300	−0.283650	+	0.958928i	$0.591545\pi$
$18$	−0.482188	−0.113653
$19$	−1.46177	−0.335353	−0.167676	−	0.985842i	$-0.553626\pi$
$19$	−1.46177	−0.335353	−0.167676	+	0.985842i	$0.553626\pi$
$20$	7.30745	1.63400
$21$	−1.00000	−0.218218
$22$	−0.480984	−0.102546
$23$	−6.00006	−1.25110	−0.625550	−	0.780184i	$-0.715125\pi$
$23$	−6.00006	−1.25110	−0.625550	+	0.780184i	$0.715125\pi$
$24$	−1.81664	−0.370820
$25$	12.0929	2.41858
$26$	−0.338842	−0.0664524
$27$	−1.00000	−0.192450
$28$	−1.76749	−0.334025
$29$	−3.91669	−0.727312	−0.363656	−	0.931533i	$-0.618472\pi$
$29$	−3.91669	−0.727312	−0.363656	+	0.931533i	$0.618472\pi$
$30$	−1.99354	−0.363968
$31$	9.76370	1.75361	0.876806	−	0.480844i	$-0.159670\pi$
$31$	9.76370	1.75361	0.876806	+	0.480844i	$0.159670\pi$
$32$	−4.91543	−0.868934
$33$	−0.997504	−0.173643
$34$	1.12786	0.193426
$35$	−4.13435	−0.698834
$36$	−1.76749	−0.294582
$37$	−7.34101	−1.20686	−0.603428	−	0.797418i	$-0.706199\pi$
$37$	−7.34101	−1.20686	−0.603428	+	0.797418i	$0.706199\pi$
$38$	0.704847	0.114341
$39$	−0.702717	−0.112525
$40$	−7.51064	−1.18754
$41$	−2.43757	−0.380684	−0.190342	−	0.981718i	$-0.560960\pi$
$41$	−2.43757	−0.380684	−0.190342	+	0.981718i	$0.560960\pi$
$42$	0.482188	0.0744032
$43$	−9.17914	−1.39981	−0.699903	−	0.714238i	$-0.746774\pi$
$43$	−9.17914	−1.39981	−0.699903	+	0.714238i	$0.746774\pi$
$44$	−1.76308	−0.265795
$45$	−4.13435	−0.616313
$46$	2.89316	0.426573
$47$	−11.9268	−1.73970	−0.869851	−	0.493315i	$-0.835785\pi$
$47$	−11.9268	−1.73970	−0.869851	+	0.493315i	$0.835785\pi$
$48$	−2.65903	−0.383798
$49$	1.00000	0.142857
$50$	−5.83105	−0.824635
$51$	2.33904	0.327531
$52$	−1.24205	−0.172241
$53$	−0.531897	−0.0730617	−0.0365309	−	0.999333i	$-0.511631\pi$
$53$	−0.531897	−0.0730617	−0.0365309	+	0.999333i	$0.511631\pi$
$54$	0.482188	0.0656175
$55$	−4.12403	−0.556085
$56$	1.81664	0.242759
$57$	1.46177	0.193616
$58$	1.88858	0.247983
$59$	9.50800	1.23784	0.618918	−	0.785455i	$-0.287571\pi$
$59$	9.50800	1.23784	0.618918	+	0.785455i	$0.287571\pi$
$60$	−7.30745	−0.943388
$61$	0.836502	0.107103	0.0535516	−	0.998565i	$-0.482946\pi$
$61$	0.836502	0.107103	0.0535516	+	0.998565i	$0.482946\pi$
$62$	−4.70794	−0.597909
$63$	1.00000	0.125988
$64$	−2.94789	−0.368486
$65$	−2.90528	−0.360356
$66$	0.480984	0.0592051
$67$	−6.93613	−0.847383	−0.423691	−	0.905807i	$-0.639266\pi$
$67$	−6.93613	−0.847383	−0.423691	+	0.905807i	$0.639266\pi$
$68$	4.13423	0.501349
$69$	6.00006	0.722323
$70$	1.99354	0.238273
$71$	−11.0801	−1.31497	−0.657483	−	0.753469i	$-0.728379\pi$
$71$	−11.0801	−1.31497	−0.657483	+	0.753469i	$0.728379\pi$
$72$	1.81664	0.214093
$73$	−8.28151	−0.969277	−0.484638	−	0.874715i	$-0.661049\pi$
$73$	−8.28151	−0.969277	−0.484638	+	0.874715i	$0.661049\pi$
$74$	3.53975	0.411487
$75$	−12.0929	−1.39637
$76$	2.58367	0.296367
$77$	0.997504	0.113676
$78$	0.338842	0.0383663
$79$	1.46338	0.164643	0.0823216	−	0.996606i	$-0.473767\pi$
$79$	1.46338	0.164643	0.0823216	+	0.996606i	$0.473767\pi$
$80$	−10.9934	−1.22910
$81$	1.00000	0.111111
$82$	1.17536	0.129797
$83$	11.2131	1.23080	0.615399	−	0.788216i	$-0.288995\pi$
$83$	11.2131	1.23080	0.615399	+	0.788216i	$0.288995\pi$
$84$	1.76749	0.192849
$85$	9.67040	1.04890
$86$	4.42607	0.477276
$87$	3.91669	0.419914
$88$	1.81211	0.193171
$89$	7.66990	0.813008	0.406504	−	0.913649i	$-0.366748\pi$
$89$	7.66990	0.813008	0.406504	+	0.913649i	$0.366748\pi$
$90$	1.99354	0.210137
$91$	0.702717	0.0736648
$92$	10.6051	1.10566
$93$	−9.76370	−1.01245
$94$	5.75096	0.593166
$95$	6.04347	0.620047
$96$	4.91543	0.501679
$97$	−15.7928	−1.60351	−0.801756	−	0.597652i	$-0.796100\pi$
$97$	−15.7928	−1.60351	−0.801756	+	0.597652i	$0.796100\pi$
$98$	−0.482188	−0.0487083
$99$	0.997504	0.100253
$100$	−21.3741	−2.13741
$101$	−1.71885	−0.171032	−0.0855161	−	0.996337i	$-0.527254\pi$
$101$	−1.71885	−0.171032	−0.0855161	+	0.996337i	$0.527254\pi$
$102$	−1.12786	−0.111674
$103$	4.80382	0.473334	0.236667	−	0.971591i	$-0.423945\pi$
$103$	4.80382	0.473334	0.236667	+	0.971591i	$0.423945\pi$
$104$	1.27658	0.125179
$105$	4.13435	0.403472
$106$	0.256474	0.0249110
$107$	−9.04526	−0.874438	−0.437219	−	0.899355i	$-0.644037\pi$
$107$	−9.04526	−0.874438	−0.437219	+	0.899355i	$0.644037\pi$
$108$	1.76749	0.170077
$109$	18.2629	1.74927	0.874634	−	0.484784i	$-0.161102\pi$
$109$	18.2629	1.74927	0.874634	+	0.484784i	$0.161102\pi$
$110$	1.98856	0.189602
$111$	7.34101	0.696778
$112$	2.65903	0.251254
$113$	−18.1350	−1.70600	−0.853000	−	0.521910i	$-0.825220\pi$
$113$	−18.1350	−1.70600	−0.853000	+	0.521910i	$0.825220\pi$
$114$	−0.704847	−0.0660150
$115$	24.8064	2.31321
$116$	6.92274	0.642760
$117$	0.702717	0.0649662
$118$	−4.58464	−0.422051
$119$	−2.33904	−0.214419
$120$	7.51064	0.685624
$121$	−10.0050	−0.909544
$122$	−0.403351	−0.0365177
$123$	2.43757	0.219788
$124$	−17.2573	−1.54975
$125$	−29.3245	−2.62287
$126$	−0.482188	−0.0429567
$127$	−7.55032	−0.669983	−0.334991	−	0.942221i	$-0.608733\pi$
$127$	−7.55032	−0.669983	−0.334991	+	0.942221i	$0.608733\pi$
$128$	11.2523	0.994572
$129$	9.17914	0.808179
$130$	1.40089	0.122866
$131$	16.6976	1.45887	0.729436	−	0.684049i	$-0.239782\pi$
$131$	16.6976	1.45887	0.729436	+	0.684049i	$0.239782\pi$
$132$	1.76308	0.153457
$133$	−1.46177	−0.126751
$134$	3.34452	0.288922
$135$	4.13435	0.355829
$136$	−4.24919	−0.364365
$137$	−1.54612	−0.132094	−0.0660470	−	0.997817i	$-0.521039\pi$
$137$	−1.54612	−0.132094	−0.0660470	+	0.997817i	$0.521039\pi$
$138$	−2.89316	−0.246282
$139$	18.8312	1.59724	0.798622	−	0.601832i	$-0.205562\pi$
