LMFDB - Embedded newform 1003.2.a.h.1.9

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:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6 x^{15} - 5 x^{14} + 90 x^{13} - 82 x^{12} - 456 x^{11} + 723 x^{10} + 951 x^{9} - 2105 x^{8} + \cdots - 1 $ x^16 - 6x^15 - 5x^14 + 90x^13 - 82x^12 - 456x^11 + 723x^10 + 951x^9 - 2105x^8 - 695x^7 + 2641x^6 - 151x^5 - 1323x^4 + 301x^3 + 179x^2 - 50*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.377947$ 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)

$f(q)$	$=$	$q-0.377947 q^{2} -1.60628 q^{3} -1.85716 q^{4} +0.658559 q^{5} +0.607088 q^{6} -1.52100 q^{7} +1.45780 q^{8} -0.419863 q^{9} +O(q^{10})$	\(q-0.377947 q^{2} -1.60628 q^{3} -1.85716 q^{4} +0.658559 q^{5} +0.607088 q^{6} -1.52100 q^{7} +1.45780 q^{8} -0.419863 q^{9} -0.248900 q^{10} +1.85546 q^{11} +2.98311 q^{12} +5.77216 q^{13} +0.574857 q^{14} -1.05783 q^{15} +3.16334 q^{16} +1.00000 q^{17} +0.158686 q^{18} -7.34219 q^{19} -1.22305 q^{20} +2.44315 q^{21} -0.701265 q^{22} +6.40008 q^{23} -2.34163 q^{24} -4.56630 q^{25} -2.18157 q^{26} +5.49326 q^{27} +2.82474 q^{28} -10.4126 q^{29} +0.399803 q^{30} +9.55058 q^{31} -4.11117 q^{32} -2.98039 q^{33} -0.377947 q^{34} -1.00167 q^{35} +0.779752 q^{36} -8.78017 q^{37} +2.77496 q^{38} -9.27171 q^{39} +0.960046 q^{40} +2.93890 q^{41} -0.923381 q^{42} -7.11730 q^{43} -3.44588 q^{44} -0.276505 q^{45} -2.41889 q^{46} -0.558492 q^{47} -5.08122 q^{48} -4.68656 q^{49} +1.72582 q^{50} -1.60628 q^{51} -10.7198 q^{52} -4.93123 q^{53} -2.07616 q^{54} +1.22193 q^{55} -2.21731 q^{56} +11.7936 q^{57} +3.93542 q^{58} +1.00000 q^{59} +1.96456 q^{60} -9.06003 q^{61} -3.60961 q^{62} +0.638612 q^{63} -4.77288 q^{64} +3.80131 q^{65} +1.12643 q^{66} +8.93361 q^{67} -1.85716 q^{68} -10.2803 q^{69} +0.378577 q^{70} -1.75795 q^{71} -0.612076 q^{72} -3.73919 q^{73} +3.31843 q^{74} +7.33476 q^{75} +13.6356 q^{76} -2.82216 q^{77} +3.50421 q^{78} -14.2159 q^{79} +2.08325 q^{80} -7.56413 q^{81} -1.11075 q^{82} +7.22380 q^{83} -4.53732 q^{84} +0.658559 q^{85} +2.68996 q^{86} +16.7256 q^{87} +2.70489 q^{88} +1.28305 q^{89} +0.104504 q^{90} -8.77947 q^{91} -11.8860 q^{92} -15.3409 q^{93} +0.211080 q^{94} -4.83526 q^{95} +6.60370 q^{96} -9.44602 q^{97} +1.77127 q^{98} -0.779040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.377947	−0.267249	−0.133624	−	0.991032i	$-0.542662\pi$
$2$	−0.377947	−0.267249	−0.133624	+	0.991032i	$0.542662\pi$
$3$	−1.60628	−0.927386	−0.463693	−	0.885996i	$-0.653476\pi$
$3$	−1.60628	−0.927386	−0.463693	+	0.885996i	$0.653476\pi$
$4$	−1.85716	−0.928578
$5$	0.658559	0.294516	0.147258	−	0.989098i	$-0.452955\pi$
$5$	0.658559	0.294516	0.147258	+	0.989098i	$0.452955\pi$
$6$	0.607088	0.247843
$7$	−1.52100	−0.574884	−0.287442	−	0.957798i	$-0.592805\pi$
$7$	−1.52100	−0.574884	−0.287442	+	0.957798i	$0.592805\pi$
$8$	1.45780	0.515410
$9$	−0.419863	−0.139954
$10$	−0.248900	−0.0787091
$11$	1.85546	0.559443	0.279721	−	0.960081i	$-0.409758\pi$
$11$	1.85546	0.559443	0.279721	+	0.960081i	$0.409758\pi$
$12$	2.98311	0.861151
$13$	5.77216	1.60091	0.800455	−	0.599393i	$-0.204591\pi$
$13$	5.77216	1.60091	0.800455	+	0.599393i	$0.204591\pi$
$14$	0.574857	0.153637
$15$	−1.05783	−0.273131
$16$	3.16334	0.790836
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.158686	0.0374026
$19$	−7.34219	−1.68441	−0.842207	−	0.539154i	$-0.818744\pi$
$19$	−7.34219	−1.68441	−0.842207	+	0.539154i	$0.818744\pi$
$20$	−1.22305	−0.273482
$21$	2.44315	0.533140
$22$	−0.701265	−0.149510
$23$	6.40008	1.33451	0.667255	−	0.744830i	$-0.267469\pi$
$23$	6.40008	1.33451	0.667255	+	0.744830i	$0.267469\pi$
$24$	−2.34163	−0.477984
$25$	−4.56630	−0.913260
$26$	−2.18157	−0.427841
$27$	5.49326	1.05718
$28$	2.82474	0.533825
$29$	−10.4126	−1.93358	−0.966789	−	0.255575i	$-0.917735\pi$
$29$	−10.4126	−1.93358	−0.966789	+	0.255575i	$0.917735\pi$
$30$	0.399803	0.0729938
$31$	9.55058	1.71534	0.857668	−	0.514204i	$-0.171913\pi$
$31$	9.55058	1.71534	0.857668	+	0.514204i	$0.171913\pi$
$32$	−4.11117	−0.726759
$33$	−2.98039	−0.518820
$34$	−0.377947	−0.0648173
$35$	−1.00167	−0.169313
$36$	0.779752	0.129959
$37$	−8.78017	−1.44345	−0.721725	−	0.692180i	$-0.756651\pi$
$37$	−8.78017	−1.44345	−0.721725	+	0.692180i	$0.756651\pi$
$38$	2.77496	0.450157
$39$	−9.27171	−1.48466
$40$	0.960046	0.151797
$41$	2.93890	0.458979	0.229489	−	0.973311i	$-0.426294\pi$
$41$	2.93890	0.458979	0.229489	+	0.973311i	$0.426294\pi$
$42$	−0.923381	−0.142481
$43$	−7.11730	−1.08538	−0.542689	−	0.839934i	$-0.682594\pi$
$43$	−7.11730	−1.08538	−0.542689	+	0.839934i	$0.682594\pi$
$44$	−3.44588	−0.519486
$45$	−0.276505	−0.0412189
$46$	−2.41889	−0.356646
$47$	−0.558492	−0.0814644	−0.0407322	−	0.999170i	$-0.512969\pi$
$47$	−0.558492	−0.0814644	−0.0407322	+	0.999170i	$0.512969\pi$
$48$	−5.08122	−0.733410
$49$	−4.68656	−0.669508
$50$	1.72582	0.244067
$51$	−1.60628	−0.224924
$52$	−10.7198	−1.48657
$53$	−4.93123	−0.677356	−0.338678	−	0.940902i	$-0.609980\pi$
$53$	−4.93123	−0.677356	−0.338678	+	0.940902i	$0.609980\pi$
$54$	−2.07616	−0.282529
$55$	1.22193	0.164765
$56$	−2.21731	−0.296301
$57$	11.7936	1.56210
$58$	3.93542	0.516746
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	1.96456	0.253623
$61$	−9.06003	−1.16002	−0.580009	−	0.814610i	$-0.696951\pi$
$61$	−9.06003	−1.16002	−0.580009	+	0.814610i	$0.696951\pi$
$62$	−3.60961	−0.458421
$63$	0.638612	0.0804576
$64$	−4.77288	−0.596610
$65$	3.80131	0.471494
$66$	1.12643	0.138654
$67$	8.93361	1.09141	0.545707	−	0.837976i	$-0.316261\pi$
$67$	8.93361	1.09141	0.545707	+	0.837976i	$0.316261\pi$
$68$	−1.85716	−0.225213
$69$	−10.2803	−1.23761
$70$	0.378577	0.0452486
$71$	−1.75795	−0.208630	−0.104315	−	0.994544i	$-0.533265\pi$
$71$	−1.75795	−0.208630	−0.104315	+	0.994544i	$0.533265\pi$
$72$	−0.612076	−0.0721339
$73$	−3.73919	−0.437639	−0.218820	−	0.975765i	$-0.570221\pi$
$73$	−3.73919	−0.437639	−0.218820	+	0.975765i	$0.570221\pi$
