LMFDB - Embedded newform 1003.2.a.h.1.13

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			1.13
Root			$-1.35393$ 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)

$f(q)$	$=$	$q+1.35393 q^{2} -1.79865 q^{3} -0.166881 q^{4} +1.77529 q^{5} -2.43525 q^{6} +2.41510 q^{7} -2.93380 q^{8} +0.235159 q^{9} +O(q^{10})$	\(q+1.35393 q^{2} -1.79865 q^{3} -0.166881 q^{4} +1.77529 q^{5} -2.43525 q^{6} +2.41510 q^{7} -2.93380 q^{8} +0.235159 q^{9} +2.40362 q^{10} -4.25084 q^{11} +0.300161 q^{12} -4.33750 q^{13} +3.26987 q^{14} -3.19314 q^{15} -3.63839 q^{16} +1.00000 q^{17} +0.318388 q^{18} -0.153548 q^{19} -0.296262 q^{20} -4.34393 q^{21} -5.75533 q^{22} +4.64401 q^{23} +5.27689 q^{24} -1.84834 q^{25} -5.87266 q^{26} +4.97299 q^{27} -0.403034 q^{28} -2.97458 q^{29} -4.32328 q^{30} -8.25288 q^{31} +0.941483 q^{32} +7.64580 q^{33} +1.35393 q^{34} +4.28751 q^{35} -0.0392434 q^{36} +2.14049 q^{37} -0.207893 q^{38} +7.80166 q^{39} -5.20835 q^{40} -11.5074 q^{41} -5.88137 q^{42} -10.8223 q^{43} +0.709384 q^{44} +0.417475 q^{45} +6.28765 q^{46} +0.456311 q^{47} +6.54421 q^{48} -1.16728 q^{49} -2.50252 q^{50} -1.79865 q^{51} +0.723844 q^{52} -8.44354 q^{53} +6.73307 q^{54} -7.54649 q^{55} -7.08542 q^{56} +0.276180 q^{57} -4.02736 q^{58} +1.00000 q^{59} +0.532873 q^{60} +13.3709 q^{61} -11.1738 q^{62} +0.567932 q^{63} +8.55148 q^{64} -7.70032 q^{65} +10.3519 q^{66} -0.309182 q^{67} -0.166881 q^{68} -8.35297 q^{69} +5.80498 q^{70} -4.54815 q^{71} -0.689908 q^{72} -3.81890 q^{73} +2.89806 q^{74} +3.32452 q^{75} +0.0256242 q^{76} -10.2662 q^{77} +10.5629 q^{78} -4.58396 q^{79} -6.45920 q^{80} -9.65018 q^{81} -15.5802 q^{82} +4.13272 q^{83} +0.724919 q^{84} +1.77529 q^{85} -14.6526 q^{86} +5.35023 q^{87} +12.4711 q^{88} +10.5650 q^{89} +0.565231 q^{90} -10.4755 q^{91} -0.774995 q^{92} +14.8441 q^{93} +0.617812 q^{94} -0.272593 q^{95} -1.69340 q^{96} +17.4879 q^{97} -1.58042 q^{98} -0.999622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.35393	0.957371	0.478686	−	0.877986i	$-0.341113\pi$
$2$	1.35393	0.957371	0.478686	+	0.877986i	$0.341113\pi$
$3$	−1.79865	−1.03845	−0.519227	−	0.854636i	$-0.673780\pi$
$3$	−1.79865	−1.03845	−0.519227	+	0.854636i	$0.673780\pi$
$4$	−0.166881	−0.0834403
$5$	1.77529	0.793935	0.396967	−	0.917833i	$-0.370063\pi$
$5$	1.77529	0.793935	0.396967	+	0.917833i	$0.370063\pi$
$6$	−2.43525	−0.994186
$7$	2.41510	0.912823	0.456411	−	0.889769i	$-0.349135\pi$
$7$	2.41510	0.912823	0.456411	+	0.889769i	$0.349135\pi$
$8$	−2.93380	−1.03725
$9$	0.235159	0.0783862
$10$	2.40362	0.760090
$11$	−4.25084	−1.28168	−0.640839	−	0.767675i	$-0.721413\pi$
$11$	−4.25084	−1.28168	−0.640839	+	0.767675i	$0.721413\pi$
$12$	0.300161	0.0866489
$13$	−4.33750	−1.20301	−0.601503	−	0.798871i	$-0.705431\pi$
$13$	−4.33750	−1.20301	−0.601503	+	0.798871i	$0.705431\pi$
