LMFDB - Embedded newform 1003.2.a.i.1.1

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			1.1
Root			$-2.55956$ 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)

$f(q)$	$=$	$q-2.55956 q^{2} -0.639116 q^{3} +4.55133 q^{4} +2.79521 q^{5} +1.63585 q^{6} -2.94129 q^{7} -6.53027 q^{8} -2.59153 q^{9} +O(q^{10})$	\(q-2.55956 q^{2} -0.639116 q^{3} +4.55133 q^{4} +2.79521 q^{5} +1.63585 q^{6} -2.94129 q^{7} -6.53027 q^{8} -2.59153 q^{9} -7.15450 q^{10} -5.77374 q^{11} -2.90883 q^{12} -1.05617 q^{13} +7.52841 q^{14} -1.78646 q^{15} +7.61194 q^{16} +1.00000 q^{17} +6.63317 q^{18} -2.27700 q^{19} +12.7219 q^{20} +1.87983 q^{21} +14.7782 q^{22} +5.87835 q^{23} +4.17360 q^{24} +2.81319 q^{25} +2.70332 q^{26} +3.57364 q^{27} -13.3868 q^{28} +2.64149 q^{29} +4.57255 q^{30} +4.52257 q^{31} -6.42265 q^{32} +3.69009 q^{33} -2.55956 q^{34} -8.22153 q^{35} -11.7949 q^{36} +4.08041 q^{37} +5.82810 q^{38} +0.675013 q^{39} -18.2535 q^{40} +1.84892 q^{41} -4.81152 q^{42} -1.63440 q^{43} -26.2782 q^{44} -7.24387 q^{45} -15.0460 q^{46} +11.0946 q^{47} -4.86491 q^{48} +1.65121 q^{49} -7.20053 q^{50} -0.639116 q^{51} -4.80697 q^{52} +9.38359 q^{53} -9.14692 q^{54} -16.1388 q^{55} +19.2074 q^{56} +1.45526 q^{57} -6.76104 q^{58} -1.00000 q^{59} -8.13078 q^{60} +4.22040 q^{61} -11.5758 q^{62} +7.62246 q^{63} +1.21525 q^{64} -2.95221 q^{65} -9.44499 q^{66} +11.3235 q^{67} +4.55133 q^{68} -3.75694 q^{69} +21.0435 q^{70} -11.1153 q^{71} +16.9234 q^{72} +1.83492 q^{73} -10.4440 q^{74} -1.79796 q^{75} -10.3634 q^{76} +16.9823 q^{77} -1.72773 q^{78} -10.2855 q^{79} +21.2770 q^{80} +5.49063 q^{81} -4.73241 q^{82} +12.7312 q^{83} +8.55571 q^{84} +2.79521 q^{85} +4.18334 q^{86} -1.68822 q^{87} +37.7041 q^{88} +17.5809 q^{89} +18.5411 q^{90} +3.10650 q^{91} +26.7543 q^{92} -2.89045 q^{93} -28.3972 q^{94} -6.36468 q^{95} +4.10481 q^{96} -1.97208 q^{97} -4.22637 q^{98} +14.9628 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.55956	−1.80988	−0.904940	−	0.425539i	$-0.860084\pi$
$2$	−2.55956	−1.80988	−0.904940	+	0.425539i	$0.860084\pi$
$3$	−0.639116	−0.368994	−0.184497	−	0.982833i	$-0.559066\pi$
$3$	−0.639116	−0.368994	−0.184497	+	0.982833i	$0.559066\pi$
$4$	4.55133	2.27566
$5$	2.79521	1.25006	0.625028	−	0.780603i	$-0.285088\pi$
$5$	2.79521	1.25006	0.625028	+	0.780603i	$0.285088\pi$
$6$	1.63585	0.667834
$7$	−2.94129	−1.11170	−0.555852	−	0.831281i	$-0.687608\pi$
$7$	−2.94129	−1.11170	−0.555852	+	0.831281i	$0.687608\pi$
$8$	−6.53027	−2.30880
$9$	−2.59153	−0.863844
$10$	−7.15450	−2.26245
$11$	−5.77374	−1.74085	−0.870425	−	0.492302i	$-0.836156\pi$
$11$	−5.77374	−1.74085	−0.870425	+	0.492302i	$0.836156\pi$
$12$	−2.90883	−0.839706
$13$	−1.05617	−0.292928	−0.146464	−	0.989216i	$-0.546789\pi$
$13$	−1.05617	−0.292928	−0.146464	+	0.989216i	$0.546789\pi$
$14$	7.52841	2.01205
$15$	−1.78646	−0.461263
$16$	7.61194	1.90298
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.63317	1.56345
$19$	−2.27700	−0.522379	−0.261189	−	0.965288i	$-0.584115\pi$
$19$	−2.27700	−0.522379	−0.261189	+	0.965288i	$0.584115\pi$
$20$	12.7219	2.84471
$21$	1.87983	0.410212
$22$	14.7782	3.15073
$23$	5.87835	1.22572	0.612860	−	0.790191i	$-0.290019\pi$
$23$	5.87835	1.22572	0.612860	+	0.790191i	$0.290019\pi$
$24$	4.17360	0.851932
$25$	2.81319	0.562639
$26$	2.70332	0.530165
$27$	3.57364	0.687746
$28$	−13.3868	−2.52987
$29$	2.64149	0.490512	0.245256	−	0.969458i	$-0.421128\pi$
$29$	2.64149	0.490512	0.245256	+	0.969458i	$0.421128\pi$
$30$	4.57255	0.834830
$31$	4.52257	0.812278	0.406139	−	0.913811i	$-0.366875\pi$
$31$	4.52257	0.812278	0.406139	+	0.913811i	$0.366875\pi$
$32$	−6.42265	−1.13537
$33$	3.69009	0.642362
$34$	−2.55956	−0.438960
$35$	−8.22153	−1.38969
$36$	−11.7949	−1.96582
$37$	4.08041	0.670816	0.335408	−	0.942073i	$-0.391126\pi$
$37$	4.08041	0.670816	0.335408	+	0.942073i	$0.391126\pi$
$38$	5.82810	0.945443
$39$	0.675013	0.108089
$40$	−18.2535	−2.88613
$41$	1.84892	0.288752	0.144376	−	0.989523i	$-0.453882\pi$
$41$	1.84892	0.288752	0.144376	+	0.989523i	$0.453882\pi$
$42$	−4.81152	−0.742434
$43$	−1.63440	−0.249243	−0.124622	−	0.992204i	$-0.539772\pi$
$43$	−1.63440	−0.249243	−0.124622	+	0.992204i	$0.539772\pi$
$44$	−26.2782	−3.96159
$45$	−7.24387	−1.07985
$46$	−15.0460	−2.21841
$47$	11.0946	1.61831	0.809156	−	0.587594i	$-0.199925\pi$
$47$	11.0946	1.61831	0.809156	+	0.587594i	$0.199925\pi$
$48$	−4.86491	−0.702189
$49$	1.65121	0.235887
$50$	−7.20053	−1.01831
$51$	−0.639116	−0.0894941
$52$	−4.80697	−0.666606
$53$	9.38359	1.28894	0.644468	−	0.764632i	$-0.277079\pi$
$53$	9.38359	1.28894	0.644468	+	0.764632i	$0.277079\pi$
$54$	−9.14692	−1.24474
$55$	−16.1388	−2.17616
$56$	19.2074	2.56670
$57$	1.45526	0.192754
$58$	−6.76104	−0.887768
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−8.13078	−1.04968
$61$	4.22040	0.540367	0.270183	−	0.962809i	$-0.412916\pi$
$61$	4.22040	0.540367	0.270183	+	0.962809i	$0.412916\pi$
$62$	−11.5758	−1.47013
$63$	7.62246	0.960339
$64$	1.21525	0.151906
$65$	−2.95221	−0.366176
$66$	−9.44499	−1.16260
$67$	11.3235	1.38339	0.691693	−	0.722192i	$-0.256865\pi$
$67$	11.3235	1.38339	0.691693	+	0.722192i	$0.256865\pi$
$68$	4.55133	0.551930
$69$	−3.75694	−0.452283
$70$	21.0435	2.51518
$71$	−11.1153	−1.31914	−0.659569	−	0.751644i	$-0.729261\pi$
$71$	−11.1153	−1.31914	−0.659569	+	0.751644i	$0.729261\pi$
$72$	16.9234	1.99444
$73$	1.83492	0.214762	0.107381	−	0.994218i	$-0.465754\pi$
$73$	1.83492	0.214762	0.107381	+	0.994218i	$0.465754\pi$
$74$	−10.4440	−1.21410
$75$	−1.79796	−0.207610