$139$	18.8312	1.59724	0.798622	+	0.601832i	$0.205562\pi$
$140$	7.30745	0.617592
$141$	11.9268	1.00442
$142$	5.34269	0.448349
$143$	0.700963	0.0586175
$144$	2.65903	0.221586
$145$	16.1930	1.34476
$146$	3.99324	0.330483
$147$	−1.00000	−0.0824786
$148$	12.9752	1.06656
$149$	13.3308	1.09210	0.546049	−	0.837753i	$-0.316131\pi$
$149$	13.3308	1.09210	0.546049	+	0.837753i	$0.316131\pi$
$150$	5.83105	0.476103
$151$	−11.2141	−0.912592	−0.456296	−	0.889828i	$-0.650824\pi$
$151$	−11.2141	−0.912592	−0.456296	+	0.889828i	$0.650824\pi$
$152$	−2.65551	−0.215390
$153$	−2.33904	−0.189100
$154$	−0.480984	−0.0387588
$155$	−40.3666	−3.24232
$156$	1.24205	0.0994435
$157$	13.1471	1.04925	0.524626	−	0.851333i	$-0.324205\pi$
$157$	13.1471	1.04925	0.524626	+	0.851333i	$0.324205\pi$
$158$	−0.705625	−0.0561365
$159$	0.531897	0.0421822
$160$	20.3221	1.60661
$161$	−6.00006	−0.472871
$162$	−0.482188	−0.0378843
$163$	1.52517	0.119461	0.0597304	−	0.998215i	$-0.480976\pi$
$163$	1.52517	0.119461	0.0597304	+	0.998215i	$0.480976\pi$
$164$	4.30838	0.336428
$165$	4.12403	0.321056
$166$	−5.40682	−0.419651
$167$	−22.7114	−1.75746	−0.878732	−	0.477315i	$-0.841610\pi$
$167$	−22.7114	−1.75746	−0.878732	+	0.477315i	$0.841610\pi$
$168$	−1.81664	−0.140157
$169$	−12.5062	−0.962014
$170$	−4.66295	−0.357632
$171$	−1.46177	−0.111784
$172$	16.2241	1.23708
$173$	23.5569	1.79100	0.895500	−	0.445062i	$-0.146819\pi$
$173$	23.5569	1.79100	0.895500	+	0.445062i	$0.146819\pi$
$174$	−1.88858	−0.143173
$175$	12.0929	0.914137
$176$	2.65239	0.199931
$177$	−9.50800	−0.714665
$178$	−3.69833	−0.277202
$179$	−10.4008	−0.777389	−0.388694	−	0.921367i	$-0.627074\pi$
$179$	−10.4008	−0.777389	−0.388694	+	0.921367i	$0.627074\pi$
$180$	7.30745	0.544665
$181$	−11.5176	−0.856096	−0.428048	−	0.903756i	$-0.640799\pi$
$181$	−11.5176	−0.856096	−0.428048	+	0.903756i	$0.640799\pi$
$182$	−0.338842	−0.0251166
$183$	−0.836502	−0.0618360
$184$	−10.9000	−0.803556
$185$	30.3504	2.23140
$186$	4.70794	0.345203
$187$	−2.33320	−0.170620
$188$	21.0805	1.53746
$189$	−1.00000	−0.0727393
$190$	−2.91409	−0.211410
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	2.94789	0.212746
$193$	21.6406	1.55773	0.778863	−	0.627194i	$-0.215797\pi$
$193$	21.6406	1.55773	0.778863	+	0.627194i	$0.215797\pi$
$194$	7.61508	0.546731
$195$	2.90528	0.208052
$196$	−1.76749	−0.126250
$197$	14.9802	1.06729	0.533647	−	0.845707i	$-0.320821\pi$
$197$	14.9802	1.06729	0.533647	+	0.845707i	$0.320821\pi$
$198$	−0.480984	−0.0341821
$199$	20.5734	1.45841	0.729204	−	0.684297i	$-0.239891\pi$
$199$	20.5734	1.45841	0.729204	+	0.684297i	$0.239891\pi$
$200$	21.9684	1.55340
$201$	6.93613	0.489237
$202$	0.828810	0.0583148
$203$	−3.91669	−0.274898
$204$	−4.13423	−0.289454
$205$	10.0778	0.703861
$206$	−2.31634	−0.161387
$207$	−6.00006	−0.417033
$208$	1.86854	0.129560
$209$	−1.45812	−0.100860
$210$	−1.99354	−0.137567
$211$	8.51737	0.586360	0.293180	−	0.956057i	$-0.405287\pi$
$211$	8.51737	0.586360	0.293180	+	0.956057i	$0.405287\pi$
$212$	0.940126	0.0645681
$213$	11.0801	0.759196
$214$	4.36152	0.298147
$215$	37.9498	2.58816
$216$	−1.81664	−0.123607
$217$	9.76370	0.662803
$218$	−8.80615	−0.596428
$219$	8.28151	0.559612
$220$	7.28921	0.491438
$221$	−1.64368	−0.110566
$222$	−3.53975	−0.237572
$223$	22.2413	1.48939	0.744694	−	0.667406i	$-0.232596\pi$
$223$	22.2413	1.48939	0.744694	+	0.667406i	$0.232596\pi$
$224$	−4.91543	−0.328426
$225$	12.0929	0.806193
$226$	8.74450	0.581675
$227$	−16.0840	−1.06753	−0.533765	−	0.845633i	$-0.679223\pi$
$227$	−16.0840	−1.06753	−0.533765	+	0.845633i	$0.679223\pi$
$228$	−2.58367	−0.171108
$229$	24.9029	1.64563	0.822814	−	0.568311i	$-0.192403\pi$
$229$	24.9029	1.64563	0.822814	+	0.568311i	$0.192403\pi$
$230$	−11.9613	−0.788708
$231$	−0.997504	−0.0656309
$232$	−7.11522	−0.467137
$233$	−6.69139	−0.438367	−0.219184	−	0.975684i	$-0.570339\pi$
$233$	−6.69139	−0.438367	−0.219184	+	0.975684i	$0.570339\pi$
$234$	−0.338842	−0.0221508
$235$	49.3096	3.21660
$236$	−16.8053	−1.09393
$237$	−1.46338	−0.0950568
$238$	1.12786	0.0731080
$239$	−11.4771	−0.742390	−0.371195	−	0.928555i	$-0.621052\pi$
$239$	−11.4771	−0.742390	−0.371195	+	0.928555i	$0.621052\pi$
$240$	10.9934	0.709618
$241$	−27.5046	−1.77172	−0.885862	−	0.463949i	$-0.846432\pi$
$241$	−27.5046	−1.77172	−0.885862	+	0.463949i	$0.846432\pi$
$242$	4.82428	0.310117
$243$	−1.00000	−0.0641500
$244$	−1.47851	−0.0946521
$245$	−4.13435	−0.264134
$246$	−1.17536	−0.0749385
$247$	−1.02721	−0.0653598
$248$	17.7371	1.12631
$249$	−11.2131	−0.710602
$250$	14.1399	0.894288
$251$	16.5037	1.04170	0.520852	−	0.853647i	$-0.325614\pi$
$251$	16.5037	1.04170	0.520852	+	0.853647i	$0.325614\pi$
$252$	−1.76749	−0.111342
$253$	−5.98508	−0.376279
$254$	3.64067	0.228436
$255$	−9.67040	−0.605584
$256$	0.470058	0.0293787
$257$	−11.5033	−0.717555	−0.358777	−	0.933423i	$-0.616806\pi$
$257$	−11.5033	−0.717555	−0.358777	+	0.933423i	$0.616806\pi$
$258$	−4.42607	−0.275555
$259$	−7.34101	−0.456148
$260$	5.13507	0.318464
$261$	−3.91669	−0.242437
$262$	−8.05136	−0.497415
$263$	11.6125	0.716057	0.358028	−	0.933711i	$-0.383449\pi$
$263$	11.6125	0.716057	0.358028	+	0.933711i	$0.383449\pi$
$264$	−1.81211	−0.111527
$265$	2.19905	0.135087
$266$	0.704847	0.0432170
$267$	−7.66990	−0.469390
$268$	12.2596	0.748872
$269$	−31.2118	−1.90302	−0.951510	−	0.307619i	$-0.900468\pi$
$269$	−31.2118	−1.90302	−0.951510	+	0.307619i	$0.900468\pi$
$270$	−1.99354	−0.121323
$271$	19.1870	1.16553	0.582765	−	0.812641i	$-0.301971\pi$