$14$	3.26987	0.873910
$15$	−3.19314	−0.824464
$16$	−3.63839	−0.909597
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.318388	0.0750447
$19$	−0.153548	−0.0352264	−0.0176132	−	0.999845i	$-0.505607\pi$
$19$	−0.153548	−0.0352264	−0.0176132	+	0.999845i	$0.505607\pi$
$20$	−0.296262	−0.0662462
$21$	−4.34393	−0.947924
$22$	−5.75533	−1.22704
$23$	4.64401	0.968342	0.484171	−	0.874973i	$-0.339121\pi$
$23$	4.64401	0.968342	0.484171	+	0.874973i	$0.339121\pi$
$24$	5.27689	1.07714
$25$	−1.84834	−0.369668
$26$	−5.87266	−1.15172
$27$	4.97299	0.957053
$28$	−0.403034	−0.0761662
$29$	−2.97458	−0.552365	−0.276182	−	0.961105i	$-0.589069\pi$
$29$	−2.97458	−0.552365	−0.276182	+	0.961105i	$0.589069\pi$
$30$	−4.32328	−0.789318
$31$	−8.25288	−1.48226	−0.741130	−	0.671361i	$-0.765710\pi$
$31$	−8.25288	−1.48226	−0.741130	+	0.671361i	$0.765710\pi$
$32$	0.941483	0.166432
$33$	7.64580	1.33096
$34$	1.35393	0.232197
$35$	4.28751	0.724721
$36$	−0.0392434	−0.00654057
$37$	2.14049	0.351894	0.175947	−	0.984400i	$-0.443701\pi$
$37$	2.14049	0.351894	0.175947	+	0.984400i	$0.443701\pi$
$38$	−0.207893	−0.0337247
$39$	7.80166	1.24927
$40$	−5.20835	−0.823512
$41$	−11.5074	−1.79716	−0.898578	−	0.438814i	$-0.855399\pi$
$41$	−11.5074	−1.79716	−0.898578	+	0.438814i	$0.855399\pi$
$42$	−5.88137	−0.907515
$43$	−10.8223	−1.65038	−0.825192	−	0.564853i	$-0.808933\pi$
$43$	−10.8223	−1.65038	−0.825192	+	0.564853i	$0.808933\pi$
$44$	0.709384	0.106944
$45$	0.417475	0.0622335
$46$	6.28765	0.927063
$47$	0.456311	0.0665598	0.0332799	−	0.999446i	$-0.489405\pi$
$47$	0.456311	0.0665598	0.0332799	+	0.999446i	$0.489405\pi$
$48$	6.54421	0.944575
$49$	−1.16728	−0.166755
$50$	−2.50252	−0.353909
$51$	−1.79865	−0.251862
$52$	0.723844	0.100379
$53$	−8.44354	−1.15981	−0.579905	−	0.814684i	$-0.696910\pi$
$53$	−8.44354	−1.15981	−0.579905	+	0.814684i	$0.696910\pi$
$54$	6.73307	0.916255
$55$	−7.54649	−1.01757
$56$	−7.08542	−0.946829
$57$	0.276180	0.0365810
$58$	−4.02736	−0.528818
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.532873	0.0687936
$61$	13.3709	1.71197	0.855986	−	0.516998i	$-0.172951\pi$
$61$	13.3709	1.71197	0.855986	+	0.516998i	$0.172951\pi$
$62$	−11.1738	−1.41907
$63$	0.567932	0.0715527
$64$	8.55148	1.06893
$65$	−7.70032	−0.955107
$66$	10.3519	1.27423
$67$	−0.309182	−0.0377725	−0.0188863	−	0.999822i	$-0.506012\pi$
$67$	−0.309182	−0.0377725	−0.0188863	+	0.999822i	$0.506012\pi$
$68$	−0.166881	−0.0202373
$69$	−8.35297	−1.00558
$70$	5.80498	0.693827
$71$	−4.54815	−0.539767	−0.269883	−	0.962893i	$-0.586985\pi$
$71$	−4.54815	−0.539767	−0.269883	+	0.962893i	$0.586985\pi$
$72$	−0.689908	−0.0813064
$73$	−3.81890	−0.446969	−0.223484	−	0.974708i	$-0.571743\pi$
$73$	−3.81890	−0.446969	−0.223484	+	0.974708i	$0.571743\pi$
$74$	2.89806	0.336893
$75$	3.32452	0.383883