$76$	−10.3634	−1.18876
$77$	16.9823	1.93531
$78$	−1.72773	−0.195627
$79$	−10.2855	−1.15721	−0.578606	−	0.815607i	$-0.696403\pi$
$79$	−10.2855	−1.15721	−0.578606	+	0.815607i	$0.696403\pi$
$80$	21.2770	2.37884
$81$	5.49063	0.610070
$82$	−4.73241	−0.522607
$83$	12.7312	1.39743	0.698714	−	0.715401i	$-0.253756\pi$
$83$	12.7312	1.39743	0.698714	+	0.715401i	$0.253756\pi$
$84$	8.55571	0.933505
$85$	2.79521	0.303183
$86$	4.18334	0.451101
$87$	−1.68822	−0.180996
$88$	37.7041	4.01927
$89$	17.5809	1.86357	0.931787	−	0.363005i	$-0.118249\pi$
$89$	17.5809	1.86357	0.931787	+	0.363005i	$0.118249\pi$
$90$	18.5411	1.95440
$91$	3.10650	0.325650
$92$	26.7543	2.78933
$93$	−2.89045	−0.299726
$94$	−28.3972	−2.92895
$95$	−6.36468	−0.653002
$96$	4.10481	0.418946
$97$	−1.97208	−0.200234	−0.100117	−	0.994976i	$-0.531922\pi$
$97$	−1.97208	−0.200234	−0.100117	+	0.994976i	$0.531922\pi$
$98$	−4.22637	−0.426928
$99$	14.9628	1.50382
$100$	12.8038	1.28038
$101$	2.11812	0.210761	0.105380	−	0.994432i	$-0.466394\pi$
$101$	2.11812	0.210761	0.105380	+	0.994432i	$0.466394\pi$
$102$	1.63585	0.161974
$103$	−16.1680	−1.59308	−0.796541	−	0.604585i	$-0.793339\pi$
$103$	−16.1680	−1.59308	−0.796541	+	0.604585i	$0.793339\pi$
$104$	6.89706	0.676312
$105$	5.25451	0.512788
$106$	−24.0178	−2.33282
$107$	−7.44009	−0.719261	−0.359631	−	0.933095i	$-0.617097\pi$
$107$	−7.44009	−0.719261	−0.359631	+	0.933095i	$0.617097\pi$
$108$	16.2648	1.56508
$109$	3.01645	0.288923	0.144462	−	0.989510i	$-0.453855\pi$
$109$	3.01645	0.288923	0.144462	+	0.989510i	$0.453855\pi$
$110$	41.3082	3.93858
$111$	−2.60786	−0.247527
$112$	−22.3890	−2.11556
$113$	11.7016	1.10080	0.550398	−	0.834902i	$-0.314476\pi$
$113$	11.7016	1.10080	0.550398	+	0.834902i	$0.314476\pi$
$114$	−3.72483	−0.348862
$115$	16.4312	1.53222
$116$	12.0223	1.11624
$117$	2.73709	0.253044
$118$	2.55956	0.235626
$119$	−2.94129	−0.269628
$120$	11.6661	1.06496
$121$	22.3361	2.03056
$122$	−10.8023	−0.977999
$123$	−1.18167	−0.106548
$124$	20.5837	1.84847
$125$	−6.11258	−0.546726
$126$	−19.5101	−1.73810
$127$	−21.3408	−1.89369	−0.946844	−	0.321694i	$-0.895748\pi$
$127$	−21.3408	−1.89369	−0.946844	+	0.321694i	$0.895748\pi$
$128$	9.73480	0.860443
$129$	1.04457	0.0919692
$130$	7.55634	0.662735
$131$	7.39943	0.646491	0.323245	−	0.946315i	$-0.395226\pi$
$131$	7.39943	0.646491	0.323245	+	0.946315i	$0.395226\pi$
$132$	16.7948	1.46180
$133$	6.69731	0.580731
$134$	−28.9831	−2.50376
$135$	9.98906	0.859721
$136$	−6.53027	−0.559966
$137$	11.1840	0.955510	0.477755	−	0.878493i	$-0.341451\pi$
$137$	11.1840	0.955510	0.477755	+	0.878493i	$0.341451\pi$
$138$	9.61611	0.818578
$139$	−11.5107	−0.976326	−0.488163	−	0.872752i	$-0.662333\pi$
$139$	−11.5107	−0.976326	−0.488163	+	0.872752i	$0.662333\pi$
$140$	−37.4189	−3.16247
$141$	−7.09072	−0.597147
$142$	28.4501	2.38748
$143$	6.09804	0.509944
$144$	−19.7266	−1.64388
$145$	7.38351	0.613167
$146$	−4.69659	−0.388693
$147$	−1.05532	−0.0870409
$148$	18.5713	1.52655
$149$	−11.4083	−0.934604	−0.467302	−	0.884098i	$-0.654774\pi$
$149$	−11.4083	−0.934604	−0.467302	+	0.884098i	$0.654774\pi$
$150$	4.60197	0.375749
$151$	11.7410	0.955470	0.477735	−	0.878504i	$-0.341458\pi$
$151$	11.7410	0.955470	0.477735	+	0.878504i	$0.341458\pi$
$152$	14.8694	1.20607
$153$	−2.59153	−0.209513
$154$	−43.4671	−3.50268
$155$	12.6415	1.01539
$156$	3.07221	0.245973
$157$	−17.1846	−1.37148	−0.685741	−	0.727845i	$-0.740522\pi$
$157$	−17.1846	−1.37148	−0.685741	+	0.727845i	$0.740522\pi$
$158$	26.3264	2.09441
$159$	−5.99720	−0.475609
$160$	−17.9526	−1.41928
$161$	−17.2900	−1.36264
$162$	−14.0536	−1.10415
$163$	−1.89620	−0.148522	−0.0742608	−	0.997239i	$-0.523660\pi$
$163$	−1.89620	−0.148522	−0.0742608	+	0.997239i	$0.523660\pi$
$164$	8.41503	0.657104
$165$	10.3146	0.802988
$166$	−32.5862	−2.52918
$167$	7.18826	0.556244	0.278122	−	0.960546i	$-0.410288\pi$
$167$	7.18826	0.556244	0.278122	+	0.960546i	$0.410288\pi$
$168$	−12.2758	−0.947097
$169$	−11.8845	−0.914193
$170$	−7.15450	−0.548725
$171$	5.90091	0.451254
$172$	−7.43869	−0.567194
$173$	5.43379	0.413123	0.206562	−	0.978434i	$-0.433773\pi$
$173$	5.43379	0.413123	0.206562	+	0.978434i	$0.433773\pi$
$174$	4.32109	0.327581
$175$	−8.27443	−0.625488
$176$	−43.9494	−3.31281
$177$	0.639116	0.0480389
$178$	−44.9994	−3.37285
$179$	1.42152	0.106249	0.0531245	−	0.998588i	$-0.483082\pi$
$179$	1.42152	0.106249	0.0531245	+	0.998588i	$0.483082\pi$
$180$	−32.9692	−2.45738
$181$	9.90416	0.736170	0.368085	−	0.929792i	$-0.380013\pi$
$181$	9.90416	0.736170	0.368085	+	0.929792i	$0.380013\pi$
$182$	−7.95126	−0.589387
$183$	−2.69732	−0.199392
$184$	−38.3872	−2.82994
$185$	11.4056	0.838557
$186$	7.39827	0.542467
$187$	−5.77374	−0.422218
$188$	50.4951	3.68273
$189$	−10.5111	−0.764571
$190$	16.2908	1.18186
$191$	−23.6409	−1.71060	−0.855299	−	0.518136i	$-0.826626\pi$
$191$	−23.6409	−1.71060	−0.855299	+	0.518136i	$0.826626\pi$
$192$	−0.776684	−0.0560523
$193$	13.9846	1.00664	0.503318	−	0.864101i	$-0.332112\pi$
$193$	13.9846	1.00664	0.503318	+	0.864101i	$0.332112\pi$
$194$	5.04765	0.362400
$195$	1.88680	0.135117
$196$	7.51521	0.536801
$197$	26.7570	1.90636	0.953179	−	0.302408i	$-0.0977904\pi$
$197$	26.7570	1.90636	0.953179	+	0.302408i	$0.0977904\pi$
$198$	−38.2982	−2.72174
$199$	−5.47765	−0.388300	−0.194150	−	0.980972i	$-0.562195\pi$
$199$	−5.47765	−0.388300	−0.194150	+	0.980972i	$0.562195\pi$
$200$	−18.3709	−1.29902
$201$	−7.23702	−0.510460
$202$	−5.42145	−0.381452
$203$	−7.76939	−0.545304
$204$	−2.90883	−0.203659
$205$	5.16811	0.360956
$206$	41.3829	2.88329
