LMFDB - Embedded newform 1003.2.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} - 16 x^{16} + 112 x^{15} + 52 x^{14} - 984 x^{13} + 431 x^{12} + 4304 x^{11} + \cdots + 28 $ x^18 - 5x^17 - 16x^16 + 112x^15 + 52x^14 - 984x^13 + 431x^12 + 4304x^11 - 3825x^10 - 9826x^9 + 11533x^8 + 11182x^7 - 15697x^6 - 5604x^5 + 9201x^4 + 1189x^3 - 1952x^2 - 100*x + 28
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.26170$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.26170 q^{2} -1.91993 q^{3} +3.11529 q^{4} -0.621807 q^{5} -4.34231 q^{6} +3.74378 q^{7} +2.52246 q^{8} +0.686140 q^{9} +O(q^{10})$	\(q+2.26170 q^{2} -1.91993 q^{3} +3.11529 q^{4} -0.621807 q^{5} -4.34231 q^{6} +3.74378 q^{7} +2.52246 q^{8} +0.686140 q^{9} -1.40634 q^{10} +0.321664 q^{11} -5.98115 q^{12} +3.48531 q^{13} +8.46731 q^{14} +1.19383 q^{15} -0.525530 q^{16} +1.00000 q^{17} +1.55184 q^{18} +2.69260 q^{19} -1.93711 q^{20} -7.18780 q^{21} +0.727509 q^{22} +6.35005 q^{23} -4.84296 q^{24} -4.61336 q^{25} +7.88273 q^{26} +4.44245 q^{27} +11.6630 q^{28} +3.46358 q^{29} +2.70008 q^{30} -0.773818 q^{31} -6.23352 q^{32} -0.617574 q^{33} +2.26170 q^{34} -2.32791 q^{35} +2.13753 q^{36} +1.43459 q^{37} +6.08986 q^{38} -6.69156 q^{39} -1.56849 q^{40} +8.61209 q^{41} -16.2567 q^{42} +4.87081 q^{43} +1.00208 q^{44} -0.426647 q^{45} +14.3619 q^{46} -4.13587 q^{47} +1.00898 q^{48} +7.01587 q^{49} -10.4340 q^{50} -1.91993 q^{51} +10.8578 q^{52} -1.27463 q^{53} +10.0475 q^{54} -0.200013 q^{55} +9.44354 q^{56} -5.16961 q^{57} +7.83358 q^{58} -1.00000 q^{59} +3.71912 q^{60} +0.0869327 q^{61} -1.75014 q^{62} +2.56876 q^{63} -13.0473 q^{64} -2.16719 q^{65} -1.39677 q^{66} -13.0113 q^{67} +3.11529 q^{68} -12.1917 q^{69} -5.26503 q^{70} +8.33863 q^{71} +1.73076 q^{72} -9.87137 q^{73} +3.24460 q^{74} +8.85733 q^{75} +8.38825 q^{76} +1.20424 q^{77} -15.1343 q^{78} -12.7910 q^{79} +0.326778 q^{80} -10.5876 q^{81} +19.4780 q^{82} +1.60842 q^{83} -22.3921 q^{84} -0.621807 q^{85} +11.0163 q^{86} -6.64984 q^{87} +0.811387 q^{88} +4.51219 q^{89} -0.964947 q^{90} +13.0482 q^{91} +19.7823 q^{92} +1.48568 q^{93} -9.35410 q^{94} -1.67428 q^{95} +11.9679 q^{96} -12.8517 q^{97} +15.8678 q^{98} +0.220707 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * 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 $

$2$	2.26170	1.59926	0.799632	−	0.600490i	$-0.205028\pi$
$2$	2.26170	1.59926	0.799632	+	0.600490i	$0.205028\pi$
$3$	−1.91993	−1.10847	−0.554237	−	0.832359i	$-0.686990\pi$
$3$	−1.91993	−1.10847	−0.554237	+	0.832359i	$0.686990\pi$
$4$	3.11529	1.55765
$5$	−0.621807	−0.278081	−0.139040	−	0.990287i	$-0.544402\pi$
$5$	−0.621807	−0.278081	−0.139040	+	0.990287i	$0.544402\pi$
$6$	−4.34231	−1.77274
$7$	3.74378	1.41502	0.707508	−	0.706706i	$-0.249820\pi$
$7$	3.74378	1.41502	0.707508	+	0.706706i	$0.249820\pi$
$8$	2.52246	0.891825
$9$	0.686140	0.228713
$10$	−1.40634	−0.444724
$11$	0.321664	0.0969855	0.0484927	−	0.998824i	$-0.484558\pi$
$11$	0.321664	0.0969855	0.0484927	+	0.998824i	$0.484558\pi$
$12$	−5.98115	−1.72661
$13$	3.48531	0.966651	0.483325	−	0.875441i	$-0.339429\pi$
$13$	3.48531	0.966651	0.483325	+	0.875441i	$0.339429\pi$
$14$	8.46731	2.26298
$15$	1.19383	0.308245
$16$	−0.525530	−0.131382
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.55184	0.365773
$19$	2.69260	0.617725	0.308863	−	0.951107i	$-0.400052\pi$
$19$	2.69260	0.617725	0.308863	+	0.951107i	$0.400052\pi$
$20$	−1.93711	−0.433151
$21$	−7.18780	−1.56851
$22$	0.727509	0.155105
$23$	6.35005	1.32408	0.662039	−	0.749470i	$-0.269691\pi$
$23$	6.35005	1.32408	0.662039	+	0.749470i	$0.269691\pi$
$24$	−4.84296	−0.988565
$25$	−4.61336	−0.922671
$26$	7.88273	1.54593
$27$	4.44245	0.854951
$28$	11.6630	2.20409
$29$	3.46358	0.643170	0.321585	−	0.946881i	$-0.395784\pi$
$29$	3.46358	0.643170	0.321585	+	0.946881i	$0.395784\pi$
$30$	2.70008	0.492965
$31$	−0.773818	−0.138982	−0.0694909	−	0.997583i	$-0.522137\pi$
$31$	−0.773818	−0.138982	−0.0694909	+	0.997583i	$0.522137\pi$
$32$	−6.23352	−1.10194
$33$	−0.617574	−0.107506
$34$	2.26170	0.387879
$35$	−2.32791	−0.393488
$36$	2.13753	0.356255
$37$	1.43459	0.235844	0.117922	−	0.993023i	$-0.462377\pi$
$37$	1.43459	0.235844	0.117922	+	0.993023i	$0.462377\pi$
$38$	6.08986	0.987906
$39$	−6.69156	−1.07151
$40$	−1.56849	−0.247999
$41$	8.61209	1.34498	0.672492	−	0.740105i	$-0.265224\pi$
$41$	8.61209	1.34498	0.672492	+	0.740105i	$0.265224\pi$
$42$	−16.2567	−2.50846
$43$	4.87081	0.742791	0.371396	−	0.928475i	$-0.378879\pi$
$43$	4.87081	0.742791	0.371396	+	0.928475i	$0.378879\pi$
$44$	1.00208	0.151069
$45$	−0.426647	−0.0636007
$46$	14.3619	2.11755
$47$	−4.13587	−0.603278	−0.301639	−	0.953422i	$-0.597534\pi$
$47$	−4.13587	−0.603278	−0.301639	+	0.953422i	$0.597534\pi$
$48$	1.00898	0.145634
$49$	7.01587	1.00227
$50$	−10.4340	−1.47560
$51$	−1.91993	−0.268844
$52$	10.8578	1.50570
$53$	−1.27463	−0.175084	−0.0875420	−	0.996161i	$-0.527901\pi$
$53$	−1.27463	−0.175084	−0.0875420	+	0.996161i	$0.527901\pi$
$54$	10.0475	1.36729
$55$	−0.200013	−0.0269698
$56$	9.44354	1.26195
$57$	−5.16961	−0.684732
$58$	7.83358	1.02860
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.71912	0.480137
$61$	0.0869327	0.0111306	0.00556530	−	0.999985i	$-0.498229\pi$
$61$	0.0869327	0.0111306	0.00556530	+	0.999985i	$0.498229\pi$
$62$	−1.75014	−0.222269
$63$	2.56876	0.323633
$64$	−13.0473	−1.63091
$65$	−2.16719	−0.268807
$66$	−1.39677	−0.171930
$67$	−13.0113	−1.58958	−0.794791	−	0.606883i	$-0.792420\pi$
$67$	−13.0113	−1.58958	−0.794791	+	0.606883i	$0.792420\pi$
$68$	3.11529	0.377785
$69$	−12.1917	−1.46770
$70$	−5.26503	−0.629292
