LMFDB - Embedded newform 1003.2.a.h.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:	$1$
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			1.1
Root			$2.74400$ 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)

$f(q)$	$=$	$q-2.74400 q^{2} -0.794276 q^{3} +5.52956 q^{4} -3.63969 q^{5} +2.17950 q^{6} -4.59580 q^{7} -9.68512 q^{8} -2.36913 q^{9} +O(q^{10})$	\(q-2.74400 q^{2} -0.794276 q^{3} +5.52956 q^{4} -3.63969 q^{5} +2.17950 q^{6} -4.59580 q^{7} -9.68512 q^{8} -2.36913 q^{9} +9.98732 q^{10} +3.75984 q^{11} -4.39200 q^{12} +5.08816 q^{13} +12.6109 q^{14} +2.89092 q^{15} +15.5169 q^{16} +1.00000 q^{17} +6.50089 q^{18} +6.51215 q^{19} -20.1259 q^{20} +3.65033 q^{21} -10.3170 q^{22} +1.37101 q^{23} +7.69266 q^{24} +8.24734 q^{25} -13.9619 q^{26} +4.26457 q^{27} -25.4128 q^{28} -2.06074 q^{29} -7.93269 q^{30} -3.21776 q^{31} -23.2082 q^{32} -2.98635 q^{33} -2.74400 q^{34} +16.7273 q^{35} -13.1002 q^{36} +2.18765 q^{37} -17.8694 q^{38} -4.04140 q^{39} +35.2508 q^{40} -5.62856 q^{41} -10.0165 q^{42} -8.67901 q^{43} +20.7903 q^{44} +8.62288 q^{45} -3.76205 q^{46} -7.91941 q^{47} -12.3247 q^{48} +14.1214 q^{49} -22.6307 q^{50} -0.794276 q^{51} +28.1353 q^{52} +2.24930 q^{53} -11.7020 q^{54} -13.6847 q^{55} +44.5109 q^{56} -5.17244 q^{57} +5.65468 q^{58} +1.00000 q^{59} +15.9855 q^{60} +4.17311 q^{61} +8.82954 q^{62} +10.8880 q^{63} +32.6496 q^{64} -18.5193 q^{65} +8.19456 q^{66} +7.70359 q^{67} +5.52956 q^{68} -1.08896 q^{69} -45.8998 q^{70} -7.33536 q^{71} +22.9453 q^{72} -12.9414 q^{73} -6.00291 q^{74} -6.55066 q^{75} +36.0093 q^{76} -17.2795 q^{77} +11.0896 q^{78} +0.0406167 q^{79} -56.4767 q^{80} +3.72013 q^{81} +15.4448 q^{82} +1.31290 q^{83} +20.1847 q^{84} -3.63969 q^{85} +23.8152 q^{86} +1.63680 q^{87} -36.4145 q^{88} +5.21909 q^{89} -23.6612 q^{90} -23.3842 q^{91} +7.58107 q^{92} +2.55579 q^{93} +21.7309 q^{94} -23.7022 q^{95} +18.4337 q^{96} -4.44838 q^{97} -38.7491 q^{98} -8.90754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.74400	−1.94030	−0.970152	−	0.242498i	$-0.922033\pi$
$2$	−2.74400	−1.94030	−0.970152	+	0.242498i	$0.922033\pi$
$3$	−0.794276	−0.458575	−0.229288	−	0.973359i	$-0.573640\pi$
$3$	−0.794276	−0.458575	−0.229288	+	0.973359i	$0.573640\pi$
$4$	5.52956	2.76478
$5$	−3.63969	−1.62772	−0.813859	−	0.581062i	$-0.802637\pi$
$5$	−3.63969	−1.62772	−0.813859	+	0.581062i	$0.802637\pi$
$6$	2.17950	0.889776
$7$	−4.59580	−1.73705	−0.868525	−	0.495646i	$-0.834931\pi$
$7$	−4.59580	−1.73705	−0.868525	+	0.495646i	$0.834931\pi$
$8$	−9.68512	−3.42421
$9$	−2.36913	−0.789709
$10$	9.98732	3.15827
$11$	3.75984	1.13364	0.566818	−	0.823843i	$-0.308174\pi$
$11$	3.75984	1.13364	0.566818	+	0.823843i	$0.308174\pi$
$12$	−4.39200	−1.26786
$13$	5.08816	1.41120	0.705601	−	0.708609i	$-0.250677\pi$
$13$	5.08816	1.41120	0.705601	+	0.708609i	$0.250677\pi$
$14$	12.6109	3.37040
$15$	2.89092	0.746432
$16$	15.5169	3.87922
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	6.50089	1.53227
$19$	6.51215	1.49399	0.746995	−	0.664830i	$-0.231496\pi$
$19$	6.51215	1.49399	0.746995	+	0.664830i	$0.231496\pi$
$20$	−20.1259	−4.50028
$21$	3.65033	0.796568
$22$	−10.3170	−2.19960
$23$	1.37101	0.285875	0.142938	−	0.989732i	$-0.454345\pi$
$23$	1.37101	0.285875	0.142938	+	0.989732i	$0.454345\pi$
$24$	7.69266	1.57026
$25$	8.24734	1.64947
$26$	−13.9619	−2.73816
$27$	4.26457	0.820716
$28$	−25.4128	−4.80256
$29$	−2.06074	−0.382670	−0.191335	−	0.981525i	$-0.561282\pi$
$29$	−2.06074	−0.382670	−0.191335	+	0.981525i	$0.561282\pi$
$30$	−7.93269	−1.44830
$31$	−3.21776	−0.577926	−0.288963	−	0.957340i	$-0.593311\pi$
$31$	−3.21776	−0.577926	−0.288963	+	0.957340i	$0.593311\pi$
$32$	−23.2082	−4.10267
$33$	−2.98635	−0.519857
$34$	−2.74400	−0.470593
$35$	16.7273	2.82743
$36$	−13.1002	−2.18337
$37$	2.18765	0.359647	0.179823	−	0.983699i	$-0.442447\pi$
$37$	2.18765	0.359647	0.179823	+	0.983699i	$0.442447\pi$
$38$	−17.8694	−2.89879
$39$	−4.04140	−0.647143
$40$	35.2508	5.57365
$41$	−5.62856	−0.879034	−0.439517	−	0.898234i	$-0.644850\pi$
$41$	−5.62856	−0.879034	−0.439517	+	0.898234i	$0.644850\pi$
$42$	−10.0165	−1.54558
$43$	−8.67901	−1.32354	−0.661768	−	0.749709i	$-0.730194\pi$
$43$	−8.67901	−1.32354	−0.661768	+	0.749709i	$0.730194\pi$
$44$	20.7903	3.13425
$45$	8.62288	1.28542
$46$	−3.76205	−0.554684
$47$	−7.91941	−1.15516	−0.577582	−	0.816332i	$-0.696004\pi$
$47$	−7.91941	−1.15516	−0.577582	+	0.816332i	$0.696004\pi$
$48$	−12.3247	−1.77892
$49$	14.1214	2.01734
$50$	−22.6307	−3.20047
$51$	−0.794276	−0.111221
$52$	28.1353	3.90166
$53$	2.24930	0.308966	0.154483	−	0.987995i	$-0.450629\pi$
$53$	2.24930	0.308966	0.154483	+	0.987995i	$0.450629\pi$
$54$	−11.7020	−1.59244
$55$	−13.6847	−1.84524
$56$	44.5109	5.94802
$57$	−5.17244	−0.685107
$58$	5.65468	0.742496
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	15.9855	2.06372
$61$	4.17311	0.534313	0.267156	−	0.963653i	$-0.413916\pi$
$61$	4.17311	0.534313	0.267156	+	0.963653i	$0.413916\pi$
$62$	8.82954	1.12135
$63$	10.8880	1.37176
$64$	32.6496	4.08120
$65$	−18.5193	−2.29704
$66$	8.19456	1.00868
$67$	7.70359	0.941144	0.470572	−	0.882362i	$-0.344048\pi$
$67$	7.70359	0.941144	0.470572	+	0.882362i	$0.344048\pi$
$68$	5.52956	0.670557
$69$	−1.08896	−0.131095
$70$	−45.8998	−5.48607
$71$	−7.33536	−0.870547	−0.435273	−	0.900298i	$-0.643348\pi$
$71$	−7.33536	−0.870547	−0.435273	+	0.900298i	$0.643348\pi$
$72$	22.9453	2.70413
$73$	−12.9414	−1.51467	−0.757337	−	0.653025i	$-0.773500\pi$
$73$	−12.9414	−1.51467	−0.757337	+	0.653025i	$0.773500\pi$