$74$	3.31843	0.385760
$75$	7.33476	0.846945
$76$	13.6356	1.56411
$77$	−2.82216	−0.321615
$78$	3.50421	0.396774
$79$	−14.2159	−1.59942	−0.799708	−	0.600389i	$-0.795013\pi$
$79$	−14.2159	−1.59942	−0.799708	+	0.600389i	$0.795013\pi$
$80$	2.08325	0.232914
$81$	−7.56413	−0.840458
$82$	−1.11075	−0.122661
$83$	7.22380	0.792915	0.396457	−	0.918053i	$-0.370239\pi$
$83$	7.22380	0.792915	0.396457	+	0.918053i	$0.370239\pi$
$84$	−4.53732	−0.495062
$85$	0.658559	0.0714307
$86$	2.68996	0.290066
$87$	16.7256	1.79317
$88$	2.70489	0.288342
$89$	1.28305	0.136003	0.0680014	−	0.997685i	$-0.478338\pi$
$89$	1.28305	0.136003	0.0680014	+	0.997685i	$0.478338\pi$
$90$	0.104504	0.0110157
$91$	−8.77947	−0.920338
$92$	−11.8860	−1.23920
$93$	−15.3409	−1.59078
$94$	0.211080	0.0217713
$95$	−4.83526	−0.496088
$96$	6.60370	0.673987
$97$	−9.44602	−0.959098	−0.479549	−	0.877515i	$-0.659200\pi$
$97$	−9.44602	−0.959098	−0.479549	+	0.877515i	$0.659200\pi$
$98$	1.77127	0.178925
$99$	−0.779040	−0.0782965
$100$	8.48033	0.848033
$101$	−3.52408	−0.350660	−0.175330	−	0.984510i	$-0.556099\pi$
$101$	−3.52408	−0.350660	−0.175330	+	0.984510i	$0.556099\pi$
$102$	0.607088	0.0601107
$103$	−1.45734	−0.143596	−0.0717978	−	0.997419i	$-0.522874\pi$
$103$	−1.45734	−0.143596	−0.0717978	+	0.997419i	$0.522874\pi$
$104$	8.41466	0.825125
$105$	1.60896	0.157018
$106$	1.86374	0.181023
$107$	−3.32884	−0.321811	−0.160906	−	0.986970i	$-0.551441\pi$
$107$	−3.32884	−0.321811	−0.160906	+	0.986970i	$0.551441\pi$
$108$	−10.2018	−0.981673
$109$	5.45061	0.522073	0.261037	−	0.965329i	$-0.415936\pi$
$109$	5.45061	0.522073	0.261037	+	0.965329i	$0.415936\pi$
$110$	−0.461825	−0.0440332
$111$	14.1034	1.33864
$112$	−4.81145	−0.454639
$113$	−17.3287	−1.63015	−0.815073	−	0.579358i	$-0.803303\pi$
$113$	−17.3287	−1.63015	−0.815073	+	0.579358i	$0.803303\pi$
$114$	−4.45736	−0.417470
$115$	4.21483	0.393035
$116$	19.3379	1.79548
$117$	−2.42352	−0.224054
$118$	−0.377947	−0.0347928
$119$	−1.52100	−0.139430
$120$	−1.54210	−0.140774
$121$	−7.55726	−0.687024
$122$	3.42421	0.310013
$123$	−4.72069	−0.425651
$124$	−17.7369	−1.59282
$125$	−6.29997	−0.563487
$126$	−0.241361	−0.0215022
$127$	2.73655	0.242829	0.121415	−	0.992602i	$-0.461257\pi$
$127$	2.73655	0.242829	0.121415	+	0.992602i	$0.461257\pi$
$128$	10.0262	0.886203
$129$	11.4324	1.00656
$130$	−1.43669	−0.126006
$131$	−16.0179	−1.39949	−0.699745	−	0.714393i	$-0.746703\pi$
$131$	−16.0179	−1.39949	−0.699745	+	0.714393i	$0.746703\pi$
$132$	5.53505	0.481765
$133$	11.1675	0.968343
$134$	−3.37643	−0.291679
$135$	3.61763	0.311356
$136$	1.45780	0.125005
$137$	−15.0456	−1.28543	−0.642715	−	0.766105i	$-0.722192\pi$
$137$	−15.0456	−1.28543	−0.642715	+	0.766105i	$0.722192\pi$
$138$	3.88541	0.330748
$139$	18.2129	1.54480	0.772399	−	0.635137i	$-0.219057\pi$
$139$	18.2129	1.54480	0.772399	+	0.635137i	$0.219057\pi$
$140$	1.86025	0.157220
$141$	0.897095	0.0755490
$142$	0.664411	0.0557561
$143$	10.7100	0.895618
$144$	−1.32817	−0.110681
$145$	−6.85733	−0.569471
$146$	1.41321	0.116958
$147$	7.52792	0.620893
$148$	16.3061	1.34036
$149$	21.2333	1.73950	0.869749	−	0.493495i	$-0.164281\pi$
$149$	21.2333	1.73950	0.869749	+	0.493495i	$0.164281\pi$
$150$	−2.77215	−0.226345
$151$	9.24117	0.752036	0.376018	−	0.926612i	$-0.377293\pi$
$151$	9.24117	0.752036	0.376018	+	0.926612i	$0.377293\pi$
$152$	−10.7034	−0.868163
$153$	−0.419863	−0.0339439
$154$	1.06663	0.0859511
$155$	6.28962	0.505195
$156$	17.2190	1.37863
$157$	−1.36456	−0.108904	−0.0544520	−	0.998516i	$-0.517341\pi$
$157$	−1.36456	−0.108904	−0.0544520	+	0.998516i	$0.517341\pi$
$158$	5.37286	0.427442
$159$	7.92094	0.628171
$160$	−2.70745	−0.214043
$161$	−9.73453	−0.767188
$162$	2.85884	0.224611
$163$	−2.79539	−0.218952	−0.109476	−	0.993989i	$-0.534917\pi$
$163$	−2.79539	−0.218952	−0.109476	+	0.993989i	$0.534917\pi$
$164$	−5.45799	−0.426198
$165$	−1.96276	−0.152801
$166$	−2.73021	−0.211905
$167$	9.78723	0.757359	0.378679	−	0.925528i	$-0.376378\pi$
$167$	9.78723	0.757359	0.378679	+	0.925528i	$0.376378\pi$
$168$	3.56163	0.274785
$169$	20.3179	1.56291
$170$	−0.248900	−0.0190898
$171$	3.08272	0.235741
$172$	13.2179	1.00786
$173$	−9.45979	−0.719215	−0.359607	−	0.933104i	$-0.617089\pi$
$173$	−9.45979	−0.719215	−0.359607	+	0.933104i	$0.617089\pi$
$174$	−6.32139	−0.479223
$175$	6.94535	0.525019
$176$	5.86946	0.442427
$177$	−1.60628	−0.120735
$178$	−0.484924	−0.0363466
$179$	−9.17293	−0.685617	−0.342809	−	0.939405i	$-0.611378\pi$
$179$	−9.17293	−0.685617	−0.342809	+	0.939405i	$0.611378\pi$
$180$	0.513512	0.0382750
$181$	1.87729	0.139538	0.0697689	−	0.997563i	$-0.477774\pi$
$181$	1.87729	0.139538	0.0697689	+	0.997563i	$0.477774\pi$
$182$	3.31817	0.245959
$183$	14.5529	1.07578
$184$	9.33003	0.687819
$185$	−5.78226	−0.425120
$186$	5.79805	0.425133
$187$	1.85546	0.135685
$188$	1.03721	0.0756461
$189$	−8.35525	−0.607755
$190$	1.82747	0.132579
$191$	−4.54803	−0.329084	−0.164542	−	0.986370i	$-0.552615\pi$
$191$	−4.54803	−0.329084	−0.164542	+	0.986370i	$0.552615\pi$
$192$	7.66659	0.553288
$193$	1.38980	0.100040	0.0500202	−	0.998748i	$-0.484071\pi$
$193$	1.38980	0.100040	0.0500202	+	0.998748i	$0.484071\pi$
$194$	3.57009	0.256318
$195$	−6.10597	−0.437258
$196$	8.70367	0.621691
$197$	12.0914	0.861478	0.430739	−	0.902476i	$-0.358253\pi$
$197$	12.0914	0.861478	0.430739	+	0.902476i	$0.358253\pi$
$198$	0.294436	0.0209246
$199$	5.34941	0.379210	0.189605	−	0.981860i	$-0.439279\pi$
$199$	5.34941	0.379210	0.189605	+	0.981860i	$0.439279\pi$
$200$	−6.65675	−0.470703
$201$	−14.3499	−1.01216
$202$	1.33192	0.0937133
$203$	15.8376	1.11158
$204$	2.98311	0.208860
$205$	1.93544	0.135177
$206$	0.550795	0.0383757
$207$	−2.68716	−0.186770
$208$	18.2593	1.26606
$209$	−13.6232	−0.942333
$210$	−0.608101	−0.0419630
$211$	−22.4478	−1.54537	−0.772684	−	0.634791i	$-0.781086\pi$
$211$	−22.4478	−1.54537	−0.772684	+	0.634791i	$0.781086\pi$
$212$	9.15806	0.628978