$271$	19.1870	1.16553	0.582765	+	0.812641i	$0.301971\pi$
$272$	−6.21956	−0.377116
$273$	−0.702717	−0.0425304
$274$	0.745521	0.0450386
$275$	12.0627	0.727408
$276$	−10.6051	−0.638351
$277$	8.37683	0.503315	0.251658	−	0.967816i	$-0.419024\pi$
$277$	8.37683	0.503315	0.251658	+	0.967816i	$0.419024\pi$
$278$	−9.08020	−0.544594
$279$	9.76370	0.584537
$280$	−7.51064	−0.448846
$281$	−10.8066	−0.644665	−0.322333	−	0.946626i	$-0.604467\pi$
$281$	−10.8066	−0.644665	−0.322333	+	0.946626i	$0.604467\pi$
$282$	−5.75096	−0.342465
$283$	17.5690	1.04437	0.522184	−	0.852833i	$-0.325118\pi$
$283$	17.5690	1.04437	0.522184	+	0.852833i	$0.325118\pi$
$284$	19.5840	1.16210
$285$	−6.04347	−0.357984
$286$	−0.337996	−0.0199861
$287$	−2.43757	−0.143885
$288$	−4.91543	−0.289645
$289$	−11.5289	−0.678171
$290$	−7.80807	−0.458506
$291$	15.7928	0.925788
$292$	14.6375	0.856596
$293$	25.0315	1.46236	0.731178	−	0.682187i	$-0.238971\pi$
$293$	25.0315	1.46236	0.731178	+	0.682187i	$0.238971\pi$
$294$	0.482188	0.0281218
$295$	−39.3095	−2.28868
$296$	−13.3360	−0.775138
$297$	−0.997504	−0.0578810
$298$	−6.42793	−0.372360
$299$	−4.21635	−0.243838
$300$	21.3741	1.23404
$301$	−9.17914	−0.529077
$302$	5.40732	0.311156
$303$	1.71885	0.0987454
$304$	−3.88688	−0.222928
$305$	−3.45840	−0.198027
$306$	1.12786	0.0644752
$307$	3.98673	0.227535	0.113767	−	0.993507i	$-0.463708\pi$
$307$	3.98673	0.227535	0.113767	+	0.993507i	$0.463708\pi$
$308$	−1.76308	−0.100461
$309$	−4.80382	−0.273280
$310$	19.4643	1.10550
$311$	15.8134	0.896694	0.448347	−	0.893860i	$-0.352013\pi$
$311$	15.8134	0.896694	0.448347	+	0.893860i	$0.352013\pi$
$312$	−1.27658	−0.0722724
$313$	−11.6769	−0.660020	−0.330010	−	0.943977i	$-0.607052\pi$
$313$	−11.6769	−0.660020	−0.330010	+	0.943977i	$0.607052\pi$
$314$	−6.33937	−0.357751
$315$	−4.13435	−0.232945
$316$	−2.58652	−0.145503
$317$	−5.94931	−0.334147	−0.167073	−	0.985944i	$-0.553432\pi$
$317$	−5.94931	−0.334147	−0.167073	+	0.985944i	$0.553432\pi$
$318$	−0.256474	−0.0143824
$319$	−3.90692	−0.218745
$320$	12.1876	0.681309
$321$	9.04526	0.504857
$322$	2.89316	0.161229
$323$	3.41913	0.190245
$324$	−1.76749	−0.0981942
$325$	8.49788	0.471378
$326$	−0.735420	−0.0407311
$327$	−18.2629	−1.00994
$328$	−4.42818	−0.244505
$329$	−11.9268	−0.657545
$330$	−1.98856	−0.109467
$331$	−27.8415	−1.53031	−0.765154	−	0.643848i	$-0.777337\pi$
$331$	−27.8415	−1.53031	−0.765154	+	0.643848i	$0.777337\pi$
$332$	−19.8191	−1.08771
$333$	−7.34101	−0.402285
$334$	10.9512	0.599222
$335$	28.6764	1.56676
$336$	−2.65903	−0.145062
$337$	30.8476	1.68038	0.840189	−	0.542294i	$-0.182444\pi$
$337$	30.8476	1.68038	0.840189	+	0.542294i	$0.182444\pi$
$338$	6.03033	0.328007
$339$	18.1350	0.984960
$340$	−17.0924	−0.926965
$341$	9.73933	0.527414
$342$	0.704847	0.0381138
$343$	1.00000	0.0539949
$344$	−16.6752	−0.899067
$345$	−24.8064	−1.33553
$346$	−11.3589	−0.610656
$347$	−1.62161	−0.0870525	−0.0435263	−	0.999052i	$-0.513859\pi$
$347$	−1.62161	−0.0870525	−0.0435263	+	0.999052i	$0.513859\pi$
$348$	−6.92274	−0.371098
$349$	3.92886	0.210307	0.105154	−	0.994456i	$-0.466467\pi$
$349$	3.92886	0.210307	0.105154	+	0.994456i	$0.466467\pi$
$350$	−5.83105	−0.311683
$351$	−0.702717	−0.0375083
$352$	−4.90316	−0.261339
$353$	6.90972	0.367767	0.183884	−	0.982948i	$-0.441133\pi$
$353$	6.90972	0.367767	0.183884	+	0.982948i	$0.441133\pi$
$354$	4.58464	0.243671
$355$	45.8091	2.43129
$356$	−13.5565	−0.718494
$357$	2.33904	0.123795
$358$	5.01512	0.265057
$359$	24.4506	1.29045	0.645226	−	0.763992i	$-0.276763\pi$
$359$	24.4506	1.29045	0.645226	+	0.763992i	$0.276763\pi$
$360$	−7.51064	−0.395845
$361$	−16.8632	−0.887539
$362$	5.55365	0.291893
$363$	10.0050	0.525126
$364$	−1.24205	−0.0651011
$365$	34.2387	1.79213
$366$	0.403351	0.0210835
$367$	9.81317	0.512243	0.256122	−	0.966645i	$-0.417555\pi$
$367$	9.81317	0.512243	0.256122	+	0.966645i	$0.417555\pi$
$368$	−15.9543	−0.831677
$369$	−2.43757	−0.126895
$370$	−14.6346	−0.760815
$371$	−0.531897	−0.0276147
$372$	17.2573	0.894749
$373$	−26.0314	−1.34786	−0.673928	−	0.738797i	$-0.735394\pi$
$373$	−26.0314	−1.34786	−0.673928	+	0.738797i	$0.735394\pi$
$374$	1.12504	0.0581744
$375$	29.3245	1.51431
$376$	−21.6667	−1.11737
$377$	−2.75233	−0.141752
$378$	0.482188	0.0248011
$379$	26.8930	1.38140	0.690701	−	0.723140i	$-0.257302\pi$
$379$	26.8930	1.38140	0.690701	+	0.723140i	$0.257302\pi$
$380$	−10.6818	−0.547965
$381$	7.55032	0.386815
$382$	0.482188	0.0246709
$383$	−30.0292	−1.53442	−0.767210	−	0.641396i	$-0.778356\pi$
$383$	−30.0292	−1.53442	−0.767210	+	0.641396i	$0.778356\pi$
$384$	−11.2523	−0.574217
$385$	−4.12403	−0.210180
$386$	−10.4348	−0.531120
$387$	−9.17914	−0.466602
$388$	27.9136	1.41710
$389$	28.5529	1.44769	0.723844	−	0.689963i	$-0.242373\pi$
$389$	28.5529	1.44769	0.723844	+	0.689963i	$0.242373\pi$
$390$	−1.40089	−0.0709369
$391$	14.0344	0.709748
$392$	1.81664	0.0917542
$393$	−16.6976	−0.842281
$394$	−7.22327	−0.363903
$395$	−6.05014	−0.304415
$396$	−1.76308	−0.0885982
$397$	−13.3638	−0.670711	−0.335355	−	0.942092i	$-0.608856\pi$
$397$	−13.3638	−0.670711	−0.335355	+	0.942092i	$0.608856\pi$
$398$	−9.92023	−0.497256
$399$	1.46177	0.0731800
$400$	32.1553	1.60777
$401$	−20.6193	−1.02968	−0.514839	−	0.857287i	$-0.672148\pi$
$401$	−20.6193	−1.02968	−0.514839	+	0.857287i	$0.672148\pi$
$402$	−3.34452	−0.166809
$403$	6.86112	0.341777
$404$	3.03806	0.151149
$405$	−4.13435	−0.205438
$406$	1.88858	0.0937288
$407$	−7.32269	−0.362972
$408$	4.24919	0.210366