$74$	−6.00291	−0.697824
$75$	−6.55066	−0.756406
$76$	36.0093	4.13055
$77$	−17.2795	−1.96918
$78$	11.0896	1.25565
$79$	0.0406167	0.00456974	0.00228487	−	0.999997i	$-0.499273\pi$
$79$	0.0406167	0.00456974	0.00228487	+	0.999997i	$0.499273\pi$
$80$	−56.4767	−6.31429
$81$	3.72013	0.413348
$82$	15.4448	1.70559
$83$	1.31290	0.144109	0.0720547	−	0.997401i	$-0.477044\pi$
$83$	1.31290	0.144109	0.0720547	+	0.997401i	$0.477044\pi$
$84$	20.1847	2.20234
$85$	−3.63969	−0.394780
$86$	23.8152	2.56806
$87$	1.63680	0.175483
$88$	−36.4145	−3.88180
$89$	5.21909	0.553222	0.276611	−	0.960982i	$-0.410789\pi$
$89$	5.21909	0.553222	0.276611	+	0.960982i	$0.410789\pi$
$90$	−23.6612	−2.49411
$91$	−23.3842	−2.45133
$92$	7.58107	0.790381
$93$	2.55579	0.265023
$94$	21.7309	2.24137
$95$	−23.7022	−2.43179
$96$	18.4337	1.88138
$97$	−4.44838	−0.451665	−0.225832	−	0.974166i	$-0.572510\pi$
$97$	−4.44838	−0.451665	−0.225832	+	0.974166i	$0.572510\pi$
$98$	−38.7491	−3.91426
$99$	−8.90754	−0.895242
$100$	45.6041	4.56041
$101$	11.6496	1.15918	0.579589	−	0.814909i	$-0.303213\pi$
$101$	11.6496	1.15918	0.579589	+	0.814909i	$0.303213\pi$
$102$	2.17950	0.215802
$103$	−10.0433	−0.989596	−0.494798	−	0.869008i	$-0.664758\pi$
$103$	−10.0433	−0.989596	−0.494798	+	0.869008i	$0.664758\pi$
$104$	−49.2795	−4.83225
$105$	−13.2861	−1.29659
$106$	−6.17210	−0.599487
$107$	17.0440	1.64771	0.823855	−	0.566801i	$-0.191819\pi$
$107$	17.0440	1.64771	0.823855	+	0.566801i	$0.191819\pi$
$108$	23.5812	2.26910
$109$	0.654870	0.0627252	0.0313626	−	0.999508i	$-0.490015\pi$
$109$	0.654870	0.0627252	0.0313626	+	0.999508i	$0.490015\pi$
$110$	37.5508	3.58033
$111$	−1.73760	−0.164925
$112$	−71.3126	−6.73841
$113$	−14.9665	−1.40793	−0.703963	−	0.710237i	$-0.748588\pi$
$113$	−14.9665	−1.40793	−0.703963	+	0.710237i	$0.748588\pi$
$114$	14.1932	1.32932
$115$	−4.99005	−0.465324
$116$	−11.3950	−1.05800
$117$	−12.0545	−1.11444
$118$	−2.74400	−0.252606
$119$	−4.59580	−0.421296
$120$	−27.9989	−2.55594
$121$	3.13642	0.285129
$122$	−11.4510	−1.03673
$123$	4.47063	0.403103
$124$	−17.7928	−1.59784
$125$	−11.8193	−1.05715
$126$	−29.8768	−2.66164
$127$	−0.670167	−0.0594677	−0.0297338	−	0.999558i	$-0.509466\pi$
$127$	−0.670167	−0.0594677	−0.0297338	+	0.999558i	$0.509466\pi$
$128$	−43.1742	−3.81609
$129$	6.89353	0.606941
$130$	50.8171	4.45695
$131$	5.67180	0.495547	0.247774	−	0.968818i	$-0.420301\pi$
$131$	5.67180	0.495547	0.247774	+	0.968818i	$0.420301\pi$
$132$	−16.5132	−1.43729
$133$	−29.9285	−2.59513
$134$	−21.1387	−1.82610
$135$	−15.5217	−1.33590
$136$	−9.68512	−0.830492
$137$	−4.02015	−0.343465	−0.171732	−	0.985144i	$-0.554936\pi$
$137$	−4.02015	−0.343465	−0.171732	+	0.985144i	$0.554936\pi$
$138$	2.98811	0.254365
$139$	12.5933	1.06815	0.534076	−	0.845437i	$-0.320660\pi$
$139$	12.5933	1.06815	0.534076	+	0.845437i	$0.320660\pi$
$140$	92.4945	7.81721
$141$	6.29020	0.529730
$142$	20.1282	1.68913
$143$	19.1307	1.59979
$144$	−36.7615	−3.06346
$145$	7.50046	0.622879
$146$	35.5112	2.93893
$147$	−11.2163	−0.925103
$148$	12.0967	0.994344
$149$	−7.58311	−0.621232	−0.310616	−	0.950535i	$-0.600535\pi$
$149$	−7.58311	−0.621232	−0.310616	+	0.950535i	$0.600535\pi$
$150$	17.9750	1.46766
$151$	−2.29757	−0.186974	−0.0934870	−	0.995621i	$-0.529801\pi$
$151$	−2.29757	−0.186974	−0.0934870	+	0.995621i	$0.529801\pi$
$152$	−63.0710	−5.11573
$153$	−2.36913	−0.191532
$154$	47.4150	3.82081
$155$	11.7116	0.940701
$156$	−22.3472	−1.78921
$157$	17.3792	1.38701	0.693505	−	0.720452i	$-0.256065\pi$
$157$	17.3792	1.38701	0.693505	+	0.720452i	$0.256065\pi$
$158$	−0.111452	−0.00886668
$159$	−1.78657	−0.141684
$160$	84.4706	6.67799
$161$	−6.30088	−0.496579
$162$	−10.2081	−0.802021
$163$	13.9017	1.08887	0.544435	−	0.838803i	$-0.316744\pi$
$163$	13.9017	1.08887	0.544435	+	0.838803i	$0.316744\pi$
$164$	−31.1235	−2.43033
$165$	10.8694	0.846181
$166$	−3.60260	−0.279616
$167$	15.6535	1.21131	0.605654	−	0.795728i	$-0.292912\pi$
$167$	15.6535	1.21131	0.605654	+	0.795728i	$0.292912\pi$
$168$	−35.3539	−2.72762
$169$	12.8894	0.991491
$170$	9.98732	0.765993
$171$	−15.4281	−1.17982
$172$	−47.9911	−3.65929
$173$	−7.84378	−0.596352	−0.298176	−	0.954511i	$-0.596378\pi$
$173$	−7.84378	−0.596352	−0.298176	+	0.954511i	$0.596378\pi$
$174$	−4.49138	−0.340491
$175$	−37.9031	−2.86521
$176$	58.3411	4.39763
$177$	−0.794276	−0.0597014
$178$	−14.3212	−1.07342
$179$	3.59444	0.268661	0.134331	−	0.990937i	$-0.457112\pi$
$179$	3.59444	0.268661	0.134331	+	0.990937i	$0.457112\pi$
$180$	47.6807	3.55391
$181$	−15.1651	−1.12721	−0.563607	−	0.826043i	$-0.690587\pi$
$181$	−15.1651	−1.12721	−0.563607	+	0.826043i	$0.690587\pi$
$182$	64.1663	4.75632
$183$	−3.31460	−0.245023
$184$	−13.2784	−0.978896
$185$	−7.96236	−0.585404
$186$	−7.01309	−0.514225
$187$	3.75984	0.274947
$188$	−43.7908	−3.19378
$189$	−19.5991	−1.42563
$190$	65.0389	4.71842
$191$	−3.79561	−0.274640	−0.137320	−	0.990527i	$-0.543849\pi$
$191$	−3.79561	−0.274640	−0.137320	+	0.990527i	$0.543849\pi$
$192$	−25.9328	−1.87154
$193$	−3.04928	−0.219492	−0.109746	−	0.993960i	$-0.535004\pi$
$193$	−3.04928	−0.219492	−0.109746	+	0.993960i	$0.535004\pi$
$194$	12.2064	0.876367
$195$	14.7095	1.05337
$196$	78.0850	5.57750
$197$	−22.8829	−1.63034	−0.815171	−	0.579221i	$-0.803357\pi$
$197$	−22.8829	−1.63034	−0.815171	+	0.579221i	$0.803357\pi$
$198$	24.4423	1.73704
$199$	−16.7857	−1.18991	−0.594955	−	0.803759i	$-0.702830\pi$
$199$	−16.7857	−1.18991	−0.594955	+	0.803759i	$0.702830\pi$
$200$	−79.8765	−5.64812
$201$	−6.11878	−0.431585
$202$	−31.9665	−2.24916
