LMFDB - Embedded newform 4011.2.a.e.1.1

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:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.86081$ of defining polynomial
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)

$f(q)$	$=$	$q-1.86081 q^{2} -1.00000 q^{3} +1.46260 q^{4} +1.46260 q^{5} +1.86081 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.86081 q^{2} -1.00000 q^{3} +1.46260 q^{4} +1.46260 q^{5} +1.86081 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.72161 q^{10} -2.92520 q^{11} -1.46260 q^{12} +0.676596 q^{13} +1.86081 q^{14} -1.46260 q^{15} -4.78600 q^{16} -7.11982 q^{17} -1.86081 q^{18} +7.32340 q^{19} +2.13919 q^{20} +1.00000 q^{21} +5.44322 q^{22} -6.72161 q^{23} -1.00000 q^{24} -2.86081 q^{25} -1.25901 q^{26} -1.00000 q^{27} -1.46260 q^{28} +3.00000 q^{29} +2.72161 q^{30} -9.04502 q^{31} +6.90582 q^{32} +2.92520 q^{33} +13.2486 q^{34} -1.46260 q^{35} +1.46260 q^{36} -3.25901 q^{37} -13.6274 q^{38} -0.676596 q^{39} +1.46260 q^{40} +11.0450 q^{41} -1.86081 q^{42} +0.278388 q^{43} -4.27839 q^{44} +1.46260 q^{45} +12.5076 q^{46} +7.76663 q^{47} +4.78600 q^{48} +1.00000 q^{49} +5.32340 q^{50} +7.11982 q^{51} +0.989588 q^{52} -9.30403 q^{53} +1.86081 q^{54} -4.27839 q^{55} -1.00000 q^{56} -7.32340 q^{57} -5.58242 q^{58} +4.71120 q^{59} -2.13919 q^{60} +10.7860 q^{61} +16.8310 q^{62} -1.00000 q^{63} -3.27839 q^{64} +0.989588 q^{65} -5.44322 q^{66} -6.46260 q^{67} -10.4134 q^{68} +6.72161 q^{69} +2.72161 q^{70} -11.2936 q^{71} +1.00000 q^{72} +5.74099 q^{73} +6.06439 q^{74} +2.86081 q^{75} +10.7112 q^{76} +2.92520 q^{77} +1.25901 q^{78} +6.39821 q^{79} -7.00000 q^{80} +1.00000 q^{81} -20.5526 q^{82} -11.1198 q^{83} +1.46260 q^{84} -10.4134 q^{85} -0.518027 q^{86} -3.00000 q^{87} -2.92520 q^{88} -5.90582 q^{89} -2.72161 q^{90} -0.676596 q^{91} -9.83102 q^{92} +9.04502 q^{93} -14.4522 q^{94} +10.7112 q^{95} -6.90582 q^{96} +17.5976 q^{97} -1.86081 q^{98} -2.92520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 2 q^{15} - 4 q^{16} - 7 q^{17} + 14 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 5 q^{26} - 3 q^{27} - 2 q^{28} + 9 q^{29} - 3 q^{30} - 8 q^{31} - 4 q^{32} + 4 q^{33} + 27 q^{34} - 2 q^{35} + 2 q^{36} - q^{37} - 5 q^{38} - 10 q^{39} + 2 q^{40} + 14 q^{41} + 12 q^{43} - 24 q^{44} + 2 q^{45} + 16 q^{46} - 7 q^{47} + 4 q^{48} + 3 q^{49} + 8 q^{50} + 7 q^{51} - q^{52} - 24 q^{55} - 3 q^{56} - 14 q^{57} - q^{59} - 12 q^{60} + 22 q^{61} + 21 q^{62} - 3 q^{63} - 21 q^{64} - q^{65} + 6 q^{66} - 17 q^{67} + 15 q^{68} + 9 q^{69} - 3 q^{70} - 2 q^{71} + 3 q^{72} + 26 q^{73} + 19 q^{74} + 3 q^{75} + 17 q^{76} + 4 q^{77} - 5 q^{78} + 16 q^{79} - 21 q^{80} + 3 q^{81} - 21 q^{82} - 19 q^{83} + 2 q^{84} + 15 q^{85} + 16 q^{86} - 9 q^{87} - 4 q^{88} + 7 q^{89} + 3 q^{90} - 10 q^{91} + 8 q^{93} - 37 q^{94} + 17 q^{95} + 4 q^{96} - 7 q^{97} - 4 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 2 * q^15 - 4 * q^16 - 7 * q^17 + 14 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 5 * q^26 - 3 * q^27 - 2 * q^28 + 9 * q^29 - 3 * q^30 - 8 * q^31 - 4 * q^32 + 4 * q^33 + 27 * q^34 - 2 * q^35 + 2 * q^36 - q^37 - 5 * q^38 - 10 * q^39 + 2 * q^40 + 14 * q^41 + 12 * q^43 - 24 * q^44 + 2 * q^45 + 16 * q^46 - 7 * q^47 + 4 * q^48 + 3 * q^49 + 8 * q^50 + 7 * q^51 - q^52 - 24 * q^55 - 3 * q^56 - 14 * q^57 - q^59 - 12 * q^60 + 22 * q^61 + 21 * q^62 - 3 * q^63 - 21 * q^64 - q^65 + 6 * q^66 - 17 * q^67 + 15 * q^68 + 9 * q^69 - 3 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 19 * q^74 + 3 * q^75 + 17 * q^76 + 4 * q^77 - 5 * q^78 + 16 * q^79 - 21 * q^80 + 3 * q^81 - 21 * q^82 - 19 * q^83 + 2 * q^84 + 15 * q^85 + 16 * q^86 - 9 * q^87 - 4 * q^88 + 7 * q^89 + 3 * q^90 - 10 * q^91 + 8 * q^93 - 37 * q^94 + 17 * q^95 + 4 * q^96 - 7 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.86081	−1.31579	−0.657894	−	0.753110i	$-0.728553\pi$
$2$	−1.86081	−1.31579	−0.657894	+	0.753110i	$0.728553\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.46260	0.731299
$5$	1.46260	0.654094	0.327047	−	0.945008i	$-0.393946\pi$
$5$	1.46260	0.654094	0.327047	+	0.945008i	$0.393946\pi$
$6$	1.86081	0.759671
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.72161	−0.860649
$11$	−2.92520	−0.881980	−0.440990	−	0.897512i	$-0.645373\pi$
$11$	−2.92520	−0.881980	−0.440990	+	0.897512i	$0.645373\pi$
$12$	−1.46260	−0.422216
$13$	0.676596	0.187654	0.0938269	−	0.995589i	$-0.470090\pi$
$13$	0.676596	0.187654	0.0938269	+	0.995589i	$0.470090\pi$
$14$	1.86081	0.497321
$15$	−1.46260	−0.377641
$16$	−4.78600	−1.19650
$17$	−7.11982	−1.72681	−0.863405	−	0.504512i	$-0.831673\pi$
$17$	−7.11982	−1.72681	−0.863405	+	0.504512i	$0.831673\pi$
$18$	−1.86081	−0.438596
$19$	7.32340	1.68010	0.840052	−	0.542506i	$-0.182524\pi$
$19$	7.32340	1.68010	0.840052	+	0.542506i	$0.182524\pi$
$20$	2.13919	0.478338
$21$	1.00000	0.218218
$22$	5.44322	1.16050
$23$	−6.72161	−1.40155	−0.700776	−	0.713381i	$-0.747163\pi$
$23$	−6.72161	−1.40155	−0.700776	+	0.713381i	$0.747163\pi$
$24$	−1.00000	−0.204124
$25$	−2.86081	−0.572161
$26$	−1.25901	−0.246913
$27$	−1.00000	−0.192450
$28$	−1.46260	−0.276405
$29$	3.00000	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$30$	2.72161	0.496896
$31$	−9.04502	−1.62453	−0.812266	−	0.583287i	$-0.801766\pi$
$31$	−9.04502	−1.62453	−0.812266	+	0.583287i	$0.801766\pi$
$32$	6.90582	1.22079
$33$	2.92520	0.509211
$34$	13.2486	2.27212
$35$	−1.46260	−0.247224
$36$	1.46260	0.243766
$37$	−3.25901	−0.535778	−0.267889	−	0.963450i	$-0.586326\pi$
$37$	−3.25901	−0.535778	−0.267889	+	0.963450i	$0.586326\pi$
$38$	−13.6274	−2.21066
$39$	−0.676596	−0.108342
$40$	1.46260	0.231257
$41$	11.0450	1.72494	0.862471	−	0.506107i	$-0.168916\pi$
$41$	11.0450	1.72494	0.862471	+	0.506107i	$0.168916\pi$
$42$	−1.86081	−0.287129
$43$	0.278388	0.0424538	0.0212269	−	0.999775i	$-0.493243\pi$
$43$	0.278388	0.0424538	0.0212269	+	0.999775i	$0.493243\pi$
$44$	−4.27839	−0.644991
$45$	1.46260	0.218031
$46$	12.5076	1.84415
$47$	7.76663	1.13288	0.566440	−	0.824103i	$-0.308320\pi$