$213$	2.82376	0.193481
$214$	1.25812	0.0860036
$215$	−4.68716	−0.319662
$216$	8.00807	0.544880
$217$	−14.5264	−0.986119
$218$	−2.06004	−0.139523
$219$	6.00619	0.405861
$220$	−2.26932	−0.152997
$221$	5.77216	0.388278
$222$	−5.33033	−0.357749
$223$	−2.40935	−0.161342	−0.0806711	−	0.996741i	$-0.525706\pi$
$223$	−2.40935	−0.161342	−0.0806711	+	0.996741i	$0.525706\pi$
$224$	6.25310	0.417803
$225$	1.91722	0.127815
$226$	6.54932	0.435654
$227$	−7.83573	−0.520075	−0.260038	−	0.965598i	$-0.583735\pi$
$227$	−7.83573	−0.520075	−0.260038	+	0.965598i	$0.583735\pi$
$228$	−21.9026	−1.45053
$229$	7.56354	0.499813	0.249906	−	0.968270i	$-0.419600\pi$
$229$	7.56354	0.499813	0.249906	+	0.968270i	$0.419600\pi$
$230$	−1.59298	−0.105038
$231$	4.53318	0.298261
$232$	−15.1795	−0.996585
$233$	−21.9590	−1.43858	−0.719291	−	0.694709i	$-0.755533\pi$
$233$	−21.9590	−1.43858	−0.719291	+	0.694709i	$0.755533\pi$
$234$	0.915961	0.0598782
$235$	−0.367800	−0.0239926
$236$	−1.85716	−0.120891
$237$	22.8348	1.48328
$238$	0.574857	0.0372624
$239$	10.4705	0.677278	0.338639	−	0.940916i	$-0.390033\pi$
$239$	10.4705	0.677278	0.338639	+	0.940916i	$0.390033\pi$
$240$	−3.34628	−0.216001
$241$	9.24341	0.595421	0.297710	−	0.954656i	$-0.403777\pi$
$241$	9.24341	0.595421	0.297710	+	0.954656i	$0.403777\pi$
$242$	2.85624	0.183606
$243$	−4.32967	−0.277749
$244$	16.8259	1.07717
$245$	−3.08637	−0.197181
$246$	1.78417	0.113755
$247$	−42.3803	−2.69660
$248$	13.9228	0.884101
$249$	−11.6034	−0.735338
$250$	2.38105	0.150591
$251$	−27.9602	−1.76483	−0.882417	−	0.470469i	$-0.844085\pi$
$251$	−27.9602	−1.76483	−0.882417	+	0.470469i	$0.844085\pi$
$252$	−1.18600	−0.0747112
$253$	11.8751	0.746582
$254$	−1.03427	−0.0648958
$255$	−1.05783	−0.0662439
$256$	5.75638	0.359774
$257$	−1.21022	−0.0754916	−0.0377458	−	0.999287i	$-0.512018\pi$
$257$	−1.21022	−0.0754916	−0.0377458	+	0.999287i	$0.512018\pi$
$258$	−4.32083	−0.269003
$259$	13.3546	0.829817
$260$	−7.05963	−0.437820
$261$	4.37188	0.270613
$262$	6.05391	0.374012
$263$	5.38585	0.332106	0.166053	−	0.986117i	$-0.446898\pi$
$263$	5.38585	0.332106	0.166053	+	0.986117i	$0.446898\pi$
$264$	−4.34481	−0.267405
$265$	−3.24750	−0.199493
$266$	−4.22071	−0.258788
$267$	−2.06093	−0.126127
$268$	−16.5911	−1.01346
$269$	12.8039	0.780665	0.390332	−	0.920674i	$-0.372360\pi$
$269$	12.8039	0.780665	0.390332	+	0.920674i	$0.372360\pi$
$270$	−1.36727	−0.0832096
$271$	23.4543	1.42475	0.712374	−	0.701800i	$-0.247620\pi$
$271$	23.4543	1.42475	0.712374	+	0.701800i	$0.247620\pi$
$272$	3.16334	0.191806
$273$	14.1023	0.853509
$274$	5.68642	0.343529
$275$	−8.47260	−0.510917
$276$	19.0922	1.14921
$277$	7.62681	0.458251	0.229125	−	0.973397i	$-0.426413\pi$
$277$	7.62681	0.458251	0.229125	+	0.973397i	$0.426413\pi$
$278$	−6.88350	−0.412845
$279$	−4.00994	−0.240069
$280$	−1.46023	−0.0872655
$281$	12.3776	0.738387	0.369193	−	0.929353i	$-0.379634\pi$
$281$	12.3776	0.738387	0.369193	+	0.929353i	$0.379634\pi$
$282$	−0.339054	−0.0201904
$283$	−12.0788	−0.718012	−0.359006	−	0.933335i	$-0.616884\pi$
$283$	−12.0788	−0.718012	−0.359006	+	0.933335i	$0.616884\pi$
$284$	3.26479	0.193729
$285$	7.76679	0.460065
$286$	−4.04782	−0.239353
$287$	−4.47007	−0.263860
$288$	1.72613	0.101713
$289$	1.00000	0.0588235
$290$	2.59171	0.152190
$291$	15.1730	0.889454
$292$	6.94426	0.406382
$293$	−13.3024	−0.777136	−0.388568	−	0.921420i	$-0.627030\pi$
$293$	−13.3024	−0.777136	−0.388568	+	0.921420i	$0.627030\pi$
$294$	−2.84515	−0.165933
$295$	0.658559	0.0383428
$296$	−12.7997	−0.743968
$297$	10.1925	0.591431
$298$	−8.02504	−0.464878
$299$	36.9423	2.13643
$300$	−13.6218	−0.786455
$301$	10.8254	0.623967
$302$	−3.49267	−0.200981
$303$	5.66067	0.325197
$304$	−23.2259	−1.33209
$305$	−5.96656	−0.341644
$306$	0.158686	0.00907147
$307$	−23.4486	−1.33828	−0.669140	−	0.743136i	$-0.733337\pi$
$307$	−23.4486	−1.33828	−0.669140	+	0.743136i	$0.733337\pi$
$308$	5.24119	0.298645
$309$	2.34089	0.133169
$310$	−2.37714	−0.135013
$311$	−23.7700	−1.34787	−0.673936	−	0.738790i	$-0.735397\pi$
$311$	−23.7700	−1.34787	−0.673936	+	0.738790i	$0.735397\pi$
$312$	−13.5163	−0.765210
$313$	1.85812	0.105027	0.0525136	−	0.998620i	$-0.483277\pi$
$313$	1.85812	0.105027	0.0525136	+	0.998620i	$0.483277\pi$
$314$	0.515732	0.0291044
$315$	0.420564	0.0236961
$316$	26.4012	1.48518
$317$	−9.02175	−0.506712	−0.253356	−	0.967373i	$-0.581534\pi$
$317$	−9.02175	−0.506712	−0.253356	+	0.967373i	$0.581534\pi$
$318$	−2.99369	−0.167878
$319$	−19.3203	−1.08173
$320$	−3.14322	−0.175712
$321$	5.34705	0.298443
$322$	3.67913	0.205030
$323$	−7.34219	−0.408530
$324$	14.0478	0.780431
$325$	−26.3574	−1.46205
$326$	1.05651	0.0585145
$327$	−8.75520	−0.484164
$328$	4.28432	0.236562
$329$	0.849467	0.0468326
$330$	0.741820	0.0408358
$331$	−6.54029	−0.359487	−0.179743	−	0.983714i	$-0.557527\pi$
$331$	−6.54029	−0.359487	−0.179743	+	0.983714i	$0.557527\pi$
$332$	−13.4157	−0.736283
$333$	3.68647	0.202017
$334$	−3.69905	−0.202403
$335$	5.88331	0.321439
$336$	7.72853	0.421626
$337$	19.0322	1.03675	0.518375	−	0.855154i	$-0.326537\pi$
$337$	19.0322	1.03675	0.518375	+	0.855154i	$0.326537\pi$
$338$	−7.67907	−0.417687
$339$	27.8347	1.51178
$340$	−1.22305	−0.0663290
$341$	17.7207	0.959632
$342$	−1.16510	−0.0630015
$343$	17.7753	0.959774
$344$	−10.3756	−0.559415
$345$	−6.77020	−0.364495
$346$	3.57530	0.192209
$347$	−31.5550	−1.69396	−0.846981	−	0.531623i	$-0.821582\pi$
$347$	−31.5550	−1.69396	−0.846981	+	0.531623i	$0.821582\pi$
$348$	−31.0621	−1.66510
$349$	19.9058	1.06554	0.532768	−	0.846261i	$-0.321152\pi$
$349$	19.9058	1.06554	0.532768	+	0.846261i	$0.321152\pi$
$350$	−2.62497	−0.140311
$351$	31.7080	1.69245
$352$	−7.62812	−0.406580
$353$	−32.6207	−1.73622	−0.868111	−	0.496370i	$-0.834666\pi$
$353$	−32.6207	−1.73622	−0.868111	+	0.496370i	$0.834666\pi$
$354$	0.607088	0.0322664
$355$	−1.15771	−0.0614450
$356$	−2.38282	−0.126289
$357$	2.44315	0.129305