$203$	9.47076	0.664717
$204$	−4.39200	−0.307501
$205$	20.4862	1.43082
$206$	27.5589	1.92012
$207$	−3.24809	−0.225758
$208$	78.9525	5.47437
$209$	24.4847	1.69364
$210$	36.4571	2.51578
$211$	−2.91727	−0.200833	−0.100417	−	0.994945i	$-0.532018\pi$
$211$	−2.91727	−0.200833	−0.100417	+	0.994945i	$0.532018\pi$
$212$	12.4377	0.854222
$213$	5.82630	0.399211
$214$	−46.7689	−3.19706
$215$	31.5889	2.15434
$216$	−41.3029	−2.81030
$217$	14.7882	1.00389
$218$	−1.79697	−0.121706
$219$	10.2790	0.694592
$220$	−75.6701	−5.10168
$221$	5.08816	0.342267
$222$	4.76797	0.320005
$223$	−5.74649	−0.384814	−0.192407	−	0.981315i	$-0.561629\pi$
$223$	−5.74649	−0.384814	−0.192407	+	0.981315i	$0.561629\pi$
$224$	106.660	7.12654
$225$	−19.5390	−1.30260
$226$	41.0680	2.73180
$227$	−19.2588	−1.27825	−0.639126	−	0.769102i	$-0.720704\pi$
$227$	−19.2588	−1.27825	−0.639126	+	0.769102i	$0.720704\pi$
$228$	−28.6013	−1.89417
$229$	−20.1519	−1.33167	−0.665836	−	0.746098i	$-0.731925\pi$
$229$	−20.1519	−1.33167	−0.665836	+	0.746098i	$0.731925\pi$
$230$	13.6927	0.902870
$231$	13.7247	0.903018
$232$	19.9585	1.31034
$233$	24.7881	1.62392	0.811962	−	0.583710i	$-0.198399\pi$
$233$	24.7881	1.62392	0.811962	+	0.583710i	$0.198399\pi$
$234$	33.0776	2.16235
$235$	28.8242	1.88028
$236$	5.52956	0.359944
$237$	−0.0322609	−0.00209557
$238$	12.6109	0.817443
$239$	2.91263	0.188402	0.0942011	−	0.995553i	$-0.469970\pi$
$239$	2.91263	0.188402	0.0942011	+	0.995553i	$0.469970\pi$
$240$	44.8581	2.89558
$241$	−25.2490	−1.62643	−0.813214	−	0.581964i	$-0.802284\pi$
$241$	−25.2490	−1.62643	−0.813214	+	0.581964i	$0.802284\pi$
$242$	−8.60635	−0.553237
$243$	−15.7485	−1.01027
$244$	23.0755	1.47726
$245$	−51.3975	−3.28366
$246$	−12.2674	−0.782143
$247$	33.1349	2.10832
$248$	31.1644	1.97894
$249$	−1.04280	−0.0660851
$250$	32.4322	2.05119
$251$	−6.16174	−0.388925	−0.194463	−	0.980910i	$-0.562296\pi$
$251$	−6.16174	−0.388925	−0.194463	+	0.980910i	$0.562296\pi$
$252$	60.2060	3.79262
$253$	5.15478	0.324078
$254$	1.83894	0.115385
$255$	2.89092	0.181036
$256$	53.1709	3.32318
$257$	11.6853	0.728911	0.364455	−	0.931221i	$-0.381255\pi$
$257$	11.6853	0.728911	0.364455	+	0.931221i	$0.381255\pi$
$258$	−18.9159	−1.17765
$259$	−10.0540	−0.624725
$260$	−102.404	−6.35081
$261$	4.88216	0.302198
$262$	−15.5634	−0.961512
$263$	−16.7844	−1.03497	−0.517484	−	0.855693i	$-0.673131\pi$
$263$	−16.7844	−1.03497	−0.517484	+	0.855693i	$0.673131\pi$
$264$	28.9232	1.78010
$265$	−8.18677	−0.502909
$266$	82.1240	5.03535
$267$	−4.14540	−0.253694
$268$	42.5975	2.60205
$269$	−0.175066	−0.0106739	−0.00533697	−	0.999986i	$-0.501699\pi$
$269$	−0.175066	−0.0106739	−0.00533697	+	0.999986i	$0.501699\pi$
$270$	42.5916	2.59204
$271$	−23.7321	−1.44162	−0.720811	−	0.693132i	$-0.756230\pi$
$271$	−23.7321	−1.44162	−0.720811	+	0.693132i	$0.756230\pi$
$272$	15.5169	0.940850
$273$	18.5735	1.12412
$274$	11.0313	0.666426
$275$	31.0087	1.86990
$276$	−6.02146	−0.362449
$277$	−8.35902	−0.502245	−0.251122	−	0.967955i	$-0.580800\pi$
$277$	−8.35902	−0.502245	−0.251122	+	0.967955i	$0.580800\pi$
$278$	−34.5561	−2.07254
$279$	7.62327	0.456393
$280$	−162.006	−9.68170
$281$	−30.3534	−1.81073	−0.905367	−	0.424629i	$-0.860404\pi$
$281$	−30.3534	−1.81073	−0.905367	+	0.424629i	$0.860404\pi$
$282$	−17.2603	−1.02784
$283$	−5.98287	−0.355645	−0.177822	−	0.984063i	$-0.556905\pi$
$283$	−5.98287	−0.355645	−0.177822	+	0.984063i	$0.556905\pi$
$284$	−40.5613	−2.40687
$285$	18.8261	1.11516
$286$	−52.4947	−3.10408
$287$	25.8678	1.52693
$288$	54.9831	3.23991
$289$	1.00000	0.0588235
$290$	−20.5813	−1.20858
$291$	3.53324	0.207122
$292$	−71.5601	−4.18774
$293$	−18.5785	−1.08537	−0.542684	−	0.839937i	$-0.682592\pi$
$293$	−18.5785	−1.08537	−0.542684	+	0.839937i	$0.682592\pi$
$294$	30.7775	1.79498
$295$	−3.63969	−0.211911
$296$	−21.1876	−1.23151
$297$	16.0341	0.930393
$298$	20.8081	1.20538
$299$	6.97591	0.403427
$300$	−36.2223	−2.09129
$301$	39.8870	2.29905
$302$	6.30455	0.362786
$303$	−9.25299	−0.531571
$304$	101.048	5.79552
$305$	−15.1888	−0.869711
$306$	6.50089	0.371631
$307$	18.0939	1.03267	0.516337	−	0.856386i	$-0.327295\pi$
$307$	18.0939	1.03267	0.516337	+	0.856386i	$0.327295\pi$
$308$	−95.5480	−5.44435
$309$	7.97716	0.453805
$310$	−32.1368	−1.82525
$311$	−17.8656	−1.01307	−0.506534	−	0.862220i	$-0.669073\pi$
$311$	−17.8656	−1.01307	−0.506534	+	0.862220i	$0.669073\pi$
$312$	39.1415	2.21595
$313$	−9.16054	−0.517784	−0.258892	−	0.965906i	$-0.583357\pi$
$313$	−9.16054	−0.517784	−0.258892	+	0.965906i	$0.583357\pi$
$314$	−47.6886	−2.69122
$315$	−39.6291	−2.23284
$316$	0.224592	0.0126343
$317$	−0.746909	−0.0419506	−0.0209753	−	0.999780i	$-0.506677\pi$
$317$	−0.746909	−0.0419506	−0.0209753	+	0.999780i	$0.506677\pi$
$318$	4.90235	0.274910
$319$	−7.74807	−0.433808
$320$	−118.834	−6.64304
$321$	−13.5377	−0.755599
$322$	17.2896	0.963514
$323$	6.51215	0.362346
$324$	20.5707	1.14282
$325$	41.9638	2.32773
$326$	−38.1465	−2.11274
$327$	−0.520147	−0.0287642
$328$	54.5133	3.01000
$329$	36.3960	2.00658
$330$	−29.8257	−1.64185
$331$	−32.4381	−1.78296	−0.891479	−	0.453062i	$-0.850332\pi$
$331$	−32.4381	−1.78296	−0.891479	+	0.453062i	$0.850332\pi$
$332$	7.25976	0.398431
$333$	−5.18281	−0.284016
$334$	−42.9534	−2.35031
$335$	−28.0387	−1.53192
$336$	56.6419	3.09007
$337$	3.26916	0.178082	0.0890412	−	0.996028i	$-0.471620\pi$
$337$	3.26916	0.178082	0.0890412	+	0.996028i	$0.471620\pi$
$338$	−35.3685	−1.92379
$339$	11.8875	0.645640
$340$	−20.1259	−1.09148
$341$	−12.0983	−0.655158
$342$	42.3348	2.28920
$343$	−32.7285	−1.76717