$47$	7.76663	1.13288	0.566440	+	0.824103i	$0.308320\pi$
$48$	4.78600	0.690800
$49$	1.00000	0.142857
$50$	5.32340	0.752843
$51$	7.11982	0.996974
$52$	0.989588	0.137231
$53$	−9.30403	−1.27801	−0.639003	−	0.769204i	$-0.720653\pi$
$53$	−9.30403	−1.27801	−0.639003	+	0.769204i	$0.720653\pi$
$54$	1.86081	0.253224
$55$	−4.27839	−0.576898
$56$	−1.00000	−0.133631
$57$	−7.32340	−0.970009
$58$	−5.58242	−0.733007
$59$	4.71120	0.613346	0.306673	−	0.951815i	$-0.400784\pi$
$59$	4.71120	0.613346	0.306673	+	0.951815i	$0.400784\pi$
$60$	−2.13919	−0.276169
$61$	10.7860	1.38101	0.690503	−	0.723329i	$-0.257389\pi$
$61$	10.7860	1.38101	0.690503	+	0.723329i	$0.257389\pi$
$62$	16.8310	2.13754
$63$	−1.00000	−0.125988
$64$	−3.27839	−0.409799
$65$	0.989588	0.122743
$66$	−5.44322	−0.670014
$67$	−6.46260	−0.789532	−0.394766	−	0.918782i	$-0.629174\pi$
$67$	−6.46260	−0.789532	−0.394766	+	0.918782i	$0.629174\pi$
$68$	−10.4134	−1.26281
$69$	6.72161	0.809187
$70$	2.72161	0.325295
$71$	−11.2936	−1.34031	−0.670153	−	0.742223i	$-0.733771\pi$
$71$	−11.2936	−1.34031	−0.670153	+	0.742223i	$0.733771\pi$
$72$	1.00000	0.117851
$73$	5.74099	0.671932	0.335966	−	0.941874i	$-0.390937\pi$
$73$	5.74099	0.671932	0.335966	+	0.941874i	$0.390937\pi$
$74$	6.06439	0.704971
$75$	2.86081	0.330337
$76$	10.7112	1.22866
$77$	2.92520	0.333357
$78$	1.25901	0.142555
$79$	6.39821	0.719855	0.359927	−	0.932980i	$-0.382801\pi$
$79$	6.39821	0.719855	0.359927	+	0.932980i	$0.382801\pi$
$80$	−7.00000	−0.782624
$81$	1.00000	0.111111
$82$	−20.5526	−2.26966
$83$	−11.1198	−1.22056	−0.610279	−	0.792186i	$-0.708943\pi$
$83$	−11.1198	−1.22056	−0.610279	+	0.792186i	$0.708943\pi$
$84$	1.46260	0.159583
$85$	−10.4134	−1.12950
$86$	−0.518027	−0.0558602
$87$	−3.00000	−0.321634
$88$	−2.92520	−0.311827
$89$	−5.90582	−0.626016	−0.313008	−	0.949751i	$-0.601337\pi$
$89$	−5.90582	−0.626016	−0.313008	+	0.949751i	$0.601337\pi$
$90$	−2.72161	−0.286883
$91$	−0.676596	−0.0709265
$92$	−9.83102	−1.02495
$93$	9.04502	0.937924
$94$	−14.4522	−1.49063
$95$	10.7112	1.09895
$96$	−6.90582	−0.704822
$97$	17.5976	1.78677	0.893385	−	0.449292i	$-0.148324\pi$
$97$	17.5976	1.78677	0.893385	+	0.449292i	$0.148324\pi$
$98$	−1.86081	−0.187970
$99$	−2.92520	−0.293993
$100$	−4.18421	−0.418421
$101$	12.3684	1.23070	0.615352	−	0.788253i	$-0.289014\pi$
$101$	12.3684	1.23070	0.615352	+	0.788253i	$0.289014\pi$
$102$	−13.2486	−1.31181
$103$	−2.72161	−0.268168	−0.134084	−	0.990970i	$-0.542809\pi$
$103$	−2.72161	−0.268168	−0.134084	+	0.990970i	$0.542809\pi$
$104$	0.676596	0.0663457
$105$	1.46260	0.142735
$106$	17.3130	1.68159
$107$	−0.0297872	−0.00287963	−0.00143982	−	0.999999i	$-0.500458\pi$
$107$	−0.0297872	−0.00287963	−0.00143982	+	0.999999i	$0.500458\pi$
$108$	−1.46260	−0.140739
$109$	16.9404	1.62260	0.811299	−	0.584631i	$-0.198761\pi$
$109$	16.9404	1.62260	0.811299	+	0.584631i	$0.198761\pi$
$110$	7.96125	0.759075
$111$	3.25901	0.309332
$112$	4.78600	0.452235
$113$	14.1648	1.33252	0.666258	−	0.745721i	$-0.267895\pi$
$113$	14.1648	1.33252	0.666258	+	0.745721i	$0.267895\pi$
$114$	13.6274	1.27633
$115$	−9.83102	−0.916747
$116$	4.38780	0.407397
$117$	0.676596	0.0625513
$118$	−8.76663	−0.807033
$119$	7.11982	0.652673
$120$	−1.46260	−0.133516
$121$	−2.44322	−0.222111
$122$	−20.0707	−1.81711
$123$	−11.0450	−0.995896
$124$	−13.2292	−1.18802
$125$	−11.4972	−1.02834
$126$	1.86081	0.165774
$127$	16.0990	1.42855	0.714277	−	0.699863i	$-0.246755\pi$
$127$	16.0990	1.42855	0.714277	+	0.699863i	$0.246755\pi$
$128$	−7.71120	−0.681580
$129$	−0.278388	−0.0245107
$130$	−1.84143	−0.161504
$131$	−7.31299	−0.638939	−0.319470	−	0.947597i	$-0.603505\pi$
$131$	−7.31299	−0.638939	−0.319470	+	0.947597i	$0.603505\pi$
$132$	4.27839	0.372386
$133$	−7.32340	−0.635020
$134$	12.0256	1.03886
$135$	−1.46260	−0.125880
$136$	−7.11982	−0.610519
$137$	−5.75622	−0.491787	−0.245893	−	0.969297i	$-0.579081\pi$
$137$	−5.75622	−0.491787	−0.245893	+	0.969297i	$0.579081\pi$
$138$	−12.5076	−1.06472
$139$	−2.71120	−0.229961	−0.114980	−	0.993368i	$-0.536681\pi$
$139$	−2.71120	−0.229961	−0.114980	+	0.993368i	$0.536681\pi$
$140$	−2.13919	−0.180795
$141$	−7.76663	−0.654068
$142$	21.0152	1.76356
$143$	−1.97918	−0.165507
$144$	−4.78600	−0.398834
$145$	4.38780	0.364387
$146$	−10.6829	−0.884120
$147$	−1.00000	−0.0824786
$148$	−4.76663	−0.391814
$149$	−20.6814	−1.69429	−0.847144	−	0.531364i	$-0.821680\pi$
$149$	−20.6814	−1.69429	−0.847144	+	0.531364i	$0.821680\pi$
$150$	−5.32340	−0.434654
$151$	3.54781	0.288717	0.144358	−	0.989525i	$-0.453888\pi$
$151$	3.54781	0.288717	0.144358	+	0.989525i	$0.453888\pi$
$152$	7.32340	0.594007
$153$	−7.11982	−0.575603
$154$	−5.44322	−0.438627
$155$	−13.2292	−1.06260
$156$	−0.989588	−0.0792304
$157$	−15.0900	−1.20432	−0.602158	−	0.798377i	$-0.705692\pi$
$157$	−15.0900	−1.20432	−0.602158	+	0.798377i	$0.705692\pi$
$158$	−11.9058	−0.947176
$159$	9.30403	0.737858
$160$	10.1004	0.798510
$161$	6.72161	0.529737
$162$	−1.86081	−0.146199
$163$	0.547814	0.0429081	0.0214540	−	0.999770i	$-0.493170\pi$
$163$	0.547814	0.0429081	0.0214540	+	0.999770i	$0.493170\pi$
$164$	16.1544	1.26145
$165$	4.27839	0.333072
$166$	20.6918	1.60600
$167$	−9.87603	−0.764231	−0.382115	−	0.924115i	$-0.624804\pi$
$167$	−9.87603	−0.764231	−0.382115	+	0.924115i	$0.624804\pi$
$168$	1.00000	0.0771517
$169$	−12.5422	−0.964786
$170$	19.3774	1.48618
$171$	7.32340	0.560035
$172$	0.407170	0.0310464
$173$	−6.30818	−0.479602	−0.239801	−	0.970822i	$-0.577082\pi$
$173$	−6.30818	−0.479602	−0.239801	+	0.970822i	$0.577082\pi$
$174$	5.58242	0.423202
$175$	2.86081	0.216257
$176$	14.0000	1.05529
$177$	−4.71120	−0.354115
$178$	10.9896	0.823704
$179$	12.4626	0.931498	0.465749	−	0.884917i	$-0.345785\pi$
$179$	12.4626	0.931498	0.465749	+	0.884917i	$0.345785\pi$
$180$	2.13919	0.159446
$181$	−9.06439	−0.673751	−0.336875	−	0.941549i	$-0.609370\pi$
$181$	−9.06439	−0.673751	−0.336875	+	0.941549i	$0.609370\pi$
$182$	1.25901	0.0933243
$183$	−10.7860	−0.797324
$184$	−6.72161	−0.495524