$207$	−15.2339	−1.05883
$208$	−8.03948	−0.557438
$209$	13.1468	0.909382
$210$	−13.4492	−0.928084
$211$	20.0962	1.38348	0.691740	−	0.722147i	$-0.256845\pi$
$211$	20.0962	1.38348	0.691740	+	0.722147i	$0.256845\pi$
$212$	42.7078	2.93318
$213$	7.10394	0.486754
$214$	19.0433	1.30178
$215$	−4.56849	−0.311568
$216$	−23.3368	−1.58787
$217$	−13.3022	−0.903014
$218$	−7.72077	−0.522917
$219$	−1.17273	−0.0792457
$220$	−73.4531	−4.95221
$221$	−1.05617	−0.0710455
$222$	6.67495	0.447994
$223$	12.1609	0.814353	0.407176	−	0.913350i	$-0.366513\pi$
$223$	12.1609	0.814353	0.407176	+	0.913350i	$0.366513\pi$
$224$	18.8909	1.26220
$225$	−7.29048	−0.486032
$226$	−29.9510	−1.99231
$227$	−20.1321	−1.33622	−0.668109	−	0.744064i	$-0.732896\pi$
$227$	−20.1321	−1.33622	−0.668109	+	0.744064i	$0.732896\pi$
$228$	6.62339	0.438644
$229$	14.4785	0.956769	0.478384	−	0.878151i	$-0.341223\pi$
$229$	14.4785	0.956769	0.478384	+	0.878151i	$0.341223\pi$
$230$	−42.0566	−2.77313
$231$	−10.8536	−0.714117
$232$	−17.2496	−1.13249
$233$	0.123412	0.00808501	0.00404250	−	0.999992i	$-0.498713\pi$
$233$	0.123412	0.00808501	0.00404250	+	0.999992i	$0.498713\pi$
$234$	−7.00574	−0.457979
$235$	31.0117	2.02298
$236$	−4.55133	−0.296266
$237$	6.57364	0.427004
$238$	7.52841	0.487994
$239$	17.1908	1.11198	0.555992	−	0.831188i	$-0.312339\pi$
$239$	17.1908	1.11198	0.555992	+	0.831188i	$0.312339\pi$
$240$	−13.5984	−0.877776
$241$	19.5004	1.25613	0.628065	−	0.778161i	$-0.283847\pi$
$241$	19.5004	1.25613	0.628065	+	0.778161i	$0.283847\pi$
$242$	−57.1705	−3.67506
$243$	−14.2301	−0.912858
$244$	19.2084	1.22969
$245$	4.61548	0.294872
$246$	3.02456	0.192839
$247$	2.40489	0.153019
$248$	−29.5336	−1.87539
$249$	−8.13670	−0.515642
$250$	15.6455	0.989508
$251$	7.81759	0.493442	0.246721	−	0.969087i	$-0.420647\pi$
$251$	7.81759	0.493442	0.246721	+	0.969087i	$0.420647\pi$
$252$	34.6923	2.18541
$253$	−33.9401	−2.13379
$254$	54.6229	3.42735
$255$	−1.78646	−0.111873
$256$	−27.3473	−1.70920
$257$	−6.88087	−0.429217	−0.214608	−	0.976700i	$-0.568848\pi$
$257$	−6.88087	−0.429217	−0.214608	+	0.976700i	$0.568848\pi$
$258$	−2.67364	−0.166453
$259$	−12.0017	−0.745749
$260$	−13.4365	−0.833295
$261$	−6.84550	−0.423726
$262$	−18.9392	−1.17007
$263$	14.7153	0.907385	0.453692	−	0.891158i	$-0.350107\pi$
$263$	14.7153	0.907385	0.453692	+	0.891158i	$0.350107\pi$
$264$	−24.0973	−1.48309
$265$	26.2291	1.61124
$266$	−17.1422	−1.05105
$267$	−11.2362	−0.687647
$268$	51.5370	3.14812
$269$	−6.63436	−0.404504	−0.202252	−	0.979334i	$-0.564826\pi$
$269$	−6.63436	−0.404504	−0.202252	+	0.979334i	$0.564826\pi$
$270$	−25.5676	−1.55599
$271$	−3.17317	−0.192756	−0.0963782	−	0.995345i	$-0.530726\pi$
$271$	−3.17317	−0.192756	−0.0963782	+	0.995345i	$0.530726\pi$
$272$	7.61194	0.461542
$273$	−1.98541	−0.120163
$274$	−28.6260	−1.72936
$275$	−16.2427	−0.979469
$276$	−17.0991	−1.02924
$277$	21.7891	1.30918	0.654591	−	0.755983i	$-0.272841\pi$
$277$	21.7891	1.30918	0.654591	+	0.755983i	$0.272841\pi$
$278$	29.4623	1.76703
$279$	−11.7204	−0.701682
$280$	53.6888	3.20852
$281$	−17.1082	−1.02059	−0.510296	−	0.859999i	$-0.670464\pi$
$281$	−17.1082	−1.02059	−0.510296	+	0.859999i	$0.670464\pi$
$282$	18.1491	1.08076
$283$	−29.1134	−1.73061	−0.865306	−	0.501243i	$-0.832876\pi$
$283$	−29.1134	−1.73061	−0.865306	+	0.501243i	$0.832876\pi$
$284$	−50.5892	−3.00192
$285$	4.06777	0.240954
$286$	−15.6083	−0.922937
$287$	−5.43821	−0.321007
$288$	16.6445	0.980786
$289$	1.00000	0.0588235
$290$	−18.8985	−1.10976
$291$	1.26039	0.0738851
$292$	8.35134	0.488725
$293$	−9.92135	−0.579611	−0.289806	−	0.957085i	$-0.593591\pi$
$293$	−9.92135	−0.579611	−0.289806	+	0.957085i	$0.593591\pi$
$294$	2.70114	0.157534
$295$	−2.79521	−0.162743
$296$	−26.6462	−1.54878
$297$	−20.6333	−1.19726
$298$	29.2002	1.69152
$299$	−6.20852	−0.359048
$300$	−8.18309	−0.472451
$301$	4.80725	0.277085
$302$	−30.0518	−1.72929
$303$	−1.35372	−0.0777694
$304$	−17.3324	−0.994079
$305$	11.7969	0.675488
$306$	6.63317	0.379193
$307$	11.8081	0.673922	0.336961	−	0.941519i	$-0.390601\pi$
$307$	11.8081	0.673922	0.336961	+	0.941519i	$0.390601\pi$
$308$	77.2919	4.40412
$309$	10.3332	0.587837
$310$	−32.3567	−1.83774
$311$	21.9514	1.24475	0.622375	−	0.782720i	$-0.286168\pi$
$311$	21.9514	1.24475	0.622375	+	0.782720i	$0.286168\pi$
$312$	−4.40802	−0.249555
$313$	−4.66198	−0.263511	−0.131755	−	0.991282i	$-0.542061\pi$
$313$	−4.66198	−0.263511	−0.131755	+	0.991282i	$0.542061\pi$
$314$	43.9850	2.48222
$315$	21.3064	1.20048
$316$	−46.8128	−2.63343
$317$	−4.38636	−0.246362	−0.123181	−	0.992384i	$-0.539310\pi$
$317$	−4.38636	−0.246362	−0.123181	+	0.992384i	$0.539310\pi$
$318$	15.3502	0.860795
$319$	−15.2513	−0.853907
$320$	3.39687	0.189891
$321$	4.75508	0.265403
$322$	44.2546	2.46621
$323$	−2.27700	−0.126695
$324$	24.9896	1.38831
$325$	−2.97120	−0.164813
$326$	4.85342	0.268806
$327$	−1.92786	−0.106611
$328$	−12.0739	−0.666671
$329$	−32.6324	−1.79908
$330$	−26.4007	−1.45331
$331$	24.5642	1.35017	0.675084	−	0.737741i	$-0.264107\pi$
$331$	24.5642	1.35017	0.675084	+	0.737741i	$0.264107\pi$
$332$	57.9438	3.18008
$333$	−10.5745	−0.579480
$334$	−18.3988	−1.00674
$335$	31.6515	1.72931
$336$	14.3091	0.780627
$337$	−4.61541	−0.251418	−0.125709	−	0.992067i	$-0.540121\pi$
$337$	−4.61541	−0.251418	−0.125709	+	0.992067i	$0.540121\pi$
$338$	30.4191	1.65458
$339$	−7.47870	−0.406187
$340$	12.7219	0.689943
$341$	−26.1122	−1.41405
$342$	−15.1037	−0.816715
$343$	15.7324	0.849468
$344$	10.6731	0.575453
$345$	−10.5014	−0.565379
$346$	−13.9081	−0.747704