$344$	84.0572	4.53206
$345$	3.96347	0.213386
$346$	21.5234	1.15710
$347$	27.8949	1.49748	0.748739	−	0.662865i	$-0.230660\pi$
$347$	27.8949	1.49748	0.748739	+	0.662865i	$0.230660\pi$
$348$	9.05077	0.485172
$349$	−9.50724	−0.508911	−0.254455	−	0.967085i	$-0.581896\pi$
$349$	−9.50724	−0.508911	−0.254455	+	0.967085i	$0.581896\pi$
$350$	104.006	5.55937
$351$	21.6988	1.15820
$352$	−87.2591	−4.65093
$353$	5.05151	0.268865	0.134432	−	0.990923i	$-0.457079\pi$
$353$	5.05151	0.268865	0.134432	+	0.990923i	$0.457079\pi$
$354$	2.17950	0.115839
$355$	26.6984	1.41701
$356$	28.8592	1.52954
$357$	3.65033	0.193196
$358$	−9.86317	−0.521285
$359$	34.3172	1.81119	0.905597	−	0.424140i	$-0.139423\pi$
$359$	34.3172	1.81119	0.905597	+	0.424140i	$0.139423\pi$
$360$	−83.5137	−4.40156
$361$	23.4081	1.23200
$362$	41.6131	2.18714
$363$	−2.49118	−0.130753
$364$	−129.304	−6.77738
$365$	47.1026	2.46546
$366$	9.09529	0.475418
$367$	−7.42075	−0.387360	−0.193680	−	0.981065i	$-0.562042\pi$
$367$	−7.42075	−0.387360	−0.193680	+	0.981065i	$0.562042\pi$
$368$	21.2738	1.10897
$369$	13.3348	0.694181
$370$	21.8487	1.13586
$371$	−10.3374	−0.536689
$372$	14.1324	0.732730
$373$	−14.6045	−0.756194	−0.378097	−	0.925766i	$-0.623421\pi$
$373$	−14.6045	−0.756194	−0.378097	+	0.925766i	$0.623421\pi$
$374$	−10.3170	−0.533481
$375$	9.38779	0.484784
$376$	76.7005	3.95552
$377$	−10.4854	−0.540025
$378$	53.7800	2.76615
$379$	−2.32251	−0.119299	−0.0596497	−	0.998219i	$-0.518998\pi$
$379$	−2.32251	−0.119299	−0.0596497	+	0.998219i	$0.518998\pi$
$380$	−131.063	−6.72337
$381$	0.532297	0.0272704
$382$	10.4152	0.532886
$383$	37.0264	1.89196	0.945980	−	0.324225i	$-0.105103\pi$
$383$	37.0264	1.89196	0.945980	+	0.324225i	$0.105103\pi$
$384$	34.2922	1.74997
$385$	62.8920	3.20527
$386$	8.36724	0.425881
$387$	20.5617	1.04521
$388$	−24.5976	−1.24875
$389$	18.4814	0.937044	0.468522	−	0.883452i	$-0.344787\pi$
$389$	18.4814	0.937044	0.468522	+	0.883452i	$0.344787\pi$
$390$	−40.3628	−2.04385
$391$	1.37101	0.0693349
$392$	−136.767	−6.90780
$393$	−4.50497	−0.227246
$394$	62.7909	3.16336
$395$	−0.147832	−0.00743825
$396$	−49.2548	−2.47515
$397$	−9.06764	−0.455092	−0.227546	−	0.973767i	$-0.573070\pi$
$397$	−9.06764	−0.455092	−0.227546	+	0.973767i	$0.573070\pi$
$398$	46.0601	2.30879
$399$	23.7715	1.19006
$400$	127.973	6.39866
$401$	−11.9147	−0.594992	−0.297496	−	0.954723i	$-0.596151\pi$
$401$	−11.9147	−0.594992	−0.297496	+	0.954723i	$0.596151\pi$
$402$	16.7900	0.837407
$403$	−16.3725	−0.815571
$404$	64.4171	3.20487
$405$	−13.5401	−0.672815
$406$	−25.9878	−1.28975
$407$	8.22521	0.407709
$408$	7.69266	0.380843
$409$	−15.7199	−0.777299	−0.388650	−	0.921386i	$-0.627058\pi$
$409$	−15.7199	−0.777299	−0.388650	+	0.921386i	$0.627058\pi$
$410$	−56.2143	−2.77623
$411$	3.19311	0.157504
$412$	−55.5350	−2.73602
$413$	−4.59580	−0.226145
$414$	8.91278	0.438039
$415$	−4.77855	−0.234570
$416$	−118.087	−5.78969
$417$	−10.0026	−0.489828
$418$	−67.1860	−3.28617
$419$	−18.3537	−0.896637	−0.448319	−	0.893874i	$-0.647977\pi$
$419$	−18.3537	−0.896637	−0.448319	+	0.893874i	$0.647977\pi$
$420$	−73.4662	−3.58478
$421$	−23.3263	−1.13686	−0.568428	−	0.822733i	$-0.692448\pi$
$421$	−23.3263	−1.13686	−0.568428	+	0.822733i	$0.692448\pi$
$422$	8.00500	0.389677
$423$	18.7621	0.912243
$424$	−21.7848	−1.05796
$425$	8.24734	0.400055
$426$	−15.9874	−0.774591
$427$	−19.1788	−0.928127
$428$	94.2460	4.55555
$429$	−15.1950	−0.733624
$430$	−86.6800	−4.18008
$431$	−4.48423	−0.215998	−0.107999	−	0.994151i	$-0.534444\pi$
$431$	−4.48423	−0.215998	−0.107999	+	0.994151i	$0.534444\pi$
$432$	66.1729	3.18374
$433$	−20.0668	−0.964349	−0.482175	−	0.876075i	$-0.660153\pi$
$433$	−20.0668	−0.964349	−0.482175	+	0.876075i	$0.660153\pi$
$434$	−40.5788	−1.94785
$435$	−5.95744	−0.285637
$436$	3.62114	0.173421
$437$	8.92821	0.427094
$438$	−28.2057	−1.34772
$439$	−5.04831	−0.240943	−0.120471	−	0.992717i	$-0.538441\pi$
$439$	−5.04831	−0.240943	−0.120471	+	0.992717i	$0.538441\pi$
$440$	132.538	6.31848
$441$	−33.4553	−1.59311
$442$	−13.9619	−0.664101
$443$	−34.1199	−1.62109	−0.810543	−	0.585679i	$-0.800828\pi$
$443$	−34.1199	−1.62109	−0.810543	+	0.585679i	$0.800828\pi$
$444$	−9.60814	−0.455982
$445$	−18.9959	−0.900490
$446$	15.7684	0.746655
$447$	6.02308	0.284882
$448$	−150.051	−7.08924
$449$	14.4887	0.683762	0.341881	−	0.939743i	$-0.388936\pi$
$449$	14.4887	0.683762	0.341881	+	0.939743i	$0.388936\pi$
$450$	53.6151	2.52744
$451$	−21.1625	−0.996504
$452$	−82.7579	−3.89260
$453$	1.82491	0.0857416
$454$	52.8462	2.48020
$455$	85.1111	3.99007
$456$	50.0957	2.34595
$457$	19.9190	0.931771	0.465886	−	0.884845i	$-0.345736\pi$
$457$	19.9190	0.931771	0.465886	+	0.884845i	$0.345736\pi$
$458$	55.2968	2.58385
$459$	4.26457	0.199053
$460$	−27.5927	−1.28652
$461$	−9.44722	−0.440001	−0.220000	−	0.975500i	$-0.570606\pi$
$461$	−9.44722	−0.440001	−0.220000	+	0.975500i	$0.570606\pi$
$462$	−37.6606	−1.75213
$463$	−0.651970	−0.0302996	−0.0151498	−	0.999885i	$-0.504823\pi$
$463$	−0.651970	−0.0302996	−0.0151498	+	0.999885i	$0.504823\pi$
$464$	−31.9763	−1.48446
$465$	−9.30227	−0.431383
$466$	−68.0187	−3.15091
$467$	12.9367	0.598638	0.299319	−	0.954153i	$-0.403241\pi$
$467$	12.9367	0.598638	0.299319	+	0.954153i	$0.403241\pi$
$468$	−66.6560	−3.08118
$469$	−35.4042	−1.63481
$470$	−79.0937	−3.64832
$471$	−13.8039	−0.636049
$472$	−9.68512	−0.445794
$473$	−32.6317	−1.50041
$474$	0.0885240	0.00406604
$475$	53.7079	2.46429
$476$	−25.4128	−1.16479
$477$	−5.32888	−0.243993
$478$	−7.99226	−0.365557