$409$	−13.6973	−0.677287	−0.338643	−	0.940915i	$-0.609968\pi$
$409$	−13.6973	−0.677287	−0.338643	+	0.940915i	$0.609968\pi$
$410$	−4.85937	−0.239987
$411$	1.54612	0.0762645
$412$	−8.49072	−0.418308
$413$	9.50800	0.467858
$414$	2.89316	0.142191
$415$	−46.3589	−2.27567
$416$	−3.45416	−0.169354
$417$	−18.8312	−0.922170
$418$	0.703088	0.0343892
$419$	−1.44478	−0.0705821	−0.0352910	−	0.999377i	$-0.511236\pi$
$419$	−1.44478	−0.0705821	−0.0352910	+	0.999377i	$0.511236\pi$
$420$	−7.30745	−0.356567
$421$	5.80540	0.282938	0.141469	−	0.989943i	$-0.454817\pi$
$421$	5.80540	0.282938	0.141469	+	0.989943i	$0.454817\pi$
$422$	−4.10697	−0.199924
$423$	−11.9268	−0.579901
$424$	−0.966266	−0.0469260
$425$	−28.2857	−1.37206
$426$	−5.34269	−0.258854
$427$	0.836502	0.0404812
$428$	15.9875	0.772783
$429$	−0.700963	−0.0338428
$430$	−18.2990	−0.882454
$431$	28.2360	1.36008	0.680039	−	0.733175i	$-0.261963\pi$
$431$	28.2360	1.36008	0.680039	+	0.733175i	$0.261963\pi$
$432$	−2.65903	−0.127933
$433$	−13.3156	−0.639907	−0.319953	−	0.947433i	$-0.603667\pi$
$433$	−13.3156	−0.639907	−0.319953	+	0.947433i	$0.603667\pi$
$434$	−4.70794	−0.225988
$435$	−16.1930	−0.776395
$436$	−32.2796	−1.54591
$437$	8.77070	0.419560
$438$	−3.99324	−0.190805
$439$	6.69269	0.319425	0.159712	−	0.987164i	$-0.448943\pi$
$439$	6.69269	0.319425	0.159712	+	0.987164i	$0.448943\pi$
$440$	−7.49189	−0.357162
$441$	1.00000	0.0476190
$442$	0.792563	0.0376984
$443$	10.0344	0.476749	0.238374	−	0.971173i	$-0.423385\pi$
$443$	10.0344	0.476749	0.238374	+	0.971173i	$0.423385\pi$
$444$	−12.9752	−0.615776
$445$	−31.7101	−1.50320
$446$	−10.7245	−0.507819
$447$	−13.3308	−0.630523
$448$	−2.94789	−0.139275
$449$	9.77498	0.461310	0.230655	−	0.973036i	$-0.425913\pi$
$449$	9.77498	0.461310	0.230655	+	0.973036i	$0.425913\pi$
$450$	−5.83105	−0.274878
$451$	−2.43148	−0.114494
$452$	32.0536	1.50767
$453$	11.2141	0.526885
$454$	7.75549	0.363983
$455$	−2.90528	−0.136202
$456$	2.65551	0.124356
$457$	16.5366	0.773550	0.386775	−	0.922174i	$-0.373589\pi$
$457$	16.5366	0.773550	0.386775	+	0.922174i	$0.373589\pi$
$458$	−12.0079	−0.561090
$459$	2.33904	0.109177
$460$	−43.8452	−2.04429
$461$	−6.79472	−0.316461	−0.158231	−	0.987402i	$-0.550579\pi$
$461$	−6.79472	−0.316461	−0.158231	+	0.987402i	$0.550579\pi$
$462$	0.480984	0.0223774
$463$	1.60269	0.0744835	0.0372418	−	0.999306i	$-0.488143\pi$
$463$	1.60269	0.0744835	0.0372418	+	0.999306i	$0.488143\pi$
$464$	−10.4146	−0.483485
$465$	40.3666	1.87196
$466$	3.22651	0.149465
$467$	−17.9561	−0.830911	−0.415455	−	0.909614i	$-0.636378\pi$
$467$	−17.9561	−0.830911	−0.415455	+	0.909614i	$0.636378\pi$
$468$	−1.24205	−0.0574137
$469$	−6.93613	−0.320281
$470$	−23.7765	−1.09673
$471$	−13.1471	−0.605786
$472$	17.2726	0.795037
$473$	−9.15623	−0.421004
$474$	0.705625	0.0324104
$475$	−17.6770	−0.811077
$476$	4.13423	0.189492
$477$	−0.531897	−0.0243539
$478$	5.53411	0.253124
$479$	−10.6449	−0.486380	−0.243190	−	0.969979i	$-0.578194\pi$
$479$	−10.6449	−0.486380	−0.243190	+	0.969979i	$0.578194\pi$
$480$	−20.3221	−0.927575
$481$	−5.15866	−0.235215
$482$	13.2624	0.604084
$483$	6.00006	0.273012
$484$	17.6838	0.803807
$485$	65.2928	2.96480
$486$	0.482188	0.0218725
$487$	−24.6498	−1.11699	−0.558495	−	0.829508i	$-0.688621\pi$
$487$	−24.6498	−1.11699	−0.558495	+	0.829508i	$0.688621\pi$
$488$	1.51962	0.0687901
$489$	−1.52517	−0.0689707
$490$	1.99354	0.0900588
$491$	8.62076	0.389049	0.194525	−	0.980898i	$-0.437684\pi$
$491$	8.62076	0.389049	0.194525	+	0.980898i	$0.437684\pi$
$492$	−4.30838	−0.194237
$493$	9.16129	0.412604
$494$	0.495308	0.0222850
$495$	−4.12403	−0.185362
$496$	25.9619	1.16573
$497$	−11.0801	−0.497011
$498$	5.40682	0.242286
$499$	15.8785	0.710820	0.355410	−	0.934711i	$-0.384341\pi$
$499$	15.8785	0.710820	0.355410	+	0.934711i	$0.384341\pi$
$500$	51.8309	2.31795
$501$	22.7114	1.01467
$502$	−7.95788	−0.355178
$503$	−7.89783	−0.352147	−0.176073	−	0.984377i	$-0.556340\pi$
$503$	−7.89783	−0.352147	−0.176073	+	0.984377i	$0.556340\pi$
$504$	1.81664	0.0809196
$505$	7.10634	0.316228
$506$	2.88594	0.128296
$507$	12.5062	0.555419
$508$	13.3452	0.592095
$509$	1.84329	0.0817025	0.0408513	−	0.999165i	$-0.486993\pi$
$509$	1.84329	0.0817025	0.0408513	+	0.999165i	$0.486993\pi$
$510$	4.66295	0.206479
$511$	−8.28151	−0.366352
$512$	−22.7313	−1.00459
$513$	1.46177	0.0645387
$514$	5.54674	0.244656
$515$	−19.8607	−0.875167
$516$	−16.2241	−0.714226
$517$	−11.8970	−0.523231
$518$	3.53975	0.155528
$519$	−23.5569	−1.03403
$520$	−5.27786	−0.231449
$521$	−3.19210	−0.139849	−0.0699243	−	0.997552i	$-0.522276\pi$
$521$	−3.19210	−0.139849	−0.0699243	+	0.997552i	$0.522276\pi$
$522$	1.88858	0.0826610
$523$	−33.9792	−1.48581	−0.742904	−	0.669398i	$-0.766552\pi$
$523$	−33.9792	−1.48581	−0.742904	+	0.669398i	$0.766552\pi$
$524$	−29.5129	−1.28927
$525$	−12.0929	−0.527777
$526$	−5.59940	−0.244146
$527$	−22.8376	−0.994824
$528$	−2.65239	−0.115430
$529$	13.0007	0.565250
$530$	−1.06036	−0.0460589
$531$	9.50800	0.412612
$532$	2.58367	0.112016
$533$	−1.71292	−0.0741948
$534$	3.69833	0.160043
$535$	37.3963	1.61678
$536$	−12.6005	−0.544257
$537$	10.4008	0.448826
$538$	15.0500	0.648850
$539$	0.997504	0.0429655
$540$	−7.30745	−0.314463
$541$	−15.0752	−0.648134	−0.324067	−	0.946034i	$-0.605050\pi$
$541$	−15.0752	−0.648134	−0.324067	+	0.946034i	$0.605050\pi$
$542$	−9.25176	−0.397397
$543$	11.5176	0.494267
$544$	11.4974	0.492946
$545$	−75.5053	−3.23429
$546$	0.338842	0.0145011
$547$	27.9749	1.19612	0.598061	−	0.801450i	$-0.295938\pi$