$347$	−8.29965	−0.445548	−0.222774	−	0.974870i	$-0.571511\pi$
$347$	−8.29965	−0.445548	−0.222774	+	0.974870i	$0.571511\pi$
$348$	−7.68363	−0.411886
$349$	−4.71383	−0.252325	−0.126163	−	0.992010i	$-0.540266\pi$
$349$	−4.71383	−0.252325	−0.126163	+	0.992010i	$0.540266\pi$
$350$	21.1789	1.13206
$351$	−3.77436	−0.201460
$352$	37.0827	1.97652
$353$	36.0142	1.91684	0.958421	−	0.285359i	$-0.0921129\pi$
$353$	36.0142	1.91684	0.958421	+	0.285359i	$0.0921129\pi$
$354$	−1.63585	−0.0869446
$355$	−31.0695	−1.64900
$356$	80.0166	4.24087
$357$	1.87983	0.0994910
$358$	−3.63845	−0.192298
$359$	−10.9855	−0.579790	−0.289895	−	0.957058i	$-0.593620\pi$
$359$	−10.9855	−0.579790	−0.289895	+	0.957058i	$0.593620\pi$
$360$	47.3044	2.49316
$361$	−13.8153	−0.727121
$362$	−25.3503	−1.33238
$363$	−14.2754	−0.749262
$364$	14.1387	0.741069
$365$	5.12900	0.268464
$366$	6.90395	0.360875
$367$	28.4763	1.48645	0.743226	−	0.669041i	$-0.233295\pi$
$367$	28.4763	1.48645	0.743226	+	0.669041i	$0.233295\pi$
$368$	44.7456	2.33253
$369$	−4.79153	−0.249437
$370$	−29.1933	−1.51769
$371$	−27.5999	−1.43292
$372$	−13.1554	−0.682075
$373$	−2.95996	−0.153261	−0.0766305	−	0.997060i	$-0.524416\pi$
$373$	−2.95996	−0.153261	−0.0766305	+	0.997060i	$0.524416\pi$
$374$	14.7782	0.764164
$375$	3.90665	0.201738
$376$	−72.4506	−3.73636
$377$	−2.78985	−0.143685
$378$	26.9038	1.38378
$379$	−4.08772	−0.209972	−0.104986	−	0.994474i	$-0.533480\pi$
$379$	−4.08772	−0.209972	−0.104986	+	0.994474i	$0.533480\pi$
$380$	−28.9678	−1.48601
$381$	13.6392	0.698759
$382$	60.5103	3.09597
$383$	−0.812311	−0.0415072	−0.0207536	−	0.999785i	$-0.506607\pi$
$383$	−0.812311	−0.0415072	−0.0207536	+	0.999785i	$0.506607\pi$
$384$	−6.22166	−0.317498
$385$	47.4690	2.41925
$386$	−35.7945	−1.82189
$387$	4.23559	0.215307
$388$	−8.97558	−0.455666
$389$	−4.33823	−0.219957	−0.109979	−	0.993934i	$-0.535078\pi$
$389$	−4.33823	−0.219957	−0.109979	+	0.993934i	$0.535078\pi$
$390$	−4.82938	−0.244545
$391$	5.87835	0.297281
$392$	−10.7829	−0.544617
$393$	−4.72909	−0.238551
$394$	−68.4861	−3.45028
$395$	−28.7502	−1.44658
$396$	68.1008	3.42219
$397$	−7.18377	−0.360543	−0.180272	−	0.983617i	$-0.557698\pi$
$397$	−7.18377	−0.360543	−0.180272	+	0.983617i	$0.557698\pi$
$398$	14.0204	0.702777
$399$	−4.28036	−0.214286
$400$	21.4139	1.07069
$401$	−17.9423	−0.895994	−0.447997	−	0.894035i	$-0.647862\pi$
$401$	−17.9423	−0.895994	−0.447997	+	0.894035i	$0.647862\pi$
$402$	18.5236	0.923872
$403$	−4.77660	−0.237939
$404$	9.64026	0.479621
$405$	15.3474	0.762621
$406$	19.8862	0.986936
$407$	−23.5593	−1.16779
$408$	4.17360	0.206624
$409$	17.1079	0.845932	0.422966	−	0.906146i	$-0.360989\pi$
$409$	17.1079	0.845932	0.422966	+	0.906146i	$0.360989\pi$
$410$	−13.2281	−0.653288
$411$	−7.14784	−0.352577
$412$	−73.5859	−3.62532
$413$	2.94129	0.144732
$414$	38.9921	1.91636
$415$	35.5863	1.74686
$416$	6.78339	0.332583
$417$	7.35668	0.360258
$418$	−33.6500	−1.64587
$419$	1.79138	0.0875148	0.0437574	−	0.999042i	$-0.486067\pi$
$419$	1.79138	0.0875148	0.0437574	+	0.999042i	$0.486067\pi$
$420$	23.9150	1.16693
$421$	0.566227	0.0275962	0.0137981	−	0.999905i	$-0.495608\pi$
$421$	0.566227	0.0275962	0.0137981	+	0.999905i	$0.495608\pi$
$422$	−51.4373	−2.50393
$423$	−28.7520	−1.39797
$424$	−61.2774	−2.97589
$425$	2.81319	0.136460
$426$	−18.1829	−0.880966
$427$	−12.4134	−0.600728
$428$	−33.8623	−1.63680
$429$	−3.89735	−0.188166
$430$	11.6933	0.563901
$431$	22.7643	1.09652	0.548259	−	0.836309i	$-0.315291\pi$
$431$	22.7643	1.09652	0.548259	+	0.836309i	$0.315291\pi$
$432$	27.2023	1.30877
$433$	−3.39324	−0.163069	−0.0815344	−	0.996671i	$-0.525982\pi$
$433$	−3.39324	−0.163069	−0.0815344	+	0.996671i	$0.525982\pi$
$434$	34.0478	1.63435
$435$	−4.71892	−0.226255
$436$	13.7289	0.657493
$437$	−13.3850	−0.640290
$438$	3.00167	0.143425
$439$	−35.9987	−1.71813	−0.859063	−	0.511870i	$-0.828953\pi$
$439$	−35.9987	−1.71813	−0.859063	+	0.511870i	$0.828953\pi$
$440$	105.391	5.02431
$441$	−4.27917	−0.203770
$442$	2.70332	0.128584
$443$	29.0732	1.38131	0.690655	−	0.723184i	$-0.257322\pi$
$443$	29.0732	1.38131	0.690655	+	0.723184i	$0.257322\pi$
$444$	−11.8692	−0.563288
$445$	49.1424	2.32957
$446$	−31.1265	−1.47388
$447$	7.29122	0.344863
$448$	−3.57440	−0.168874
$449$	22.7471	1.07350	0.536752	−	0.843740i	$-0.319651\pi$
$449$	22.7471	1.07350	0.536752	+	0.843740i	$0.319651\pi$
$450$	18.6604	0.879659
$451$	−10.6752	−0.502674
$452$	53.2580	2.50504
$453$	−7.50387	−0.352562
$454$	51.5294	2.41839
$455$	8.68331	0.407080
$456$	−9.50327	−0.445031
$457$	7.70816	0.360573	0.180286	−	0.983614i	$-0.442298\pi$
$457$	7.70816	0.360573	0.180286	+	0.983614i	$0.442298\pi$
$458$	−37.0586	−1.73164
$459$	3.57364	0.166803
$460$	74.7839	3.48682
$461$	−5.60825	−0.261202	−0.130601	−	0.991435i	$-0.541691\pi$
$461$	−5.60825	−0.261202	−0.130601	+	0.991435i	$0.541691\pi$
$462$	27.7805	1.29247
$463$	37.8856	1.76069	0.880346	−	0.474331i	$-0.157310\pi$
$463$	37.8856	1.76069	0.880346	+	0.474331i	$0.157310\pi$
$464$	20.1068	0.933437
$465$	−8.07941	−0.374674
$466$	−0.315881	−0.0146329
$467$	−13.8625	−0.641478	−0.320739	−	0.947168i	$-0.603931\pi$
$467$	−13.8625	−0.641478	−0.320739	+	0.947168i	$0.603931\pi$
$468$	12.4574	0.575844
$469$	−33.3057	−1.53792
$470$	−79.3761	−3.66135
$471$	10.9830	0.506068
$472$	6.53027	0.300580
$473$	9.43660	0.433895
$474$	−16.8256	−0.772826
$475$	−6.40563	−0.293910
$476$	−13.3868	−0.613583
$477$	−24.3179	−1.11344
$478$	−44.0009	−2.01256
$479$	−0.330482	−0.0151001	−0.00755005	−	0.999971i	$-0.502403\pi$