$479$	37.5615	1.71623	0.858113	−	0.513460i	$-0.171637\pi$
$479$	37.5615	1.71623	0.858113	+	0.513460i	$0.171637\pi$
$480$	−67.0930	−3.06236
$481$	11.1311	0.507534
$482$	69.2833	3.15577
$483$	5.00464	0.227719
$484$	17.3430	0.788319
$485$	16.1907	0.735183
$486$	43.2140	1.96023
$487$	−4.05583	−0.183787	−0.0918936	−	0.995769i	$-0.529292\pi$
$487$	−4.05583	−0.183787	−0.0918936	+	0.995769i	$0.529292\pi$
$488$	−40.4171	−1.82960
$489$	−11.0418	−0.499329
$490$	141.035	6.37131
$491$	36.6621	1.65454	0.827269	−	0.561807i	$-0.189893\pi$
$491$	36.6621	1.65454	0.827269	+	0.561807i	$0.189893\pi$
$492$	24.7206	1.11449
$493$	−2.06074	−0.0928111
$494$	−90.9222	−4.09078
$495$	32.4207	1.45720
$496$	−49.9296	−2.24191
$497$	33.7118	1.51218
$498$	2.86146	0.128225
$499$	−2.42307	−0.108472	−0.0542358	−	0.998528i	$-0.517272\pi$
$499$	−2.42307	−0.108472	−0.0542358	+	0.998528i	$0.517272\pi$
$500$	−65.3556	−2.92279
$501$	−12.4332	−0.555476
$502$	16.9078	0.754634
$503$	−29.5336	−1.31684	−0.658418	−	0.752652i	$-0.728774\pi$
$503$	−29.5336	−1.31684	−0.658418	+	0.752652i	$0.728774\pi$
$504$	−105.452	−4.69720
$505$	−42.4009	−1.88682
$506$	−14.1447	−0.628810
$507$	−10.2377	−0.454673
$508$	−3.70573	−0.164415
$509$	−32.1055	−1.42305	−0.711526	−	0.702660i	$-0.751996\pi$
$509$	−32.1055	−1.42305	−0.711526	+	0.702660i	$0.751996\pi$
$510$	−7.93269	−0.351265
$511$	59.4760	2.63106
$512$	−59.5530	−2.63189
$513$	27.7715	1.22614
$514$	−32.0646	−1.41431
$515$	36.5545	1.61078
$516$	38.1182	1.67806
$517$	−29.7757	−1.30954
$518$	27.5882	1.21216
$519$	6.23013	0.273472
$520$	179.362	7.86554
$521$	−24.9986	−1.09521	−0.547605	−	0.836737i	$-0.684460\pi$
$521$	−24.9986	−1.09521	−0.547605	+	0.836737i	$0.684460\pi$
$522$	−13.3967	−0.586356
$523$	5.15223	0.225291	0.112646	−	0.993635i	$-0.464068\pi$
$523$	5.15223	0.225291	0.112646	+	0.993635i	$0.464068\pi$
$524$	31.3625	1.37008
$525$	30.1055	1.31391
$526$	46.0563	2.00815
$527$	−3.21776	−0.140168
$528$	−46.3389	−2.01664
$529$	−21.1203	−0.918275
$530$	22.4645	0.975796
$531$	−2.36913	−0.102811
$532$	−165.492	−7.17497
$533$	−28.6390	−1.24049
$534$	11.3750	0.492244
$535$	−62.0350	−2.68201
$536$	−74.6102	−3.22267
$537$	−2.85498	−0.123202
$538$	0.480381	0.0207107
$539$	53.0942	2.28693
$540$	−85.8282	−3.69346
$541$	−33.0744	−1.42198	−0.710989	−	0.703203i	$-0.751753\pi$
$541$	−33.0744	−1.42198	−0.710989	+	0.703203i	$0.751753\pi$
$542$	65.1210	2.79718
$543$	12.0453	0.516912
$544$	−23.2082	−0.995043
$545$	−2.38352	−0.102099
$546$	−50.9657	−2.18113
$547$	13.9936	0.598322	0.299161	−	0.954203i	$-0.403293\pi$
$547$	13.9936	0.598322	0.299161	+	0.954203i	$0.403293\pi$
$548$	−22.2297	−0.949604
$549$	−9.88663	−0.421951
$550$	−85.0880	−3.62817
$551$	−13.4199	−0.571705
$552$	10.5467	0.448897
$553$	−0.186666	−0.00793786
$554$	22.9372	0.974507
$555$	6.32431	0.268452
$556$	69.6355	2.95320
$557$	15.9906	0.677545	0.338772	−	0.940868i	$-0.389988\pi$
$557$	15.9906	0.677545	0.338772	+	0.940868i	$0.389988\pi$
$558$	−20.9183	−0.885542
$559$	−44.1602	−1.86778
$560$	259.556	10.9682
$561$	−2.98635	−0.126084
$562$	83.2900	3.51338
$563$	36.0006	1.51724	0.758622	−	0.651531i	$-0.225873\pi$
$563$	36.0006	1.51724	0.758622	+	0.651531i	$0.225873\pi$
$564$	34.7820	1.46459
$565$	54.4733	2.29171
$566$	16.4170	0.690059
$567$	−17.0970	−0.718006
$568$	71.0438	2.98093
$569$	−5.61119	−0.235233	−0.117617	−	0.993059i	$-0.537525\pi$
$569$	−5.61119	−0.235233	−0.117617	+	0.993059i	$0.537525\pi$
$570$	−51.6589	−2.16375
$571$	−21.8128	−0.912835	−0.456418	−	0.889766i	$-0.650868\pi$
$571$	−21.8128	−0.912835	−0.456418	+	0.889766i	$0.650868\pi$
$572$	105.784	4.42306
$573$	3.01476	0.125943
$574$	−70.9812	−2.96270
$575$	11.3072	0.471542
$576$	−77.3509	−3.22296
$577$	−30.1339	−1.25449	−0.627245	−	0.778822i	$-0.715818\pi$
$577$	−30.1339	−1.25449	−0.627245	+	0.778822i	$0.715818\pi$
$578$	−2.74400	−0.114136
$579$	2.42197	0.100654
$580$	41.4742	1.72212
$581$	−6.03383	−0.250325
$582$	−9.69524	−0.401880
$583$	8.45703	0.350254
$584$	125.339	5.18656
$585$	43.8746	1.81399
$586$	50.9795	2.10594
$587$	−15.7126	−0.648530	−0.324265	−	0.945966i	$-0.605117\pi$
$587$	−15.7126	−0.648530	−0.324265	+	0.945966i	$0.605117\pi$
$588$	−62.0211	−2.55771
$589$	−20.9545	−0.863416
$590$	9.98732	0.411172
$591$	18.1754	0.747635
$592$	33.9455	1.39515
$593$	−17.4194	−0.715330	−0.357665	−	0.933850i	$-0.616427\pi$
$593$	−17.4194	−0.715330	−0.357665	+	0.933850i	$0.616427\pi$
$594$	−43.9976	−1.80525
$595$	16.7273	0.685752
$596$	−41.9312	−1.71757
$597$	13.3325	0.545663
$598$	−19.1419	−0.782772
$599$	8.30960	0.339521	0.169761	−	0.985485i	$-0.445701\pi$
$599$	8.30960	0.339521	0.169761	+	0.985485i	$0.445701\pi$
$600$	63.4440	2.59009
$601$	19.1161	0.779763	0.389882	−	0.920865i	$-0.372516\pi$
$601$	19.1161	0.779763	0.389882	+	0.920865i	$0.372516\pi$
$602$	−109.450	−4.46085
$603$	−18.2508	−0.743229
$604$	−12.7046	−0.516942
$605$	−11.4156	−0.464110
$606$	25.3902	1.03141
$607$	14.9370	0.606272	0.303136	−	0.952947i	$-0.401966\pi$
$607$	14.9370	0.606272	0.303136	+	0.952947i	$0.401966\pi$
$608$	−151.135	−6.12934
$609$	−7.52240	−0.304823
$610$	41.6782	1.68750
$611$	−40.2952	−1.63017
$612$	−13.1002	−0.529545
$613$	41.6179	1.68093	0.840466	−	0.541864i	$-0.182281\pi$
$613$	41.6179	1.68093	0.840466	+	0.541864i	$0.182281\pi$
$614$	−49.6497	−2.00370
$615$	−16.2717	−0.656139
$616$	167.354	6.74288
$617$	18.1049	0.728878	0.364439	−	0.931227i	$-0.381261\pi$
$617$	18.1049	0.728878	0.364439	+	0.931227i	$0.381261\pi$
$618$	−21.8893	−0.880519
$619$	0.151262	0.00607975	0.00303988	−	0.999995i	$-0.499032\pi$