$547$	27.9749	1.19612	0.598061	+	0.801450i	$0.295938\pi$
$548$	2.73276	0.116738
$549$	0.836502	0.0357010
$550$	−5.81649	−0.248016
$551$	5.72530	0.243906
$552$	10.9000	0.463933
$553$	1.46338	0.0622293
$554$	−4.03921	−0.171609
$555$	−30.3504	−1.28830
$556$	−33.2841	−1.41156
$557$	3.94321	0.167079	0.0835396	−	0.996504i	$-0.473377\pi$
$557$	3.94321	0.167079	0.0835396	+	0.996504i	$0.473377\pi$
$558$	−4.70794	−0.199303
$559$	−6.45034	−0.272820
$560$	−10.9934	−0.464554
$561$	2.33320	0.0985077
$562$	5.21079	0.219804
$563$	−20.6132	−0.868744	−0.434372	−	0.900734i	$-0.643030\pi$
$563$	−20.6132	−0.868744	−0.434372	+	0.900734i	$0.643030\pi$
$564$	−21.0805	−0.887651
$565$	74.9767	3.15429
$566$	−8.47155	−0.356086
$567$	1.00000	0.0419961
$568$	−20.1286	−0.844576
$569$	−0.658791	−0.0276180	−0.0138090	−	0.999905i	$-0.504396\pi$
$569$	−0.658791	−0.0276180	−0.0138090	+	0.999905i	$0.504396\pi$
$570$	2.91409	0.122058
$571$	−12.9397	−0.541510	−0.270755	−	0.962648i	$-0.587273\pi$
$571$	−12.9397	−0.541510	−0.270755	+	0.962648i	$0.587273\pi$
$572$	−1.23895	−0.0518031
$573$	1.00000	0.0417756
$574$	1.17536	0.0490588
$575$	−72.5581	−3.02588
$576$	−2.94789	−0.122829
$577$	28.0362	1.16716	0.583580	−	0.812055i	$-0.301651\pi$
$577$	28.0362	1.16716	0.583580	+	0.812055i	$0.301651\pi$
$578$	5.55910	0.231228
$579$	−21.6406	−0.899353
$580$	−28.6210	−1.18842
$581$	11.2131	0.465198
$582$	−7.61508	−0.315655
$583$	−0.530570	−0.0219739
$584$	−15.0445	−0.622547
$585$	−2.90528	−0.120119
$586$	−12.0699	−0.498603
$587$	−4.76119	−0.196515	−0.0982577	−	0.995161i	$-0.531327\pi$
$587$	−4.76119	−0.196515	−0.0982577	+	0.995161i	$0.531327\pi$
$588$	1.76749	0.0728903
$589$	−14.2723	−0.588079
$590$	18.9545	0.780346
$591$	−14.9802	−0.616203
$592$	−19.5200	−0.802265
$593$	−13.7306	−0.563848	−0.281924	−	0.959437i	$-0.590973\pi$
$593$	−13.7306	−0.563848	−0.281924	+	0.959437i	$0.590973\pi$
$594$	0.480984	0.0197350
$595$	9.67040	0.396448
$596$	−23.5620	−0.965139
$597$	−20.5734	−0.842012
$598$	2.03307	0.0831385
$599$	28.7948	1.17652	0.588261	−	0.808671i	$-0.299813\pi$
$599$	28.7948	1.17652	0.588261	+	0.808671i	$0.299813\pi$
$600$	−21.9684	−0.896858
$601$	13.5715	0.553594	0.276797	−	0.960928i	$-0.410727\pi$
$601$	13.5715	0.553594	0.276797	+	0.960928i	$0.410727\pi$
$602$	4.42607	0.180393
$603$	−6.93613	−0.282461
$604$	19.8209	0.806501
$605$	41.3642	1.68169
$606$	−0.828810	−0.0336681
$607$	35.3913	1.43649	0.718245	−	0.695790i	$-0.244946\pi$
$607$	35.3913	1.43649	0.718245	+	0.695790i	$0.244946\pi$
$608$	7.18523	0.291399
$609$	3.91669	0.158712
$610$	1.66760	0.0675190
$611$	−8.38117	−0.339066
$612$	4.13423	0.167116
$613$	10.7505	0.434207	0.217103	−	0.976149i	$-0.430339\pi$
$613$	10.7505	0.434207	0.217103	+	0.976149i	$0.430339\pi$
$614$	−1.92235	−0.0775799
$615$	−10.0778	−0.406374
$616$	1.81211	0.0730118
$617$	−28.4006	−1.14336	−0.571682	−	0.820475i	$-0.693709\pi$
$617$	−28.4006	−1.14336	−0.571682	+	0.820475i	$0.693709\pi$
$618$	2.31634	0.0931770
$619$	−14.2460	−0.572597	−0.286299	−	0.958140i	$-0.592425\pi$
$619$	−14.2460	−0.572597	−0.286299	+	0.958140i	$0.592425\pi$
$620$	71.3478	2.86540
$621$	6.00006	0.240774
$622$	−7.62501	−0.305735
$623$	7.66990	0.307288
$624$	−1.86854	−0.0748016
$625$	60.7735	2.43094
$626$	5.63048	0.225039
$627$	1.45812	0.0582317
$628$	−23.2374	−0.927274
$629$	17.1709	0.684648
$630$	1.99354	0.0794244
$631$	38.0568	1.51502	0.757509	−	0.652825i	$-0.226416\pi$
$631$	38.0568	1.51502	0.757509	+	0.652825i	$0.226416\pi$
$632$	2.65844	0.105747
$633$	−8.51737	−0.338535
$634$	2.86869	0.113930
$635$	31.2157	1.23876
$636$	−0.940126	−0.0372784
$637$	0.702717	0.0278427
$638$	1.88387	0.0745831
$639$	−11.0801	−0.438322
$640$	−46.5210	−1.83890
$641$	−44.2616	−1.74823	−0.874114	−	0.485720i	$-0.838557\pi$
$641$	−44.2616	−1.74823	−0.874114	+	0.485720i	$0.838557\pi$
$642$	−4.36152	−0.172135
$643$	3.12064	0.123066	0.0615331	−	0.998105i	$-0.480401\pi$
$643$	3.12064	0.123066	0.0615331	+	0.998105i	$0.480401\pi$
$644$	10.6051	0.417899
$645$	−37.9498	−1.49427
$646$	−1.64866	−0.0648658
$647$	12.0105	0.472180	0.236090	−	0.971731i	$-0.424134\pi$
$647$	12.0105	0.472180	0.236090	+	0.971731i	$0.424134\pi$
$648$	1.81664	0.0713644
$649$	9.48427	0.372290
$650$	−4.09758	−0.160720
$651$	−9.76370	−0.382670
$652$	−2.69573	−0.105573
$653$	24.9817	0.977610	0.488805	−	0.872393i	$-0.337433\pi$
$653$	24.9817	0.977610	0.488805	+	0.872393i	$0.337433\pi$
$654$	8.80615	0.344348
$655$	−69.0336	−2.69737
$656$	−6.48155	−0.253062
$657$	−8.28151	−0.323092
$658$	5.75096	0.224196
$659$	30.9680	1.20634	0.603170	−	0.797612i	$-0.293904\pi$
$659$	30.9680	1.20634	0.603170	+	0.797612i	$0.293904\pi$
$660$	−7.28921	−0.283732
$661$	20.9266	0.813951	0.406976	−	0.913439i	$-0.366583\pi$
$661$	20.9266	0.813951	0.406976	+	0.913439i	$0.366583\pi$
$662$	13.4248	0.521771
$663$	1.64368	0.0638353
$664$	20.3702	0.790516
$665$	6.04347	0.234356
$666$	3.53975	0.137162
$667$	23.5004	0.909939
$668$	40.1424	1.55315
$669$	−22.2413	−0.859898
$670$	−13.8274	−0.534200
$671$	0.834414	0.0322122
$672$	4.91543	0.189617
$673$	35.8417	1.38160	0.690798	−	0.723048i	$-0.257260\pi$
$673$	35.8417	1.38160	0.690798	+	0.723048i	$0.257260\pi$
$674$	−14.8744	−0.572939
$675$	−12.0929	−0.465456
$676$	22.1046	0.850178
$677$	25.6544	0.985979	0.492989	−	0.870035i	$-0.335904\pi$
$677$	25.6544	0.985979	0.492989	+	0.870035i	$0.335904\pi$
$678$	−8.74450	−0.335830
$679$	−15.7928	−0.606070
$680$	17.5677	0.673689
$681$	16.0840	0.616339
$682$	−4.69619	−0.179826