$185$	−4.76663	−0.350449
$186$	−16.8310	−1.23411
$187$	20.8269	1.52301
$188$	11.3595	0.828474
$189$	1.00000	0.0727393
$190$	−19.9315	−1.44598
$191$	1.00000	0.0723575
$191$	1.00000	0.0723575
$192$	3.27839	0.236597
$193$	−0.293617	−0.0211350	−0.0105675	−	0.999944i	$-0.503364\pi$
$193$	−0.293617	−0.0211350	−0.0105675	+	0.999944i	$0.503364\pi$
$194$	−32.7458	−2.35101
$195$	−0.989588	−0.0708659
$196$	1.46260	0.104471
$197$	10.9508	0.780215	0.390107	−	0.920769i	$-0.372438\pi$
$197$	10.9508	0.780215	0.390107	+	0.920769i	$0.372438\pi$
$198$	5.44322	0.386833
$199$	24.6081	1.74442	0.872210	−	0.489132i	$-0.162687\pi$
$199$	24.6081	1.74442	0.872210	+	0.489132i	$0.162687\pi$
$200$	−2.86081	−0.202290
$201$	6.46260	0.455837
$202$	−23.0152	−1.61935
$203$	−3.00000	−0.210559
$204$	10.4134	0.729086
$205$	16.1544	1.12827
$206$	5.06439	0.352853
$207$	−6.72161	−0.467184
$208$	−3.23819	−0.224528
$209$	−21.4224	−1.48182
$210$	−2.72161	−0.187809
$211$	−9.54222	−0.656913	−0.328457	−	0.944519i	$-0.606529\pi$
$211$	−9.54222	−0.656913	−0.328457	+	0.944519i	$0.606529\pi$
$212$	−13.6081	−0.934605
$213$	11.2936	0.773826
$214$	0.0554281	0.00378899
$215$	0.407170	0.0277688
$216$	−1.00000	−0.0680414
$217$	9.04502	0.614016
$218$	−31.5228	−2.13500
$219$	−5.74099	−0.387940
$220$	−6.25756	−0.421885
$221$	−4.81724	−0.324043
$222$	−6.06439	−0.407015
$223$	15.3040	1.02483	0.512417	−	0.858737i	$-0.328750\pi$
$223$	15.3040	1.02483	0.512417	+	0.858737i	$0.328750\pi$
$224$	−6.90582	−0.461415
$225$	−2.86081	−0.190720
$226$	−26.3580	−1.75331
$227$	23.8206	1.58103	0.790515	−	0.612443i	$-0.209813\pi$
$227$	23.8206	1.58103	0.790515	+	0.612443i	$0.209813\pi$
$228$	−10.7112	−0.709367
$229$	27.9211	1.84507	0.922537	−	0.385907i	$-0.126112\pi$
$229$	27.9211	1.84507	0.922537	+	0.385907i	$0.126112\pi$
$230$	18.2936	1.20625
$231$	−2.92520	−0.192464
$232$	3.00000	0.196960
$233$	−1.73684	−0.113784	−0.0568921	−	0.998380i	$-0.518119\pi$
$233$	−1.73684	−0.113784	−0.0568921	+	0.998380i	$0.518119\pi$
$234$	−1.25901	−0.0823043
$235$	11.3595	0.741009
$236$	6.89059	0.448539
$237$	−6.39821	−0.415608
$238$	−13.2486	−0.858779
$239$	−15.2292	−0.985097	−0.492548	−	0.870285i	$-0.663935\pi$
$239$	−15.2292	−0.985097	−0.492548	+	0.870285i	$0.663935\pi$
$240$	7.00000	0.451848
$241$	12.2188	0.787083	0.393541	−	0.919307i	$-0.371250\pi$
$241$	12.2188	0.787083	0.393541	+	0.919307i	$0.371250\pi$
$242$	4.54636	0.292251
$243$	−1.00000	−0.0641500
$244$	15.7756	1.00993
$245$	1.46260	0.0934420
$246$	20.5526	1.31039
$247$	4.95498	0.315278
$248$	−9.04502	−0.574359
$249$	11.1198	0.704690
$250$	21.3941	1.35308
$251$	−18.6468	−1.17698	−0.588488	−	0.808506i	$-0.700277\pi$
$251$	−18.6468	−1.17698	−0.588488	+	0.808506i	$0.700277\pi$
$252$	−1.46260	−0.0921350
$253$	19.6620	1.23614
$254$	−29.9571	−1.87968
$255$	10.4134	0.652115
$256$	20.9058	1.30661
$257$	12.1752	0.759471	0.379736	−	0.925095i	$-0.376015\pi$
$257$	12.1752	0.759471	0.379736	+	0.925095i	$0.376015\pi$
$258$	0.518027	0.0322509
$259$	3.25901	0.202505
$260$	1.44737	0.0897621
$261$	3.00000	0.185695
$262$	13.6081	0.840709
$263$	3.19317	0.196899	0.0984497	−	0.995142i	$-0.468612\pi$
$263$	3.19317	0.196899	0.0984497	+	0.995142i	$0.468612\pi$
$264$	2.92520	0.180033
$265$	−13.6081	−0.835936
$266$	13.6274	0.835552
$267$	5.90582	0.361430
$268$	−9.45219	−0.577384
$269$	−28.9854	−1.76727	−0.883637	−	0.468173i	$-0.844912\pi$
$269$	−28.9854	−1.76727	−0.883637	+	0.468173i	$0.844912\pi$
$270$	2.72161	0.165632
$271$	−3.06439	−0.186148	−0.0930742	−	0.995659i	$-0.529669\pi$
$271$	−3.06439	−0.186148	−0.0930742	+	0.995659i	$0.529669\pi$
$272$	34.0755	2.06613
$273$	0.676596	0.0409494
$274$	10.7112	0.647087
$275$	8.36842	0.504635
$276$	9.83102	0.591758
$277$	2.75140	0.165316	0.0826578	−	0.996578i	$-0.473659\pi$
$277$	2.75140	0.165316	0.0826578	+	0.996578i	$0.473659\pi$
$278$	5.04502	0.302580
$279$	−9.04502	−0.541511
$280$	−1.46260	−0.0874070
$281$	11.4343	0.682111	0.341055	−	0.940043i	$-0.389216\pi$
$281$	11.4343	0.682111	0.341055	+	0.940043i	$0.389216\pi$
$282$	14.4522	0.860615
$283$	8.00000	0.475551	0.237775	−	0.971320i	$-0.423582\pi$
$283$	8.00000	0.475551	0.237775	+	0.971320i	$0.423582\pi$
$284$	−16.5180	−0.980165
$285$	−10.7112	−0.634477
$286$	3.68286	0.217772
$287$	−11.0450	−0.651967
$288$	6.90582	0.406929
$289$	33.6918	1.98187
$290$	−8.16484	−0.479456
$291$	−17.5976	−1.03159
$292$	8.39676	0.491383
$293$	26.6918	1.55935	0.779677	−	0.626183i	$-0.215384\pi$
$293$	26.6918	1.55935	0.779677	+	0.626183i	$0.215384\pi$
$294$	1.86081	0.108524
$295$	6.89059	0.401186
$296$	−3.25901	−0.189426
$297$	2.92520	0.169737
$298$	38.4841	2.22932
$299$	−4.54781	−0.263007
$300$	4.18421	0.241575
$301$	−0.278388	−0.0160460
$302$	−6.60179	−0.379890
$303$	−12.3684	−0.710547
$304$	−35.0498	−2.01025
$305$	15.7756	0.903308
$306$	13.2486	0.757372
$307$	21.6710	1.23683	0.618415	−	0.785852i	$-0.287775\pi$
$307$	21.6710	1.23683	0.618415	+	0.785852i	$0.287775\pi$
$308$	4.27839	0.243784
$309$	2.72161	0.154827
$310$	24.6170	1.39815
$311$	6.65577	0.377414	0.188707	−	0.982033i	$-0.439570\pi$
$311$	6.65577	0.377414	0.188707	+	0.982033i	$0.439570\pi$
$312$	−0.676596	−0.0383047
$313$	−20.1946	−1.14147	−0.570734	−	0.821135i	$-0.693341\pi$
$313$	−20.1946	−1.14147	−0.570734	+	0.821135i	$0.693341\pi$
$314$	28.0796	1.58462
$315$	−1.46260	−0.0824081
$316$	9.35801	0.526429
$317$	12.0498	0.676786	0.338393	−	0.941005i	$-0.390117\pi$
$317$	12.0498	0.676786	0.338393	+	0.941005i	$0.390117\pi$
$318$	−17.3130	−0.970864
$319$	−8.77559	−0.491339
$320$	−4.79497	−0.268047
$321$	0.0297872	0.00166256
$322$	−12.5076	−0.697022
$323$	−52.1413	−2.90122
$324$	1.46260	0.0812555
$325$	−1.93561	−0.107368
$326$	−1.01938	−0.0564580
$327$	−16.9404	−0.936808
$328$	11.0450	0.609859
$329$	−7.76663	−0.428188
$330$	−7.96125	−0.438252
$331$	9.80683	0.539032	0.269516	−	0.962996i	$-0.413136\pi$
$331$	9.80683	0.539032	0.269516	+	0.962996i	$0.413136\pi$
$332$	−16.2638	−0.892594
$333$	−3.25901	−0.178593
$334$	18.3774	1.00557
$335$	−9.45219	−0.516428