$76$	0.0256242	0.00293930
$77$	−10.2662	−1.16994
$78$	10.5629	1.19601
$79$	−4.58396	−0.515735	−0.257868	−	0.966180i	$-0.583020\pi$
$79$	−4.58396	−0.515735	−0.257868	+	0.966180i	$0.583020\pi$
$80$	−6.45920	−0.722161
$81$	−9.65018	−1.07224
$82$	−15.5802	−1.72055
$83$	4.13272	0.453624	0.226812	−	0.973939i	$-0.427170\pi$
$83$	4.13272	0.453624	0.226812	+	0.973939i	$0.427170\pi$
$84$	0.724919	0.0790951
$85$	1.77529	0.192557
$86$	−14.6526	−1.58003
$87$	5.35023	0.573605
$88$	12.4711	1.32943
$89$	10.5650	1.11988	0.559941	−	0.828532i	$-0.310824\pi$
$89$	10.5650	1.11988	0.559941	+	0.828532i	$0.310824\pi$
$90$	0.565231	0.0595806
$91$	−10.4755	−1.09813
$92$	−0.774995	−0.0807988
$93$	14.8441	1.53926
$94$	0.617812	0.0637224
$95$	−0.272593	−0.0279674
$96$	−1.69340	−0.172832
$97$	17.4879	1.77563	0.887813	−	0.460204i	$-0.152224\pi$
$97$	17.4879	1.77563	0.887813	+	0.460204i	$0.152224\pi$
$98$	−1.58042	−0.159646
$99$	−0.999622	−0.100466
$100$	0.308452	0.0308452
$101$	−6.80653	−0.677275	−0.338638	−	0.940917i	$-0.609966\pi$
$101$	−6.80653	−0.677275	−0.338638	+	0.940917i	$0.609966\pi$
$102$	−2.43525	−0.241125
$103$	16.8319	1.65850	0.829249	−	0.558880i	$-0.188769\pi$
$103$	16.8319	1.65850	0.829249	+	0.558880i	$0.188769\pi$
$104$	12.7253	1.24782
$105$	−7.71175	−0.752590
$106$	−11.4319	−1.11037
$107$	18.7646	1.81404	0.907022	−	0.421084i	$-0.138350\pi$
$107$	18.7646	1.81404	0.907022	+	0.421084i	$0.138350\pi$
$108$	−0.829897	−0.0798569
$109$	−13.2776	−1.27176	−0.635881	−	0.771787i	$-0.719363\pi$
$109$	−13.2776	−1.27176	−0.635881	+	0.771787i	$0.719363\pi$
$110$	−10.2174	−0.974190
$111$	−3.84999	−0.365425
$112$	−8.78708	−0.830301
$113$	−12.9487	−1.21811	−0.609054	−	0.793129i	$-0.708451\pi$
$113$	−12.9487	−1.21811	−0.609054	+	0.793129i	$0.708451\pi$
$114$	0.373928	0.0350216
$115$	8.24447	0.768801
$116$	0.496399	0.0460895
$117$	−1.02000	−0.0942990
$118$	1.35393	0.124639
$119$	2.41510	0.221392
$120$	9.36802	0.855179
$121$	7.06967	0.642697
$122$	18.1033	1.63899
$123$	20.6979	1.86626
$124$	1.37725	0.123680
$125$	−12.1578	−1.08743
$126$	0.768938	0.0685025
$127$	11.7485	1.04251	0.521256	−	0.853400i	$-0.325464\pi$
$127$	11.7485	1.04251	0.521256	+	0.853400i	$0.325464\pi$
$128$	9.69511	0.856935
$129$	19.4656	1.71385
$130$	−10.4257	−0.914392
$131$	−3.52268	−0.307778	−0.153889	−	0.988088i	$-0.549180\pi$
$131$	−3.52268	−0.307778	−0.153889	+	0.988088i	$0.549180\pi$
$132$	−1.27594	−0.111056
$133$	−0.370834	−0.0321554
$134$	−0.418609	−0.0361623
$135$	8.82852	0.759838
$136$	−2.93380	−0.251571
$137$	−9.03807	−0.772175	−0.386087	−	0.922462i	$-0.626174\pi$
$137$	−9.03807	−0.772175	−0.386087	+	0.922462i	$0.626174\pi$
$138$	−11.3093	−0.962712
$139$	−18.4390	−1.56398	−0.781988	−	0.623293i	$-0.785794\pi$
$139$	−18.4390	−1.56398	−0.781988	+	0.623293i	$0.785794\pi$
$140$	−0.715503	−0.0604710