$683$	35.8438	1.37153	0.685763	−	0.727825i	$-0.259469\pi$
$683$	35.8438	1.37153	0.685763	+	0.727825i	$0.259469\pi$
$684$	2.58367	0.0987890
$685$	6.39221	0.244234
$686$	−0.482188	−0.0184100
$687$	−24.9029	−0.950103
$688$	−24.4076	−0.930531
$689$	−0.373773	−0.0142396
$690$	11.9613	0.455360
$691$	22.8819	0.870468	0.435234	−	0.900317i	$-0.356666\pi$
$691$	22.8819	0.870468	0.435234	+	0.900317i	$0.356666\pi$
$692$	−41.6367	−1.58279
$693$	0.997504	0.0378920
$694$	0.781920	0.0296813
$695$	−77.8550	−2.95321
$696$	7.11522	0.269702
$697$	5.70155	0.215962
$698$	−1.89445	−0.0717060
$699$	6.69139	0.253092
$700$	−21.3741	−0.807866
$701$	6.26507	0.236628	0.118314	−	0.992976i	$-0.462251\pi$
$701$	6.26507	0.236628	0.118314	+	0.992976i	$0.462251\pi$
$702$	0.338842	0.0127888
$703$	10.7309	0.404722
$704$	−2.94053	−0.110826
$705$	−49.3096	−1.85711
$706$	−3.33179	−0.125393
$707$	−1.71885	−0.0646441
$708$	16.8053	0.631583
$709$	−25.2434	−0.948035	−0.474017	−	0.880515i	$-0.657197\pi$
$709$	−25.2434	−0.948035	−0.474017	+	0.880515i	$0.657197\pi$
$710$	−22.0886	−0.828970
$711$	1.46338	0.0548811
$712$	13.9335	0.522178
$713$	−58.5828	−2.19394
$714$	−1.12786	−0.0422089
$715$	−2.89803	−0.108380
$716$	18.3833	0.687015
$717$	11.4771	0.428619
$718$	−11.7898	−0.439990
$719$	−27.6998	−1.03303	−0.516515	−	0.856278i	$-0.672771\pi$
$719$	−27.6998	−1.03303	−0.516515	+	0.856278i	$0.672771\pi$
$720$	−10.9934	−0.409698
$721$	4.80382	0.178904
$722$	8.13125	0.302614
$723$	27.5046	1.02291
$724$	20.3573	0.756573
$725$	−47.3641	−1.75906
$726$	−4.82428	−0.179046
$727$	19.7569	0.732743	0.366371	−	0.930469i	$-0.380600\pi$
$727$	19.7569	0.732743	0.366371	+	0.930469i	$0.380600\pi$
$728$	1.27658	0.0473134
$729$	1.00000	0.0370370
$730$	−16.5095	−0.611043
$731$	21.4703	0.794109
$732$	1.47851	0.0546474
$733$	0.240975	0.00890060	0.00445030	−	0.999990i	$-0.498583\pi$
$733$	0.240975	0.00890060	0.00445030	+	0.999990i	$0.498583\pi$
$734$	−4.73179	−0.174654
$735$	4.13435	0.152498
$736$	29.4929	1.08712
$737$	−6.91881	−0.254858
$738$	1.17536	0.0432658
$739$	−40.5856	−1.49297	−0.746483	−	0.665405i	$-0.768259\pi$
$739$	−40.5856	−1.49297	−0.746483	+	0.665405i	$0.768259\pi$
$740$	−53.6441	−1.97200
$741$	1.02721	0.0377355
$742$	0.256474	0.00941547
$743$	34.0534	1.24930	0.624650	−	0.780905i	$-0.285242\pi$
$743$	34.0534	1.24930	0.624650	+	0.780905i	$0.285242\pi$
$744$	−17.7371	−0.650275
$745$	−55.1141	−2.01922
$746$	12.5520	0.459563
$747$	11.2131	0.410266
$748$	4.12391	0.150785
$749$	−9.04526	−0.330507
$750$	−14.1399	−0.516317
$751$	8.93402	0.326007	0.163004	−	0.986625i	$-0.447882\pi$
$751$	8.93402	0.326007	0.163004	+	0.986625i	$0.447882\pi$
$752$	−31.7137	−1.15648
$753$	−16.5037	−0.601428
$754$	1.32714	0.0483316
$755$	46.3632	1.68733
$756$	1.76749	0.0642832
$757$	54.5644	1.98318	0.991588	−	0.129434i	$-0.0413161\pi$
$757$	54.5644	1.98318	0.991588	+	0.129434i	$0.0413161\pi$
$758$	−12.9675	−0.471001
$759$	5.98508	0.217245
$760$	10.9788	0.398244
$761$	19.0051	0.688936	0.344468	−	0.938798i	$-0.388059\pi$
$761$	19.0051	0.688936	0.344468	+	0.938798i	$0.388059\pi$
$762$	−3.64067	−0.131888
$763$	18.2629	0.661161
$764$	1.76749	0.0639457
$765$	9.67040	0.349634
$766$	14.4797	0.523173
$767$	6.68144	0.241253
$768$	−0.470058	−0.0169618
$769$	49.3233	1.77864	0.889322	−	0.457282i	$-0.151177\pi$
$769$	49.3233	1.77864	0.889322	+	0.457282i	$0.151177\pi$
$770$	1.98856	0.0716627
$771$	11.5033	0.414280
$772$	−38.2497	−1.37664
$773$	41.1780	1.48107	0.740534	−	0.672019i	$-0.234573\pi$
$773$	41.1780	1.48107	0.740534	+	0.672019i	$0.234573\pi$
$774$	4.42607	0.159092
$775$	118.071	4.24125
$776$	−28.6898	−1.02990
$777$	7.34101	0.263357
$778$	−13.7679	−0.493602
$779$	3.56316	0.127663
$780$	−5.13507	−0.183865
$781$	−11.0524	−0.395488
$782$	−6.76720	−0.241995
$783$	3.91669	0.139971
$784$	2.65903	0.0949653
$785$	−54.3547	−1.94000
$786$	8.05136	0.287183
$787$	44.2586	1.57765	0.788825	−	0.614618i	$-0.210690\pi$
$787$	44.2586	1.57765	0.788825	+	0.614618i	$0.210690\pi$
$788$	−26.4774	−0.943219
$789$	−11.6125	−0.413416
$790$	2.91730	0.103793
$791$	−18.1350	−0.644808
$792$	1.81211	0.0643904
$793$	0.587824	0.0208743
$794$	6.44387	0.228684
$795$	−2.19905	−0.0779923
$796$	−36.3633	−1.28886
$797$	36.5405	1.29433	0.647166	−	0.762349i	$-0.275954\pi$
$797$	36.5405	1.29433	0.647166	+	0.762349i	$0.275954\pi$
$798$	−0.704847	−0.0249513
$799$	27.8972	0.986932
$800$	−59.4418	−2.10158
$801$	7.66990	0.271003
$802$	9.94238	0.351078
$803$	−8.26083	−0.291518
$804$	−12.2596	−0.432362
$805$	24.8064	0.874310
$806$	−3.30835	−0.116532
$807$	31.2118	1.09871
$808$	−3.12254	−0.109850
$809$	28.9280	1.01705	0.508527	−	0.861046i	$-0.330190\pi$
$809$	28.9280	1.01705	0.508527	+	0.861046i	$0.330190\pi$
$810$	1.99354	0.0700457
$811$	−24.3387	−0.854646	−0.427323	−	0.904099i	$-0.640543\pi$
$811$	−24.3387	−0.854646	−0.427323	+	0.904099i	$0.640543\pi$
$812$	6.92274	0.242940
$813$	−19.1870	−0.672919
$814$	3.53091	0.123758
$815$	−6.30561	−0.220876
$816$	6.21956	0.217728
$817$	13.4178	0.469429
$818$	6.60466	0.230927
$819$	0.702717	0.0245549
$820$	−17.8124	−0.622036
$821$	3.80498	0.132795	0.0663974	−	0.997793i	$-0.478849\pi$
$821$	3.80498	0.132795	0.0663974	+	0.997793i	$0.478849\pi$
$822$	−0.745521	−0.0260030
$823$	8.69576	0.303115	0.151558	−	0.988448i	$-0.451571\pi$
$823$	8.69576	0.303115	0.151558	+	0.988448i	$0.451571\pi$
$824$	8.72681	0.304013
$825$	−12.0627	−0.419969
$826$	−4.58464	−0.159520
$827$	43.6574	1.51812	0.759059	−	0.651022i	$-0.225659\pi$