$71$	8.33863	0.989613	0.494807	−	0.869003i	$-0.335239\pi$
$71$	8.33863	0.989613	0.494807	+	0.869003i	$0.335239\pi$
$72$	1.73076	0.203972
$73$	−9.87137	−1.15536	−0.577678	−	0.816265i	$-0.696041\pi$
$73$	−9.87137	−1.15536	−0.577678	+	0.816265i	$0.696041\pi$
$74$	3.24460	0.377178
$75$	8.85733	1.02276
$76$	8.38825	0.962198
$77$	1.20424	0.137236
$78$	−15.1343	−1.71362
$79$	−12.7910	−1.43910	−0.719551	−	0.694440i	$-0.755652\pi$
$79$	−12.7910	−1.43910	−0.719551	+	0.694440i	$0.755652\pi$
$80$	0.326778	0.0365349
$81$	−10.5876	−1.17640
$82$	19.4780	2.15098
$83$	1.60842	0.176548	0.0882738	−	0.996096i	$-0.471865\pi$
$83$	1.60842	0.176548	0.0882738	+	0.996096i	$0.471865\pi$
$84$	−22.3921	−2.44318
$85$	−0.621807	−0.0674444
$86$	11.0163	1.18792
$87$	−6.64984	−0.712937
$88$	0.811387	0.0864941
$89$	4.51219	0.478291	0.239145	−	0.970984i	$-0.423133\pi$
$89$	4.51219	0.478291	0.239145	+	0.970984i	$0.423133\pi$
$90$	−0.964947	−0.101714
$91$	13.0482	1.36783
$92$	19.7823	2.06245
$93$	1.48568	0.154058
$94$	−9.35410	−0.964802
$95$	−1.67428	−0.171777
$96$	11.9679	1.22147
$97$	−12.8517	−1.30489	−0.652444	−	0.757837i	$-0.726256\pi$
$97$	−12.8517	−1.30489	−0.652444	+	0.757837i	$0.726256\pi$
$98$	15.8678	1.60289
$99$	0.220707	0.0221819
$100$	−14.3720	−1.43720
$101$	1.79474	0.178583	0.0892917	−	0.996006i	$-0.471540\pi$
$101$	1.79474	0.178583	0.0892917	+	0.996006i	$0.471540\pi$
$102$	−4.34231	−0.429953
$103$	−3.42362	−0.337339	−0.168670	−	0.985673i	$-0.553947\pi$
$103$	−3.42362	−0.337339	−0.168670	+	0.985673i	$0.553947\pi$
$104$	8.79156	0.862084
$105$	4.46942	0.436171
$106$	−2.88284	−0.280006
$107$	−17.1925	−1.66206	−0.831030	−	0.556228i	$-0.812248\pi$
$107$	−17.1925	−1.66206	−0.831030	+	0.556228i	$0.812248\pi$
$108$	13.8396	1.33171
$109$	2.53026	0.242355	0.121178	−	0.992631i	$-0.461333\pi$
$109$	2.53026	0.242355	0.121178	+	0.992631i	$0.461333\pi$
$110$	−0.452370	−0.0431318
$111$	−2.75431	−0.261427
$112$	−1.96747	−0.185908
$113$	1.00439	0.0944848	0.0472424	−	0.998883i	$-0.484957\pi$
$113$	1.00439	0.0944848	0.0472424	+	0.998883i	$0.484957\pi$
$114$	−11.6921	−1.09507
$115$	−3.94851	−0.368200
$116$	10.7901	1.00183
$117$	2.39141	0.221086
$118$	−2.26170	−0.208207
$119$	3.74378	0.343192
$120$	3.01139	0.274901
$121$	−10.8965	−0.990594
$122$	0.196616	0.0178008
$123$	−16.5346	−1.49088
$124$	−2.41067	−0.216485
$125$	5.97765	0.534657
$126$	5.80976	0.517574
$127$	−12.5756	−1.11591	−0.557953	−	0.829873i	$-0.688413\pi$
$127$	−12.5756	−1.11591	−0.557953	+	0.829873i	$0.688413\pi$
$128$	−17.0421	−1.50632
$129$	−9.35162	−0.823364
$130$	−4.90154	−0.429893
$131$	18.4472	1.61174	0.805869	−	0.592094i	$-0.201699\pi$
$131$	18.4472	1.61174	0.805869	+	0.592094i	$0.201699\pi$
$132$	−1.92392	−0.167456
$133$	10.0805	0.874091
$134$	−29.4277	−2.54216
$135$	−2.76235	−0.237745
$136$	2.52246	0.216299
$137$	−5.00080	−0.427247	−0.213624	−	0.976916i	$-0.568527\pi$
$137$	−5.00080	−0.427247	−0.213624	+	0.976916i	$0.568527\pi$
$138$	−27.5739	−2.34725
$139$	0.154868	0.0131357	0.00656787	−	0.999978i	$-0.497909\pi$
$139$	0.154868	0.0131357	0.00656787	+	0.999978i	$0.497909\pi$
$140$	−7.25212	−0.612916
$141$	7.94059	0.668718
$142$	18.8595	1.58265
$143$	1.12110	0.0937511
$144$	−0.360587	−0.0300489
$145$	−2.15368	−0.178853
$146$	−22.3261	−1.84772
$147$	−13.4700	−1.11099
$148$	4.46916	0.367362
$149$	−5.59273	−0.458174	−0.229087	−	0.973406i	$-0.573574\pi$
$149$	−5.59273	−0.458174	−0.229087	+	0.973406i	$0.573574\pi$
$150$	20.0326	1.63566
$151$	−10.2330	−0.832748	−0.416374	−	0.909193i	$-0.636699\pi$
$151$	−10.2330	−0.832748	−0.416374	+	0.909193i	$0.636699\pi$
$152$	6.79199	0.550903
$153$	0.686140	0.0554711
$154$	2.72363	0.219477
$155$	0.481165	0.0386481
$156$	−20.8462	−1.66903
$157$	9.19717	0.734014	0.367007	−	0.930218i	$-0.380383\pi$
$157$	9.19717	0.734014	0.367007	+	0.930218i	$0.380383\pi$
$158$	−28.9295	−2.30150
$159$	2.44721	0.194076
$160$	3.87604	0.306428
$161$	23.7732	1.87359
$162$	−23.9461	−1.88138
$163$	−9.55403	−0.748329	−0.374165	−	0.927362i	$-0.622071\pi$
$163$	−9.55403	−0.748329	−0.374165	+	0.927362i	$0.622071\pi$
$164$	26.8292	2.09501
$165$	0.384012	0.0298953
$166$	3.63778	0.282346
$167$	8.61979	0.667020	0.333510	−	0.942747i	$-0.391767\pi$
$167$	8.61979	0.667020	0.333510	+	0.942747i	$0.391767\pi$
$168$	−18.1310	−1.39883
$169$	−0.852625	−0.0655866
$170$	−1.40634	−0.107861
$171$	1.84750	0.141282
$172$	15.1740	1.15701
$173$	−0.690554	−0.0525019	−0.0262509	−	0.999655i	$-0.508357\pi$
$173$	−0.690554	−0.0525019	−0.0262509	+	0.999655i	$0.508357\pi$
$174$	−15.0399	−1.14018
$175$	−17.2714	−1.30559
$176$	−0.169044	−0.0127422
$177$	1.91993	0.144311
$178$	10.2052	0.764914
$179$	16.9540	1.26720	0.633600	−	0.773661i	$-0.281577\pi$
$179$	16.9540	1.26720	0.633600	+	0.773661i	$0.281577\pi$
$180$	−1.32913	−0.0990675
$181$	24.7789	1.84180	0.920902	−	0.389795i	$-0.127454\pi$
$181$	24.7789	1.84180	0.920902	+	0.389795i	$0.127454\pi$
$182$	29.5112	2.18751
$183$	−0.166905	−0.0123380
$184$	16.0178	1.18085
$185$	−0.892035	−0.0655837
$186$	3.36016	0.246379
$187$	0.321664	0.0235224
$188$	−12.8844	−0.939695
$189$	16.6316	1.20977
$190$	−3.78672	−0.274718
$191$	−9.50854	−0.688014	−0.344007	−	0.938967i	$-0.611784\pi$
$191$	−9.50854	−0.688014	−0.344007	+	0.938967i	$0.611784\pi$
$192$	25.0499	1.80782
$193$	10.5903	0.762309	0.381154	−	0.924511i	$-0.375527\pi$
$193$	10.5903	0.762309	0.381154	+	0.924511i	$0.375527\pi$
$194$	−29.0666	−2.08686
$195$	4.16086	0.297965
$196$	21.8565	1.56118
$197$	5.51935	0.393237	0.196619	−	0.980480i	$-0.437004\pi$
$197$	5.51935	0.393237	0.196619	+	0.980480i	$0.437004\pi$