$479$	−0.330482	−0.0151001	−0.00755005	+	0.999971i	$0.502403\pi$
$480$	11.4738	0.523706
$481$	−4.30960	−0.196501
$482$	−49.9123	−2.27344
$483$	11.0503	0.502805
$484$	101.659	4.62086
$485$	−5.51237	−0.250304
$486$	36.4226	1.65216
$487$	−24.1132	−1.09267	−0.546337	−	0.837565i	$-0.683978\pi$
$487$	−24.1132	−1.09267	−0.546337	+	0.837565i	$0.683978\pi$
$488$	−27.5603	−1.24760
$489$	1.21189	0.0548035
$490$	−11.8136	−0.533683
$491$	3.56712	0.160982	0.0804909	−	0.996755i	$-0.474351\pi$
$491$	3.56712	0.160982	0.0804909	+	0.996755i	$0.474351\pi$
$492$	−5.37818	−0.242467
$493$	2.64149	0.118967
$494$	−6.15545	−0.276947
$495$	41.8243	1.87986
$496$	34.4256	1.54575
$497$	32.6933	1.46649
$498$	20.8263	0.933251
$499$	32.4893	1.45442	0.727210	−	0.686415i	$-0.240817\pi$
$499$	32.4893	1.45442	0.727210	+	0.686415i	$0.240817\pi$
$500$	−27.8204	−1.24416
$501$	−4.59413	−0.205251
$502$	−20.0096	−0.893071
$503$	39.3380	1.75400	0.876998	−	0.480494i	$-0.159543\pi$
$503$	39.3380	1.75400	0.876998	+	0.480494i	$0.159543\pi$
$504$	−49.7767	−2.21723
$505$	5.92059	0.263463
$506$	86.8715	3.86191
$507$	7.59558	0.337331
$508$	−97.1289	−4.30940
$509$	−35.4633	−1.57189	−0.785943	−	0.618300i	$-0.787822\pi$
$509$	−35.4633	−1.57189	−0.785943	+	0.618300i	$0.787822\pi$
$510$	4.57255	0.202476
$511$	−5.39705	−0.238751
$512$	50.5273	2.23301
$513$	−8.13715	−0.359264
$514$	17.6120	0.776831
$515$	−45.1930	−1.99144
$516$	4.75418	0.209291
$517$	−64.0573	−2.81724
$518$	30.7190	1.34972
$519$	−3.47282	−0.152440
$520$	19.2787	0.845428
$521$	−16.8425	−0.737884	−0.368942	−	0.929452i	$-0.620280\pi$
$521$	−16.8425	−0.737884	−0.368942	+	0.929452i	$0.620280\pi$
$522$	17.5214	0.766893
$523$	−27.9712	−1.22310	−0.611548	−	0.791207i	$-0.709453\pi$
$523$	−27.9712	−1.22310	−0.611548	+	0.791207i	$0.709453\pi$
$524$	33.6772	1.47120
$525$	5.28832	0.230801
$526$	−37.6647	−1.64226
$527$	4.52257	0.197006
$528$	28.0887	1.22241
$529$	11.5550	0.502390
$530$	−67.1349	−2.91615
$531$	2.59153	0.112463
$532$	30.4817	1.32155
$533$	−1.95277	−0.0845837
$534$	28.7598	1.24456
$535$	−20.7966	−0.899116
$536$	−73.9455	−3.19396
$537$	−0.908513	−0.0392052
$538$	16.9810	0.732103
$539$	−9.53367	−0.410644
$540$	45.4635	1.95644
$541$	−35.4262	−1.52309	−0.761545	−	0.648112i	$-0.775559\pi$
$541$	−35.4262	−1.52309	−0.761545	+	0.648112i	$0.775559\pi$
$542$	8.12191	0.348866
$543$	−6.32990	−0.271642
$544$	−6.42265	−0.275369
$545$	8.43160	0.361170
$546$	5.08178	0.217480
$547$	27.0739	1.15760	0.578798	−	0.815471i	$-0.303522\pi$
$547$	27.0739	1.15760	0.578798	+	0.815471i	$0.303522\pi$
$548$	50.9019	2.17442
$549$	−10.9373	−0.466792
$550$	41.5740	1.77272
$551$	−6.01466	−0.256233
$552$	24.5339	1.04423
$553$	30.2528	1.28648
$554$	−55.7705	−2.36946
$555$	−7.28950	−0.309422
$556$	−52.3891	−2.22179
$557$	22.3451	0.946791	0.473395	−	0.880850i	$-0.343028\pi$
$557$	22.3451	0.946791	0.473395	+	0.880850i	$0.343028\pi$
$558$	29.9990	1.26996
$559$	1.72620	0.0730104
$560$	−62.5818	−2.64456
$561$	3.69009	0.155796
$562$	43.7895	1.84715
$563$	−16.9497	−0.714343	−0.357172	−	0.934039i	$-0.616259\pi$
$563$	−16.9497	−0.714343	−0.357172	+	0.934039i	$0.616259\pi$
$564$	−32.2722	−1.35891
$565$	32.7085	1.37606
$566$	74.5174	3.13220
$567$	−16.1495	−0.678217
$568$	72.5857	3.04563
$569$	−23.6795	−0.992697	−0.496349	−	0.868123i	$-0.665326\pi$
$569$	−23.6795	−0.992697	−0.496349	+	0.868123i	$0.665326\pi$
$570$	−10.4117	−0.436097
$571$	47.2823	1.97870	0.989350	−	0.145553i	$-0.0464961\pi$
$571$	47.2823	1.97870	0.989350	+	0.145553i	$0.0464961\pi$
$572$	27.7542	1.16046
$573$	15.1093	0.631199
$574$	13.9194	0.580985
$575$	16.5369	0.689638
$576$	−3.14935	−0.131223
$577$	−4.13908	−0.172312	−0.0861560	−	0.996282i	$-0.527458\pi$
$577$	−4.13908	−0.172312	−0.0861560	+	0.996282i	$0.527458\pi$
$578$	−2.55956	−0.106464
$579$	−8.93780	−0.371442
$580$	33.6048	1.39536
$581$	−37.4462	−1.55353
$582$	−3.22603	−0.133723
$583$	−54.1784	−2.24384
$584$	−11.9826	−0.495841
$585$	7.65074	0.316319
$586$	25.3943	1.04903
$587$	−38.8337	−1.60284	−0.801420	−	0.598102i	$-0.795922\pi$
$587$	−38.8337	−1.60284	−0.801420	+	0.598102i	$0.795922\pi$
$588$	−4.80309	−0.198076
$589$	−10.2979	−0.424317
$590$	7.15450	0.294546
$591$	−17.1008	−0.703434
$592$	31.0599	1.27655
$593$	−14.5874	−0.599033	−0.299517	−	0.954091i	$-0.596825\pi$
$593$	−14.5874	−0.599033	−0.299517	+	0.954091i	$0.596825\pi$
$594$	52.8120	2.16690
$595$	−8.22153	−0.337050
$596$	−51.9229	−2.12685
$597$	3.50085	0.143280
$598$	15.8911	0.649834
$599$	22.1276	0.904108	0.452054	−	0.891991i	$-0.350691\pi$
$599$	22.1276	0.904108	0.452054	+	0.891991i	$0.350691\pi$
$600$	11.7411	0.479330
$601$	21.4367	0.874420	0.437210	−	0.899359i	$-0.355967\pi$
$601$	21.4367	0.874420	0.437210	+	0.899359i	$0.355967\pi$
$602$	−12.3044	−0.501491
$603$	−29.3452	−1.19503
$604$	53.4372	2.17433
$605$	62.4341	2.53831
$606$	3.46493	0.140753
$607$	−22.8614	−0.927917	−0.463959	−	0.885857i	$-0.653571\pi$
$607$	−22.8614	−0.927917	−0.463959	+	0.885857i	$0.653571\pi$
$608$	14.6243	0.593095
$609$	4.96554	0.201214
$610$	−30.1948	−1.22255
$611$	−11.7177	−0.474049
$612$	−11.7949	−0.476781
$613$	36.4375	1.47170	0.735849	−	0.677146i	$-0.236783\pi$
$613$	36.4375	1.47170	0.735849	+	0.677146i	$0.236783\pi$
$614$	−30.2234	−1.21972
$615$	−3.30302	−0.133191
$616$	−110.899	−4.46824
$617$	−3.75297	−0.151089	−0.0755445	−	0.997142i	$-0.524070\pi$
$617$	−3.75297	−0.151089	−0.0755445	+	0.997142i	$0.524070\pi$
$618$	−26.4485	−1.06391
$619$	22.0141	0.884823	0.442411	−	0.896812i	$-0.354123\pi$
$619$	22.0141	0.884823	0.442411	+	0.896812i	$0.354123\pi$