$358$	3.46688	0.183230
$359$	−12.2356	−0.645772	−0.322886	−	0.946438i	$-0.604653\pi$
$359$	−12.2356	−0.645772	−0.322886	+	0.946438i	$0.604653\pi$
$360$	−0.403088	−0.0212446
$361$	34.9078	1.83725
$362$	−0.709515	−0.0372913
$363$	12.1391	0.637137
$364$	16.3048	0.854606
$365$	−2.46248	−0.128892
$366$	−5.50023	−0.287502
$367$	−0.734103	−0.0383199	−0.0191599	−	0.999816i	$-0.506099\pi$
$367$	−0.734103	−0.0383199	−0.0191599	+	0.999816i	$0.506099\pi$
$368$	20.2457	1.05538
$369$	−1.23394	−0.0642361
$370$	2.18538	0.113613
$371$	7.50040	0.389401
$372$	28.4905	1.47716
$373$	−21.8376	−1.13071	−0.565354	−	0.824849i	$-0.691260\pi$
$373$	−21.8376	−1.13071	−0.565354	+	0.824849i	$0.691260\pi$
$374$	−0.701265	−0.0362616
$375$	10.1195	0.522570
$376$	−0.814169	−0.0419876
$377$	−60.1035	−3.09549
$378$	3.15784	0.162422
$379$	−28.2298	−1.45007	−0.725034	−	0.688713i	$-0.758176\pi$
$379$	−28.2298	−1.45007	−0.725034	+	0.688713i	$0.758176\pi$
$380$	8.97984	0.460656
$381$	−4.39566	−0.225197
$382$	1.71891	0.0879472
$383$	−19.7266	−1.00798	−0.503990	−	0.863709i	$-0.668135\pi$
$383$	−19.7266	−1.00798	−0.503990	+	0.863709i	$0.668135\pi$
$384$	−16.1050	−0.821852
$385$	−1.85856	−0.0947209
$386$	−0.525272	−0.0267356
$387$	2.98829	0.151903
$388$	17.5427	0.890597
$389$	18.6524	0.945713	0.472857	−	0.881139i	$-0.343223\pi$
$389$	18.6524	0.945713	0.472857	+	0.881139i	$0.343223\pi$
$390$	2.30773	0.116856
$391$	6.40008	0.323666
$392$	−6.83206	−0.345071
$393$	25.7292	1.29787
$394$	−4.56991	−0.230229
$395$	−9.36202	−0.471055
$396$	1.44680	0.0727044
$397$	−4.80233	−0.241022	−0.120511	−	0.992712i	$-0.538453\pi$
$397$	−4.80233	−0.241022	−0.120511	+	0.992712i	$0.538453\pi$
$398$	−2.02179	−0.101343
$399$	−17.9381	−0.898028
$400$	−14.4448	−0.722239
$401$	−31.4689	−1.57148	−0.785741	−	0.618555i	$-0.787718\pi$
$401$	−31.4689	−1.57148	−0.785741	+	0.618555i	$0.787718\pi$
$402$	5.42349	0.270499
$403$	55.1275	2.74610
$404$	6.54478	0.325615
$405$	−4.98142	−0.247529
$406$	−5.98578	−0.297069
$407$	−16.2913	−0.807528
$408$	−2.34163	−0.115928
$409$	26.2991	1.30041	0.650204	−	0.759760i	$-0.274683\pi$
$409$	26.2991	1.30041	0.650204	+	0.759760i	$0.274683\pi$
$410$	−0.731492	−0.0361258
$411$	24.1674	1.19209
$412$	2.70650	0.133340
$413$	−1.52100	−0.0748435
$414$	1.01560	0.0499141
$415$	4.75729	0.233526
$416$	−23.7304	−1.16348
$417$	−29.2550	−1.43262
$418$	5.14882	0.251837
$419$	22.0023	1.07488	0.537442	−	0.843301i	$-0.319391\pi$
$419$	22.0023	1.07488	0.537442	+	0.843301i	$0.319391\pi$
$420$	−2.98809	−0.145804
$421$	31.5235	1.53636	0.768180	−	0.640234i	$-0.221163\pi$
$421$	31.5235	1.53636	0.768180	+	0.640234i	$0.221163\pi$
$422$	8.48405	0.412997
$423$	0.234490	0.0114013
$424$	−7.18874	−0.349116
$425$	−4.56630	−0.221498
$426$	−1.06723	−0.0517074
$427$	13.7803	0.666876
$428$	6.18218	0.298827
$429$	−17.2033	−0.830584
$430$	1.77150	0.0854291
$431$	32.4749	1.56426	0.782130	−	0.623116i	$-0.214133\pi$
$431$	32.4749	1.56426	0.782130	+	0.623116i	$0.214133\pi$
$432$	17.3771	0.836054
$433$	3.13451	0.150635	0.0753175	−	0.997160i	$-0.476003\pi$
$433$	3.13451	0.150635	0.0753175	+	0.997160i	$0.476003\pi$
$434$	5.49022	0.263539
$435$	11.0148	0.528119
$436$	−10.1226	−0.484786
$437$	−46.9906	−2.24787
$438$	−2.27002	−0.108466
$439$	−39.3891	−1.87994	−0.939970	−	0.341256i	$-0.889148\pi$
$439$	−39.3891	−1.87994	−0.939970	+	0.341256i	$0.889148\pi$
$440$	1.78133	0.0849216
$441$	1.96771	0.0937006
$442$	−2.18157	−0.103767
$443$	−34.0554	−1.61802	−0.809009	−	0.587796i	$-0.799996\pi$
$443$	−34.0554	−1.61802	−0.809009	+	0.587796i	$0.799996\pi$
$444$	−26.1922	−1.24303
$445$	0.844963	0.0400551
$446$	0.910606	0.0431185
$447$	−34.1066	−1.61319
$448$	7.25956	0.342982
$449$	−23.4942	−1.10876	−0.554380	−	0.832263i	$-0.687045\pi$
$449$	−23.4942	−1.10876	−0.554380	+	0.832263i	$0.687045\pi$
$450$	−0.724607	−0.0341583
$451$	5.45301	0.256772
$452$	32.1821	1.51372
$453$	−14.8439	−0.697428
$454$	2.96149	0.138989
$455$	−5.78180	−0.271055
$456$	17.1927	0.805123
$457$	30.8505	1.44313	0.721563	−	0.692349i	$-0.243424\pi$
$457$	30.8505	1.44313	0.721563	+	0.692349i	$0.243424\pi$
$458$	−2.85861	−0.133574
$459$	5.49326	0.256403
$460$	−7.82760	−0.364964
$461$	−25.4979	−1.18755	−0.593777	−	0.804630i	$-0.702364\pi$
$461$	−25.4979	−1.18755	−0.593777	+	0.804630i	$0.702364\pi$
$462$	−1.71330	−0.0797099
$463$	27.0839	1.25870	0.629348	−	0.777124i	$-0.283322\pi$
$463$	27.0839	1.25870	0.629348	+	0.777124i	$0.283322\pi$
$464$	−32.9387	−1.52914
$465$	−10.1029	−0.468511
$466$	8.29932	0.384459
$467$	3.86600	0.178897	0.0894485	−	0.995991i	$-0.471490\pi$
$467$	3.86600	0.178897	0.0894485	+	0.995991i	$0.471490\pi$
$468$	4.50086	0.208052
$469$	−13.5880	−0.627437
$470$	0.139009	0.00641199
$471$	2.19187	0.100996
$472$	1.45780	0.0671006
$473$	−13.2059	−0.607207
$474$	−8.63032	−0.396404
$475$	33.5266	1.53831
$476$	2.82474	0.129472
$477$	2.07044	0.0947990
$478$	−3.95728	−0.181002
$479$	−3.33843	−0.152537	−0.0762683	−	0.997087i	$-0.524301\pi$
$479$	−3.33843	−0.152537	−0.0762683	+	0.997087i	$0.524301\pi$
$480$	4.34892	0.198500
$481$	−50.6806	−2.31083
$482$	−3.49352	−0.159125
$483$	15.6364	0.711480
$484$	14.0350	0.637955
$485$	−6.22076	−0.282470
$486$	1.63638	0.0742279
$487$	16.5931	0.751905	0.375953	−	0.926639i	$-0.377316\pi$
$487$	16.5931	0.751905	0.375953	+	0.926639i	$0.377316\pi$
$488$	−13.2077	−0.597884
$489$	4.49018	0.203053
$490$	1.16648	0.0526964
$491$	23.4540	1.05847	0.529233	−	0.848476i	$-0.322480\pi$
$491$	23.4540	1.05847	0.529233	+	0.848476i	$0.322480\pi$
$492$	8.76707	0.395250
$493$	−10.4126	−0.468962
$494$	16.0175	0.720661
$495$	−0.513044	−0.0230596
$496$	30.2118	1.35655
$497$	2.67384	0.119938
$498$	4.38548	0.196518
$499$	−5.18583	−0.232150	−0.116075	−	0.993240i	$-0.537031\pi$
$499$	−5.18583	−0.232150	−0.116075	+	0.993240i	$0.537031\pi$
$500$	11.7000	0.523241
$501$	−15.7210	−0.702364
$502$	10.5675	0.471649