$336$	−4.78600	−0.261098
$337$	19.2501	1.04862	0.524309	−	0.851528i	$-0.324324\pi$
$337$	19.2501	1.04862	0.524309	+	0.851528i	$0.324324\pi$
$338$	23.3386	1.26945
$339$	−14.1648	−0.769328
$340$	−15.2307	−0.825999
$341$	26.4585	1.43281
$342$	−13.6274	−0.736887
$343$	−1.00000	−0.0539949
$344$	0.278388	0.0150097
$345$	9.83102	0.529284
$346$	11.7383	0.631054
$347$	−0.104590	−0.00561470	−0.00280735	−	0.999996i	$-0.500894\pi$
$347$	−0.104590	−0.00561470	−0.00280735	+	0.999996i	$0.500894\pi$
$348$	−4.38780	−0.235211
$349$	24.0811	1.28903	0.644515	−	0.764592i	$-0.277059\pi$
$349$	24.0811	1.28903	0.644515	+	0.764592i	$0.277059\pi$
$350$	−5.32340	−0.284548
$351$	−0.676596	−0.0361140
$352$	−20.2009	−1.07671
$353$	−34.0361	−1.81156	−0.905778	−	0.423752i	$-0.860713\pi$
$353$	−34.0361	−1.81156	−0.905778	+	0.423752i	$0.860713\pi$
$354$	8.76663	0.465941
$355$	−16.5180	−0.876686
$356$	−8.63785	−0.457805
$357$	−7.11982	−0.376821
$358$	−23.1905	−1.22565
$359$	26.5616	1.40187	0.700934	−	0.713226i	$-0.252767\pi$
$359$	26.5616	1.40187	0.700934	+	0.713226i	$0.252767\pi$
$360$	1.46260	0.0770857
$361$	34.6323	1.82275
$362$	16.8671	0.886514
$363$	2.44322	0.128236
$364$	−0.989588	−0.0518685
$365$	8.39676	0.439506
$366$	20.0707	1.04911
$367$	16.5735	0.865127	0.432564	−	0.901603i	$-0.357609\pi$
$367$	16.5735	0.865127	0.432564	+	0.901603i	$0.357609\pi$
$368$	32.1697	1.67696
$369$	11.0450	0.574981
$370$	8.86977	0.461117
$371$	9.30403	0.483041
$372$	13.2292	0.685903
$373$	22.9162	1.18656	0.593279	−	0.804997i	$-0.297833\pi$
$373$	22.9162	1.18656	0.593279	+	0.804997i	$0.297833\pi$
$374$	−38.7548	−2.00396
$375$	11.4972	0.593713
$376$	7.76663	0.400533
$377$	2.02979	0.104539
$378$	−1.86081	−0.0957095
$379$	−14.4176	−0.740581	−0.370291	−	0.928916i	$-0.620742\pi$
$379$	−14.4176	−0.740581	−0.370291	+	0.928916i	$0.620742\pi$
$380$	15.6662	0.803658
$381$	−16.0990	−0.824776
$382$	−1.86081	−0.0952071
$383$	−22.8954	−1.16990	−0.584950	−	0.811069i	$-0.698886\pi$
$383$	−22.8954	−1.16990	−0.584950	+	0.811069i	$0.698886\pi$
$384$	7.71120	0.393511
$385$	4.27839	0.218047
$386$	0.546364	0.0278092
$387$	0.278388	0.0141513
$388$	25.7383	1.30666
$389$	3.00896	0.152560	0.0762802	−	0.997086i	$-0.475696\pi$
$389$	3.00896	0.152560	0.0762802	+	0.997086i	$0.475696\pi$
$390$	1.84143	0.0932445
$391$	47.8567	2.42022
$392$	1.00000	0.0505076
$393$	7.31299	0.368892
$394$	−20.3774	−1.02660
$395$	9.35801	0.470852
$396$	−4.27839	−0.214997
$397$	8.85184	0.444261	0.222131	−	0.975017i	$-0.428699\pi$
$397$	8.85184	0.444261	0.222131	+	0.975017i	$0.428699\pi$
$398$	−45.7908	−2.29529
$399$	7.32340	0.366629
$400$	13.6918	0.684591
$401$	−12.5076	−0.624600	−0.312300	−	0.949983i	$-0.601099\pi$
$401$	−12.5076	−0.624600	−0.312300	+	0.949983i	$0.601099\pi$
$402$	−12.0256	−0.599784
$403$	−6.11982	−0.304850
$404$	18.0900	0.900013
$405$	1.46260	0.0726771
$406$	5.58242	0.277051
$407$	9.53326	0.472546
$408$	7.11982	0.352484
$409$	30.9508	1.53042	0.765210	−	0.643780i	$-0.222635\pi$
$409$	30.9508	1.53042	0.765210	+	0.643780i	$0.222635\pi$
$410$	−30.0602	−1.48457
$411$	5.75622	0.283933
$412$	−3.98062	−0.196111
$413$	−4.71120	−0.231823
$414$	12.5076	0.614716
$415$	−16.2638	−0.798360
$416$	4.67245	0.229086
$417$	2.71120	0.132768
$418$	39.8629	1.94976
$419$	−10.2486	−0.500677	−0.250338	−	0.968158i	$-0.580542\pi$
$419$	−10.2486	−0.500677	−0.250338	+	0.968158i	$0.580542\pi$
$420$	2.13919	0.104382
$421$	34.3788	1.67552	0.837761	−	0.546037i	$-0.183864\pi$
$421$	34.3788	1.67552	0.837761	+	0.546037i	$0.183864\pi$
$422$	17.7562	0.864359
$423$	7.76663	0.377626
$424$	−9.30403	−0.451844
$425$	20.3684	0.988014
$426$	−21.0152	−1.01819
$427$	−10.7860	−0.521971
$428$	−0.0435667	−0.00210587
$429$	1.97918	0.0955555
$430$	−0.757665	−0.0365378
$431$	38.9155	1.87449	0.937246	−	0.348669i	$-0.113366\pi$
$431$	38.9155	1.87449	0.937246	+	0.348669i	$0.113366\pi$
$432$	4.78600	0.230267
$433$	27.0152	1.29827	0.649135	−	0.760674i	$-0.275131\pi$
$433$	27.0152	1.29827	0.649135	+	0.760674i	$0.275131\pi$
$434$	−16.8310	−0.807915
$435$	−4.38780	−0.210379
$436$	24.7770	1.18661
$437$	−49.2251	−2.35475
$438$	10.6829	0.510447
$439$	9.03605	0.431267	0.215634	−	0.976474i	$-0.430818\pi$
$439$	9.03605	0.431267	0.215634	+	0.976474i	$0.430818\pi$
$440$	−4.27839	−0.203964
$441$	1.00000	0.0476190
$442$	8.96395	0.426371
$443$	7.58387	0.360320	0.180160	−	0.983637i	$-0.442338\pi$
$443$	7.58387	0.360320	0.180160	+	0.983637i	$0.442338\pi$
$444$	4.76663	0.226214
$445$	−8.63785	−0.409473
$446$	−28.4778	−1.34846
$447$	20.6814	0.978197
$448$	3.27839	0.154889
$449$	12.4972	0.589779	0.294890	−	0.955531i	$-0.404717\pi$
$449$	12.4972	0.589779	0.294890	+	0.955531i	$0.404717\pi$
$450$	5.32340	0.250948
$451$	−32.3088	−1.52136
$452$	20.7175	0.974468
$453$	−3.54781	−0.166691
$454$	−44.3255	−2.08030
$455$	−0.989588	−0.0463926
$456$	−7.32340	−0.342950
$457$	−22.7610	−1.06472	−0.532358	−	0.846519i	$-0.678694\pi$
$457$	−22.7610	−1.06472	−0.532358	+	0.846519i	$0.678694\pi$
$458$	−51.9557	−2.42773
$459$	7.11982	0.332325
$460$	−14.3788	−0.670417
$461$	−6.78455	−0.315988	−0.157994	−	0.987440i	$-0.550503\pi$
$461$	−6.78455	−0.315988	−0.157994	+	0.987440i	$0.550503\pi$
$462$	5.44322	0.253242
$463$	−31.6274	−1.46985	−0.734926	−	0.678148i	$-0.762783\pi$
$463$	−31.6274	−1.46985	−0.734926	+	0.678148i	$0.762783\pi$
$464$	−14.3580	−0.666554
$465$	13.2292	0.613491
$466$	3.23192	0.149716
$467$	−29.9494	−1.38589	−0.692946	−	0.720989i	$-0.743688\pi$
$467$	−29.9494	−1.38589	−0.692946	+	0.720989i	$0.743688\pi$
$468$	0.989588	0.0457437
$469$	6.46260	0.298415
$470$	−21.1377	−0.975011
$471$	15.0900	0.695312
$472$	4.71120	0.216851
$473$	−0.814341	−0.0374434
$474$	11.9058	0.546853
$475$	−20.9508	−0.961290
$476$	10.4134	0.477299
$477$	−9.30403	−0.426002
$478$	28.3386	1.29618
$479$	20.5180	0.937493	0.468746	−	0.883333i	$-0.344706\pi$
$479$	20.5180	0.937493	0.468746	+	0.883333i	$0.344706\pi$
$480$	−10.1004	−0.461020
$481$	−2.20503	−0.100541
$482$	−22.7368	−1.03563
$483$	−6.72161	−0.305844