$620$	57.5358	2.31069
$621$	21.0071	0.842985
$622$	−56.1858	−2.25285
$623$	−51.7107	−2.07174
$624$	5.13816	0.205691
$625$	−31.1519	−1.24608
$626$	11.9326	0.476922
$627$	−8.40232	−0.335556
$628$	−78.2129	−3.12104
$629$	4.08041	0.162697
$630$	−54.5348	−2.17272
$631$	−37.1510	−1.47896	−0.739478	−	0.673180i	$-0.764928\pi$
$631$	−37.1510	−1.47896	−0.739478	+	0.673180i	$0.764928\pi$
$632$	67.1673	2.67177
$633$	−12.8438	−0.510495
$634$	11.2271	0.445886
$635$	−59.6519	−2.36721
$636$	−27.2952	−1.08233
$637$	−1.74396	−0.0690980
$638$	39.0365	1.54547
$639$	28.8055	1.13953
$640$	27.2108	1.07560
$641$	10.0821	0.398220	0.199110	−	0.979977i	$-0.436195\pi$
$641$	10.0821	0.398220	0.199110	+	0.979977i	$0.436195\pi$
$642$	−12.1709	−0.480347
$643$	41.5715	1.63942	0.819709	−	0.572780i	$-0.194135\pi$
$643$	41.5715	1.63942	0.819709	+	0.572780i	$0.194135\pi$
$644$	−78.6923	−3.10091
$645$	2.91979	0.114967
$646$	5.82810	0.229304
$647$	4.56809	0.179590	0.0897950	−	0.995960i	$-0.471379\pi$
$647$	4.56809	0.179590	0.0897950	+	0.995960i	$0.471379\pi$
$648$	−35.8553	−1.40853
$649$	5.77374	0.226639
$650$	7.60496	0.298291
$651$	8.50166	0.333206
$652$	−8.63021	−0.337985
$653$	4.39327	0.171922	0.0859609	−	0.996299i	$-0.472604\pi$
$653$	4.39327	0.171922	0.0859609	+	0.996299i	$0.472604\pi$
$654$	4.93447	0.192953
$655$	20.6829	0.808149
$656$	14.0738	0.549491
$657$	−4.75526	−0.185520
$658$	83.5246	3.25613
$659$	38.3546	1.49408	0.747041	−	0.664778i	$-0.231474\pi$
$659$	38.3546	1.49408	0.747041	+	0.664778i	$0.231474\pi$
$660$	46.9450	1.82733
$661$	−41.8278	−1.62691	−0.813457	−	0.581625i	$-0.802417\pi$
$661$	−41.8278	−1.62691	−0.813457	+	0.581625i	$0.802417\pi$
$662$	−62.8733	−2.44364
$663$	0.675013	0.0262153
$664$	−83.1381	−3.22638
$665$	18.7204	0.725946
$666$	27.0661	1.04879
$667$	15.5276	0.601231
$668$	32.7162	1.26583
$669$	−7.77221	−0.300491
$670$	−81.0139	−3.12984
$671$	−24.3675	−0.940697
$672$	−12.0735	−0.465744
$673$	−6.63204	−0.255646	−0.127823	−	0.991797i	$-0.540799\pi$
$673$	−6.63204	−0.255646	−0.127823	+	0.991797i	$0.540799\pi$
$674$	11.8134	0.455036
$675$	10.0533	0.386953
$676$	−54.0903	−2.08040
$677$	16.7491	0.643722	0.321861	−	0.946787i	$-0.395692\pi$
$677$	16.7491	0.643722	0.321861	+	0.946787i	$0.395692\pi$
$678$	19.1421	0.735150
$679$	5.80046	0.222601
$680$	−18.2535	−0.699989
$681$	12.8668	0.493056
$682$	66.8356	2.55927
$683$	47.3820	1.81302	0.906511	−	0.422183i	$-0.138736\pi$
$683$	47.3820	1.81302	0.906511	+	0.422183i	$0.138736\pi$
$684$	26.8570	1.02690
$685$	31.2615	1.19444
$686$	−40.2679	−1.53743
$687$	−9.25346	−0.353042
$688$	−12.4409	−0.474307
$689$	−9.91064	−0.377565
$690$	26.8790	1.02327
$691$	12.2497	0.466000	0.233000	−	0.972477i	$-0.425146\pi$
$691$	12.2497	0.466000	0.233000	+	0.972477i	$0.425146\pi$
$692$	24.7310	0.940130
$693$	−44.0101	−1.67181
$694$	21.2434	0.806389
$695$	−32.1749	−1.22046
$696$	11.0245	0.417883
$697$	1.84892	0.0700327
$698$	12.0653	0.456679
$699$	−0.0788748	−0.00298332
$700$	−37.6596	−1.42340
$701$	−10.5742	−0.399384	−0.199692	−	0.979859i	$-0.563994\pi$
$701$	−10.5742	−0.399384	−0.199692	+	0.979859i	$0.563994\pi$
$702$	9.66068	0.364619
$703$	−9.29108	−0.350420
$704$	−7.01652	−0.264445
$705$	−19.8201	−0.746466
$706$	−92.1803	−3.46925
$707$	−6.23001	−0.234304
$708$	2.90883	0.109320
$709$	0.990634	0.0372041	0.0186020	−	0.999827i	$-0.494078\pi$
$709$	0.990634	0.0372041	0.0186020	+	0.999827i	$0.494078\pi$
$710$	79.5241	2.98449
$711$	26.6553	0.999650
$712$	−114.808	−4.30262
$713$	26.5853	0.995626
$714$	−4.81152	−0.180067
$715$	17.0453	0.637458
$716$	6.46979	0.241787
$717$	−10.9869	−0.410315
$718$	28.1179	1.04935
$719$	36.6619	1.36726	0.683630	−	0.729829i	$-0.260400\pi$
$719$	36.6619	1.36726	0.683630	+	0.729829i	$0.260400\pi$
$720$	−55.1399	−2.05494
$721$	47.5549	1.77104
$722$	35.3610	1.31600
$723$	−12.4630	−0.463504
$724$	45.0771	1.67528
$725$	7.43102	0.275981
$726$	36.5386	1.35607
$727$	−47.4305	−1.75910	−0.879549	−	0.475808i	$-0.842156\pi$
$727$	−47.4305	−1.75910	−0.879549	+	0.475808i	$0.842156\pi$
$728$	−20.2863	−0.751860
$729$	−7.37723	−0.273231
$730$	−13.1280	−0.485887
$731$	−1.63440	−0.0604504
$732$	−12.2764	−0.453749
$733$	0.473992	0.0175073	0.00875364	−	0.999962i	$-0.497214\pi$
$733$	0.473992	0.0175073	0.00875364	+	0.999962i	$0.497214\pi$
$734$	−72.8867	−2.69030
$735$	−2.94983	−0.108806
$736$	−37.7546	−1.39165
$737$	−65.3790	−2.40826
$738$	12.2642	0.451451
$739$	−18.2625	−0.671796	−0.335898	−	0.941898i	$-0.609040\pi$
$739$	−18.2625	−0.671796	−0.335898	+	0.941898i	$0.609040\pi$
$740$	51.9107	1.90827
$741$	−1.53700	−0.0564632
$742$	70.6435	2.59340
$743$	−25.6311	−0.940313	−0.470157	−	0.882583i	$-0.655803\pi$
$743$	−25.6311	−0.940313	−0.470157	+	0.882583i	$0.655803\pi$
$744$	18.8754	0.692006
$745$	−31.8886	−1.16831
$746$	7.57619	0.277384
$747$	−32.9933	−1.20716
$748$	−26.2782	−0.960826
$749$	21.8835	0.799606
$750$	−9.99929	−0.365122
$751$	38.7283	1.41322	0.706609	−	0.707605i	$-0.250224\pi$
$751$	38.7283	1.41322	0.706609	+	0.707605i	$0.250224\pi$
$752$	84.4513	3.07962
$753$	−4.99635	−0.182077
$754$	7.14079	0.260052
$755$	32.8186	1.19439
$756$	−47.8395	−1.73991
$757$	53.6303	1.94923	0.974614	−	0.223892i	$-0.0718762\pi$
$757$	53.6303	1.94923	0.974614	+	0.223892i	$0.0718762\pi$
$758$	10.4628	0.380025
$759$	21.6916	0.787357
$760$	41.5631	1.50765
$761$	−35.7056	−1.29433	−0.647163	−	0.762352i	$-0.724045\pi$
$761$	−35.7056	−1.29433	−0.647163	+	0.762352i	$0.724045\pi$
$762$	−34.9104	−1.26467
$763$	−8.87226	−0.321197