$619$	0.151262	0.00607975	0.00303988	+	0.999995i	$0.499032\pi$
$620$	64.7602	2.60083
$621$	5.84676	0.234622
$622$	49.0234	1.96566
$623$	−23.9859	−0.960974
$624$	−62.7101	−2.51041
$625$	1.78192	0.0712767
$626$	25.1365	1.00466
$627$	−19.4476	−0.776661
$628$	96.0992	3.83478
$629$	2.18765	0.0872272
$630$	108.742	4.33240
$631$	−27.7533	−1.10484	−0.552422	−	0.833565i	$-0.686296\pi$
$631$	−27.7533	−1.10484	−0.552422	+	0.833565i	$0.686296\pi$
$632$	−0.393378	−0.0156477
$633$	2.31712	0.0920972
$634$	2.04952	0.0813969
$635$	2.43920	0.0967967
$636$	−9.87893	−0.391725
$637$	71.8519	2.84688
$638$	21.2607	0.841720
$639$	17.3784	0.687478
$640$	157.141	6.21153
$641$	−19.2753	−0.761329	−0.380665	−	0.924713i	$-0.624305\pi$
$641$	−19.2753	−0.761329	−0.380665	+	0.924713i	$0.624305\pi$
$642$	37.1474	1.46609
$643$	23.3114	0.919313	0.459657	−	0.888097i	$-0.347972\pi$
$643$	23.3114	0.919313	0.459657	+	0.888097i	$0.347972\pi$
$644$	−34.8411	−1.37293
$645$	−25.0903	−0.987930
$646$	−17.8694	−0.703061
$647$	0.300867	0.0118283	0.00591414	−	0.999983i	$-0.498117\pi$
$647$	0.300867	0.0118283	0.00591414	+	0.999983i	$0.498117\pi$
$648$	−36.0300	−1.41539
$649$	3.75984	0.147587
$650$	−115.149	−4.51651
$651$	−11.7459	−0.460358
$652$	76.8705	3.01048
$653$	−35.7465	−1.39887	−0.699434	−	0.714697i	$-0.746565\pi$
$653$	−35.7465	−1.39887	−0.699434	+	0.714697i	$0.746565\pi$
$654$	1.42729	0.0558113
$655$	−20.6436	−0.806611
$656$	−87.3379	−3.40997
$657$	30.6597	1.19615
$658$	−99.8709	−3.89337
$659$	8.11720	0.316201	0.158101	−	0.987423i	$-0.449463\pi$
$659$	8.11720	0.316201	0.158101	+	0.987423i	$0.449463\pi$
$660$	60.1030	2.33950
$661$	14.8580	0.577909	0.288955	−	0.957343i	$-0.406692\pi$
$661$	14.8580	0.577909	0.288955	+	0.957343i	$0.406692\pi$
$662$	89.0102	3.45948
$663$	−4.04140	−0.156955
$664$	−12.7156	−0.493461
$665$	108.931	4.22415
$666$	14.2217	0.551078
$667$	−2.82529	−0.109396
$668$	86.5572	3.34900
$669$	4.56430	0.176466
$670$	76.9383	2.97238
$671$	15.6903	0.605716
$672$	−84.7176	−3.26805
$673$	−8.79690	−0.339095	−0.169548	−	0.985522i	$-0.554231\pi$
$673$	−8.79690	−0.339095	−0.169548	+	0.985522i	$0.554231\pi$
$674$	−8.97058	−0.345534
$675$	35.1713	1.35375
$676$	71.2726	2.74125
$677$	−2.28222	−0.0877129	−0.0438564	−	0.999038i	$-0.513964\pi$
$677$	−2.28222	−0.0877129	−0.0438564	+	0.999038i	$0.513964\pi$
$678$	−32.6193	−1.25274
$679$	20.4439	0.784564
$680$	35.2508	1.35181
$681$	15.2968	0.586175
$682$	33.1977	1.27121
$683$	9.34313	0.357505	0.178752	−	0.983894i	$-0.442794\pi$
$683$	9.34313	0.357505	0.178752	+	0.983894i	$0.442794\pi$
$684$	−85.3106	−3.26193
$685$	14.6321	0.559064
$686$	89.8071	3.42885
$687$	16.0061	0.610673
$688$	−134.671	−5.13429
$689$	11.4448	0.436013
$690$	−10.8758	−0.414034
$691$	50.9465	1.93810	0.969048	−	0.246872i	$-0.0794028\pi$
$691$	50.9465	1.93810	0.969048	+	0.246872i	$0.0794028\pi$
$692$	−43.3727	−1.64878
$693$	40.9373	1.55508
$694$	−76.5438	−2.90556
$695$	−45.8358	−1.73865
$696$	−15.8526	−0.600891
$697$	−5.62856	−0.213197
$698$	26.0879	0.987442
$699$	−19.6886	−0.744692
$700$	−209.588	−7.92167
$701$	20.1202	0.759929	0.379964	−	0.925001i	$-0.375936\pi$
$701$	20.1202	0.759929	0.379964	+	0.925001i	$0.375936\pi$
$702$	−59.5416	−2.24725
$703$	14.2463	0.537309
$704$	122.757	4.62659
$705$	−22.8944	−0.862252
$706$	−13.8614	−0.521679
$707$	−53.5392	−2.01355
$708$	−4.39200	−0.165061
$709$	−19.1700	−0.719946	−0.359973	−	0.932963i	$-0.617214\pi$
$709$	−19.1700	−0.719946	−0.359973	+	0.932963i	$0.617214\pi$
$710$	−73.2606	−2.74942
$711$	−0.0962261	−0.00360876
$712$	−50.5475	−1.89435
$713$	−4.41157	−0.165215
$714$	−10.0165	−0.374859
$715$	−69.6298	−2.60401
$716$	19.8757	0.742789
$717$	−2.31343	−0.0863966
$718$	−94.1666	−3.51427
$719$	−48.4152	−1.80558	−0.902792	−	0.430078i	$-0.858486\pi$
$719$	−48.4152	−1.80558	−0.902792	+	0.430078i	$0.858486\pi$
$720$	133.800	4.98645
$721$	46.1570	1.71898
$722$	−64.2319	−2.39046
$723$	20.0546	0.745840
$724$	−83.8563	−3.11650
$725$	−16.9956	−0.631202
$726$	6.83582	0.253701
$727$	−33.9764	−1.26012	−0.630058	−	0.776548i	$-0.716969\pi$
$727$	−33.9764	−1.26012	−0.630058	+	0.776548i	$0.716969\pi$
$728$	226.479	8.39386
$729$	1.34827	0.0499358
$730$	−129.250	−4.78374
$731$	−8.67901	−0.321005
$732$	−18.3283	−0.677433
$733$	11.8725	0.438522	0.219261	−	0.975666i	$-0.429635\pi$
$733$	11.8725	0.438522	0.219261	+	0.975666i	$0.429635\pi$
$734$	20.3626	0.751597
$735$	40.8238	1.50581
$736$	−31.8186	−1.17285
$737$	28.9643	1.06691
$738$	−36.5907	−1.34692
$739$	22.8916	0.842080	0.421040	−	0.907042i	$-0.361665\pi$
$739$	22.8916	0.842080	0.421040	+	0.907042i	$0.361665\pi$
$740$	−44.0283	−1.61851
$741$	−26.3182	−0.966824
$742$	28.3657	1.04134
$743$	20.1547	0.739405	0.369702	−	0.929150i	$-0.379460\pi$
$743$	20.1547	0.739405	0.369702	+	0.929150i	$0.379460\pi$
$744$	−24.7531	−0.907493
$745$	27.6002	1.01119
$746$	40.0749	1.46725
$747$	−3.11042	−0.113804
$748$	20.7903	0.760168
$749$	−78.3310	−2.86215
$750$	−25.7601	−0.940627
$751$	37.2235	1.35830	0.679152	−	0.733997i	$-0.262348\pi$
$751$	37.2235	1.35830	0.679152	+	0.733997i	$0.262348\pi$
$752$	−122.885	−4.48114
$753$	4.89412	0.178352
$754$	28.7719	1.04781
$755$	8.36246	0.304341
$756$	−108.374	−3.94154
$757$	9.24760	0.336110	0.168055	−	0.985778i	$-0.446251\pi$
$757$	9.24760	0.336110	0.168055	+	0.985778i	$0.446251\pi$
$758$	6.37298	0.231477
$759$	−4.09432	−0.148614
$760$	229.559	8.32697
$761$	6.33211	0.229539	0.114769	−	0.993392i	$-0.463387\pi$
$761$	6.33211	0.229539	0.114769	+	0.993392i	$0.463387\pi$