$503$	−1.36167	−0.0607141	−0.0303570	−	0.999539i	$-0.509664\pi$
$503$	−1.36167	−0.0607141	−0.0303570	+	0.999539i	$0.509664\pi$
$504$	0.930968	0.0414686
$505$	−2.32082	−0.103275
$506$	−4.48816	−0.199523
$507$	−32.6362	−1.44943
$508$	−5.08220	−0.225486
$509$	−19.0945	−0.846349	−0.423175	−	0.906048i	$-0.639084\pi$
$509$	−19.0945	−0.846349	−0.423175	+	0.906048i	$0.639084\pi$
$510$	0.399803	0.0177036
$511$	5.68731	0.251592
$512$	−22.2281	−0.982352
$513$	−40.3326	−1.78073
$514$	0.457399	0.0201750
$515$	−0.959741	−0.0422913
$516$	−21.2317	−0.934674
$517$	−1.03626	−0.0455747
$518$	−5.04734	−0.221767
$519$	15.1951	0.666990
$520$	5.54155	0.243013
$521$	6.00129	0.262921	0.131461	−	0.991321i	$-0.458033\pi$
$521$	6.00129	0.262921	0.131461	+	0.991321i	$0.458033\pi$
$522$	−1.65234	−0.0723209
$523$	6.44324	0.281743	0.140872	−	0.990028i	$-0.455010\pi$
$523$	6.44324	0.281743	0.140872	+	0.990028i	$0.455010\pi$
$524$	29.7477	1.29954
$525$	−11.1562	−0.486895
$526$	−2.03556	−0.0887548
$527$	9.55058	0.416030
$528$	−9.42800	−0.410301
$529$	17.9610	0.780915
$530$	1.22738	0.0533141
$531$	−0.419863	−0.0182205
$532$	−20.7398	−0.899182
$533$	16.9638	0.734784
$534$	0.778923	0.0337073
$535$	−2.19224	−0.0947787
$536$	13.0234	0.562526
$537$	14.7343	0.635832
$538$	−4.83917	−0.208631
$539$	−8.69573	−0.374552
$540$	−6.71851	−0.289119
$541$	−31.3007	−1.34572	−0.672861	−	0.739768i	$-0.734935\pi$
$541$	−31.3007	−1.34572	−0.672861	+	0.739768i	$0.734935\pi$
$542$	−8.86448	−0.380762
$543$	−3.01545	−0.129405
$544$	−4.11117	−0.176265
$545$	3.58954	0.153759
$546$	−5.32991	−0.228099
$547$	36.7931	1.57316	0.786581	−	0.617487i	$-0.211849\pi$
$547$	36.7931	1.57316	0.786581	+	0.617487i	$0.211849\pi$
$548$	27.9420	1.19362
$549$	3.80397	0.162350
$550$	3.20219	0.136542
$551$	76.4516	3.25695
$552$	−14.9866	−0.637874
$553$	21.6224	0.919479
$554$	−2.88253	−0.122467
$555$	9.28793	0.394250
$556$	−33.8242	−1.43447
$557$	−25.5350	−1.08195	−0.540976	−	0.841038i	$-0.681945\pi$
$557$	−25.5350	−1.08195	−0.540976	+	0.841038i	$0.681945\pi$
$558$	1.51554	0.0641580
$559$	−41.0822	−1.73759
$560$	−3.16862	−0.133899
$561$	−2.98039	−0.125832
$562$	−4.67808	−0.197333
$563$	24.5506	1.03469	0.517343	−	0.855778i	$-0.326921\pi$
$563$	24.5506	1.03469	0.517343	+	0.855778i	$0.326921\pi$
$564$	−1.66605	−0.0701532
$565$	−11.4120	−0.480105
$566$	4.56515	0.191888
$567$	11.5050	0.483166
$568$	−2.56274	−0.107530
$569$	−20.4512	−0.857361	−0.428680	−	0.903456i	$-0.641021\pi$
$569$	−20.4512	−0.857361	−0.428680	+	0.903456i	$0.641021\pi$
$570$	−2.93543	−0.122952
$571$	−18.3757	−0.768999	−0.384500	−	0.923125i	$-0.625626\pi$
$571$	−18.3757	−0.768999	−0.384500	+	0.923125i	$0.625626\pi$
$572$	−19.8902	−0.831651
$573$	7.30541	0.305188
$574$	1.68945	0.0705161
$575$	−29.2247	−1.21875
$576$	2.00396	0.0834982
$577$	16.0759	0.669247	0.334624	−	0.942352i	$-0.391391\pi$
$577$	16.0759	0.669247	0.334624	+	0.942352i	$0.391391\pi$
$578$	−0.377947	−0.0157205
$579$	−2.23242	−0.0927760
$580$	12.7351	0.528798
$581$	−10.9874	−0.455834
$582$	−5.73457	−0.237705
$583$	−9.14971	−0.378942
$584$	−5.45099	−0.225564
$585$	−1.59603	−0.0659877
$586$	5.02761	0.207689
$587$	7.97075	0.328988	0.164494	−	0.986378i	$-0.447401\pi$
$587$	7.97075	0.328988	0.164494	+	0.986378i	$0.447401\pi$
$588$	−13.9805	−0.576547
$589$	−70.1222	−2.88934
$590$	−0.248900	−0.0102471
$591$	−19.4222	−0.798923
$592$	−27.7747	−1.14153
$593$	21.8021	0.895307	0.447653	−	0.894207i	$-0.352260\pi$
$593$	21.8021	0.895307	0.447653	+	0.894207i	$0.352260\pi$
$594$	−3.85223	−0.158059
$595$	−1.00167	−0.0410644
$596$	−39.4335	−1.61526
$597$	−8.59265	−0.351674
$598$	−13.9622	−0.570958
$599$	25.7571	1.05241	0.526204	−	0.850358i	$-0.323615\pi$
$599$	25.7571	1.05241	0.526204	+	0.850358i	$0.323615\pi$
$600$	10.6926	0.436524
$601$	−6.36653	−0.259696	−0.129848	−	0.991534i	$-0.541449\pi$
$601$	−6.36653	−0.259696	−0.129848	+	0.991534i	$0.541449\pi$
$602$	−4.09143	−0.166754
$603$	−3.75089	−0.152748
$604$	−17.1623	−0.698324
$605$	−4.97690	−0.202340
$606$	−2.13943	−0.0869084
$607$	−4.77568	−0.193839	−0.0969194	−	0.995292i	$-0.530899\pi$
$607$	−4.77568	−0.193839	−0.0969194	+	0.995292i	$0.530899\pi$
$608$	30.1850	1.22416
$609$	−25.4397	−1.03087
$610$	2.25504	0.0913039
$611$	−3.22371	−0.130417
$612$	0.779752	0.0315196
$613$	−32.3865	−1.30808	−0.654040	−	0.756460i	$-0.726927\pi$
$613$	−32.3865	−1.30808	−0.654040	+	0.756460i	$0.726927\pi$
$614$	8.86231	0.357654
$615$	−3.10886	−0.125361
$616$	−4.11414	−0.165763
$617$	19.4667	0.783701	0.391850	−	0.920029i	$-0.371835\pi$
$617$	19.4667	0.783701	0.391850	+	0.920029i	$0.371835\pi$
$618$	−0.884731	−0.0355891
$619$	−4.91935	−0.197725	−0.0988626	−	0.995101i	$-0.531520\pi$
$619$	−4.91935	−0.197725	−0.0988626	+	0.995101i	$0.531520\pi$
$620$	−11.6808	−0.469113
$621$	35.1573	1.41081
$622$	8.98378	0.360217
$623$	−1.95152	−0.0781859
$624$	−29.3296	−1.17412
$625$	18.6826	0.747304
$626$	−0.702270	−0.0280684
$627$	21.8826	0.873907
$628$	2.53421	0.101126
$629$	−8.78017	−0.350088
$630$	−0.158951	−0.00633274
$631$	−19.7113	−0.784694	−0.392347	−	0.919817i	$-0.628337\pi$
$631$	−19.7113	−0.784694	−0.392347	+	0.919817i	$0.628337\pi$
$632$	−20.7240	−0.824355
$633$	36.0574	1.43315
$634$	3.40974	0.135418
$635$	1.80218	0.0715172
$636$	−14.7104	−0.583306
$637$	−27.0516	−1.07182
$638$	7.30202	0.289090
$639$	0.738098	0.0291987
$640$	6.60287	0.261001
$641$	−31.5208	−1.24500	−0.622499	−	0.782620i	$-0.713883\pi$
$641$	−31.5208	−1.24500	−0.622499	+	0.782620i	$0.713883\pi$
$642$	−2.02090	−0.0797586
$643$	−10.6435	−0.419737	−0.209869	−	0.977730i	$-0.567304\pi$
$643$	−10.6435	−0.419737	−0.209869	+	0.977730i	$0.567304\pi$
$644$	18.0785	0.712394
$645$	7.52890	0.296450
$646$	2.77496	0.109179
$647$	36.6094	1.43926	0.719632	−	0.694356i	$-0.244311\pi$
$647$	36.6094	1.43926	0.719632	+	0.694356i	$0.244311\pi$
$648$	−11.0270	−0.433180
$649$	1.85546	0.0728332
$650$	9.96170	0.390730
$651$	23.3335	0.914514