$764$	−107.598	−3.89275
$765$	−7.24387	−0.261903
$766$	2.07916	0.0751230
$767$	1.05617	0.0381360
$768$	17.4781	0.630685
$769$	48.9644	1.76570	0.882851	−	0.469652i	$-0.155621\pi$
$769$	48.9644	1.76570	0.882851	+	0.469652i	$0.155621\pi$
$770$	−121.500	−4.37854
$771$	4.39767	0.158378
$772$	63.6487	2.29077
$773$	−38.8273	−1.39652	−0.698260	−	0.715844i	$-0.746042\pi$
$773$	−38.8273	−1.39652	−0.698260	+	0.715844i	$0.746042\pi$
$774$	−10.8412	−0.389680
$775$	12.7229	0.457019
$776$	12.8782	0.462301
$777$	7.67047	0.275177
$778$	11.1040	0.398096
$779$	−4.20998	−0.150838
$780$	8.58746	0.307480
$781$	64.1767	2.29642
$782$	−15.0460	−0.538043
$783$	9.43972	0.337348
$784$	12.5689	0.448890
$785$	−48.0346	−1.71443
$786$	12.1044	0.431749
$787$	0.751978	0.0268051	0.0134026	−	0.999910i	$-0.495734\pi$
$787$	0.751978	0.0268051	0.0134026	+	0.999910i	$0.495734\pi$
$788$	121.780	4.33823
$789$	−9.40478	−0.334819
$790$	73.5877	2.61813
$791$	−34.4179	−1.22376
$792$	−97.7114	−3.47202
$793$	−4.45745	−0.158289
$794$	18.3873	0.652540
$795$	−16.7634	−0.594538
$796$	−24.9306	−0.883641
$797$	−10.5327	−0.373089	−0.186544	−	0.982447i	$-0.559729\pi$
$797$	−10.5327	−0.373089	−0.186544	+	0.982447i	$0.559729\pi$
$798$	10.9558	0.387832
$799$	11.0946	0.392498
$800$	−18.0681	−0.638805
$801$	−45.5615	−1.60984
$802$	45.9242	1.62164
$803$	−10.5944	−0.373868
$804$	−32.9381	−1.16164
$805$	−48.3290	−1.70337
$806$	12.2260	0.430641
$807$	4.24012	0.149259
$808$	−13.8319	−0.486604
$809$	12.2778	0.431665	0.215833	−	0.976430i	$-0.430753\pi$
$809$	12.2778	0.431665	0.215833	+	0.976430i	$0.430753\pi$
$810$	−39.2827	−1.38025
$811$	−21.9018	−0.769075	−0.384538	−	0.923109i	$-0.625639\pi$
$811$	−21.9018	−0.769075	−0.384538	+	0.923109i	$0.625639\pi$
$812$	−35.3611	−1.24093
$813$	2.02802	0.0711259
$814$	60.3012	2.11356
$815$	−5.30027	−0.185660
$816$	−4.86491	−0.170306
$817$	3.72152	0.130199
$818$	−43.7887	−1.53104
$819$	−8.05059	−0.281310
$820$	23.5218	0.821416
$821$	−8.23022	−0.287237	−0.143618	−	0.989633i	$-0.545874\pi$
$821$	−8.23022	−0.287237	−0.143618	+	0.989633i	$0.545874\pi$
$822$	18.2953	0.638122
$823$	17.8805	0.623276	0.311638	−	0.950201i	$-0.399122\pi$
$823$	17.8805	0.623276	0.311638	+	0.950201i	$0.399122\pi$
$824$	105.581	3.67811
$825$	10.3809	0.361418
$826$	−7.52841	−0.261947
$827$	−32.8093	−1.14089	−0.570446	−	0.821335i	$-0.693229\pi$
$827$	−32.8093	−1.14089	−0.570446	+	0.821335i	$0.693229\pi$
$828$	−69.3346	−2.40954
$829$	20.0249	0.695492	0.347746	−	0.937589i	$-0.386947\pi$
$829$	20.0249	0.695492	0.347746	+	0.937589i	$0.386947\pi$
$830$	−91.0852	−3.16161
$831$	−13.9258	−0.483080
$832$	−1.28350	−0.0444975
$833$	1.65121	0.0572111
$834$	−18.8298	−0.652024
$835$	20.0927	0.695336
$836$	59.8354	2.06945
$837$	16.1620	0.558642
$838$	−4.58515	−0.158391
$839$	−51.1312	−1.76524	−0.882622	−	0.470083i	$-0.844224\pi$
$839$	−51.1312	−1.76524	−0.882622	+	0.470083i	$0.844224\pi$
$840$	−34.3134	−1.18392
$841$	−22.0225	−0.759398
$842$	−1.44929	−0.0499458
$843$	10.9341	0.376592
$844$	91.4644	3.14833
$845$	−33.2197	−1.14279
$846$	73.5923	2.53015
$847$	−65.6971	−2.25738
$848$	71.4273	2.45282
$849$	18.6068	0.638585
$850$	−7.20053	−0.246976
$851$	23.9861	0.822232
$852$	32.3324	1.10769
$853$	15.6347	0.535322	0.267661	−	0.963513i	$-0.413749\pi$
$853$	15.6347	0.535322	0.267661	+	0.963513i	$0.413749\pi$
$854$	31.7729	1.08725
$855$	16.4943	0.564092
$856$	48.5858	1.66063
$857$	−36.9619	−1.26259	−0.631297	−	0.775541i	$-0.717477\pi$
$857$	−36.9619	−1.26259	−0.631297	+	0.775541i	$0.717477\pi$
$858$	9.97550	0.340558
$859$	50.0389	1.70730	0.853652	−	0.520844i	$-0.174383\pi$
$859$	50.0389	1.70730	0.853652	+	0.520844i	$0.174383\pi$
$860$	−20.7927	−0.709025
$861$	3.47565	0.118450
$862$	−58.2665	−1.98456
$863$	−11.7317	−0.399350	−0.199675	−	0.979862i	$-0.563989\pi$
$863$	−11.7317	−0.399350	−0.199675	+	0.979862i	$0.563989\pi$
$864$	−22.9522	−0.780850
$865$	15.1886	0.516427
$866$	8.68519	0.295135
$867$	−0.639116	−0.0217055
$868$	−60.5428	−2.05496
$869$	59.3860	2.01453
$870$	12.0783	0.409494
$871$	−11.9595	−0.405232
$872$	−19.6982	−0.667066
$873$	5.11070	0.172971
$874$	34.2596	1.15885
$875$	17.9789	0.607798
$876$	−5.33747	−0.180337
$877$	−22.9295	−0.774275	−0.387137	−	0.922022i	$-0.626536\pi$
$877$	−22.9295	−0.774275	−0.387137	+	0.922022i	$0.626536\pi$
$878$	92.1408	3.10960
$879$	6.34089	0.213873
$880$	−122.848	−4.14120
$881$	14.6058	0.492082	0.246041	−	0.969259i	$-0.420870\pi$
$881$	14.6058	0.492082	0.246041	+	0.969259i	$0.420870\pi$
$882$	10.9528	0.368799
$883$	−7.45649	−0.250931	−0.125465	−	0.992098i	$-0.540042\pi$
$883$	−7.45649	−0.250931	−0.125465	+	0.992098i	$0.540042\pi$
$884$	−4.80697	−0.161676
$885$	1.78646	0.0600513
$886$	−74.4145	−2.50001
$887$	−24.0887	−0.808820	−0.404410	−	0.914578i	$-0.632523\pi$
$887$	−24.0887	−0.808820	−0.404410	+	0.914578i	$0.632523\pi$
$888$	17.0300	0.571490
$889$	62.7695	2.10522
$890$	−125.783	−4.21624
$891$	−31.7015	−1.06204
$892$	55.3482	1.85319
$893$	−25.2623	−0.845371
$894$	−18.6623	−0.624160
$895$	3.97343	0.132817
$896$	−28.6329	−0.956558
$897$	3.96796	0.132486
$898$	−58.2226	−1.94291
$899$	11.9463	0.398432
$900$	−33.1814	−1.10605
$901$	9.38359	0.312613
$902$	27.3237	0.909780
$903$	−3.07239	−0.102243
$904$	−76.4148	−2.54152
$905$	27.6842	0.920254
$906$	19.2066	0.638096
$907$	38.0695	1.26408	0.632038	−	0.774938i	$-0.282219\pi$
$907$	38.0695	1.26408	0.632038	+	0.774938i	$0.282219\pi$
$908$	−91.6280	−3.04078
$909$	−5.48917	−0.182064
$910$	−22.2254	−0.736766
$911$	38.8480	1.28709	0.643545	−	0.765408i	$-0.277463\pi$