$198$	0.499173	0.0354747
$199$	−21.4850	−1.52303	−0.761514	−	0.648148i	$-0.775544\pi$
$199$	−21.4850	−1.52303	−0.761514	+	0.648148i	$0.775544\pi$
$200$	−11.6370	−0.822862
$201$	24.9808	1.76201
$202$	4.05917	0.285602
$203$	12.9669	0.910096
$204$	−5.98115	−0.418765
$205$	−5.35506	−0.374014
$206$	−7.74321	−0.539495
$207$	4.35703	0.302834
$208$	−1.83163	−0.127001
$209$	0.866114	0.0599104
$210$	10.1085	0.697553
$211$	−25.8846	−1.78197	−0.890986	−	0.454032i	$-0.849985\pi$
$211$	−25.8846	−1.78197	−0.890986	+	0.454032i	$0.849985\pi$
$212$	−3.97085	−0.272719
$213$	−16.0096	−1.09696
$214$	−38.8843	−2.65807
$215$	−3.02870	−0.206556
$216$	11.2059	0.762467
$217$	−2.89700	−0.196661
$218$	5.72270	0.387590
$219$	18.9524	1.28068
$220$	−0.623100	−0.0420094
$221$	3.48531	0.234447
$222$	−6.22942	−0.418091
$223$	−8.04441	−0.538694	−0.269347	−	0.963043i	$-0.586808\pi$
$223$	−8.04441	−0.538694	−0.269347	+	0.963043i	$0.586808\pi$
$224$	−23.3369	−1.55926
$225$	−3.16541	−0.211027
$226$	2.27162	0.151106
$227$	−17.9759	−1.19310	−0.596552	−	0.802575i	$-0.703463\pi$
$227$	−17.9759	−1.19310	−0.596552	+	0.802575i	$0.703463\pi$
$228$	−16.1049	−1.06657
$229$	−14.7913	−0.977434	−0.488717	−	0.872442i	$-0.662535\pi$
$229$	−14.7913	−0.977434	−0.488717	+	0.872442i	$0.662535\pi$
$230$	−8.93035	−0.588850
$231$	−2.31206	−0.152122
$232$	8.73675	0.573596
$233$	25.7710	1.68831	0.844156	−	0.536097i	$-0.180102\pi$
$233$	25.7710	1.68831	0.844156	+	0.536097i	$0.180102\pi$
$234$	5.40865	0.353575
$235$	2.57171	0.167760
$236$	−3.11529	−0.202788
$237$	24.5579	1.59521
$238$	8.46731	0.548854
$239$	−16.0067	−1.03539	−0.517695	−	0.855565i	$-0.673210\pi$
$239$	−16.0067	−1.03539	−0.517695	+	0.855565i	$0.673210\pi$
$240$	−0.627392	−0.0404980
$241$	20.1639	1.29887	0.649437	−	0.760415i	$-0.275005\pi$
$241$	20.1639	1.29887	0.649437	+	0.760415i	$0.275005\pi$
$242$	−24.6447	−1.58422
$243$	7.00017	0.449061
$244$	0.270821	0.0173375
$245$	−4.36252	−0.278711
$246$	−37.3964	−2.38431
$247$	9.38455	0.597125
$248$	−1.95193	−0.123947
$249$	−3.08807	−0.195698
$250$	13.5197	0.855059
$251$	−2.37502	−0.149910	−0.0749549	−	0.997187i	$-0.523881\pi$
$251$	−2.37502	−0.149910	−0.0749549	+	0.997187i	$0.523881\pi$
$252$	8.00243	0.504106
$253$	2.04259	0.128416
$254$	−28.4423	−1.78463
$255$	1.19383	0.0747604
$256$	−12.4495	−0.778091
$257$	10.8533	0.677010	0.338505	−	0.940965i	$-0.390079\pi$
$257$	10.8533	0.677010	0.338505	+	0.940965i	$0.390079\pi$
$258$	−21.1506	−1.31678
$259$	5.37077	0.333723
$260$	−6.75143	−0.418706
$261$	2.37650	0.147102
$262$	41.7220	2.57759
$263$	9.43443	0.581752	0.290876	−	0.956761i	$-0.406053\pi$
$263$	9.43443	0.581752	0.290876	+	0.956761i	$0.406053\pi$
$264$	−1.55781	−0.0958764
$265$	0.792575	0.0486875
$266$	22.7991	1.39790
$267$	−8.66309	−0.530173
$268$	−40.5340	−2.47601
$269$	−3.31620	−0.202192	−0.101096	−	0.994877i	$-0.532235\pi$
$269$	−3.31620	−0.202192	−0.101096	+	0.994877i	$0.532235\pi$
$270$	−6.24761	−0.380217
$271$	−18.8987	−1.14802	−0.574008	−	0.818849i	$-0.694612\pi$
$271$	−18.8987	−1.14802	−0.574008	+	0.818849i	$0.694612\pi$
$272$	−0.525530	−0.0318649
$273$	−25.0517	−1.51620
$274$	−11.3103	−0.683281
$275$	−1.48395	−0.0894857
$276$	−37.9807	−2.28617
$277$	−12.7483	−0.765972	−0.382986	−	0.923754i	$-0.625104\pi$
$277$	−12.7483	−0.765972	−0.382986	+	0.923754i	$0.625104\pi$
$278$	0.350265	0.0210075
$279$	−0.530947	−0.0317870
$280$	−5.87206	−0.350923
$281$	12.0256	0.717385	0.358693	−	0.933456i	$-0.383223\pi$
$281$	12.0256	0.717385	0.358693	+	0.933456i	$0.383223\pi$
$282$	17.9592	1.06946
$283$	26.1701	1.55565	0.777825	−	0.628481i	$-0.216323\pi$
$283$	26.1701	1.55565	0.777825	+	0.628481i	$0.216323\pi$
$284$	25.9773	1.54147
$285$	3.21450	0.190411
$286$	2.53559	0.149933
$287$	32.2418	1.90317
$288$	−4.27707	−0.252029
$289$	1.00000	0.0588235
$290$	−4.87098	−0.286034
$291$	24.6743	1.44643
$292$	−30.7522	−1.79964
$293$	4.36554	0.255037	0.127519	−	0.991836i	$-0.459299\pi$
$293$	4.36554	0.255037	0.127519	+	0.991836i	$0.459299\pi$
$294$	−30.4651	−1.77676
$295$	0.621807	0.0362030
$296$	3.61869	0.210332
$297$	1.42898	0.0829178
$298$	−12.6491	−0.732741
$299$	22.1319	1.27992
$300$	27.5932	1.59309
$301$	18.2352	1.05106
$302$	−23.1440	−1.33179
$303$	−3.44578	−0.197955
$304$	−1.41504	−0.0811582
$305$	−0.0540554	−0.00309520
$306$	1.55184	0.0887130
$307$	26.8874	1.53455	0.767274	−	0.641320i	$-0.221613\pi$
$307$	26.8874	1.53455	0.767274	+	0.641320i	$0.221613\pi$
$308$	3.75156	0.213765
$309$	6.57312	0.373932
$310$	1.08825	0.0618086
$311$	−14.1862	−0.804424	−0.402212	−	0.915547i	$-0.631759\pi$
$311$	−14.1862	−0.804424	−0.402212	+	0.915547i	$0.631759\pi$
$312$	−16.8792	−0.955597
$313$	15.3722	0.868888	0.434444	−	0.900699i	$-0.356945\pi$
$313$	15.3722	0.868888	0.434444	+	0.900699i	$0.356945\pi$
$314$	20.8012	1.17388
$315$	−1.59727	−0.0899960
$316$	−39.8478	−2.24161
$317$	−19.5721	−1.09928	−0.549641	−	0.835401i	$-0.685235\pi$
$317$	−19.5721	−1.09928	−0.549641	+	0.835401i	$0.685235\pi$
$318$	5.53485	0.310379
$319$	1.11411	0.0623782
$320$	8.11290	0.453525
$321$	33.0084	1.84235
$322$	53.7679	2.99637
$323$	2.69260	0.149820
$324$	−32.9836	−1.83242
$325$	−16.0790	−0.891901
$326$	−21.6084	−1.19678
$327$	−4.85793	−0.268644
$328$	21.7237	1.19949
$329$	−15.4838	−0.853648
$330$	0.868520	0.0478105
$331$	16.4984	0.906835	0.453417	−	0.891298i	$-0.350205\pi$
$331$	16.4984	0.906835	0.453417	+	0.891298i	$0.350205\pi$
$332$	5.01072	0.274999
$333$	0.984326	0.0539408
$334$	19.4954	1.06674
$335$	8.09052	0.442032
$336$	3.77740	0.206074
$337$	−14.0102	−0.763183	−0.381591	−	0.924331i	$-0.624624\pi$