$827$	43.6574	1.51812	0.759059	+	0.651022i	$0.225659\pi$
$828$	10.6051	0.368552
$829$	−2.65304	−0.0921438	−0.0460719	−	0.998938i	$-0.514670\pi$
$829$	−2.65304	−0.0921438	−0.0460719	+	0.998938i	$0.514670\pi$
$830$	22.3537	0.775909
$831$	−8.37683	−0.290589
$832$	−2.07153	−0.0718175
$833$	−2.33904	−0.0810428
$834$	9.08020	0.314422
$835$	93.8972	3.24945
$836$	2.57722	0.0891350
$837$	−9.76370	−0.337483
$838$	0.696655	0.0240655
$839$	−40.4459	−1.39635	−0.698173	−	0.715929i	$-0.746003\pi$
$839$	−40.4459	−1.39635	−0.698173	+	0.715929i	$0.746003\pi$
$840$	7.51064	0.259142
$841$	−13.6595	−0.471018
$842$	−2.79929	−0.0964700
$843$	10.8066	0.372198
$844$	−15.0544	−0.518194
$845$	51.7050	1.77871
$846$	5.75096	0.197722
$847$	−10.0050	−0.343775
$848$	−1.41433	−0.0485683
$849$	−17.5690	−0.602966
$850$	13.6390	0.467815
$851$	44.0465	1.50990
$852$	−19.5840	−0.670938
$853$	−45.6157	−1.56185	−0.780926	−	0.624624i	$-0.785252\pi$
$853$	−45.6157	−1.56185	−0.780926	+	0.624624i	$0.785252\pi$
$854$	−0.403351	−0.0138024
$855$	6.04347	0.206682
$856$	−16.4320	−0.561634
$857$	32.0881	1.09611	0.548055	−	0.836442i	$-0.315368\pi$
$857$	32.0881	1.09611	0.548055	+	0.836442i	$0.315368\pi$
$858$	0.337996	0.0115390
$859$	13.4212	0.457924	0.228962	−	0.973435i	$-0.426467\pi$
$859$	13.4212	0.457924	0.228962	+	0.973435i	$0.426467\pi$
$860$	−67.0761	−2.28728
$861$	2.43757	0.0830720
$862$	−13.6150	−0.463730
$863$	−12.5105	−0.425864	−0.212932	−	0.977067i	$-0.568301\pi$
$863$	−12.5105	−0.425864	−0.212932	+	0.977067i	$0.568301\pi$
$864$	4.91543	0.167226
$865$	−97.3926	−3.31145
$866$	6.42062	0.218182
$867$	11.5289	0.391542
$868$	−17.2573	−0.585751
$869$	1.45973	0.0495179
$870$	7.80807	0.264718
$871$	−4.87414	−0.165154
$872$	33.1771	1.12352
$873$	−15.7928	−0.534504
$874$	−4.22913	−0.143052
$875$	−29.3245	−0.991350
$876$	−14.6375	−0.494556
$877$	−48.5197	−1.63839	−0.819197	−	0.573512i	$-0.805581\pi$
$877$	−48.5197	−1.63839	−0.819197	+	0.573512i	$0.805581\pi$
$878$	−3.22713	−0.108911
$879$	−25.0315	−0.844292
$880$	−10.9659	−0.369661
$881$	−36.3124	−1.22340	−0.611698	−	0.791091i	$-0.709513\pi$
$881$	−36.3124	−1.22340	−0.611698	+	0.791091i	$0.709513\pi$
$882$	−0.482188	−0.0162361
$883$	−2.95751	−0.0995282	−0.0497641	−	0.998761i	$-0.515847\pi$
$883$	−2.95751	−0.0995282	−0.0497641	+	0.998761i	$0.515847\pi$
$884$	2.90520	0.0977124
$885$	39.3095	1.32137
$886$	−4.83847	−0.162552
$887$	−14.8873	−0.499866	−0.249933	−	0.968263i	$-0.580409\pi$
$887$	−14.8873	−0.499866	−0.249933	+	0.968263i	$0.580409\pi$
$888$	13.3360	0.447526
$889$	−7.55032	−0.253230
$890$	15.2902	0.512530
$891$	0.997504	0.0334176
$892$	−39.3114	−1.31624
$893$	17.4342	0.583414
$894$	6.42793	0.214982
$895$	43.0004	1.43735
$896$	11.2523	0.375913
$897$	4.21635	0.140780
$898$	−4.71338	−0.157288
$899$	−38.2414	−1.27542
$900$	−21.3741	−0.712471
$901$	1.24413	0.0414479
$902$	1.17243	0.0390377
$903$	9.17914	0.305463
$904$	−32.9448	−1.09573
$905$	47.6178	1.58287
$906$	−5.40732	−0.179646
$907$	−33.2948	−1.10554	−0.552768	−	0.833335i	$-0.686428\pi$
$907$	−33.2948	−1.10554	−0.552768	+	0.833335i	$0.686428\pi$
$908$	28.4283	0.943427
$909$	−1.71885	−0.0570107
$910$	1.40089	0.0464391
$911$	−26.2123	−0.868453	−0.434226	−	0.900804i	$-0.642978\pi$
$911$	−26.2123	−0.868453	−0.434226	+	0.900804i	$0.642978\pi$
$912$	3.88688	0.128708
$913$	11.1851	0.370173
$914$	−7.97375	−0.263748
$915$	3.45840	0.114331
$916$	−44.0157	−1.45432
$917$	16.6976	0.551402
$918$	−1.12786	−0.0372248
$919$	14.1267	0.465997	0.232998	−	0.972477i	$-0.425146\pi$
$919$	14.1267	0.465997	0.232998	+	0.972477i	$0.425146\pi$
$920$	45.0643	1.48573
$921$	−3.98673	−0.131367
$922$	3.27633	0.107900
$923$	−7.78618	−0.256285
$924$	1.76308	0.0580012
$925$	−88.7741	−2.91887
$926$	−0.772800	−0.0253958
$927$	4.80382	0.157778
$928$	19.2522	0.631986
$929$	22.9888	0.754238	0.377119	−	0.926165i	$-0.376915\pi$
$929$	22.9888	0.754238	0.377119	+	0.926165i	$0.376915\pi$
$930$	−19.4643	−0.638259
$931$	−1.46177	−0.0479075
$932$	11.8270	0.387406
$933$	−15.8134	−0.517706
$934$	8.65823	0.283306
$935$	9.64627	0.315467
$936$	1.27658	0.0417265
$937$	2.16799	0.0708253	0.0354126	−	0.999373i	$-0.488725\pi$
$937$	2.16799	0.0708253	0.0354126	+	0.999373i	$0.488725\pi$
$938$	3.34452	0.109202
$939$	11.6769	0.381063
$940$	−87.1545	−2.84267
$941$	37.9491	1.23711	0.618553	−	0.785743i	$-0.287719\pi$
$941$	37.9491	1.23711	0.618553	+	0.785743i	$0.287719\pi$
$942$	6.33937	0.206548
$943$	14.6255	0.476273
$944$	25.2820	0.822860
$945$	4.13435	0.134491
$946$	4.41502	0.143545
$947$	−14.3486	−0.466265	−0.233133	−	0.972445i	$-0.574898\pi$
$947$	−14.3486	−0.466265	−0.233133	+	0.972445i	$0.574898\pi$
$948$	2.58652	0.0840062
$949$	−5.81956	−0.188911
$950$	8.52364	0.276543
$951$	5.94931	0.192920
$952$	−4.24919	−0.137717
$953$	40.2665	1.30436	0.652179	−	0.758065i	$-0.273855\pi$
$953$	40.2665	1.30436	0.652179	+	0.758065i	$0.273855\pi$
$954$	0.256474	0.00830367
$955$	4.13435	0.133785
$956$	20.2857	0.656085
$957$	3.90692	0.126293
$958$	5.13286	0.165835
$959$	−1.54612	−0.0499268
$960$	−12.1876	−0.393354
$961$	64.3299	2.07516
$962$	2.48744	0.0801984
$963$	−9.04526	−0.291479
$964$	48.6142	1.56576
$965$	−89.4700	−2.88014
$966$	−2.89316	−0.0930858
$967$	−13.6675	−0.439517	−0.219759	−	0.975554i	$-0.570527\pi$
$967$	−13.6675	−0.439517	−0.219759	+	0.975554i	$0.570527\pi$
$968$	−18.1755	−0.584182
$969$	−3.41913	−0.109838
$970$	−31.4834	−1.01087
$971$	−4.15189	−0.133240	−0.0666202	−	0.997778i	$-0.521222\pi$
$971$	−4.15189	−0.133240	−0.0666202	+	0.997778i	$0.521222\pi$