$484$	−3.57345	−0.162430
$485$	25.7383	1.16872
$486$	1.86081	0.0844079
$487$	−27.8116	−1.26027	−0.630133	−	0.776487i	$-0.717000\pi$
$487$	−27.8116	−1.26027	−0.630133	+	0.776487i	$0.717000\pi$
$488$	10.7860	0.488259
$489$	−0.547814	−0.0247730
$490$	−2.72161	−0.122950
$491$	19.2445	0.868490	0.434245	−	0.900795i	$-0.357015\pi$
$491$	19.2445	0.868490	0.434245	+	0.900795i	$0.357015\pi$
$492$	−16.1544	−0.728298
$493$	−21.3595	−0.961982
$494$	−9.22026	−0.414839
$495$	−4.27839	−0.192299
$496$	43.2895	1.94375
$497$	11.2936	0.506588
$498$	−20.6918	−0.927223
$499$	−17.5512	−0.785699	−0.392849	−	0.919603i	$-0.628511\pi$
$499$	−17.5512	−0.785699	−0.392849	+	0.919603i	$0.628511\pi$
$500$	−16.8158	−0.752025
$501$	9.87603	0.441229
$502$	34.6981	1.54865
$503$	30.5228	1.36095	0.680473	−	0.732773i	$-0.261774\pi$
$503$	30.5228	1.36095	0.680473	+	0.732773i	$0.261774\pi$
$504$	−1.00000	−0.0445435
$505$	18.0900	0.804996
$506$	−36.5872	−1.62650
$507$	12.5422	0.557019
$508$	23.5464	1.04470
$509$	−12.6032	−0.558629	−0.279314	−	0.960200i	$-0.590107\pi$
$509$	−12.6032	−0.558629	−0.279314	+	0.960200i	$0.590107\pi$
$510$	−19.3774	−0.858045
$511$	−5.74099	−0.253966
$512$	−23.4793	−1.03765
$513$	−7.32340	−0.323336
$514$	−22.6558	−0.999303
$515$	−3.98062	−0.175407
$516$	−0.407170	−0.0179247
$517$	−22.7189	−0.999177
$518$	−6.06439	−0.266454
$519$	6.30818	0.276898
$520$	0.989588	0.0433963
$521$	30.8954	1.35355	0.676776	−	0.736189i	$-0.263376\pi$
$521$	30.8954	1.35355	0.676776	+	0.736189i	$0.263376\pi$
$522$	−5.58242	−0.244336
$523$	18.5962	0.813155	0.406577	−	0.913616i	$-0.366722\pi$
$523$	18.5962	0.813155	0.406577	+	0.913616i	$0.366722\pi$
$524$	−10.6960	−0.467256
$525$	−2.86081	−0.124856
$526$	−5.94187	−0.259078
$527$	64.3989	2.80526
$528$	−14.0000	−0.609272
$529$	22.1801	0.964351
$530$	25.3220	1.09992
$531$	4.71120	0.204449
$532$	−10.7112	−0.464389
$533$	7.47301	0.323692
$534$	−10.9896	−0.475566
$535$	−0.0435667	−0.00188355
$536$	−6.46260	−0.279142
$537$	−12.4626	−0.537801
$538$	53.9363	2.32536
$539$	−2.92520	−0.125997
$540$	−2.13919	−0.0920563
$541$	5.66137	0.243401	0.121701	−	0.992567i	$-0.461165\pi$
$541$	5.66137	0.243401	0.121701	+	0.992567i	$0.461165\pi$
$542$	5.70224	0.244932
$543$	9.06439	0.388990
$544$	−49.1682	−2.10807
$545$	24.7770	1.06133
$546$	−1.25901	−0.0538808
$547$	−4.11086	−0.175768	−0.0878838	−	0.996131i	$-0.528010\pi$
$547$	−4.11086	−0.175768	−0.0878838	+	0.996131i	$0.528010\pi$
$548$	−8.41903	−0.359643
$549$	10.7860	0.460335
$550$	−15.5720	−0.663993
$551$	21.9702	0.935963
$552$	6.72161	0.286091
$553$	−6.39821	−0.272079
$554$	−5.11982	−0.217520
$555$	4.76663	0.202332
$556$	−3.96540	−0.168170
$557$	14.6316	0.619960	0.309980	−	0.950743i	$-0.399678\pi$
$557$	14.6316	0.619960	0.309980	+	0.950743i	$0.399678\pi$
$558$	16.8310	0.712514
$559$	0.188356	0.00796662
$560$	7.00000	0.295804
$561$	−20.8269	−0.879311
$562$	−21.2769	−0.897514
$563$	−41.3822	−1.74405	−0.872026	−	0.489460i	$-0.837194\pi$
$563$	−41.3822	−1.74405	−0.872026	+	0.489460i	$0.837194\pi$
$564$	−11.3595	−0.478319
$565$	20.7175	0.871590
$566$	−14.8864	−0.625724
$567$	−1.00000	−0.0419961
$568$	−11.2936	−0.473870
$569$	44.1413	1.85050	0.925250	−	0.379358i	$-0.123855\pi$
$569$	44.1413	1.85050	0.925250	+	0.379358i	$0.123855\pi$
$570$	19.9315	0.834837
$571$	−5.06024	−0.211765	−0.105882	−	0.994379i	$-0.533767\pi$
$571$	−5.06024	−0.211765	−0.105882	+	0.994379i	$0.533767\pi$
$572$	−2.89474	−0.121035
$573$	−1.00000	−0.0417756
$574$	20.5526	0.857850
$575$	19.2292	0.801914
$576$	−3.27839	−0.136600
$577$	−12.4536	−0.518452	−0.259226	−	0.965817i	$-0.583467\pi$
$577$	−12.4536	−0.518452	−0.259226	+	0.965817i	$0.583467\pi$
$578$	−62.6939	−2.60772
$579$	0.293617	0.0122023
$580$	6.41758	0.266476
$581$	11.1198	0.461328
$582$	32.7458	1.35736
$583$	27.2161	1.12718
$584$	5.74099	0.237564
$585$	0.989588	0.0409144
$586$	−49.6683	−2.05178
$587$	3.59138	0.148232	0.0741161	−	0.997250i	$-0.476386\pi$
$587$	3.59138	0.148232	0.0741161	+	0.997250i	$0.476386\pi$
$588$	−1.46260	−0.0603165
$589$	−66.2403	−2.72938
$590$	−12.8221	−0.527876
$591$	−10.9508	−0.450457
$592$	15.5976	0.641059
$593$	23.3532	0.959001	0.479500	−	0.877542i	$-0.340818\pi$
$593$	23.3532	0.959001	0.479500	+	0.877542i	$0.340818\pi$
$594$	−5.44322	−0.223338
$595$	10.4134	0.426909
$596$	−30.2486	−1.23903
$597$	−24.6081	−1.00714
$598$	8.46260	0.346061
$599$	20.3747	0.832487	0.416244	−	0.909253i	$-0.363346\pi$
$599$	20.3747	0.832487	0.416244	+	0.909253i	$0.363346\pi$
$600$	2.86081	0.116792
$601$	−5.70079	−0.232540	−0.116270	−	0.993218i	$-0.537094\pi$
$601$	−5.70079	−0.232540	−0.116270	+	0.993218i	$0.537094\pi$
$602$	0.518027	0.0211132
$603$	−6.46260	−0.263177
$604$	5.18903	0.211139
$605$	−3.57345	−0.145282
$606$	23.0152	0.934930
$607$	39.5872	1.60680	0.803398	−	0.595442i	$-0.203023\pi$
$607$	39.5872	1.60680	0.803398	+	0.595442i	$0.203023\pi$
$608$	50.5741	2.05105
$609$	3.00000	0.121566
$610$	−29.3553	−1.18856
$611$	5.25487	0.212589
$612$	−10.4134	−0.420938
$613$	7.99518	0.322922	0.161461	−	0.986879i	$-0.448379\pi$
$613$	7.99518	0.322922	0.161461	+	0.986879i	$0.448379\pi$
$614$	−40.3255	−1.62741
$615$	−16.1544	−0.651409
$616$	2.92520	0.117860
$617$	−28.1232	−1.13220	−0.566098	−	0.824338i	$-0.691548\pi$
$617$	−28.1232	−1.13220	−0.566098	+	0.824338i	$0.691548\pi$
$618$	−5.06439	−0.203720
$619$	−28.6579	−1.15186	−0.575929	−	0.817500i	$-0.695360\pi$
$619$	−28.6579	−1.15186	−0.575929	+	0.817500i	$0.695360\pi$
$620$	−19.3490	−0.777076
$621$	6.72161	0.269729
$622$	−12.3851	−0.496597
$623$	5.90582	0.236612
$624$	3.23819	0.129631
$625$	−2.51176	−0.100470
$626$	37.5783	1.50193
$627$	21.4224	0.855528
$628$	−22.0707	−0.880715
$629$	23.2036	0.925188
$630$	2.72161	0.108432
$631$	20.0811	0.799415	0.399707	−	0.916643i	$-0.369112\pi$
$631$	20.0811	0.799415	0.399707	+	0.916643i	$0.369112\pi$
$632$	6.39821	0.254507
$633$	9.54222	0.379269
$634$	−22.4224	−0.890507
$635$	23.5464	0.934409
$636$	13.6081	0.539595
$637$	0.676596	0.0268077