$141$	−0.820746	−0.0691193
$142$	−6.15787	−0.516757
$143$	18.4380	1.54186
$144$	−0.855598	−0.0712999
$145$	−5.28074	−0.438541
$146$	−5.17052	−0.427915
$147$	2.09954	0.173167
$148$	−0.357206	−0.0293621
$149$	14.9028	1.22089	0.610443	−	0.792060i	$-0.290991\pi$
$149$	14.9028	1.22089	0.610443	+	0.792060i	$0.290991\pi$
$150$	4.50116	0.367519
$151$	15.0387	1.22383	0.611917	−	0.790922i	$-0.290399\pi$
$151$	15.0387	1.22383	0.611917	+	0.790922i	$0.290399\pi$
$152$	0.450480	0.0365387
$153$	0.235159	0.0190114
$154$	−13.8997	−1.12007
$155$	−14.6513	−1.17682
$156$	−1.30195	−0.104239
$157$	−14.7158	−1.17445	−0.587226	−	0.809423i	$-0.699780\pi$
$157$	−14.7158	−1.17445	−0.587226	+	0.809423i	$0.699780\pi$
$158$	−6.20635	−0.493750
$159$	15.1870	1.20441
$160$	1.67141	0.132136
$161$	11.2158	0.883925
$162$	−13.0656	−1.02653
$163$	20.1436	1.57777	0.788885	−	0.614541i	$-0.210659\pi$
$163$	20.1436	1.57777	0.788885	+	0.614541i	$0.210659\pi$
$164$	1.92037	0.149955
$165$	13.5735	1.05670
$166$	5.59540	0.434287
$167$	19.5524	1.51301	0.756507	−	0.653986i	$-0.226905\pi$
$167$	19.5524	1.51301	0.756507	+	0.653986i	$0.226905\pi$
$168$	12.7442	0.983239
$169$	5.81388	0.447221
$170$	2.40362	0.184349
$171$	−0.0361082	−0.00276126
$172$	1.80603	0.137709
$173$	−8.14965	−0.619606	−0.309803	−	0.950801i	$-0.600263\pi$
$173$	−8.14965	−0.619606	−0.309803	+	0.950801i	$0.600263\pi$
$174$	7.24383	0.549153
$175$	−4.46393	−0.337441
$176$	15.4662	1.16581
$177$	−1.79865	−0.135195
$178$	14.3042	1.07214
$179$	3.37621	0.252350	0.126175	−	0.992008i	$-0.459730\pi$
$179$	3.37621	0.252350	0.126175	+	0.992008i	$0.459730\pi$
$180$	−0.0696685	−0.00519278
$181$	5.10781	0.379661	0.189830	−	0.981817i	$-0.439206\pi$
$181$	5.10781	0.379661	0.189830	+	0.981817i	$0.439206\pi$
$182$	−14.1831	−1.05132
$183$	−24.0497	−1.77780
$184$	−13.6246	−1.00442
$185$	3.79999	0.279380
$186$	20.0978	1.47364
$187$	−4.25084	−0.310852
$188$	−0.0761495	−0.00555377
$189$	12.0103	0.873620
$190$	−0.369071	−0.0267752
$191$	13.8611	1.00295	0.501476	−	0.865171i	$-0.332790\pi$
$191$	13.8611	1.00295	0.501476	+	0.865171i	$0.332790\pi$
$192$	−15.3812	−1.11004
$193$	6.00754	0.432432	0.216216	−	0.976346i	$-0.430628\pi$
$193$	6.00754	0.432432	0.216216	+	0.976346i	$0.430628\pi$
$194$	23.6773	1.69993
$195$	13.8502	0.991835
$196$	0.194797	0.0139141
$197$	−16.8165	−1.19813	−0.599063	−	0.800702i	$-0.704460\pi$
$197$	−16.8165	−1.19813	−0.599063	+	0.800702i	$0.704460\pi$
$198$	−1.35342	−0.0961831
$199$	−18.3220	−1.29881	−0.649406	−	0.760442i	$-0.724982\pi$
$199$	−18.3220	−1.29881	−0.649406	+	0.760442i	$0.724982\pi$
$200$	5.42266	0.383440
$201$	0.556111	0.0392250
$202$	−9.21555	−0.648404
$203$	−7.18390	−0.504211
$204$	0.300161	0.0210155
$205$	−20.4290	−1.42682
$206$	22.7892	1.58780
$207$	1.09208	0.0759047
$208$	15.7815	1.09425