$337$	−14.0102	−0.763183	−0.381591	+	0.924331i	$0.624624\pi$
$338$	−1.92838	−0.104890
$339$	−1.92836	−0.104734
$340$	−1.93711	−0.105055
$341$	−0.248910	−0.0134792
$342$	4.17850	0.225947
$343$	0.0594248	0.00320864
$344$	12.2864	0.662440
$345$	7.58087	0.408140
$346$	−1.56183	−0.0839644
$347$	−10.7168	−0.575307	−0.287653	−	0.957735i	$-0.592875\pi$
$347$	−10.7168	−0.575307	−0.287653	+	0.957735i	$0.592875\pi$
$348$	−20.7162	−1.11050
$349$	16.9883	0.909362	0.454681	−	0.890654i	$-0.349753\pi$
$349$	16.9883	0.909362	0.454681	+	0.890654i	$0.349753\pi$
$350$	−39.0627	−2.08799
$351$	15.4833	0.826439
$352$	−2.00510	−0.106872
$353$	31.1572	1.65833	0.829165	−	0.559005i	$-0.188817\pi$
$353$	31.1572	1.65833	0.829165	+	0.559005i	$0.188817\pi$
$354$	4.34231	0.230791
$355$	−5.18502	−0.275192
$356$	14.0568	0.745008
$357$	−7.18780	−0.380419
$358$	38.3448	2.02659
$359$	23.9427	1.26365	0.631824	−	0.775112i	$-0.282306\pi$
$359$	23.9427	1.26365	0.631824	+	0.775112i	$0.282306\pi$
$360$	−1.07620	−0.0567207
$361$	−11.7499	−0.618415
$362$	56.0426	2.94553
$363$	20.9206	1.09805
$364$	40.6490	2.13059
$365$	6.13808	0.321282
$366$	−0.377489	−0.0197317
$367$	24.7349	1.29115	0.645575	−	0.763697i	$-0.276618\pi$
$367$	24.7349	1.29115	0.645575	+	0.763697i	$0.276618\pi$
$368$	−3.33714	−0.173961
$369$	5.90910	0.307616
$370$	−2.01752	−0.104886
$371$	−4.77194	−0.247747
$372$	4.62832	0.239967
$373$	10.5058	0.543971	0.271986	−	0.962301i	$-0.412320\pi$
$373$	10.5058	0.543971	0.271986	+	0.962301i	$0.412320\pi$
$374$	0.727509	0.0376186
$375$	−11.4767	−0.592654
$376$	−10.4326	−0.538019
$377$	12.0716	0.621721
$378$	37.6156	1.93474
$379$	32.8133	1.68550	0.842752	−	0.538302i	$-0.180934\pi$
$379$	32.8133	1.68550	0.842752	+	0.538302i	$0.180934\pi$
$380$	−5.21587	−0.267569
$381$	24.1443	1.23695
$382$	−21.5055	−1.10032
$383$	−19.5237	−0.997612	−0.498806	−	0.866714i	$-0.666228\pi$
$383$	−19.5237	−0.997612	−0.498806	+	0.866714i	$0.666228\pi$
$384$	32.7196	1.66972
$385$	−0.748805	−0.0381626
$386$	23.9522	1.21913
$387$	3.34206	0.169886
$388$	−40.0367	−2.03256
$389$	−1.57957	−0.0800874	−0.0400437	−	0.999198i	$-0.512750\pi$
$389$	−1.57957	−0.0800874	−0.0400437	+	0.999198i	$0.512750\pi$
$390$	9.41062	0.476525
$391$	6.35005	0.321136
$392$	17.6973	0.893848
$393$	−35.4173	−1.78657
$394$	12.4831	0.628891
$395$	7.95354	0.400186
$396$	0.687567	0.0345515
$397$	20.7270	1.04026	0.520129	−	0.854087i	$-0.325884\pi$
$397$	20.7270	1.04026	0.520129	+	0.854087i	$0.325884\pi$
$398$	−48.5926	−2.43572
$399$	−19.3539	−0.968906
$400$	2.42446	0.121223
$401$	−29.5267	−1.47449	−0.737247	−	0.675623i	$-0.763875\pi$
$401$	−29.5267	−1.47449	−0.737247	+	0.675623i	$0.763875\pi$
$402$	56.4991	2.81792
$403$	−2.69699	−0.134347
$404$	5.59115	0.278170
$405$	6.58346	0.327135
$406$	29.3272	1.45548
$407$	0.461455	0.0228735
$408$	−4.84296	−0.239762
$409$	−11.6866	−0.577863	−0.288931	−	0.957350i	$-0.593300\pi$
$409$	−11.6866	−0.577863	−0.288931	+	0.957350i	$0.593300\pi$
$410$	−12.1115	−0.598147
$411$	9.60120	0.473592
$412$	−10.6656	−0.525456
$413$	−3.74378	−0.184219
$414$	9.85429	0.484312
$415$	−1.00013	−0.0490944
$416$	−21.7257	−1.06519
$417$	−0.297336	−0.0145606
$418$	1.95889	0.0958126
$419$	−4.13413	−0.201965	−0.100983	−	0.994888i	$-0.532199\pi$
$419$	−4.13413	−0.201965	−0.100983	+	0.994888i	$0.532199\pi$
$420$	13.9236	0.679401
$421$	14.5215	0.707736	0.353868	−	0.935295i	$-0.384866\pi$
$421$	14.5215	0.707736	0.353868	+	0.935295i	$0.384866\pi$
$422$	−58.5433	−2.84984
$423$	−2.83778	−0.137978
$424$	−3.21521	−0.156144
$425$	−4.61336	−0.223781
$426$	−36.2089	−1.75433
$427$	0.325457	0.0157500
$428$	−53.5596	−2.58890
$429$	−2.15244	−0.103921
$430$	−6.85002	−0.330337
$431$	−21.6031	−1.04059	−0.520293	−	0.853988i	$-0.674177\pi$
$431$	−21.6031	−1.04059	−0.520293	+	0.853988i	$0.674177\pi$
$432$	−2.33464	−0.112325
$433$	9.01591	0.433277	0.216638	−	0.976252i	$-0.430491\pi$
$433$	9.01591	0.433277	0.216638	+	0.976252i	$0.430491\pi$
$434$	−6.55215	−0.314513
$435$	4.13491	0.198254
$436$	7.88251	0.377504
$437$	17.0982	0.817916
$438$	42.8646	2.04815
$439$	−21.8903	−1.04477	−0.522384	−	0.852710i	$-0.674957\pi$
$439$	−21.8903	−1.04477	−0.522384	+	0.852710i	$0.674957\pi$
$440$	−0.504526	−0.0240523
$441$	4.81387	0.229232
$442$	7.88273	0.374943
$443$	−21.3065	−1.01230	−0.506151	−	0.862445i	$-0.668932\pi$
$443$	−21.3065	−1.01230	−0.506151	+	0.862445i	$0.668932\pi$
$444$	−8.58048	−0.407211
$445$	−2.80571	−0.133003
$446$	−18.1941	−0.861514
$447$	10.7377	0.507874
$448$	−48.8462	−2.30777
$449$	−11.5301	−0.544138	−0.272069	−	0.962278i	$-0.587708\pi$
$449$	−11.5301	−0.544138	−0.272069	+	0.962278i	$0.587708\pi$
$450$	−7.15921	−0.337488
$451$	2.77020	0.130444
$452$	3.12896	0.147174
$453$	19.6466	0.923080
$454$	−40.6562	−1.90809
$455$	−8.11347	−0.380366
$456$	−13.0402	−0.610662
$457$	3.57059	0.167025	0.0835126	−	0.996507i	$-0.473386\pi$
$457$	3.57059	0.167025	0.0835126	+	0.996507i	$0.473386\pi$
$458$	−33.4534	−1.56318
$459$	4.44245	0.207356
$460$	−12.3008	−0.573526
$461$	12.3450	0.574964	0.287482	−	0.957786i	$-0.407182\pi$
$461$	12.3450	0.574964	0.287482	+	0.957786i	$0.407182\pi$
$462$	−5.22919	−0.243284
$463$	−24.6241	−1.14438	−0.572190	−	0.820121i	$-0.693906\pi$
$463$	−24.6241	−1.14438	−0.572190	+	0.820121i	$0.693906\pi$
$464$	−1.82021	−0.0845013
$465$	−0.923805	−0.0428404
$466$	58.2862	2.70006
$467$	−8.14093	−0.376717	−0.188359	−	0.982100i	$-0.560317\pi$
$467$	−8.14093	−0.376717	−0.188359	+	0.982100i	$0.560317\pi$
$468$	7.44994	0.344374
$469$	−48.7114	−2.24928
$470$	5.81644	0.268293
$471$	−17.6579	−0.813635
$472$	−2.52246	−0.116106
$473$	1.56677	0.0720400