$638$	16.3297	0.646498
$639$	−11.2936	−0.446769
$640$	−11.2784	−0.445817
$641$	33.2638	1.31384	0.656921	−	0.753959i	$-0.271858\pi$
$641$	33.2638	1.31384	0.656921	+	0.753959i	$0.271858\pi$
$642$	−0.0554281	−0.00218757
$643$	−24.9736	−0.984862	−0.492431	−	0.870352i	$-0.663892\pi$
$643$	−24.9736	−0.984862	−0.492431	+	0.870352i	$0.663892\pi$
$644$	9.83102	0.387396
$645$	−0.407170	−0.0160323
$646$	97.0249	3.81739
$647$	−2.35946	−0.0927598	−0.0463799	−	0.998924i	$-0.514768\pi$
$647$	−2.35946	−0.0927598	−0.0463799	+	0.998924i	$0.514768\pi$
$648$	1.00000	0.0392837
$649$	−13.7812	−0.540959
$650$	3.60179	0.141274
$651$	−9.04502	−0.354502
$652$	0.801232	0.0313786
$653$	25.3103	0.990468	0.495234	−	0.868760i	$-0.335082\pi$
$653$	25.3103	0.990468	0.495234	+	0.868760i	$0.335082\pi$
$654$	31.5228	1.23264
$655$	−10.6960	−0.417926
$656$	−52.8615	−2.06389
$657$	5.74099	0.223977
$658$	14.4522	0.563405
$659$	25.9452	1.01068	0.505342	−	0.862919i	$-0.331367\pi$
$659$	25.9452	1.01068	0.505342	+	0.862919i	$0.331367\pi$
$660$	6.25756	0.243575
$661$	23.2791	0.905450	0.452725	−	0.891650i	$-0.350452\pi$
$661$	23.2791	0.905450	0.452725	+	0.891650i	$0.350452\pi$
$662$	−18.2486	−0.709252
$663$	4.81724	0.187086
$664$	−11.1198	−0.431533
$665$	−10.7112	−0.415363
$666$	6.06439	0.234990
$667$	−20.1648	−0.780786
$668$	−14.4447	−0.558881
$669$	−15.3040	−0.591688
$670$	17.5887	0.679510
$671$	−31.5512	−1.21802
$672$	6.90582	0.266398
$673$	20.7908	0.801427	0.400714	−	0.916203i	$-0.368762\pi$
$673$	20.7908	0.801427	0.400714	+	0.916203i	$0.368762\pi$
$674$	−35.8206	−1.37976
$675$	2.86081	0.110112
$676$	−18.3442	−0.705547
$677$	−1.38635	−0.0532816	−0.0266408	−	0.999645i	$-0.508481\pi$
$677$	−1.38635	−0.0532816	−0.0266408	+	0.999645i	$0.508481\pi$
$678$	26.3580	1.01227
$679$	−17.5976	−0.675336
$680$	−10.4134	−0.399337
$681$	−23.8206	−0.912808
$682$	−49.2340	−1.88527
$683$	4.64681	0.177805	0.0889026	−	0.996040i	$-0.471664\pi$
$683$	4.64681	0.177805	0.0889026	+	0.996040i	$0.471664\pi$
$684$	10.7112	0.409553
$685$	−8.41903	−0.321675
$686$	1.86081	0.0710459
$687$	−27.9211	−1.06525
$688$	−1.33237	−0.0507960
$689$	−6.29507	−0.239823
$690$	−18.2936	−0.696426
$691$	−2.41903	−0.0920243	−0.0460122	−	0.998941i	$-0.514651\pi$
$691$	−2.41903	−0.0920243	−0.0460122	+	0.998941i	$0.514651\pi$
$692$	−9.22633	−0.350732
$693$	2.92520	0.111119
$694$	0.194622	0.00738776
$695$	−3.96540	−0.150416
$696$	−3.00000	−0.113715
$697$	−78.6385	−2.97865
$698$	−44.8102	−1.69609
$699$	1.73684	0.0656933
$700$	4.18421	0.158148
$701$	−2.69038	−0.101614	−0.0508070	−	0.998708i	$-0.516179\pi$
$701$	−2.69038	−0.101614	−0.0508070	+	0.998708i	$0.516179\pi$
$702$	1.25901	0.0475184
$703$	−23.8671	−0.900164
$704$	9.58993	0.361434
$705$	−11.3595	−0.427822
$706$	63.3345	2.38362
$707$	−12.3684	−0.465162
$708$	−6.89059	−0.258964
$709$	20.9404	0.786434	0.393217	−	0.919446i	$-0.371362\pi$
$709$	20.9404	0.786434	0.393217	+	0.919446i	$0.371362\pi$
$710$	30.7368	1.15353
$711$	6.39821	0.239952
$712$	−5.90582	−0.221330
$713$	60.7971	2.27687
$714$	13.2486	0.495816
$715$	−2.89474	−0.108257
$716$	18.2278	0.681204
$717$	15.2292	0.568746
$718$	−49.4260	−1.84456
$719$	0.786003	0.0293130	0.0146565	−	0.999893i	$-0.495335\pi$
$719$	0.786003	0.0293130	0.0146565	+	0.999893i	$0.495335\pi$
$720$	−7.00000	−0.260875
$721$	2.72161	0.101358
$722$	−64.4439	−2.39835
$723$	−12.2188	−0.454423
$724$	−13.2576	−0.492713
$725$	−8.58242	−0.318743
$726$	−4.54636	−0.168731
$727$	−30.7160	−1.13919	−0.569597	−	0.821924i	$-0.692901\pi$
$727$	−30.7160	−1.13919	−0.569597	+	0.821924i	$0.692901\pi$
$728$	−0.676596	−0.0250763
$729$	1.00000	0.0370370
$730$	−15.6247	−0.578297
$731$	−1.98207	−0.0733097
$732$	−15.7756	−0.583083
$733$	−51.0713	−1.88636	−0.943181	−	0.332279i	$-0.892183\pi$
$733$	−51.0713	−1.88636	−0.943181	+	0.332279i	$0.892183\pi$
$734$	−30.8400	−1.13832
$735$	−1.46260	−0.0539488
$736$	−46.4183	−1.71100
$737$	18.9044	0.696352
$738$	−20.5526	−0.756553
$739$	−47.2284	−1.73733	−0.868663	−	0.495403i	$-0.835020\pi$
$739$	−47.2284	−1.73733	−0.868663	+	0.495403i	$0.835020\pi$
$740$	−6.97166	−0.256283
$741$	−4.95498	−0.182026
$742$	−17.3130	−0.635580
$743$	−52.3047	−1.91887	−0.959437	−	0.281924i	$-0.909027\pi$
$743$	−52.3047	−1.91887	−0.959437	+	0.281924i	$0.909027\pi$
$744$	9.04502	0.331606
$745$	−30.2486	−1.10822
$746$	−42.6427	−1.56126
$747$	−11.1198	−0.406853
$748$	30.4614	1.11378
$749$	0.0297872	0.00108840
$750$	−21.3941	−0.781201
$751$	9.27424	0.338422	0.169211	−	0.985580i	$-0.445878\pi$
$751$	9.27424	0.338422	0.169211	+	0.985580i	$0.445878\pi$
$752$	−37.1711	−1.35549
$753$	18.6468	0.679527
$754$	−3.77704	−0.137552
$755$	5.18903	0.188848
$756$	1.46260	0.0531942
$757$	−5.98959	−0.217695	−0.108848	−	0.994058i	$-0.534716\pi$
$757$	−5.98959	−0.217695	−0.108848	+	0.994058i	$0.534716\pi$
$758$	26.8283	0.974449
$759$	−19.6620	−0.713687
$760$	10.7112	0.388536
$761$	−3.06999	−0.111287	−0.0556435	−	0.998451i	$-0.517721\pi$
$761$	−3.06999	−0.111287	−0.0556435	+	0.998451i	$0.517721\pi$
$762$	29.9571	1.08523
$763$	−16.9404	−0.613285
$764$	1.46260	0.0529150
$765$	−10.4134	−0.376499
$766$	42.6039	1.53934
$767$	3.18758	0.115097
$768$	−20.9058	−0.754374
$769$	−1.43908	−0.0518945	−0.0259472	−	0.999663i	$-0.508260\pi$
$769$	−1.43908	−0.0518945	−0.0259472	+	0.999663i	$0.508260\pi$
$770$	−7.96125	−0.286904
$771$	−12.1752	−0.438481
$772$	−0.429444	−0.0154560
$773$	−12.1932	−0.438558	−0.219279	−	0.975662i	$-0.570370\pi$
$773$	−12.1932	−0.438558	−0.219279	+	0.975662i	$0.570370\pi$
$774$	−0.518027	−0.0186201
$775$	25.8760	0.929495
$776$	17.5976	0.631719
$777$	−3.25901	−0.116916
$778$	−5.59910	−0.200737
$779$	80.8871	2.89808
$780$	−1.44737	−0.0518241
$781$	33.0361	1.18212
$782$	−89.0520	−3.18449
$783$	−3.00000	−0.107211
$784$	−4.78600	−0.170929
$785$	−22.0707	−0.787736
$786$	−13.6081	−0.485383
$787$	4.54636	0.162060	0.0810302	−	0.996712i	$-0.474179\pi$
$787$	4.54636	0.162060	0.0810302	+	0.996712i	$0.474179\pi$
$788$	16.0167	0.570571
$789$	−3.19317	−0.113680