$652$	5.19147	0.203314
$653$	−10.7718	−0.421532	−0.210766	−	0.977537i	$-0.567596\pi$
$653$	−10.7718	−0.421532	−0.210766	+	0.977537i	$0.567596\pi$
$654$	3.30900	0.129392
$655$	−10.5487	−0.412173
$656$	9.29674	0.362977
$657$	1.56995	0.0612496
$658$	−0.321053	−0.0125160
$659$	41.5089	1.61696	0.808478	−	0.588527i	$-0.200292\pi$
$659$	41.5089	1.61696	0.808478	+	0.588527i	$0.200292\pi$
$660$	3.64516	0.141888
$661$	33.1288	1.28856	0.644281	−	0.764789i	$-0.277157\pi$
$661$	33.1288	1.28856	0.644281	+	0.764789i	$0.277157\pi$
$662$	2.47188	0.0960723
$663$	−9.27171	−0.360084
$664$	10.5308	0.408676
$665$	7.35444	0.285193
$666$	−1.39329	−0.0539888
$667$	−66.6417	−2.58038
$668$	−18.1764	−0.703267
$669$	3.87009	0.149627
$670$	−2.22358	−0.0859042
$671$	−16.8105	−0.648963
$672$	−10.0442	−0.387464
$673$	4.66925	0.179986	0.0899931	−	0.995942i	$-0.471315\pi$
$673$	4.66925	0.179986	0.0899931	+	0.995942i	$0.471315\pi$
$674$	−7.19315	−0.277070
$675$	−25.0839	−0.965479
$676$	−37.7335	−1.45129
$677$	−33.1184	−1.27285	−0.636423	−	0.771340i	$-0.719587\pi$
$677$	−33.1184	−1.27285	−0.636423	+	0.771340i	$0.719587\pi$
$678$	−10.5200	−0.404020
$679$	14.3674	0.551370
$680$	0.960046	0.0368161
$681$	12.5864	0.482311
$682$	−6.69749	−0.256460
$683$	17.9387	0.686404	0.343202	−	0.939262i	$-0.388488\pi$
$683$	17.9387	0.686404	0.343202	+	0.939262i	$0.388488\pi$
$684$	−5.72509	−0.218904
$685$	−9.90839	−0.378580
$686$	−6.71810	−0.256498
$687$	−12.1492	−0.463520
$688$	−22.5145	−0.858356
$689$	−28.4639	−1.08439
$690$	2.55877	0.0974109
$691$	−4.27391	−0.162587	−0.0812935	−	0.996690i	$-0.525905\pi$
$691$	−4.27391	−0.162587	−0.0812935	+	0.996690i	$0.525905\pi$
$692$	17.5683	0.667847
$693$	1.18492	0.0450114
$694$	11.9261	0.452709
$695$	11.9943	0.454969
$696$	24.3826	0.924220
$697$	2.93890	0.111319
$698$	−7.52335	−0.284763
$699$	35.2723	1.33412
$700$	−12.8986	−0.487521
$701$	2.29580	0.0867111	0.0433555	−	0.999060i	$-0.486195\pi$
$701$	2.29580	0.0867111	0.0433555	+	0.999060i	$0.486195\pi$
$702$	−11.9839	−0.452304
$703$	64.4657	2.43137
$704$	−8.85590	−0.333769
$705$	0.590790	0.0222504
$706$	12.3289	0.464003
$707$	5.36013	0.201589
$708$	2.98311	0.112112
$709$	49.1236	1.84488	0.922438	−	0.386145i	$-0.126194\pi$
$709$	49.1236	1.84488	0.922438	+	0.386145i	$0.126194\pi$
$710$	0.437553	0.0164211
$711$	5.96875	0.223845
$712$	1.87043	0.0700972
$713$	61.1245	2.28913
$714$	−0.923381	−0.0345567
$715$	7.05319	0.263774
$716$	17.0356	0.636649
$717$	−16.8185	−0.628099
$718$	4.62442	0.172582
$719$	36.0694	1.34516	0.672581	−	0.740024i	$-0.265186\pi$
$719$	36.0694	1.34516	0.672581	+	0.740024i	$0.265186\pi$
$720$	−0.874679	−0.0325974
$721$	2.21661	0.0825508
$722$	−13.1933	−0.491003
$723$	−14.8475	−0.552185
$724$	−3.48642	−0.129572
$725$	47.5472	1.76586
$726$	−4.58792	−0.170274
$727$	10.9556	0.406321	0.203160	−	0.979145i	$-0.434879\pi$
$727$	10.9556	0.406321	0.203160	+	0.979145i	$0.434879\pi$
$728$	−12.7987	−0.474351
$729$	29.6470	1.09804
$730$	0.930685	0.0344462
$731$	−7.11730	−0.263243
$732$	−27.0271	−0.998950
$733$	28.8173	1.06439	0.532196	−	0.846621i	$-0.321367\pi$
$733$	28.8173	1.06439	0.532196	+	0.846621i	$0.321367\pi$
$734$	0.277452	0.0102409
$735$	4.95758	0.182863
$736$	−26.3118	−0.969867
$737$	16.5760	0.610584
$738$	0.466362	0.0171670
$739$	38.3343	1.41015	0.705076	−	0.709132i	$-0.250913\pi$
$739$	38.3343	1.41015	0.705076	+	0.709132i	$0.250913\pi$
$740$	10.7386	0.394757
$741$	68.0747	2.50079
$742$	−2.83475	−0.104067
$743$	−10.6696	−0.391429	−0.195715	−	0.980661i	$-0.562703\pi$
$743$	−10.6696	−0.391429	−0.195715	+	0.980661i	$0.562703\pi$
$744$	−22.3640	−0.819903
$745$	13.9834	0.512311
$746$	8.25344	0.302180
$747$	−3.03301	−0.110972
$748$	−3.44588	−0.125994
$749$	5.06317	0.185004
$750$	−3.82464	−0.139656
$751$	8.58364	0.313221	0.156611	−	0.987660i	$-0.449943\pi$
$751$	8.58364	0.313221	0.156611	+	0.987660i	$0.449943\pi$
$752$	−1.76670	−0.0644250
$753$	44.9120	1.63668
$754$	22.7159	0.827264
$755$	6.08586	0.221487
$756$	15.5170	0.564348
$757$	36.4552	1.32499	0.662493	−	0.749068i	$-0.269498\pi$
$757$	36.4552	1.32499	0.662493	+	0.749068i	$0.269498\pi$
$758$	10.6694	0.387529
$759$	−19.0748	−0.692370
$760$	−7.04884	−0.255688
$761$	31.9109	1.15677	0.578385	−	0.815764i	$-0.303683\pi$
$761$	31.9109	1.15677	0.578385	+	0.815764i	$0.303683\pi$
$762$	1.66133	0.0601835
$763$	−8.29037	−0.300132
$764$	8.44640	0.305580
$765$	−0.276505	−0.00999705
$766$	7.45559	0.269381
$767$	5.77216	0.208421
$768$	−9.24636	−0.333649
$769$	−11.8391	−0.426928	−0.213464	−	0.976951i	$-0.568475\pi$
$769$	−11.8391	−0.426928	−0.213464	+	0.976951i	$0.568475\pi$
$770$	0.702435	0.0253140
$771$	1.94396	0.0700099
$772$	−2.58108	−0.0928953
$773$	28.1712	1.01325	0.506624	−	0.862167i	$-0.330893\pi$
$773$	28.1712	1.01325	0.506624	+	0.862167i	$0.330893\pi$
$774$	−1.12942	−0.0405960
$775$	−43.6108	−1.56655
$776$	−13.7704	−0.494328
$777$	−21.4513	−0.769561
$778$	−7.04960	−0.252741
$779$	−21.5780	−0.773110
$780$	11.3397	0.406028
$781$	−3.26181	−0.116717
$782$	−2.41889	−0.0864993
$783$	−57.1993	−2.04414
$784$	−14.8252	−0.529471
$785$	−0.898645	−0.0320740
$786$	−9.72427	−0.346853
$787$	−16.8548	−0.600808	−0.300404	−	0.953812i	$-0.597121\pi$
$787$	−16.8548	−0.600808	−0.300404	+	0.953812i	$0.597121\pi$
$788$	−22.4557	−0.799950
$789$	−8.65119	−0.307990
$790$	3.53835	0.125889
$791$	26.3570	0.937145
$792$	−1.13568	−0.0403548
$793$	−52.2960	−1.85708
$794$	1.81503	0.0644128
$795$	5.21640	0.185007
$796$	−9.93469	−0.352126
$797$	−16.3714	−0.579905	−0.289953	−	0.957041i	$-0.593640\pi$
$797$	−16.3714	−0.579905	−0.289953	+	0.957041i	$0.593640\pi$
$798$	6.77964	0.239997
$799$	−0.558492	−0.0197580
$800$	18.7728	0.663720
$801$	−0.538705	−0.0190342
$802$	11.8936	0.419977
$803$	−6.93793	−0.244834
$804$	26.6500	0.939872
$805$	−6.41076	−0.225950
$806$	−20.8353	−0.733891
$807$	−20.5666	−0.723978
$808$	−5.13741	−0.180733