$762$	−1.46063	−0.0529129
$763$	−3.00965	−0.108957
$764$	−20.9880	−0.759320
$765$	8.62288	0.311761
$766$	−101.601	−3.67098
$767$	5.08816	0.183723
$768$	−42.2324	−1.52393
$769$	−11.4172	−0.411714	−0.205857	−	0.978582i	$-0.565998\pi$
$769$	−11.4172	−0.411714	−0.205857	+	0.978582i	$0.565998\pi$
$770$	−172.576	−6.21920
$771$	−9.28137	−0.334260
$772$	−16.8612	−0.606847
$773$	6.51830	0.234447	0.117224	−	0.993106i	$-0.462601\pi$
$773$	6.51830	0.234447	0.117224	+	0.993106i	$0.462601\pi$
$774$	−56.4213	−2.02802
$775$	−26.5379	−0.953271
$776$	43.0831	1.54659
$777$	7.98564	0.286483
$778$	−50.7130	−1.81815
$779$	−36.6540	−1.31327
$780$	81.3368	2.91232
$781$	−27.5798	−0.986883
$782$	−3.76205	−0.134531
$783$	−8.78817	−0.314064
$784$	219.120	7.82572
$785$	−63.2549	−2.25766
$786$	12.3617	0.440926
$787$	2.63566	0.0939510	0.0469755	−	0.998896i	$-0.485042\pi$
$787$	2.63566	0.0939510	0.0469755	+	0.998896i	$0.485042\pi$
$788$	−126.533	−4.50753
$789$	13.3314	0.474611
$790$	0.405652	0.0144325
$791$	68.7829	2.44564
$792$	86.2706	3.06549
$793$	21.2335	0.754023
$794$	24.8816	0.883016
$795$	6.50255	0.230622
$796$	−92.8177	−3.28984
$797$	−50.7695	−1.79835	−0.899174	−	0.437592i	$-0.855831\pi$
$797$	−50.7695	−1.79835	−0.899174	+	0.437592i	$0.855831\pi$
$798$	−65.2291	−2.30909
$799$	−7.91941	−0.280169
$800$	−191.406	−6.76722
$801$	−12.3647	−0.436884
$802$	32.6940	1.15446
$803$	−48.6575	−1.71709
$804$	−33.8341	−1.19324
$805$	22.9333	0.808291
$806$	44.9261	1.58245
$807$	0.139050	0.00489480
$808$	−112.828	−3.96927
$809$	6.08848	0.214060	0.107030	−	0.994256i	$-0.465866\pi$
$809$	6.08848	0.214060	0.107030	+	0.994256i	$0.465866\pi$
$810$	37.1542	1.30546
$811$	10.1043	0.354810	0.177405	−	0.984138i	$-0.443230\pi$
$811$	10.1043	0.354810	0.177405	+	0.984138i	$0.443230\pi$
$812$	52.3691	1.83780
$813$	18.8498	0.661092
$814$	−22.5700	−0.791078
$815$	−50.5981	−1.77237
$816$	−12.3247	−0.431451
$817$	−56.5190	−1.97735
$818$	43.1355	1.50820
$819$	55.4001	1.93583
$820$	113.280	3.95590
$821$	−19.7953	−0.690860	−0.345430	−	0.938445i	$-0.612267\pi$
$821$	−19.7953	−0.690860	−0.345430	+	0.938445i	$0.612267\pi$
$822$	−8.76190	−0.305606
$823$	10.2217	0.356307	0.178154	−	0.984003i	$-0.442988\pi$
$823$	10.2217	0.356307	0.178154	+	0.984003i	$0.442988\pi$
$824$	97.2706	3.38858
$825$	−24.6295	−0.857488
$826$	12.6109	0.438789
$827$	−45.6758	−1.58830	−0.794152	−	0.607719i	$-0.792085\pi$
$827$	−45.6758	−1.58830	−0.794152	+	0.607719i	$0.792085\pi$
$828$	−17.9605	−0.624171
$829$	−50.4646	−1.75271	−0.876354	−	0.481668i	$-0.840031\pi$
$829$	−50.4646	−1.75271	−0.876354	+	0.481668i	$0.840031\pi$
$830$	13.1124	0.455136
$831$	6.63937	0.230317
$832$	166.126	5.75939
$833$	14.1214	0.489277
$834$	27.4471	0.950415
$835$	−56.9741	−1.97167
$836$	135.389	4.68254
$837$	−13.7223	−0.474314
$838$	50.3627	1.73975
$839$	8.77905	0.303086	0.151543	−	0.988451i	$-0.451576\pi$
$839$	8.77905	0.303086	0.151543	+	0.988451i	$0.451576\pi$
$840$	128.677	4.43979
$841$	−24.7533	−0.853564
$842$	64.0076	2.20585
$843$	24.1090	0.830358
$844$	−16.1312	−0.555259
$845$	−46.9133	−1.61387
$846$	−51.4832	−1.77003
$847$	−14.4144	−0.495284
$848$	34.9022	1.19855
$849$	4.75205	0.163090
$850$	−22.6307	−0.776228
$851$	2.99928	0.102814
$852$	32.2169	1.10373
$853$	3.89882	0.133493	0.0667465	−	0.997770i	$-0.478738\pi$
$853$	3.89882	0.133493	0.0667465	+	0.997770i	$0.478738\pi$
$854$	52.6267	1.80085
$855$	56.1535	1.92041
$856$	−165.074	−5.64210
$857$	32.6707	1.11601	0.558005	−	0.829838i	$-0.311567\pi$
$857$	32.6707	1.11601	0.558005	+	0.829838i	$0.311567\pi$
$858$	41.6953	1.42345
$859$	39.5582	1.34971	0.674854	−	0.737951i	$-0.264206\pi$
$859$	39.5582	1.34971	0.674854	+	0.737951i	$0.264206\pi$
$860$	174.673	5.95629
$861$	−20.5461	−0.700211
$862$	12.3047	0.419101
$863$	−7.85880	−0.267517	−0.133758	−	0.991014i	$-0.542705\pi$
$863$	−7.85880	−0.267517	−0.133758	+	0.991014i	$0.542705\pi$
$864$	−98.9729	−3.36713
$865$	28.5489	0.970693
$866$	55.0634	1.87113
$867$	−0.794276	−0.0269750
$868$	81.7721	2.77552
$869$	0.152712	0.00518041
$870$	16.3472	0.554223
$871$	39.1971	1.32814
$872$	−6.34250	−0.214784
$873$	10.5388	0.356684
$874$	−24.4990	−0.828693
$875$	54.3192	1.83632
$876$	56.8384	1.92039
$877$	−37.8435	−1.27788	−0.638942	−	0.769255i	$-0.720627\pi$
$877$	−37.8435	−1.27788	−0.638942	+	0.769255i	$0.720627\pi$
$878$	13.8526	0.467502
$879$	14.7565	0.497723
$880$	−212.344	−7.15810
$881$	−38.0289	−1.28123	−0.640613	−	0.767864i	$-0.721320\pi$
$881$	−38.0289	−1.28123	−0.640613	+	0.767864i	$0.721320\pi$
$882$	91.8016	3.09112
$883$	53.1581	1.78891	0.894456	−	0.447156i	$-0.147563\pi$
$883$	53.1581	1.78891	0.894456	+	0.447156i	$0.147563\pi$
$884$	28.1353	0.946292
$885$	2.89092	0.0971771
$886$	93.6252	3.14540
$887$	−46.4507	−1.55966	−0.779830	−	0.625991i	$-0.784695\pi$
$887$	−46.4507	−1.55966	−0.779830	+	0.625991i	$0.784695\pi$
$888$	16.8288	0.564738
$889$	3.07995	0.103298
$890$	52.1247	1.74722
$891$	13.9871	0.468586
$892$	−31.7756	−1.06392
$893$	−51.5724	−1.72580
$894$	−16.5274	−0.552757
$895$	−13.0827	−0.437305
$896$	198.420	6.62874
$897$	−5.54080	−0.185002
$898$	−39.7569	−1.32671
$899$	6.63097	0.221155
$900$	−108.042	−3.60140
$901$	2.24930	0.0749352
$902$	58.0700	1.93352
$903$	−31.6813	−1.05429
$904$	144.952	4.82103
$905$	55.1963	1.83479
$906$	−5.00755	−0.166365
$907$	30.0477	0.997716	0.498858	−	0.866684i	$-0.333753\pi$
$907$	30.0477	0.997716	0.498858	+	0.866684i	$0.333753\pi$
$908$	−106.493	−3.53408
$909$	−27.5994	−0.915413
$910$	−233.545	−7.74195