$474$	55.5426	2.55116
$475$	−12.4219	−0.569957
$476$	11.6630	0.534571
$477$	−0.874576	−0.0400441
$478$	−36.2025	−1.65586
$479$	−29.6301	−1.35383	−0.676916	−	0.736060i	$-0.736684\pi$
$479$	−29.6301	−1.35383	−0.676916	+	0.736060i	$0.736684\pi$
$480$	−7.44174	−0.339668
$481$	4.99997	0.227979
$482$	45.6048	2.07724
$483$	−45.6429	−2.07682
$484$	−33.9459	−1.54300
$485$	7.99125	0.362864
$486$	15.8323	0.718168
$487$	39.5867	1.79384	0.896922	−	0.442189i	$-0.145798\pi$
$487$	39.5867	1.79384	0.896922	+	0.442189i	$0.145798\pi$
$488$	0.219285	0.00992654
$489$	18.3431	0.829503
$490$	−9.86672	−0.445733
$491$	35.5422	1.60400	0.801998	−	0.597327i	$-0.203770\pi$
$491$	35.5422	1.60400	0.801998	+	0.597327i	$0.203770\pi$
$492$	−51.5103	−2.32226
$493$	3.46358	0.155992
$494$	21.2251	0.954960
$495$	−0.137237	−0.00616835
$496$	0.406664	0.0182598
$497$	31.2180	1.40032
$498$	−6.98428	−0.312973
$499$	−38.3957	−1.71883	−0.859414	−	0.511280i	$-0.829172\pi$
$499$	−38.3957	−1.71883	−0.859414	+	0.511280i	$0.829172\pi$
$500$	18.6221	0.832808
$501$	−16.5494	−0.739374
$502$	−5.37158	−0.239745
$503$	−23.1752	−1.03333	−0.516666	−	0.856187i	$-0.672827\pi$
$503$	−23.1752	−1.03333	−0.516666	+	0.856187i	$0.672827\pi$
$504$	6.47959	0.288624
$505$	−1.11598	−0.0496606
$506$	4.61972	0.205372
$507$	1.63698	0.0727010
$508$	−39.1767	−1.73819
$509$	−28.4135	−1.25941	−0.629703	−	0.776836i	$-0.716823\pi$
$509$	−28.4135	−1.25941	−0.629703	+	0.776836i	$0.716823\pi$
$510$	2.70008	0.119562
$511$	−36.9562	−1.63485
$512$	5.92716	0.261946
$513$	11.9618	0.528125
$514$	24.5469	1.08272
$515$	2.12883	0.0938075
$516$	−29.1331	−1.28251
$517$	−1.33036	−0.0585092
$518$	12.1471	0.533712
$519$	1.32582	0.0581969
$520$	−5.46665	−0.239729
$521$	12.8820	0.564372	0.282186	−	0.959360i	$-0.408940\pi$
$521$	12.8820	0.564372	0.282186	+	0.959360i	$0.408940\pi$
$522$	5.37493	0.235254
$523$	−40.1668	−1.75637	−0.878187	−	0.478318i	$-0.841247\pi$
$523$	−40.1668	−1.75637	−0.878187	+	0.478318i	$0.841247\pi$
$524$	57.4684	2.51052
$525$	33.1599	1.44722
$526$	21.3379	0.930375
$527$	−0.773818	−0.0337080
$528$	0.324553	0.0141244
$529$	17.3232	0.753182
$530$	1.79257	0.0778642
$531$	−0.686140	−0.0297759
$532$	31.4037	1.36153
$533$	30.0158	1.30013
$534$	−19.5933	−0.847887
$535$	10.6904	0.462186
$536$	−32.8205	−1.41763
$537$	−32.5505	−1.40466
$538$	−7.50026	−0.323359
$539$	2.25676	0.0972054
$540$	−8.60553	−0.370323
$541$	−7.29594	−0.313677	−0.156838	−	0.987624i	$-0.550130\pi$
$541$	−7.29594	−0.313677	−0.156838	+	0.987624i	$0.550130\pi$
$542$	−42.7433	−1.83598
$543$	−47.5739	−2.04159
$544$	−6.23352	−0.267260
$545$	−1.57334	−0.0673943
$546$	−56.6595	−2.42480
$547$	2.30704	0.0986419	0.0493210	−	0.998783i	$-0.484294\pi$
$547$	2.30704	0.0986419	0.0493210	+	0.998783i	$0.484294\pi$
$548$	−15.5790	−0.665500
$549$	0.0596480	0.00254571
$550$	−3.35626	−0.143111
$551$	9.32604	0.397303
$552$	−30.7530	−1.30894
$553$	−47.8867	−2.03635
$554$	−28.8329	−1.22499
$555$	1.71265	0.0726978
$556$	0.482459	0.0204608
$557$	−14.3453	−0.607830	−0.303915	−	0.952699i	$-0.598294\pi$
$557$	−14.3453	−0.607830	−0.303915	+	0.952699i	$0.598294\pi$
$558$	−1.20084	−0.0508358
$559$	16.9763	0.718020
$560$	1.22338	0.0516974
$561$	−0.617574	−0.0260740
$562$	27.1982	1.14729
$563$	18.6747	0.787045	0.393523	−	0.919315i	$-0.371256\pi$
$563$	18.6747	0.787045	0.393523	+	0.919315i	$0.371256\pi$
$564$	24.7373	1.04163
$565$	−0.624535	−0.0262744
$566$	59.1889	2.48790
$567$	−39.6377	−1.66463
$568$	21.0339	0.882562
$569$	−1.97241	−0.0826876	−0.0413438	−	0.999145i	$-0.513164\pi$
$569$	−1.97241	−0.0826876	−0.0413438	+	0.999145i	$0.513164\pi$
$570$	7.27025	0.304517
$571$	4.62865	0.193703	0.0968515	−	0.995299i	$-0.469123\pi$
$571$	4.62865	0.193703	0.0968515	+	0.995299i	$0.469123\pi$
$572$	3.49256	0.146031
$573$	18.2558	0.762645
$574$	72.9213	3.04367
$575$	−29.2951	−1.22169
$576$	−8.95227	−0.373011
$577$	−6.22276	−0.259057	−0.129528	−	0.991576i	$-0.541346\pi$
$577$	−6.22276	−0.259057	−0.129528	+	0.991576i	$0.541346\pi$
$578$	2.26170	0.0940744
$579$	−20.3327	−0.844999
$580$	−6.70934	−0.278590
$581$	6.02158	0.249817
$582$	55.8059	2.31323
$583$	−0.410004	−0.0169806
$584$	−24.9002	−1.03038
$585$	−1.48700	−0.0614797
$586$	9.87355	0.407872
$587$	−16.2278	−0.669791	−0.334896	−	0.942255i	$-0.608701\pi$
$587$	−16.2278	−0.669791	−0.334896	+	0.942255i	$0.608701\pi$
$588$	−41.9630	−1.73053
$589$	−2.08358	−0.0858526
$590$	1.40634	0.0578982
$591$	−10.5968	−0.435893
$592$	−0.753917	−0.0309858
$593$	−24.5854	−1.00960	−0.504800	−	0.863236i	$-0.668434\pi$
$593$	−24.5854	−1.00960	−0.504800	+	0.863236i	$0.668434\pi$
$594$	3.23193	0.132607
$595$	−2.32791	−0.0954349
$596$	−17.4230	−0.713673
$597$	41.2497	1.68824
$598$	50.0557	2.04693
$599$	14.2527	0.582348	0.291174	−	0.956670i	$-0.405954\pi$
$599$	14.2527	0.582348	0.291174	+	0.956670i	$0.405954\pi$
$600$	22.3423	0.912120
$601$	−11.2470	−0.458774	−0.229387	−	0.973335i	$-0.573672\pi$
$601$	−11.2470	−0.458774	−0.229387	+	0.973335i	$0.573672\pi$
$602$	41.2426	1.68092
$603$	−8.92757	−0.363559
$604$	−31.8788	−1.29713
$605$	6.77554	0.275465
$606$	−7.79333	−0.316582
$607$	−30.2707	−1.22865	−0.614325	−	0.789053i	$-0.710572\pi$
$607$	−30.2707	−1.22865	−0.614325	+	0.789053i	$0.710572\pi$
$608$	−16.7844	−0.680697
$609$	−24.8955	−1.00882
$610$	−0.122257	−0.00495004
$611$	−14.4148	−0.583159
$612$	2.13753	0.0864045
$613$	5.13507	0.207404	0.103702	−	0.994608i	$-0.466931\pi$
$613$	5.13507	0.207404	0.103702	+	0.994608i	$0.466931\pi$
$614$	60.8114	2.45415
$615$	10.2814	0.414584
$616$	3.03765	0.122390
$617$	31.4766	1.26720	0.633600	−	0.773661i	$-0.281576\pi$