$790$	−17.4134	−0.619542
$791$	−14.1648	−0.503644
$792$	−2.92520	−0.103942
$793$	7.29776	0.259151
$794$	−16.4716	−0.584554
$795$	13.6081	0.482628
$796$	35.9917	1.27569
$797$	2.47446	0.0876499	0.0438249	−	0.999039i	$-0.486046\pi$
$797$	2.47446	0.0876499	0.0438249	+	0.999039i	$0.486046\pi$
$798$	−13.6274	−0.482406
$799$	−55.2970	−1.95627
$800$	−19.7562	−0.698488
$801$	−5.90582	−0.208672
$802$	23.2742	0.821842
$803$	−16.7935	−0.592630
$804$	9.45219	0.333353
$805$	9.83102	0.346498
$806$	11.3878	0.401118
$807$	28.9854	1.02034
$808$	12.3684	0.435120
$809$	−18.6170	−0.654540	−0.327270	−	0.944931i	$-0.606129\pi$
$809$	−18.6170	−0.654540	−0.327270	+	0.944931i	$0.606129\pi$
$810$	−2.72161	−0.0956277
$811$	−8.24860	−0.289648	−0.144824	−	0.989457i	$-0.546262\pi$
$811$	−8.24860	−0.289648	−0.144824	+	0.989457i	$0.546262\pi$
$812$	−4.38780	−0.153981
$813$	3.06439	0.107473
$814$	−17.7395	−0.621770
$815$	0.801232	0.0280659
$816$	−34.0755	−1.19288
$817$	2.03875	0.0713268
$818$	−57.5935	−2.01371
$819$	−0.676596	−0.0236422
$820$	23.6274	0.825106
$821$	−44.7610	−1.56217	−0.781085	−	0.624424i	$-0.785334\pi$
$821$	−44.7610	−1.56217	−0.781085	+	0.624424i	$0.785334\pi$
$822$	−10.7112	−0.373596
$823$	−4.77559	−0.166467	−0.0832333	−	0.996530i	$-0.526525\pi$
$823$	−4.77559	−0.166467	−0.0832333	+	0.996530i	$0.526525\pi$
$824$	−2.72161	−0.0948118
$825$	−8.36842	−0.291351
$826$	8.76663	0.305030
$827$	−26.7971	−0.931826	−0.465913	−	0.884831i	$-0.654274\pi$
$827$	−26.7971	−0.931826	−0.465913	+	0.884831i	$0.654274\pi$
$828$	−9.83102	−0.341652
$829$	30.5347	1.06051	0.530257	−	0.847837i	$-0.322095\pi$
$829$	30.5347	1.06051	0.530257	+	0.847837i	$0.322095\pi$
$830$	30.2638	1.05047
$831$	−2.75140	−0.0954450
$832$	−2.21814	−0.0769003
$833$	−7.11982	−0.246687
$834$	−5.04502	−0.174695
$835$	−14.4447	−0.499879
$836$	−31.3324	−1.08365
$837$	9.04502	0.312641
$838$	19.0707	0.658785
$839$	−12.3130	−0.425092	−0.212546	−	0.977151i	$-0.568175\pi$
$839$	−12.3130	−0.425092	−0.212546	+	0.977151i	$0.568175\pi$
$840$	1.46260	0.0504644
$841$	−20.0000	−0.689655
$842$	−63.9723	−2.20463
$843$	−11.4343	−0.393817
$844$	−13.9564	−0.480400
$845$	−18.3442	−0.631061
$846$	−14.4522	−0.496876
$847$	2.44322	0.0839501
$848$	44.5291	1.52914
$849$	−8.00000	−0.274559
$850$	−37.9017	−1.30002
$851$	21.9058	0.750922
$852$	16.5180	0.565898
$853$	45.2880	1.55063	0.775316	−	0.631573i	$-0.217591\pi$
$853$	45.2880	1.55063	0.775316	+	0.631573i	$0.217591\pi$
$854$	20.0707	0.686804
$855$	10.7112	0.366315
$856$	−0.0297872	−0.00101810
$857$	55.6073	1.89951	0.949754	−	0.312997i	$-0.101333\pi$
$857$	55.6073	1.89951	0.949754	+	0.312997i	$0.101333\pi$
$858$	−3.68286	−0.125731
$859$	36.5831	1.24820	0.624099	−	0.781345i	$-0.285466\pi$
$859$	36.5831	1.24820	0.624099	+	0.781345i	$0.285466\pi$
$860$	0.595527	0.0203073
$861$	11.0450	0.376413
$862$	−72.4141	−2.46643
$863$	−3.59765	−0.122465	−0.0612327	−	0.998124i	$-0.519503\pi$
$863$	−3.59765	−0.122465	−0.0612327	+	0.998124i	$0.519503\pi$
$864$	−6.90582	−0.234941
$865$	−9.22633	−0.313705
$866$	−50.2701	−1.70825
$867$	−33.6918	−1.14423
$868$	13.2292	0.449029
$869$	−18.7160	−0.634897
$870$	8.16484	0.276814
$871$	−4.37257	−0.148159
$872$	16.9404	0.573675
$873$	17.5976	0.595590
$874$	91.5983	3.09836
$875$	11.4972	0.388676
$876$	−8.39676	−0.283700
$877$	−11.7126	−0.395508	−0.197754	−	0.980252i	$-0.563365\pi$
$877$	−11.7126	−0.395508	−0.197754	+	0.980252i	$0.563365\pi$
$878$	−16.8143	−0.567457
$879$	−26.6918	−0.900293
$880$	20.4764	0.690259
$881$	4.76326	0.160478	0.0802392	−	0.996776i	$-0.474432\pi$
$881$	4.76326	0.160478	0.0802392	+	0.996776i	$0.474432\pi$
$882$	−1.86081	−0.0626566
$883$	−13.6289	−0.458648	−0.229324	−	0.973350i	$-0.573652\pi$
$883$	−13.6289	−0.458648	−0.229324	+	0.973350i	$0.573652\pi$
$884$	−7.04569	−0.236972
$885$	−6.89059	−0.231625
$886$	−14.1121	−0.474105
$887$	−7.45778	−0.250408	−0.125204	−	0.992131i	$-0.539959\pi$
$887$	−7.45778	−0.250408	−0.125204	+	0.992131i	$0.539959\pi$
$888$	3.25901	0.109365
$889$	−16.0990	−0.539943
$890$	16.0734	0.538780
$891$	−2.92520	−0.0979978
$892$	22.3836	0.749460
$893$	56.8782	1.90335
$894$	−38.4841	−1.28710
$895$	18.2278	0.609287
$896$	7.71120	0.257613
$897$	4.54781	0.151847
$898$	−23.2549	−0.776025
$899$	−27.1350	−0.905005
$900$	−4.18421	−0.139474
$901$	66.2430	2.20687
$902$	60.1205	2.00179
$903$	0.278388	0.00926418
$904$	14.1648	0.471115
$905$	−13.2576	−0.440696
$906$	6.60179	0.219330
$907$	−31.0048	−1.02950	−0.514749	−	0.857341i	$-0.672115\pi$
$907$	−31.0048	−1.02950	−0.514749	+	0.857341i	$0.672115\pi$
$908$	34.8400	1.15621
$909$	12.3684	0.410235
$910$	1.84143	0.0610428
$911$	−30.5381	−1.01177	−0.505886	−	0.862601i	$-0.668834\pi$
$911$	−30.5381	−1.01177	−0.505886	+	0.862601i	$0.668834\pi$
$912$	35.0498	1.16062
$913$	32.5277	1.07651
$914$	42.3539	1.40094
$915$	−15.7756	−0.521525
$916$	40.8373	1.34930
$917$	7.31299	0.241496
$918$	−13.2486	−0.437269
$919$	13.1060	0.432328	0.216164	−	0.976357i	$-0.430645\pi$
$919$	13.1060	0.432328	0.216164	+	0.976357i	$0.430645\pi$
$920$	−9.83102	−0.324119
$921$	−21.6710	−0.714084
$922$	12.6247	0.415774
$923$	−7.64121	−0.251514
$924$	−4.27839	−0.140749
$925$	9.32340	0.306552
$926$	58.8525	1.93401
$927$	−2.72161	−0.0893895
$928$	20.7175	0.680084
$929$	34.9377	1.14627	0.573135	−	0.819461i	$-0.305727\pi$
$929$	34.9377	1.14627	0.573135	+	0.819461i	$0.305727\pi$
$930$	−24.6170	−0.807224
$931$	7.32340	0.240015
$932$	−2.54030	−0.0832103
$933$	−6.65577	−0.217900
$934$	55.7300	1.82354
$935$	30.4614	0.996193
$936$	0.676596	0.0221152
$937$	5.10459	0.166760	0.0833798	−	0.996518i	$-0.473429\pi$
$937$	5.10459	0.166760	0.0833798	+	0.996518i	$0.473429\pi$
$938$	−12.0256	−0.392651
$939$	20.1946	0.659027
$940$	16.6143	0.541900
$941$	−45.3774	−1.47926	−0.739630	−	0.673013i	$-0.765000\pi$
$941$	−45.3774	−1.47926	−0.739630	+	0.673013i	$0.765000\pi$
$942$	−28.0796	−0.914883
$943$	−74.2403	−2.41760
$944$	−22.5478	−0.733869
$945$	1.46260	0.0475783
$946$	1.51533	0.0492676