$911$	−13.3321	−0.441712	−0.220856	−	0.975306i	$-0.570885\pi$
$911$	−13.3321	−0.441712	−0.220856	+	0.975306i	$0.570885\pi$
$912$	−80.2603	−2.65768
$913$	4.93630	0.163368
$914$	−54.6578	−1.80792
$915$	12.0641	0.398828
$916$	−111.431	−3.68178
$917$	−26.0665	−0.860790
$918$	−11.7020	−0.386223
$919$	5.59440	0.184542	0.0922712	−	0.995734i	$-0.470587\pi$
$919$	5.59440	0.184542	0.0922712	+	0.995734i	$0.470587\pi$
$920$	48.3292	1.59337
$921$	−14.3716	−0.473559
$922$	25.9232	0.853735
$923$	−37.3235	−1.22852
$924$	75.8914	2.49665
$925$	18.0423	0.593226
$926$	1.78901	0.0587905
$927$	23.7939	0.781493
$928$	47.8261	1.56997
$929$	−32.4945	−1.06611	−0.533055	−	0.846081i	$-0.678956\pi$
$929$	−32.4945	−1.06611	−0.533055	+	0.846081i	$0.678956\pi$
$930$	25.5255	0.837013
$931$	91.9606	3.01389
$932$	137.067	4.48979
$933$	14.1903	0.464568
$934$	−35.4983	−1.16154
$935$	−13.6847	−0.447536
$936$	116.749	3.81607
$937$	−24.2112	−0.790946	−0.395473	−	0.918478i	$-0.629419\pi$
$937$	−24.2112	−0.790946	−0.395473	+	0.918478i	$0.629419\pi$
$938$	97.1492	3.17203
$939$	7.27599	0.237443
$940$	159.385	5.19857
$941$	55.2595	1.80141	0.900703	−	0.434434i	$-0.143052\pi$
$941$	55.2595	1.80141	0.900703	+	0.434434i	$0.143052\pi$
$942$	37.8779	1.23413
$943$	−7.71681	−0.251294
$944$	15.5169	0.505032
$945$	71.3347	2.32052
$946$	89.5415	2.91125
$947$	5.12386	0.166503	0.0832516	−	0.996529i	$-0.473469\pi$
$947$	5.12386	0.166503	0.0832516	+	0.996529i	$0.473469\pi$
$948$	−0.178388	−0.00579379
$949$	−65.8478	−2.13751
$950$	−147.375	−4.78147
$951$	0.593252	0.0192375
$952$	44.5109	1.44261
$953$	−1.43554	−0.0465018	−0.0232509	−	0.999730i	$-0.507402\pi$
$953$	−1.43554	−0.0465018	−0.0232509	+	0.999730i	$0.507402\pi$
$954$	14.6225	0.473420
$955$	13.8148	0.447037
$956$	16.1055	0.520890
$957$	6.15410	0.198934
$958$	−103.069	−3.33000
$959$	18.4758	0.596615
$960$	94.3872	3.04633
$961$	−20.6460	−0.666001
$962$	−30.5438	−0.984771
$963$	−40.3795	−1.30121
$964$	−139.616	−4.49672
$965$	11.0984	0.357271
$966$	−13.7328	−0.441844
$967$	44.4029	1.42790	0.713951	−	0.700196i	$-0.246904\pi$
$967$	44.4029	1.42790	0.713951	+	0.700196i	$0.246904\pi$
$968$	−30.3766	−0.976342
$969$	−5.17244	−0.166163
$970$	−44.4274	−1.42648
$971$	23.6710	0.759638	0.379819	−	0.925061i	$-0.375986\pi$
$971$	23.6710	0.759638	0.379819	+	0.925061i	$0.375986\pi$
$972$	−87.0823	−2.79317
$973$	−57.8764	−1.85543
$974$	11.1292	0.356603
$975$	−33.3308	−1.06744
$976$	64.7538	2.07272
$977$	15.3037	0.489609	0.244804	−	0.969573i	$-0.421276\pi$
$977$	15.3037	0.489609	0.244804	+	0.969573i	$0.421276\pi$
$978$	30.2988	0.968849
$979$	19.6230	0.627152
$980$	−284.205	−9.07861
$981$	−1.55147	−0.0495346
$982$	−100.601	−3.21031
$983$	−5.24289	−0.167222	−0.0836111	−	0.996498i	$-0.526645\pi$
$983$	−5.24289	−0.167222	−0.0836111	+	0.996498i	$0.526645\pi$
$984$	−43.2986	−1.38031
$985$	83.2868	2.65374
$986$	5.65468	0.180082
$987$	−28.9085	−0.920167
$988$	183.221	5.82904
$989$	−11.8990	−0.378366
$990$	−88.9625	−2.82741
$991$	5.24448	0.166597	0.0832983	−	0.996525i	$-0.473455\pi$
$991$	5.24448	0.166597	0.0832983	+	0.996525i	$0.473455\pi$
$992$	74.6783	2.37104
$993$	25.7648	0.817621
$994$	−92.5054	−2.93409
$995$	61.0949	1.93684
$996$	−5.76625	−0.182711
$997$	−18.8809	−0.597965	−0.298983	−	0.954259i	$-0.596647\pi$
$997$	−18.8809	−0.597965	−0.298983	+	0.954259i	$0.596647\pi$
$998$	6.64892	0.210468
$999$	9.32937	0.295168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.1	✓	16
3.2	odd	2		9027.2.a.n.1.16		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.1	✓	16	1.1	even	1	trivial
9027.2.a.n.1.16		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)

\(f(q)\)	\(=\)	\(q-2.74400 q^{2} -0.794276 q^{3} +5.52956 q^{4} -3.63969 q^{5} +2.17950 q^{6} -4.59580 q^{7} -9.68512 q^{8} -2.36913 q^{9} +O(q^{10})\)	\(q-2.74400 q^{2} -0.794276 q^{3} +5.52956 q^{4} -3.63969 q^{5} +2.17950 q^{6} -4.59580 q^{7} -9.68512 q^{8} -2.36913 q^{9} +9.98732 q^{10} +3.75984 q^{11} -4.39200 q^{12} +5.08816 q^{13} +12.6109 q^{14} +2.89092 q^{15} +15.5169 q^{16} +1.00000 q^{17} +6.50089 q^{18} +6.51215 q^{19} -20.1259 q^{20} +3.65033 q^{21} -10.3170 q^{22} +1.37101 q^{23} +7.69266 q^{24} +8.24734 q^{25} -13.9619 q^{26} +4.26457 q^{27} -25.4128 q^{28} -2.06074 q^{29} -7.93269 q^{30} -3.21776 q^{31} -23.2082 q^{32} -2.98635 q^{33} -2.74400 q^{34} +16.7273 q^{35} -13.1002 q^{36} +2.18765 q^{37} -17.8694 q^{38} -4.04140 q^{39} +35.2508 q^{40} -5.62856 q^{41} -10.0165 q^{42} -8.67901 q^{43} +20.7903 q^{44} +8.62288 q^{45} -3.76205 q^{46} -7.91941 q^{47} -12.3247 q^{48} +14.1214 q^{49} -22.6307 q^{50} -0.794276 q^{51} +28.1353 q^{52} +2.24930 q^{53} -11.7020 q^{54} -13.6847 q^{55} +44.5109 q^{56} -5.17244 q^{57} +5.65468 q^{58} +1.00000 q^{59} +15.9855 q^{60} +4.17311 q^{61} +8.82954 q^{62} +10.8880 q^{63} +32.6496 q^{64} -18.5193 q^{65} +8.19456 q^{66} +7.70359 q^{67} +5.52956 q^{68} -1.08896 q^{69} -45.8998 q^{70} -7.33536 q^{71} +22.9453 q^{72} -12.9414 q^{73} -6.00291 q^{74} -6.55066 q^{75} +36.0093 q^{76} -17.2795 q^{77} +11.0896 q^{78} +0.0406167 q^{79} -56.4767 q^{80} +3.72013 q^{81} +15.4448 q^{82} +1.31290 q^{83} +20.1847 q^{84} -3.63969 q^{85} +23.8152 q^{86} +1.63680 q^{87} -36.4145 q^{88} +5.21909 q^{89} -23.6612 q^{90} -23.3842 q^{91} +7.58107 q^{92} +2.55579 q^{93} +21.7309 q^{94} -23.7022 q^{95} +18.4337 q^{96} -4.44838 q^{97} -38.7491 q^{98} -8.90754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 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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