$617$	31.4766	1.26720	0.633600	+	0.773661i	$0.281576\pi$
$618$	14.8664	0.598016
$619$	16.0582	0.645434	0.322717	−	0.946496i	$-0.395404\pi$
$619$	16.0582	0.645434	0.322717	+	0.946496i	$0.395404\pi$
$620$	1.49897	0.0602001
$621$	28.2098	1.13202
$622$	−32.0849	−1.28649
$623$	16.8926	0.676789
$624$	3.51661	0.140777
$625$	19.3498	0.773993
$626$	34.7673	1.38958
$627$	−1.66288	−0.0664091
$628$	28.6519	1.14333
$629$	1.43459	0.0572007
$630$	−3.61255	−0.143927
$631$	−34.5486	−1.37536	−0.687678	−	0.726016i	$-0.741370\pi$
$631$	−34.5486	−1.37536	−0.687678	+	0.726016i	$0.741370\pi$
$632$	−32.2649	−1.28343
$633$	49.6967	1.97527
$634$	−44.2664	−1.75804
$635$	7.81961	0.310312
$636$	7.62377	0.302302
$637$	24.4525	0.968843
$638$	2.51978	0.0997592
$639$	5.72147	0.226338
$640$	10.5969	0.418878
$641$	−38.5617	−1.52310	−0.761548	−	0.648108i	$-0.775560\pi$
$641$	−38.5617	−1.52310	−0.761548	+	0.648108i	$0.775560\pi$
$642$	74.6551	2.94640
$643$	28.6592	1.13021	0.565104	−	0.825020i	$-0.308836\pi$
$643$	28.6592	1.13021	0.565104	+	0.825020i	$0.308836\pi$
$644$	74.0605	2.91839
$645$	5.81490	0.228962
$646$	6.08986	0.239602
$647$	−14.7226	−0.578804	−0.289402	−	0.957208i	$-0.593456\pi$
$647$	−14.7226	−0.578804	−0.289402	+	0.957208i	$0.593456\pi$
$648$	−26.7069	−1.04915
$649$	−0.321664	−0.0126264
$650$	−36.3658	−1.42639
$651$	5.56205	0.217994
$652$	−29.7636	−1.16563
$653$	7.86856	0.307921	0.153960	−	0.988077i	$-0.450797\pi$
$653$	7.86856	0.307921	0.153960	+	0.988077i	$0.450797\pi$
$654$	−10.9872	−0.429633
$655$	−11.4706	−0.448193
$656$	−4.52591	−0.176707
$657$	−6.77314	−0.264245
$658$	−35.0197	−1.36521
$659$	−25.0446	−0.975601	−0.487800	−	0.872955i	$-0.662201\pi$
$659$	−25.0446	−0.975601	−0.487800	+	0.872955i	$0.662201\pi$
$660$	1.19631	0.0465663
$661$	−25.9008	−1.00742	−0.503712	−	0.863871i	$-0.668033\pi$
$661$	−25.9008	−1.00742	−0.503712	+	0.863871i	$0.668033\pi$
$662$	37.3145	1.45027
$663$	−6.69156	−0.259879
$664$	4.05719	0.157450
$665$	−6.26813	−0.243068
$666$	2.22625	0.0862655
$667$	21.9939	0.851608
$668$	26.8532	1.03898
$669$	15.4447	0.597127
$670$	18.2983	0.706926
$671$	0.0279632	0.00107951
$672$	44.8053	1.72840
$673$	15.3908	0.593271	0.296635	−	0.954991i	$-0.404135\pi$
$673$	15.3908	0.593271	0.296635	+	0.954991i	$0.404135\pi$
$674$	−31.6868	−1.22053
$675$	−20.4946	−0.788838
$676$	−2.65618	−0.102161
$677$	14.3370	0.551014	0.275507	−	0.961299i	$-0.411154\pi$
$677$	14.3370	0.551014	0.275507	+	0.961299i	$0.411154\pi$
$678$	−4.36136	−0.167497
$679$	−48.1138	−1.84644
$680$	−1.56849	−0.0601487
$681$	34.5125	1.32252
$682$	−0.562959	−0.0215568
$683$	11.8837	0.454716	0.227358	−	0.973811i	$-0.426991\pi$
$683$	11.8837	0.454716	0.227358	+	0.973811i	$0.426991\pi$
$684$	5.75551	0.220068
$685$	3.10953	0.118809
$686$	0.134401	0.00513146
$687$	28.3982	1.08346
$688$	−2.55975	−0.0975897
$689$	−4.44248	−0.169245
$690$	17.1457	0.652724
$691$	47.8283	1.81947	0.909737	−	0.415185i	$-0.136283\pi$
$691$	47.8283	1.81947	0.909737	+	0.415185i	$0.136283\pi$
$692$	−2.15128	−0.0817794
$693$	0.826277	0.0313877
$694$	−24.2382	−0.920068
$695$	−0.0962980	−0.00365279
$696$	−16.7740	−0.635816
$697$	8.61209	0.326206
$698$	38.4224	1.45431
$699$	−49.4785	−1.87145
$700$	−53.8054	−2.03365
$701$	24.9695	0.943087	0.471543	−	0.881843i	$-0.343697\pi$
$701$	24.9695	0.943087	0.471543	+	0.881843i	$0.343697\pi$
$702$	35.0187	1.32169
$703$	3.86277	0.145687
$704$	−4.19685	−0.158175
$705$	−4.93751	−0.185957
$706$	70.4682	2.65211
$707$	6.71911	0.252698
$708$	5.98115	0.224786
$709$	43.4248	1.63085	0.815427	−	0.578860i	$-0.196502\pi$
$709$	43.4248	1.63085	0.815427	+	0.578860i	$0.196502\pi$
$710$	−11.7270	−0.440105
$711$	−8.77643	−0.329142
$712$	11.3818	0.426552
$713$	−4.91378	−0.184023
$714$	−16.2567	−0.608390
$715$	−0.697108	−0.0260703
$716$	52.8166	1.97385
$717$	30.7319	1.14770
$718$	54.1513	2.02091
$719$	−50.0366	−1.86605	−0.933025	−	0.359811i	$-0.882841\pi$
$719$	−50.0366	−1.86605	−0.933025	+	0.359811i	$0.882841\pi$
$720$	0.224215	0.00835602
$721$	−12.8173	−0.477340
$722$	−26.5747	−0.989010
$723$	−38.7134	−1.43977
$724$	77.1937	2.86888
$725$	−15.9787	−0.593435
$726$	47.3162	1.75607
$727$	−6.64019	−0.246271	−0.123136	−	0.992390i	$-0.539295\pi$
$727$	−6.64019	−0.246271	−0.123136	+	0.992390i	$0.539295\pi$
$728$	32.9137	1.21986
$729$	18.3230	0.678631
$730$	13.8825	0.513815
$731$	4.87081	0.180153
$732$	−0.519958	−0.0192182
$733$	33.2080	1.22656	0.613282	−	0.789864i	$-0.289849\pi$
$733$	33.2080	1.22656	0.613282	+	0.789864i	$0.289849\pi$
$734$	55.9429	2.06489
$735$	8.37574	0.308944
$736$	−39.5832	−1.45906
$737$	−4.18527	−0.154166
$738$	13.3646	0.491959
$739$	11.2154	0.412564	0.206282	−	0.978493i	$-0.433864\pi$
$739$	11.2154	0.412564	0.206282	+	0.978493i	$0.433864\pi$
$740$	−2.77895	−0.102156
$741$	−18.0177	−0.661897
$742$	−10.7927	−0.396212
$743$	22.9972	0.843685	0.421842	−	0.906669i	$-0.361384\pi$
$743$	22.9972	0.843685	0.421842	+	0.906669i	$0.361384\pi$
$744$	3.74757	0.137392
$745$	3.47760	0.127409
$746$	23.7611	0.869954
$747$	1.10360	0.0403788
$748$	1.00208	0.0366396
$749$	−64.3648	−2.35184
$750$	−25.9568	−0.947810
$751$	9.46657	0.345440	0.172720	−	0.984971i	$-0.444744\pi$
$751$	9.46657	0.345440	0.172720	+	0.984971i	$0.444744\pi$
$752$	2.17352	0.0792601
$753$	4.55987	0.166171
$754$	27.3024	0.994296
$755$	6.36294	0.231571
$756$	51.8122	1.88439
$757$	−24.6100	−0.894465	−0.447233	−	0.894418i	$-0.647590\pi$
$757$	−24.6100	−0.894465	−0.447233	+	0.894418i	$0.647590\pi$
$758$	74.2138	2.69557
$759$	−3.92163	−0.142346
$760$	−4.22331	−0.153195
$761$	13.7151	0.497170	0.248585	−	0.968610i	$-0.420034\pi$