$809$	−9.30419	−0.327118	−0.163559	−	0.986534i	$-0.552297\pi$
$809$	−9.30419	−0.327118	−0.163559	+	0.986534i	$0.552297\pi$
$810$	1.88271	0.0661517
$811$	3.20302	0.112473	0.0562367	−	0.998417i	$-0.482090\pi$
$811$	3.20302	0.112473	0.0562367	+	0.998417i	$0.482090\pi$
$812$	−29.4130	−1.03219
$813$	−37.6742	−1.32129
$814$	6.15723	0.215811
$815$	−1.84093	−0.0644849
$816$	−5.08122	−0.177878
$817$	52.2566	1.82823
$818$	−9.93966	−0.347532
$819$	3.68618	0.128805
$820$	−3.59441	−0.125522
$821$	−27.5667	−0.962083	−0.481041	−	0.876698i	$-0.659741\pi$
$821$	−27.5667	−0.962083	−0.481041	+	0.876698i	$0.659741\pi$
$822$	−9.13399	−0.318584
$823$	−26.8489	−0.935894	−0.467947	−	0.883757i	$-0.655006\pi$
$823$	−26.8489	−0.935894	−0.467947	+	0.883757i	$0.655006\pi$
$824$	−2.12450	−0.0740106
$825$	13.6094	0.473817
$826$	0.574857	0.0200018
$827$	10.6042	0.368745	0.184373	−	0.982856i	$-0.440975\pi$
$827$	10.6042	0.368745	0.184373	+	0.982856i	$0.440975\pi$
$828$	4.99048	0.173431
$829$	−12.8559	−0.446504	−0.223252	−	0.974761i	$-0.571667\pi$
$829$	−12.8559	−0.446504	−0.223252	+	0.974761i	$0.571667\pi$
$830$	−1.79800	−0.0624096
$831$	−12.2508	−0.424975
$832$	−27.5499	−0.955120
$833$	−4.68656	−0.162380
$834$	11.0568	0.382867
$835$	6.44547	0.223055
$836$	25.3003	0.875030
$837$	52.4638	1.81342
$838$	−8.31571	−0.287261
$839$	46.6078	1.60908	0.804539	−	0.593899i	$-0.202412\pi$
$839$	46.6078	1.60908	0.804539	+	0.593899i	$0.202412\pi$
$840$	2.34554	0.0809288
$841$	79.4230	2.73872
$842$	−11.9142	−0.410590
$843$	−19.8819	−0.684770
$844$	41.6890	1.43499
$845$	13.3805	0.460304
$846$	−0.0886248	−0.00304698
$847$	11.4946	0.394959
$848$	−15.5992	−0.535678
$849$	19.4020	0.665875
$850$	1.72582	0.0591951
$851$	−56.1938	−1.92630
$852$	−5.24416	−0.179662
$853$	6.25356	0.214118	0.107059	−	0.994253i	$-0.465857\pi$
$853$	6.25356	0.214118	0.107059	+	0.994253i	$0.465857\pi$
$854$	−5.20822	−0.178222
$855$	2.03015	0.0694297
$856$	−4.85278	−0.165865
$857$	11.6567	0.398186	0.199093	−	0.979981i	$-0.436200\pi$
$857$	11.6567	0.398186	0.199093	+	0.979981i	$0.436200\pi$
$858$	6.50193	0.221972
$859$	−0.843380	−0.0287757	−0.0143879	−	0.999896i	$-0.504580\pi$
$859$	−0.843380	−0.0287757	−0.0143879	+	0.999896i	$0.504580\pi$
$860$	8.70479	0.296831
$861$	7.18018	0.244700
$862$	−12.2738	−0.418046
$863$	−40.8164	−1.38941	−0.694703	−	0.719296i	$-0.744464\pi$
$863$	−40.8164	−1.38941	−0.694703	+	0.719296i	$0.744464\pi$
$864$	−22.5837	−0.768314
$865$	−6.22983	−0.211821
$866$	−1.18468	−0.0402570
$867$	−1.60628	−0.0545521
$868$	26.9779	0.915689
$869$	−26.3771	−0.894782
$870$	−4.16301	−0.141139
$871$	51.5663	1.74726
$872$	7.94589	0.269082
$873$	3.96604	0.134230
$874$	17.7599	0.600739
$875$	9.58226	0.323940
$876$	−11.1544	−0.376873
$877$	−3.61287	−0.121998	−0.0609990	−	0.998138i	$-0.519429\pi$
$877$	−3.61287	−0.121998	−0.0609990	+	0.998138i	$0.519429\pi$
$878$	14.8870	0.502412
$879$	21.3674	0.720705
$880$	3.86539	0.130302
$881$	−34.2060	−1.15243	−0.576215	−	0.817298i	$-0.695471\pi$
$881$	−34.2060	−1.15243	−0.576215	+	0.817298i	$0.695471\pi$
$882$	−0.743690	−0.0250414
$883$	−11.5502	−0.388696	−0.194348	−	0.980933i	$-0.562259\pi$
$883$	−11.5502	−0.388696	−0.194348	+	0.980933i	$0.562259\pi$
$884$	−10.7198	−0.360546
$885$	−1.05783	−0.0355586
$886$	12.8711	0.432413
$887$	35.6645	1.19750	0.598748	−	0.800938i	$-0.295665\pi$
$887$	35.6645	1.19750	0.598748	+	0.800938i	$0.295665\pi$
$888$	20.5599	0.689946
$889$	−4.16229	−0.139599
$890$	−0.319351	−0.0107047
$891$	−14.0349	−0.470188
$892$	4.47454	0.149819
$893$	4.10056	0.137220
$894$	12.8905	0.431122
$895$	−6.04092	−0.201926
$896$	−15.2499	−0.509464
$897$	−59.3397	−1.98130
$898$	8.87956	0.296315
$899$	−99.4468	−3.31674
$900$	−3.56058	−0.118686
$901$	−4.93123	−0.164283
$902$	−2.06095	−0.0686221
$903$	−17.3887	−0.578658
$904$	−25.2617	−0.840193
$905$	1.23630	0.0410962
$906$	5.61021	0.186387
$907$	6.65530	0.220986	0.110493	−	0.993877i	$-0.464757\pi$
$907$	6.65530	0.220986	0.110493	+	0.993877i	$0.464757\pi$
$908$	14.5522	0.482931
$909$	1.47963	0.0490763
$910$	2.18521	0.0724390
$911$	−15.5079	−0.513798	−0.256899	−	0.966438i	$-0.582701\pi$
$911$	−15.5079	−0.513798	−0.256899	+	0.966438i	$0.582701\pi$
$912$	37.3073	1.23537
$913$	13.4035	0.443590
$914$	−11.6598	−0.385673
$915$	9.58397	0.316836
$916$	−14.0467	−0.464115
$917$	24.3632	0.804545
$918$	−2.07616	−0.0685234
$919$	37.1816	1.22651	0.613253	−	0.789886i	$-0.289860\pi$
$919$	37.1816	1.22651	0.613253	+	0.789886i	$0.289860\pi$
$920$	6.14438	0.202574
$921$	37.6650	1.24110
$922$	9.63683	0.317372
$923$	−10.1472	−0.333998
$924$	−8.41882	−0.276959
$925$	40.0929	1.31825
$926$	−10.2363	−0.336385
$927$	0.611882	0.0200968
$928$	42.8081	1.40525
$929$	−8.62330	−0.282921	−0.141461	−	0.989944i	$-0.545180\pi$
$929$	−8.62330	−0.282921	−0.141461	+	0.989944i	$0.545180\pi$
$930$	3.81835	0.125209
$931$	34.4096	1.12773
$932$	40.7813	1.33584
$933$	38.1812	1.25000
$934$	−1.46114	−0.0478100
$935$	1.22193	0.0399614
$936$	−3.53300	−0.115480
$937$	7.52547	0.245846	0.122923	−	0.992416i	$-0.460773\pi$
$937$	7.52547	0.245846	0.122923	+	0.992416i	$0.460773\pi$
$938$	5.13555	0.167682
$939$	−2.98466	−0.0974008
$940$	0.683062	0.0222790
$941$	19.4285	0.633350	0.316675	−	0.948534i	$-0.397434\pi$
$941$	19.4285	0.633350	0.316675	+	0.948534i	$0.397434\pi$
$942$	−0.828410	−0.0269911
$943$	18.8092	0.612511
$944$	3.16334	0.102958
$945$	−5.50242	−0.178994
$946$	4.99112	0.162275
$947$	−4.91750	−0.159797	−0.0798987	−	0.996803i	$-0.525460\pi$
$947$	−4.91750	−0.159797	−0.0798987	+	0.996803i	$0.525460\pi$
$948$	−42.4077	−1.37734
$949$	−21.5832	−0.700621
$950$	−12.6713	−0.411111
$951$	14.4915	0.469918
$952$	−2.21731	−0.0718635
$953$	3.57076	0.115668	0.0578341	−	0.998326i	$-0.481581\pi$
$953$	3.57076	0.115668	0.0578341	+	0.998326i	$0.481581\pi$
$954$	−0.782516	−0.0253349
$955$	−2.99514	−0.0969206
$956$	−19.4453	−0.628906
$957$	31.0337	1.00318
$958$	1.26175	0.0407652