$972$	1.76749	0.0566924
$973$	18.8312	0.603702
$974$	11.8858	0.380847
$975$	−8.49788	−0.272150
$976$	2.22428	0.0711975
$977$	59.5136	1.90401	0.952005	−	0.306083i	$-0.0990185\pi$
$977$	59.5136	1.90401	0.952005	+	0.306083i	$0.0990185\pi$
$978$	0.735420	0.0235161
$979$	7.65076	0.244519
$980$	7.30745	0.233428
$981$	18.2629	0.583089
$982$	−4.15683	−0.132650
$983$	22.9897	0.733257	0.366628	−	0.930367i	$-0.380512\pi$
$983$	22.9897	0.733257	0.366628	+	0.930367i	$0.380512\pi$
$984$	4.42818	0.141165
$985$	−61.9334	−1.97336
$986$	−4.41746	−0.140681
$987$	11.9268	0.379634
$988$	1.81559	0.0577616
$989$	55.0754	1.75130
$990$	1.98856	0.0632006
$991$	31.1292	0.988852	0.494426	−	0.869220i	$-0.335378\pi$
$991$	31.1292	0.988852	0.494426	+	0.869220i	$0.335378\pi$
$992$	−47.9928	−1.52377
$993$	27.8415	0.883523
$994$	5.34269	0.169460
$995$	−85.0576	−2.69651
$996$	19.8191	0.627992
$997$	32.8350	1.03990	0.519948	−	0.854198i	$-0.325951\pi$
$997$	32.8350	1.03990	0.519948	+	0.854198i	$0.325951\pi$
$998$	−7.65643	−0.242360
$999$	7.34101	0.232259

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.l.1.13	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.l.1.13	✓	28	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-0.482188 q^{2} -1.00000 q^{3} -1.76749 q^{4} -4.13435 q^{5} +0.482188 q^{6} +1.00000 q^{7} +1.81664 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.482188 q^{2} -1.00000 q^{3} -1.76749 q^{4} -4.13435 q^{5} +0.482188 q^{6} +1.00000 q^{7} +1.81664 q^{8} +1.00000 q^{9} +1.99354 q^{10} +0.997504 q^{11} +1.76749 q^{12} +0.702717 q^{13} -0.482188 q^{14} +4.13435 q^{15} +2.65903 q^{16} -2.33904 q^{17} -0.482188 q^{18} -1.46177 q^{19} +7.30745 q^{20} -1.00000 q^{21} -0.480984 q^{22} -6.00006 q^{23} -1.81664 q^{24} +12.0929 q^{25} -0.338842 q^{26} -1.00000 q^{27} -1.76749 q^{28} -3.91669 q^{29} -1.99354 q^{30} +9.76370 q^{31} -4.91543 q^{32} -0.997504 q^{33} +1.12786 q^{34} -4.13435 q^{35} -1.76749 q^{36} -7.34101 q^{37} +0.704847 q^{38} -0.702717 q^{39} -7.51064 q^{40} -2.43757 q^{41} +0.482188 q^{42} -9.17914 q^{43} -1.76308 q^{44} -4.13435 q^{45} +2.89316 q^{46} -11.9268 q^{47} -2.65903 q^{48} +1.00000 q^{49} -5.83105 q^{50} +2.33904 q^{51} -1.24205 q^{52} -0.531897 q^{53} +0.482188 q^{54} -4.12403 q^{55} +1.81664 q^{56} +1.46177 q^{57} +1.88858 q^{58} +9.50800 q^{59} -7.30745 q^{60} +0.836502 q^{61} -4.70794 q^{62} +1.00000 q^{63} -2.94789 q^{64} -2.90528 q^{65} +0.480984 q^{66} -6.93613 q^{67} +4.13423 q^{68} +6.00006 q^{69} +1.99354 q^{70} -11.0801 q^{71} +1.81664 q^{72} -8.28151 q^{73} +3.53975 q^{74} -12.0929 q^{75} +2.58367 q^{76} +0.997504 q^{77} +0.338842 q^{78} +1.46338 q^{79} -10.9934 q^{80} +1.00000 q^{81} +1.17536 q^{82} +11.2131 q^{83} +1.76749 q^{84} +9.67040 q^{85} +4.42607 q^{86} +3.91669 q^{87} +1.81211 q^{88} +7.66990 q^{89} +1.99354 q^{90} +0.702717 q^{91} +10.6051 q^{92} -9.76370 q^{93} +5.75096 q^{94} +6.04347 q^{95} +4.91543 q^{96} -15.7928 q^{97} -0.482188 q^{98} +0.997504 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9}+O(q^{10}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9	\( 28 q - 6 q^{2} - 28 q^{3} + 34 q^{4} + 8 q^{5} + 6 q^{6} + 28 q^{7} - 15 q^{8} + 28 q^{9} + 4 q^{10} - 8 q^{11} - 34 q^{12} + 26 q^{13} - 6 q^{14} - 8 q^{15} + 62 q^{16} + 9 q^{17} - 6 q^{18} + 25 q^{19} + 20 q^{20} - 28 q^{21} + 3 q^{22} - 30 q^{23} + 15 q^{24} + 42 q^{25} + 25 q^{26} - 28 q^{27} + 34 q^{28} - 5 q^{29} - 4 q^{30} + 18 q^{31} - 26 q^{32} + 8 q^{33} + 30 q^{34} + 8 q^{35} + 34 q^{36} + 36 q^{37} - 2 q^{38} - 26 q^{39} + 28 q^{40} + 21 q^{41} + 6 q^{42} + 8 q^{43} - 20 q^{44} + 8 q^{45} + 24 q^{46} + 6 q^{47} - 62 q^{48} + 28 q^{49} - 48 q^{50} - 9 q^{51} + 54 q^{52} - 12 q^{53} + 6 q^{54} + 15 q^{55} - 15 q^{56} - 25 q^{57} + 19 q^{58} + 33 q^{59} - 20 q^{60} + 48 q^{61} + 28 q^{63} + 75 q^{64} + 21 q^{65} - 3 q^{66} + 27 q^{67} + 19 q^{68} + 30 q^{69} + 4 q^{70} - 45 q^{71} - 15 q^{72} + 61 q^{73} - 31 q^{74} - 42 q^{75} + 63 q^{76} - 8 q^{77} - 25 q^{78} + 35 q^{79} + 84 q^{80} + 28 q^{81} + 11 q^{82} + 43 q^{83} - 34 q^{84} + 43 q^{85} - q^{86} + 5 q^{87} - 27 q^{88} + 25 q^{89} + 4 q^{90} + 26 q^{91} - 102 q^{92} - 18 q^{93} + 55 q^{94} - 43 q^{95} + 26 q^{96} + 40 q^{97} - 6 q^{98} - 8 q^{99}+O(q^{100}) \) 28 * q - 6 * q^2 - 28 * q^3 + 34 * q^4 + 8 * q^5 + 6 * q^6 + 28 * q^7 - 15 * q^8 + 28 * q^9 + 4 * q^10 - 8 * q^11 - 34 * q^12 + 26 * q^13 - 6 * q^14 - 8 * q^15 + 62 * q^16 + 9 * q^17 - 6 * q^18 + 25 * q^19 + 20 * q^20 - 28 * q^21 + 3 * q^22 - 30 * q^23 + 15 * q^24 + 42 * q^25 + 25 * q^26 - 28 * q^27 + 34 * q^28 - 5 * q^29 - 4 * q^30 + 18 * q^31 - 26 * q^32 + 8 * q^33 + 30 * q^34 + 8 * q^35 + 34 * q^36 + 36 * q^37 - 2 * q^38 - 26 * q^39 + 28 * q^40 + 21 * q^41 + 6 * q^42 + 8 * q^43 - 20 * q^44 + 8 * q^45 + 24 * q^46 + 6 * q^47 - 62 * q^48 + 28 * q^49 - 48 * q^50 - 9 * q^51 + 54 * q^52 - 12 * q^53 + 6 * q^54 + 15 * q^55 - 15 * q^56 - 25 * q^57 + 19 * q^58 + 33 * q^59 - 20 * q^60 + 48 * q^61 + 28 * q^63 + 75 * q^64 + 21 * q^65 - 3 * q^66 + 27 * q^67 + 19 * q^68 + 30 * q^69 + 4 * q^70 - 45 * q^71 - 15 * q^72 + 61 * q^73 - 31 * q^74 - 42 * q^75 + 63 * q^76 - 8 * q^77 - 25 * q^78 + 35 * q^79 + 84 * q^80 + 28 * q^81 + 11 * q^82 + 43 * q^83 - 34 * q^84 + 43 * q^85 - q^86 + 5 * q^87 - 27 * q^88 + 25 * q^89 + 4 * q^90 + 26 * q^91 - 102 * q^92 - 18 * q^93 + 55 * q^94 - 43 * q^95 + 26 * q^96 + 40 * q^97 - 6 * q^98 - 8 * q^99

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