$761$	13.7151	0.497170	0.248585	+	0.968610i	$0.420034\pi$
$762$	54.6073	1.97821
$763$	9.47274	0.342936
$764$	−29.6219	−1.07168
$765$	−0.426647	−0.0154254
$766$	−44.1567	−1.59545
$767$	−3.48531	−0.125847
$768$	23.9021	0.862493
$769$	17.6976	0.638190	0.319095	−	0.947723i	$-0.396621\pi$
$769$	17.6976	0.638190	0.319095	+	0.947723i	$0.396621\pi$
$770$	−1.69357	−0.0610321
$771$	−20.8376	−0.750448
$772$	32.9920	1.18741
$773$	−19.8628	−0.714415	−0.357207	−	0.934025i	$-0.616271\pi$
$773$	−19.8628	−0.714415	−0.357207	+	0.934025i	$0.616271\pi$
$774$	7.55873	0.271693
$775$	3.56990	0.128234
$776$	−32.4178	−1.16373
$777$	−10.3115	−0.369923
$778$	−3.57252	−0.128081
$779$	23.1889	0.830830
$780$	12.9623	0.464125
$781$	2.68224	0.0959781
$782$	14.3619	0.513581
$783$	15.3868	0.549879
$784$	−3.68705	−0.131680
$785$	−5.71886	−0.204115
$786$	−80.1034	−2.85719
$787$	−28.3269	−1.00975	−0.504873	−	0.863194i	$-0.668461\pi$
$787$	−28.3269	−1.00975	−0.504873	+	0.863194i	$0.668461\pi$
$788$	17.1944	0.612525
$789$	−18.1135	−0.644857
$790$	17.9885	0.640004
$791$	3.76020	0.133697
$792$	0.556725	0.0197824
$793$	0.302987	0.0107594
$794$	46.8783	1.66365
$795$	−1.52169	−0.0539688
$796$	−66.9320	−2.37234
$797$	39.6019	1.40277	0.701386	−	0.712781i	$-0.252565\pi$
$797$	39.6019	1.40277	0.701386	+	0.712781i	$0.252565\pi$
$798$	−43.7727	−1.54954
$799$	−4.13587	−0.146316
$800$	28.7574	1.01673
$801$	3.09599	0.109392
$802$	−66.7807	−2.35811
$803$	−3.17527	−0.112053
$804$	77.8226	2.74459
$805$	−14.7823	−0.521009
$806$	−6.09979	−0.214856
$807$	6.36688	0.224125
$808$	4.52717	0.159265
$809$	−4.23876	−0.149027	−0.0745134	−	0.997220i	$-0.523740\pi$
$809$	−4.23876	−0.149027	−0.0745134	+	0.997220i	$0.523740\pi$
$810$	14.8898	0.523175
$811$	0.921171	0.0323467	0.0161733	−	0.999869i	$-0.494852\pi$
$811$	0.921171	0.0323467	0.0161733	+	0.999869i	$0.494852\pi$
$812$	40.3956	1.41761
$813$	36.2843	1.27255
$814$	1.04367	0.0365807
$815$	5.94076	0.208096
$816$	1.00898	0.0353214
$817$	13.1151	0.458841
$818$	−26.4315	−0.924156
$819$	8.95291	0.312840
$820$	−16.6826	−0.582581
$821$	−0.327816	−0.0114409	−0.00572043	−	0.999984i	$-0.501821\pi$
$821$	−0.327816	−0.0114409	−0.00572043	+	0.999984i	$0.501821\pi$
$822$	21.7150	0.757399
$823$	−32.0068	−1.11569	−0.557844	−	0.829946i	$-0.688371\pi$
$823$	−32.0068	−1.11569	−0.557844	+	0.829946i	$0.688371\pi$
$824$	−8.63596	−0.300848
$825$	2.84909	0.0991925
$826$	−8.46731	−0.294615
$827$	33.1483	1.15268	0.576339	−	0.817211i	$-0.304481\pi$
$827$	33.1483	1.15268	0.576339	+	0.817211i	$0.304481\pi$
$828$	13.5734	0.471709
$829$	−53.0886	−1.84384	−0.921922	−	0.387376i	$-0.873382\pi$
$829$	−53.0886	−1.84384	−0.921922	+	0.387376i	$0.873382\pi$
$830$	−2.26199	−0.0785150
$831$	24.4759	0.849059
$832$	−45.4739	−1.57652
$833$	7.01587	0.243086
$834$	−0.672485	−0.0232863
$835$	−5.35985	−0.185485
$836$	2.69820	0.0933192
$837$	−3.43765	−0.118823
$838$	−9.35016	−0.322996
$839$	−3.67589	−0.126906	−0.0634529	−	0.997985i	$-0.520211\pi$
$839$	−3.67589	−0.126906	−0.0634529	+	0.997985i	$0.520211\pi$
$840$	11.2740	0.388989
$841$	−17.0036	−0.586332
$842$	32.8433	1.13186
$843$	−23.0883	−0.795202
$844$	−80.6382	−2.77568
$845$	0.530168	0.0182383
$846$	−6.41822	−0.220663
$847$	−40.7942	−1.40171
$848$	0.669857	0.0230030
$849$	−50.2448	−1.72440
$850$	−10.4340	−0.357884
$851$	9.10969	0.312276
$852$	−49.8746	−1.70868
$853$	2.21779	0.0759358	0.0379679	−	0.999279i	$-0.487912\pi$
$853$	2.21779	0.0759358	0.0379679	+	0.999279i	$0.487912\pi$
$854$	0.736086	0.0251883
$855$	−1.14879	−0.0392878
$856$	−43.3674	−1.48227
$857$	26.4924	0.904962	0.452481	−	0.891774i	$-0.350539\pi$
$857$	26.4924	0.904962	0.452481	+	0.891774i	$0.350539\pi$
$858$	−4.86817	−0.166196
$859$	−25.2462	−0.861388	−0.430694	−	0.902498i	$-0.641731\pi$
$859$	−25.2462	−0.861388	−0.430694	+	0.902498i	$0.641731\pi$
$860$	−9.43530	−0.321741
$861$	−61.9020	−2.10961
$862$	−48.8598	−1.66417
$863$	16.5647	0.563871	0.281935	−	0.959433i	$-0.409024\pi$
$863$	16.5647	0.563871	0.281935	+	0.959433i	$0.409024\pi$
$864$	−27.6921	−0.942105
$865$	0.429391	0.0145997
$866$	20.3913	0.692924
$867$	−1.91993	−0.0652043
$868$	−9.02501	−0.306329
$869$	−4.11442	−0.139572
$870$	9.35194	0.317061
$871$	−45.3484	−1.53657
$872$	6.38250	0.216139
$873$	−8.81804	−0.298445
$874$	38.6710	1.30806
$875$	22.3790	0.756548
$876$	59.0422	1.99485
$877$	38.8762	1.31275	0.656377	−	0.754433i	$-0.272088\pi$
$877$	38.8762	1.31275	0.656377	+	0.754433i	$0.272088\pi$
$878$	−49.5094	−1.67086
$879$	−8.38154	−0.282702
$880$	0.105113	0.00354335
$881$	−45.3017	−1.52625	−0.763126	−	0.646249i	$-0.776337\pi$
$881$	−45.3017	−1.52625	−0.763126	+	0.646249i	$0.776337\pi$
$882$	10.8875	0.366603
$883$	−28.1767	−0.948221	−0.474111	−	0.880465i	$-0.657230\pi$
$883$	−28.1767	−0.948221	−0.474111	+	0.880465i	$0.657230\pi$
$884$	10.8578	0.365186
$885$	−1.19383	−0.0401301
$886$	−48.1889	−1.61894
$887$	−33.7900	−1.13456	−0.567279	−	0.823526i	$-0.692004\pi$
$887$	−33.7900	−1.13456	−0.567279	+	0.823526i	$0.692004\pi$
$888$	−6.94764	−0.233147
$889$	−47.0803	−1.57902
$890$	−6.34568	−0.212708
$891$	−3.40566	−0.114094
$892$	−25.0607	−0.839094
$893$	−11.1362	−0.372660
$894$	24.2854	0.812224
$895$	−10.5421	−0.352383
$896$	−63.8017	−2.13146
$897$	−42.4917	−1.41876
$898$	−26.0776	−0.870220
$899$	−2.68018	−0.0893889
$900$	−9.86118	−0.328706
$901$	−1.27463	−0.0424641
$902$	6.26538	0.208614
$903$	−35.0104	−1.16507
$904$	2.53353	0.0842639
$905$	−15.4077	−0.512170
$906$	44.4348	1.47625
$907$	3.84697	0.127737	0.0638683	−	0.997958i	$-0.479656\pi$
$907$	3.84697	0.127737	0.0638683	+	0.997958i	$0.479656\pi$