$959$	22.8843	0.738973
$960$	5.04890	0.162953
$961$	60.2136	1.94238
$962$	19.1545	0.617567
$963$	1.39766	0.0450389
$964$	−17.1665	−0.552895
$965$	0.915268	0.0294635
$966$	−5.90972	−0.190142
$967$	−26.9400	−0.866333	−0.433167	−	0.901314i	$-0.642604\pi$
$967$	−26.9400	−0.866333	−0.433167	+	0.901314i	$0.642604\pi$
$968$	−11.0170	−0.354099
$969$	11.7936	0.378866
$970$	2.35111	0.0754897
$971$	19.2829	0.618818	0.309409	−	0.950929i	$-0.399869\pi$
$971$	19.2829	0.618818	0.309409	+	0.950929i	$0.399869\pi$
$972$	8.04088	0.257911
$973$	−27.7018	−0.888080
$974$	−6.27131	−0.200946
$975$	42.3374	1.35588
$976$	−28.6600	−0.917383
$977$	−40.2525	−1.28779	−0.643896	−	0.765113i	$-0.722683\pi$
$977$	−40.2525	−1.28779	−0.643896	+	0.765113i	$0.722683\pi$
$978$	−1.69705	−0.0542656
$979$	2.38065	0.0760858
$980$	5.73188	0.183098
$981$	−2.28851	−0.0730665
$982$	−8.86437	−0.282874
$983$	27.1527	0.866037	0.433019	−	0.901385i	$-0.357448\pi$
$983$	27.1527	0.866037	0.433019	+	0.901385i	$0.357448\pi$
$984$	−6.88182	−0.219385
$985$	7.96291	0.253720
$986$	3.93542	0.125329
$987$	−1.36448	−0.0434319
$988$	78.7069	2.50400
$989$	−45.5513	−1.44845
$990$	0.193903	0.00616265
$991$	11.2931	0.358737	0.179369	−	0.983782i	$-0.442595\pi$
$991$	11.2931	0.358737	0.179369	+	0.983782i	$0.442595\pi$
$992$	−39.2641	−1.24664
$993$	10.5055	0.333383
$994$	−1.01057	−0.0320533
$995$	3.52290	0.111684
$996$	21.5494	0.682819
$997$	−18.5951	−0.588912	−0.294456	−	0.955665i	$-0.595138\pi$
$997$	−18.5951	−0.588912	−0.294456	+	0.955665i	$0.595138\pi$
$998$	1.95997	0.0620417
$999$	−48.2317	−1.52598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.9	✓	16
3.2	odd	2		9027.2.a.n.1.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.9	✓	16	1.1	even	1	trivial
9027.2.a.n.1.8		16	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)

\(f(q)\)	\(=\)	\(q-0.377947 q^{2} -1.60628 q^{3} -1.85716 q^{4} +0.658559 q^{5} +0.607088 q^{6} -1.52100 q^{7} +1.45780 q^{8} -0.419863 q^{9} +O(q^{10})\)	\(q-0.377947 q^{2} -1.60628 q^{3} -1.85716 q^{4} +0.658559 q^{5} +0.607088 q^{6} -1.52100 q^{7} +1.45780 q^{8} -0.419863 q^{9} -0.248900 q^{10} +1.85546 q^{11} +2.98311 q^{12} +5.77216 q^{13} +0.574857 q^{14} -1.05783 q^{15} +3.16334 q^{16} +1.00000 q^{17} +0.158686 q^{18} -7.34219 q^{19} -1.22305 q^{20} +2.44315 q^{21} -0.701265 q^{22} +6.40008 q^{23} -2.34163 q^{24} -4.56630 q^{25} -2.18157 q^{26} +5.49326 q^{27} +2.82474 q^{28} -10.4126 q^{29} +0.399803 q^{30} +9.55058 q^{31} -4.11117 q^{32} -2.98039 q^{33} -0.377947 q^{34} -1.00167 q^{35} +0.779752 q^{36} -8.78017 q^{37} +2.77496 q^{38} -9.27171 q^{39} +0.960046 q^{40} +2.93890 q^{41} -0.923381 q^{42} -7.11730 q^{43} -3.44588 q^{44} -0.276505 q^{45} -2.41889 q^{46} -0.558492 q^{47} -5.08122 q^{48} -4.68656 q^{49} +1.72582 q^{50} -1.60628 q^{51} -10.7198 q^{52} -4.93123 q^{53} -2.07616 q^{54} +1.22193 q^{55} -2.21731 q^{56} +11.7936 q^{57} +3.93542 q^{58} +1.00000 q^{59} +1.96456 q^{60} -9.06003 q^{61} -3.60961 q^{62} +0.638612 q^{63} -4.77288 q^{64} +3.80131 q^{65} +1.12643 q^{66} +8.93361 q^{67} -1.85716 q^{68} -10.2803 q^{69} +0.378577 q^{70} -1.75795 q^{71} -0.612076 q^{72} -3.73919 q^{73} +3.31843 q^{74} +7.33476 q^{75} +13.6356 q^{76} -2.82216 q^{77} +3.50421 q^{78} -14.2159 q^{79} +2.08325 q^{80} -7.56413 q^{81} -1.11075 q^{82} +7.22380 q^{83} -4.53732 q^{84} +0.658559 q^{85} +2.68996 q^{86} +16.7256 q^{87} +2.70489 q^{88} +1.28305 q^{89} +0.104504 q^{90} -8.77947 q^{91} -11.8860 q^{92} -15.3409 q^{93} +0.211080 q^{94} -4.83526 q^{95} +6.60370 q^{96} -9.44602 q^{97} +1.77127 q^{98} -0.779040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9} + 12 q^{10} - 7 q^{11} - 4 q^{12} - 16 q^{13} + 11 q^{14} + 7 q^{15} + 22 q^{16} + 16 q^{17} + 11 q^{18} + q^{19} - 43 q^{20} - 8 q^{21} - 18 q^{22} - 8 q^{23} - 39 q^{24} + 23 q^{25} - 49 q^{26} - 7 q^{27} - 15 q^{28} - 39 q^{29} + q^{30} - 3 q^{31} - 15 q^{33} - 6 q^{34} + 9 q^{35} - 17 q^{36} - 28 q^{37} - 27 q^{38} - 4 q^{39} + 26 q^{40} - 31 q^{41} - 45 q^{42} + 5 q^{43} - 19 q^{44} - 79 q^{45} - 39 q^{46} - 47 q^{47} - 31 q^{48} + 35 q^{49} - 13 q^{50} - 7 q^{51} + 9 q^{52} - 36 q^{53} + 9 q^{54} + 32 q^{55} + 3 q^{56} + 6 q^{57} + 22 q^{58} + 16 q^{59} + 6 q^{60} - 22 q^{61} + q^{62} - 19 q^{63} + 32 q^{64} - 19 q^{65} + 48 q^{66} + 4 q^{67} + 14 q^{68} + 14 q^{69} - 11 q^{70} - 5 q^{71} + 40 q^{72} - 35 q^{73} + 31 q^{74} - 12 q^{75} + q^{76} - 79 q^{77} + 31 q^{78} - 48 q^{79} - 127 q^{80} - 28 q^{81} - 7 q^{82} - 42 q^{83} + 28 q^{84} - 21 q^{85} + 58 q^{86} - 16 q^{87} - 2 q^{88} + 20 q^{89} - 14 q^{90} + 49 q^{91} - 21 q^{92} - 55 q^{93} - 22 q^{95} + 24 q^{96} - 2 q^{97} - 78 q^{98} - 35 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 7 * q^3 + 14 * q^4 - 21 * q^5 - 5 * q^6 - 11 * q^7 - 12 * q^8 + 17 * q^9 + 12 * q^10 - 7 * q^11 - 4 * q^12 - 16 * q^13 + 11 * q^14 + 7 * q^15 + 22 * q^16 + 16 * q^17 + 11 * q^18 + q^19 - 43 * q^20 - 8 * q^21 - 18 * q^22 - 8 * q^23 - 39 * q^24 + 23 * q^25 - 49 * q^26 - 7 * q^27 - 15 * q^28 - 39 * q^29 + q^30 - 3 * q^31 - 15 * q^33 - 6 * q^34 + 9 * q^35 - 17 * q^36 - 28 * q^37 - 27 * q^38 - 4 * q^39 + 26 * q^40 - 31 * q^41 - 45 * q^42 + 5 * q^43 - 19 * q^44 - 79 * q^45 - 39 * q^46 - 47 * q^47 - 31 * q^48 + 35 * q^49 - 13 * q^50 - 7 * q^51 + 9 * q^52 - 36 * q^53 + 9 * q^54 + 32 * q^55 + 3 * q^56 + 6 * q^57 + 22 * q^58 + 16 * q^59 + 6 * q^60 - 22 * q^61 + q^62 - 19 * q^63 + 32 * q^64 - 19 * q^65 + 48 * q^66 + 4 * q^67 + 14 * q^68 + 14 * q^69 - 11 * q^70 - 5 * q^71 + 40 * q^72 - 35 * q^73 + 31 * q^74 - 12 * q^75 + q^76 - 79 * q^77 + 31 * q^78 - 48 * q^79 - 127 * q^80 - 28 * q^81 - 7 * q^82 - 42 * q^83 + 28 * q^84 - 21 * q^85 + 58 * q^86 - 16 * q^87 - 2 * q^88 + 20 * q^89 - 14 * q^90 + 49 * q^91 - 21 * q^92 - 55 * q^93 - 22 * q^95 + 24 * q^96 - 2 * q^97 - 78 * q^98 - 35 * q^99

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