$911$	38.8480	1.28709	0.643545	+	0.765408i	$0.277463\pi$
$912$	11.0774	0.366809
$913$	−73.5066	−2.43271
$914$	−19.7295	−0.652593
$915$	−7.53958	−0.249251
$916$	65.8966	2.17728
$917$	−21.7639	−0.718707
$918$	−9.14692	−0.301893
$919$	22.8965	0.755285	0.377643	−	0.925951i	$-0.376735\pi$
$919$	22.8965	0.755285	0.377643	+	0.925951i	$0.376735\pi$
$920$	−107.300	−3.53759
$921$	−7.54672	−0.248673
$922$	14.3546	0.472744
$923$	11.7396	0.386413
$924$	−49.3985	−1.62509
$925$	11.4790	0.377427
$926$	−96.9703	−3.18664
$927$	41.8999	1.37617
$928$	−16.9653	−0.556915
$929$	23.4549	0.769529	0.384765	−	0.923015i	$-0.374283\pi$
$929$	23.4549	0.769529	0.384765	+	0.923015i	$0.374283\pi$
$930$	20.6797	0.678114
$931$	−3.75980	−0.123223
$932$	0.561690	0.0183988
$933$	−14.0295	−0.459305
$934$	35.4818	1.16100
$935$	−16.1388	−0.527796
$936$	−17.8739	−0.584228
$937$	−52.1192	−1.70266	−0.851330	−	0.524631i	$-0.824203\pi$
$937$	−52.1192	−1.70266	−0.851330	+	0.524631i	$0.824203\pi$
$938$	85.2479	2.78344
$939$	2.97954	0.0972337
$940$	141.144	4.60362
$941$	25.2540	0.823255	0.411628	−	0.911352i	$-0.364960\pi$
$941$	25.2540	0.823255	0.411628	+	0.911352i	$0.364960\pi$
$942$	−28.1115	−0.915923
$943$	10.8686	0.353930
$944$	−7.61194	−0.247748
$945$	−29.3808	−0.955756
$946$	−24.1535	−0.785298
$947$	−49.4051	−1.60545	−0.802725	−	0.596349i	$-0.796617\pi$
$947$	−49.4051	−1.60545	−0.802725	+	0.596349i	$0.796617\pi$
$948$	29.9188	0.971718
$949$	−1.93799	−0.0629097
$950$	16.3956	0.531942
$951$	2.80339	0.0909062
$952$	19.2074	0.622517
$953$	−35.8886	−1.16254	−0.581272	−	0.813709i	$-0.697445\pi$
$953$	−35.8886	−1.16254	−0.581272	+	0.813709i	$0.697445\pi$
$954$	62.2429	2.01519
$955$	−66.0813	−2.13834
$956$	78.2412	2.53050
$957$	9.74733	0.315086
$958$	0.845887	0.0273294
$959$	−32.8953	−1.06224
$960$	−2.17099	−0.0700685
$961$	−10.5463	−0.340204
$962$	11.0307	0.355643
$963$	19.2812	0.621329
$964$	88.7527	2.85853
$965$	39.0900	1.25835
$966$	−28.2838	−0.910017
$967$	−52.3590	−1.68375	−0.841875	−	0.539672i	$-0.818548\pi$
$967$	−52.3590	−1.68375	−0.841875	+	0.539672i	$0.818548\pi$
$968$	−145.861	−4.68815
$969$	1.45526	0.0467498
$970$	14.1092	0.453020
$971$	−1.38019	−0.0442926	−0.0221463	−	0.999755i	$-0.507050\pi$
$971$	−1.38019	−0.0442926	−0.0221463	+	0.999755i	$0.507050\pi$
$972$	−64.7657	−2.07736
$973$	33.8564	1.08539
$974$	61.7192	1.97761
$975$	1.89894	0.0608148
$976$	32.1254	1.02831
$977$	0.785507	0.0251306	0.0125653	−	0.999921i	$-0.496000\pi$
$977$	0.785507	0.0251306	0.0125653	+	0.999921i	$0.496000\pi$
$978$	−3.10190	−0.0991878
$979$	−101.508	−3.24420
$980$	21.0066	0.671030
$981$	−7.81722	−0.249585
$982$	−9.13024	−0.291358
$983$	59.2893	1.89103	0.945517	−	0.325571i	$-0.105557\pi$
$983$	59.2893	1.89103	0.945517	+	0.325571i	$0.105557\pi$
$984$	7.71664	0.245997
$985$	74.7914	2.38305
$986$	−6.76104	−0.215315
$987$	20.8559	0.663851
$988$	10.9454	0.348221
$989$	−9.60756	−0.305503
$990$	−107.052	−3.40232
$991$	−21.7815	−0.691912	−0.345956	−	0.938251i	$-0.612445\pi$
$991$	−21.7815	−0.691912	−0.345956	+	0.938251i	$0.612445\pi$
$992$	−29.0469	−0.922240
$993$	−15.6993	−0.498203
$994$	−83.6802	−2.65418
$995$	−15.3112	−0.485397
$996$	−37.0328	−1.17343
$997$	2.03350	0.0644015	0.0322008	−	0.999481i	$-0.489748\pi$
$997$	2.03350	0.0644015	0.0322008	+	0.999481i	$0.489748\pi$
$998$	−83.1582	−2.63233
$999$	14.5819	0.461351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.1	✓	18
3.2	odd	2		9027.2.a.q.1.18		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.1	✓	18	1.1	even	1	trivial
9027.2.a.q.1.18		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)

\(f(q)\)	\(=\)	\(q-2.55956 q^{2} -0.639116 q^{3} +4.55133 q^{4} +2.79521 q^{5} +1.63585 q^{6} -2.94129 q^{7} -6.53027 q^{8} -2.59153 q^{9} +O(q^{10})\)	\(q-2.55956 q^{2} -0.639116 q^{3} +4.55133 q^{4} +2.79521 q^{5} +1.63585 q^{6} -2.94129 q^{7} -6.53027 q^{8} -2.59153 q^{9} -7.15450 q^{10} -5.77374 q^{11} -2.90883 q^{12} -1.05617 q^{13} +7.52841 q^{14} -1.78646 q^{15} +7.61194 q^{16} +1.00000 q^{17} +6.63317 q^{18} -2.27700 q^{19} +12.7219 q^{20} +1.87983 q^{21} +14.7782 q^{22} +5.87835 q^{23} +4.17360 q^{24} +2.81319 q^{25} +2.70332 q^{26} +3.57364 q^{27} -13.3868 q^{28} +2.64149 q^{29} +4.57255 q^{30} +4.52257 q^{31} -6.42265 q^{32} +3.69009 q^{33} -2.55956 q^{34} -8.22153 q^{35} -11.7949 q^{36} +4.08041 q^{37} +5.82810 q^{38} +0.675013 q^{39} -18.2535 q^{40} +1.84892 q^{41} -4.81152 q^{42} -1.63440 q^{43} -26.2782 q^{44} -7.24387 q^{45} -15.0460 q^{46} +11.0946 q^{47} -4.86491 q^{48} +1.65121 q^{49} -7.20053 q^{50} -0.639116 q^{51} -4.80697 q^{52} +9.38359 q^{53} -9.14692 q^{54} -16.1388 q^{55} +19.2074 q^{56} +1.45526 q^{57} -6.76104 q^{58} -1.00000 q^{59} -8.13078 q^{60} +4.22040 q^{61} -11.5758 q^{62} +7.62246 q^{63} +1.21525 q^{64} -2.95221 q^{65} -9.44499 q^{66} +11.3235 q^{67} +4.55133 q^{68} -3.75694 q^{69} +21.0435 q^{70} -11.1153 q^{71} +16.9234 q^{72} +1.83492 q^{73} -10.4440 q^{74} -1.79796 q^{75} -10.3634 q^{76} +16.9823 q^{77} -1.72773 q^{78} -10.2855 q^{79} +21.2770 q^{80} +5.49063 q^{81} -4.73241 q^{82} +12.7312 q^{83} +8.55571 q^{84} +2.79521 q^{85} +4.18334 q^{86} -1.68822 q^{87} +37.7041 q^{88} +17.5809 q^{89} +18.5411 q^{90} +3.10650 q^{91} +26.7543 q^{92} -2.89045 q^{93} -28.3972 q^{94} -6.36468 q^{95} +4.10481 q^{96} -1.97208 q^{97} -4.22637 q^{98} +14.9628 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 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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