$908$	−56.0003	−1.85843
$909$	1.23144	0.0408444
$910$	−18.3503	−0.608305
$911$	−12.2347	−0.405355	−0.202678	−	0.979246i	$-0.564964\pi$
$911$	−12.2347	−0.405355	−0.202678	+	0.979246i	$0.564964\pi$
$912$	2.71679	0.0899618
$913$	0.517373	0.0171225
$914$	8.07561	0.267117
$915$	0.103783	0.00343095
$916$	−46.0792	−1.52250
$917$	69.0621	2.28063
$918$	10.0475	0.331617
$919$	25.3576	0.836471	0.418235	−	0.908339i	$-0.362649\pi$
$919$	25.3576	0.836471	0.418235	+	0.908339i	$0.362649\pi$
$920$	−9.95997	−0.328370
$921$	−51.6221	−1.70101
$922$	27.9207	0.919520
$923$	29.0627	0.956610
$924$	−7.20275	−0.236953
$925$	−6.61825	−0.217607
$926$	−55.6924	−1.83017
$927$	−2.34908	−0.0771540
$928$	−21.5903	−0.708736
$929$	30.4427	0.998793	0.499396	−	0.866374i	$-0.333555\pi$
$929$	30.4427	0.998793	0.499396	+	0.866374i	$0.333555\pi$
$930$	−2.08937	−0.0685132
$931$	18.8910	0.619126
$932$	80.2841	2.62979
$933$	27.2365	0.891683
$934$	−18.4124	−0.602471
$935$	−0.200013	−0.00654113
$936$	6.03224	0.197170
$937$	−21.4893	−0.702026	−0.351013	−	0.936371i	$-0.614163\pi$
$937$	−21.4893	−0.702026	−0.351013	+	0.936371i	$0.614163\pi$
$938$	−110.171	−3.59720
$939$	−29.5136	−0.963139
$940$	8.01164	0.261311
$941$	−21.7208	−0.708077	−0.354039	−	0.935231i	$-0.615192\pi$
$941$	−21.7208	−0.708077	−0.354039	+	0.935231i	$0.615192\pi$
$942$	−39.9370	−1.30122
$943$	54.6873	1.78086
$944$	0.525530	0.0171045
$945$	−10.3416	−0.336413
$946$	3.54356	0.115211
$947$	3.75967	0.122173	0.0610864	−	0.998132i	$-0.480543\pi$
$947$	3.75967	0.122173	0.0610864	+	0.998132i	$0.480543\pi$
$948$	76.5051	2.48477
$949$	−34.4048	−1.11683
$950$	−28.0947	−0.911513
$951$	37.5772	1.21852
$952$	9.44354	0.306067
$953$	46.2241	1.49734	0.748672	−	0.662941i	$-0.230692\pi$
$953$	46.2241	1.49734	0.748672	+	0.662941i	$0.230692\pi$
$954$	−1.97803	−0.0640411
$955$	5.91248	0.191323
$956$	−49.8657	−1.61277
$957$	−2.13902	−0.0691446
$958$	−67.0143	−2.16514
$959$	−18.7219	−0.604561
$960$	−15.5762	−0.502720
$961$	−30.4012	−0.980684
$962$	11.3084	0.364599
$963$	−11.7964	−0.380135
$964$	62.8166	2.02319
$965$	−6.58514	−0.211983
$966$	−103.231	−3.32139
$967$	44.6469	1.43575	0.717874	−	0.696173i	$-0.245115\pi$
$967$	44.6469	1.43575	0.717874	+	0.696173i	$0.245115\pi$
$968$	−27.4861	−0.883437
$969$	−5.16961	−0.166072
$970$	18.0738	0.580316
$971$	21.2107	0.680683	0.340341	−	0.940302i	$-0.389457\pi$
$971$	21.2107	0.680683	0.340341	+	0.940302i	$0.389457\pi$
$972$	21.8076	0.699479
$973$	0.579791	0.0185873
$974$	89.5333	2.86883
$975$	30.8705	0.988648
$976$	−0.0456857	−0.00146236
$977$	34.5611	1.10571	0.552854	−	0.833278i	$-0.313539\pi$
$977$	34.5611	1.10571	0.552854	+	0.833278i	$0.313539\pi$
$978$	41.4866	1.32660
$979$	1.45141	0.0463873
$980$	−13.5905	−0.434134
$981$	1.73611	0.0554299
$982$	80.3858	2.56521
$983$	17.7934	0.567520	0.283760	−	0.958895i	$-0.408418\pi$
$983$	17.7934	0.567520	0.283760	+	0.958895i	$0.408418\pi$
$984$	−41.7080	−1.32960
$985$	−3.43197	−0.109352
$986$	7.83358	0.249472
$987$	29.7278	0.946246
$988$	29.2356	0.930110
$989$	30.9299	0.983513
$990$	−0.310389	−0.00986482
$991$	34.7183	1.10286	0.551431	−	0.834220i	$-0.314082\pi$
$991$	34.7183	1.10286	0.551431	+	0.834220i	$0.314082\pi$
$992$	4.82361	0.153150
$993$	−31.6758	−1.00520
$994$	70.6057	2.23948
$995$	13.3595	0.423524
$996$	−9.62023	−0.304829
$997$	11.3568	0.359672	0.179836	−	0.983697i	$-0.442443\pi$
$997$	11.3568	0.359672	0.179836	+	0.983697i	$0.442443\pi$
$998$	−86.8397	−2.74886
$999$	6.37308	0.201635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.15	✓	18
3.2	odd	2		9027.2.a.q.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.15	✓	18	1.1	even	1	trivial
9027.2.a.q.1.4		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q+2.26170 q^{2} -1.91993 q^{3} +3.11529 q^{4} -0.621807 q^{5} -4.34231 q^{6} +3.74378 q^{7} +2.52246 q^{8} +0.686140 q^{9} +O(q^{10})\)	\(q+2.26170 q^{2} -1.91993 q^{3} +3.11529 q^{4} -0.621807 q^{5} -4.34231 q^{6} +3.74378 q^{7} +2.52246 q^{8} +0.686140 q^{9} -1.40634 q^{10} +0.321664 q^{11} -5.98115 q^{12} +3.48531 q^{13} +8.46731 q^{14} +1.19383 q^{15} -0.525530 q^{16} +1.00000 q^{17} +1.55184 q^{18} +2.69260 q^{19} -1.93711 q^{20} -7.18780 q^{21} +0.727509 q^{22} +6.35005 q^{23} -4.84296 q^{24} -4.61336 q^{25} +7.88273 q^{26} +4.44245 q^{27} +11.6630 q^{28} +3.46358 q^{29} +2.70008 q^{30} -0.773818 q^{31} -6.23352 q^{32} -0.617574 q^{33} +2.26170 q^{34} -2.32791 q^{35} +2.13753 q^{36} +1.43459 q^{37} +6.08986 q^{38} -6.69156 q^{39} -1.56849 q^{40} +8.61209 q^{41} -16.2567 q^{42} +4.87081 q^{43} +1.00208 q^{44} -0.426647 q^{45} +14.3619 q^{46} -4.13587 q^{47} +1.00898 q^{48} +7.01587 q^{49} -10.4340 q^{50} -1.91993 q^{51} +10.8578 q^{52} -1.27463 q^{53} +10.0475 q^{54} -0.200013 q^{55} +9.44354 q^{56} -5.16961 q^{57} +7.83358 q^{58} -1.00000 q^{59} +3.71912 q^{60} +0.0869327 q^{61} -1.75014 q^{62} +2.56876 q^{63} -13.0473 q^{64} -2.16719 q^{65} -1.39677 q^{66} -13.0113 q^{67} +3.11529 q^{68} -12.1917 q^{69} -5.26503 q^{70} +8.33863 q^{71} +1.73076 q^{72} -9.87137 q^{73} +3.24460 q^{74} +8.85733 q^{75} +8.38825 q^{76} +1.20424 q^{77} -15.1343 q^{78} -12.7910 q^{79} +0.326778 q^{80} -10.5876 q^{81} +19.4780 q^{82} +1.60842 q^{83} -22.3921 q^{84} -0.621807 q^{85} +11.0163 q^{86} -6.64984 q^{87} +0.811387 q^{88} +4.51219 q^{89} -0.964947 q^{90} +13.0482 q^{91} +19.7823 q^{92} +1.48568 q^{93} -9.35410 q^{94} -1.67428 q^{95} +11.9679 q^{96} -12.8517 q^{97} +15.8678 q^{98} +0.220707 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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