$947$	26.5062	0.861335	0.430667	−	0.902511i	$-0.358278\pi$
$947$	26.5062	0.861335	0.430667	+	0.902511i	$0.358278\pi$
$948$	−9.35801	−0.303934
$949$	3.88433	0.126091
$950$	38.9854	1.26485
$951$	−12.0498	−0.390743
$952$	7.11982	0.230755
$953$	35.7022	1.15651	0.578254	−	0.815856i	$-0.303734\pi$
$953$	35.7022	1.15651	0.578254	+	0.815856i	$0.303734\pi$
$954$	17.3130	0.560529
$955$	1.46260	0.0473286
$956$	−22.2742	−0.720400
$957$	8.77559	0.283675
$958$	−38.1801	−1.23354
$959$	5.75622	0.185878
$960$	4.79497	0.154757
$961$	50.8123	1.63911
$962$	4.10314	0.132291
$963$	−0.0297872	−0.000959878 0
$964$	17.8712	0.575593
$965$	−0.429444	−0.0138243
$966$	12.5076	0.402426
$967$	−48.4287	−1.55736	−0.778680	−	0.627421i	$-0.784111\pi$
$967$	−48.4287	−1.55736	−0.778680	+	0.627421i	$0.784111\pi$
$968$	−2.44322	−0.0785282
$969$	52.1413	1.67502
$970$	−47.8940	−1.53778
$971$	−22.7022	−0.728549	−0.364275	−	0.931292i	$-0.618683\pi$
$971$	−22.7022	−0.728549	−0.364275	+	0.931292i	$0.618683\pi$
$972$	−1.46260	−0.0469129
$973$	2.71120	0.0869171
$974$	51.7521	1.65824
$975$	1.93561	0.0619891
$976$	−51.6218	−1.65237
$977$	−10.1980	−0.326263	−0.163131	−	0.986604i	$-0.552159\pi$
$977$	−10.1980	−0.326263	−0.163131	+	0.986604i	$0.552159\pi$
$978$	1.01938	0.0325960
$979$	17.2757	0.552133
$980$	2.13919	0.0683341
$981$	16.9404	0.540866
$982$	−35.8102	−1.14275
$983$	0.378832	0.0120829	0.00604144	−	0.999982i	$-0.498077\pi$
$983$	0.378832	0.0120829	0.00604144	+	0.999982i	$0.498077\pi$
$984$	−11.0450	−0.352102
$985$	16.0167	0.510334
$986$	39.7458	1.26576
$987$	7.76663	0.247214
$988$	7.24715	0.230563
$989$	−1.87122	−0.0595013
$990$	7.96125	0.253025
$991$	2.93416	0.0932067	0.0466033	−	0.998913i	$-0.485160\pi$
$991$	2.93416	0.0932067	0.0466033	+	0.998913i	$0.485160\pi$
$992$	−62.4633	−1.98321
$993$	−9.80683	−0.311210
$994$	−21.0152	−0.666563
$995$	35.9917	1.14101
$996$	16.2638	0.515339
$997$	3.27839	0.103828	0.0519138	−	0.998652i	$-0.483468\pi$
$997$	3.27839	0.103828	0.0519138	+	0.998652i	$0.483468\pi$
$998$	32.6593	1.03381
$999$	3.25901	0.103111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.e.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.e.1.1	✓	3	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)

\(f(q)\)	\(=\)	\(q-1.86081 q^{2} -1.00000 q^{3} +1.46260 q^{4} +1.46260 q^{5} +1.86081 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.86081 q^{2} -1.00000 q^{3} +1.46260 q^{4} +1.46260 q^{5} +1.86081 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.72161 q^{10} -2.92520 q^{11} -1.46260 q^{12} +0.676596 q^{13} +1.86081 q^{14} -1.46260 q^{15} -4.78600 q^{16} -7.11982 q^{17} -1.86081 q^{18} +7.32340 q^{19} +2.13919 q^{20} +1.00000 q^{21} +5.44322 q^{22} -6.72161 q^{23} -1.00000 q^{24} -2.86081 q^{25} -1.25901 q^{26} -1.00000 q^{27} -1.46260 q^{28} +3.00000 q^{29} +2.72161 q^{30} -9.04502 q^{31} +6.90582 q^{32} +2.92520 q^{33} +13.2486 q^{34} -1.46260 q^{35} +1.46260 q^{36} -3.25901 q^{37} -13.6274 q^{38} -0.676596 q^{39} +1.46260 q^{40} +11.0450 q^{41} -1.86081 q^{42} +0.278388 q^{43} -4.27839 q^{44} +1.46260 q^{45} +12.5076 q^{46} +7.76663 q^{47} +4.78600 q^{48} +1.00000 q^{49} +5.32340 q^{50} +7.11982 q^{51} +0.989588 q^{52} -9.30403 q^{53} +1.86081 q^{54} -4.27839 q^{55} -1.00000 q^{56} -7.32340 q^{57} -5.58242 q^{58} +4.71120 q^{59} -2.13919 q^{60} +10.7860 q^{61} +16.8310 q^{62} -1.00000 q^{63} -3.27839 q^{64} +0.989588 q^{65} -5.44322 q^{66} -6.46260 q^{67} -10.4134 q^{68} +6.72161 q^{69} +2.72161 q^{70} -11.2936 q^{71} +1.00000 q^{72} +5.74099 q^{73} +6.06439 q^{74} +2.86081 q^{75} +10.7112 q^{76} +2.92520 q^{77} +1.25901 q^{78} +6.39821 q^{79} -7.00000 q^{80} +1.00000 q^{81} -20.5526 q^{82} -11.1198 q^{83} +1.46260 q^{84} -10.4134 q^{85} -0.518027 q^{86} -3.00000 q^{87} -2.92520 q^{88} -5.90582 q^{89} -2.72161 q^{90} -0.676596 q^{91} -9.83102 q^{92} +9.04502 q^{93} -14.4522 q^{94} +10.7112 q^{95} -6.90582 q^{96} +17.5976 q^{97} -1.86081 q^{98} -2.92520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} + 2 q^{5} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 2 q^{15} - 4 q^{16} - 7 q^{17} + 14 q^{19} + 12 q^{20} + 3 q^{21} - 6 q^{22} - 9 q^{23} - 3 q^{24} - 3 q^{25} + 5 q^{26} - 3 q^{27} - 2 q^{28} + 9 q^{29} - 3 q^{30} - 8 q^{31} - 4 q^{32} + 4 q^{33} + 27 q^{34} - 2 q^{35} + 2 q^{36} - q^{37} - 5 q^{38} - 10 q^{39} + 2 q^{40} + 14 q^{41} + 12 q^{43} - 24 q^{44} + 2 q^{45} + 16 q^{46} - 7 q^{47} + 4 q^{48} + 3 q^{49} + 8 q^{50} + 7 q^{51} - q^{52} - 24 q^{55} - 3 q^{56} - 14 q^{57} - q^{59} - 12 q^{60} + 22 q^{61} + 21 q^{62} - 3 q^{63} - 21 q^{64} - q^{65} + 6 q^{66} - 17 q^{67} + 15 q^{68} + 9 q^{69} - 3 q^{70} - 2 q^{71} + 3 q^{72} + 26 q^{73} + 19 q^{74} + 3 q^{75} + 17 q^{76} + 4 q^{77} - 5 q^{78} + 16 q^{79} - 21 q^{80} + 3 q^{81} - 21 q^{82} - 19 q^{83} + 2 q^{84} + 15 q^{85} + 16 q^{86} - 9 q^{87} - 4 q^{88} + 7 q^{89} + 3 q^{90} - 10 q^{91} + 8 q^{93} - 37 q^{94} + 17 q^{95} + 4 q^{96} - 7 q^{97} - 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 + 2 * q^5 - 3 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 2 * q^15 - 4 * q^16 - 7 * q^17 + 14 * q^19 + 12 * q^20 + 3 * q^21 - 6 * q^22 - 9 * q^23 - 3 * q^24 - 3 * q^25 + 5 * q^26 - 3 * q^27 - 2 * q^28 + 9 * q^29 - 3 * q^30 - 8 * q^31 - 4 * q^32 + 4 * q^33 + 27 * q^34 - 2 * q^35 + 2 * q^36 - q^37 - 5 * q^38 - 10 * q^39 + 2 * q^40 + 14 * q^41 + 12 * q^43 - 24 * q^44 + 2 * q^45 + 16 * q^46 - 7 * q^47 + 4 * q^48 + 3 * q^49 + 8 * q^50 + 7 * q^51 - q^52 - 24 * q^55 - 3 * q^56 - 14 * q^57 - q^59 - 12 * q^60 + 22 * q^61 + 21 * q^62 - 3 * q^63 - 21 * q^64 - q^65 + 6 * q^66 - 17 * q^67 + 15 * q^68 + 9 * q^69 - 3 * q^70 - 2 * q^71 + 3 * q^72 + 26 * q^73 + 19 * q^74 + 3 * q^75 + 17 * q^76 + 4 * q^77 - 5 * q^78 + 16 * q^79 - 21 * q^80 + 3 * q^81 - 21 * q^82 - 19 * q^83 + 2 * q^84 + 15 * q^85 + 16 * q^86 - 9 * q^87 - 4 * q^88 + 7 * q^89 + 3 * q^90 - 10 * q^91 + 8 * q^93 - 37 * q^94 + 17 * q^95 + 4 * q^96 - 7 * q^97 - 4 * q^99

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