$209$	0.652709	0.0451488
$210$	−10.4411	−0.720508
$211$	−2.42356	−0.166845	−0.0834224	−	0.996514i	$-0.526585\pi$
$211$	−2.42356	−0.166845	−0.0834224	+	0.996514i	$0.526585\pi$
$212$	1.40906	0.0967749
$213$	8.18056	0.560523
$214$	25.4059	1.73671
$215$	−19.2127	−1.31030
$216$	−14.5898	−0.992708
$217$	−19.9315	−1.35304
$218$	−17.9769	−1.21755
$219$	6.86889	0.464156
$220$	1.25936	0.0849062
$221$	−4.33750	−0.291772
$222$	−5.21261	−0.349848
$223$	16.5366	1.10737	0.553686	−	0.832725i	$-0.313221\pi$
$223$	16.5366	1.10737	0.553686	+	0.832725i	$0.313221\pi$
$224$	2.27378	0.151923
$225$	−0.434653	−0.0289769
$226$	−17.5316	−1.16618
$227$	−28.0037	−1.85867	−0.929336	−	0.369235i	$-0.879620\pi$
$227$	−28.0037	−1.85867	−0.929336	+	0.369235i	$0.879620\pi$
$228$	−0.0460891	−0.00305233
$229$	0.581148	0.0384033	0.0192017	−	0.999816i	$-0.493888\pi$
$229$	0.581148	0.0384033	0.0192017	+	0.999816i	$0.493888\pi$
$230$	11.1624	0.736028
$231$	18.4654	1.21493
$232$	8.72681	0.572943
$233$	−17.2017	−1.12692	−0.563461	−	0.826143i	$-0.690531\pi$
$233$	−17.2017	−1.12692	−0.563461	+	0.826143i	$0.690531\pi$
$234$	−1.38100	−0.0902791
$235$	0.810085	0.0528441
$236$	−0.166881	−0.0108630
$237$	8.24496	0.535567
$238$	3.26987	0.211954
$239$	17.9618	1.16185	0.580925	−	0.813957i	$-0.302691\pi$
$239$	17.9618	1.16185	0.580925	+	0.813957i	$0.302691\pi$
$240$	11.6179	0.749931
$241$	23.2637	1.49855	0.749275	−	0.662259i	$-0.230402\pi$
$241$	23.2637	1.49855	0.749275	+	0.662259i	$0.230402\pi$
$242$	9.57182	0.615300
$243$	2.43835	0.156420
$244$	−2.23135	−0.142848
$245$	−2.07227	−0.132392
$246$	28.0234	1.78671
$247$	0.666015	0.0423775
$248$	24.2123	1.53748
$249$	−7.43333	−0.471068
$250$	−16.4608	−1.04107
$251$	13.6575	0.862051	0.431025	−	0.902340i	$-0.358152\pi$
$251$	13.6575	0.862051	0.431025	+	0.902340i	$0.358152\pi$
$252$	−0.0947768	−0.00597038
$253$	−19.7409	−1.24110
$254$	15.9066	0.998071
$255$	−3.19314	−0.199962
$256$	−3.97648	−0.248530
$257$	−4.63325	−0.289014	−0.144507	−	0.989504i	$-0.546160\pi$
$257$	−4.63325	−0.289014	−0.144507	+	0.989504i	$0.546160\pi$
$258$	26.3550	1.64079
$259$	5.16949	0.321216
$260$	1.28504	0.0796945
$261$	−0.699497	−0.0432978
$262$	−4.76946	−0.294658
$263$	22.0591	1.36022	0.680111	−	0.733110i	$-0.261932\pi$
$263$	22.0591	1.36022	0.680111	+	0.733110i	$0.261932\pi$
$264$	−22.4312	−1.38055
$265$	−14.9898	−0.920813
$266$	−0.502083	−0.0307847
$267$	−19.0027	−1.16295
$268$	0.0515964	0.00315175
$269$	−25.4625	−1.55248	−0.776238	−	0.630440i	$-0.782874\pi$
$269$	−25.4625	−1.55248	−0.776238	+	0.630440i	$0.782874\pi$
$270$	11.9532	0.727447
$271$	−8.03810	−0.488280	−0.244140	−	0.969740i	$-0.578506\pi$
$271$	−8.03810	−0.488280	−0.244140	+	0.969740i	$0.578506\pi$
$272$	−3.63839	−0.220610
$273$	18.8418	1.14036
$274$	−12.2369	−0.739258
$275$	7.85700	0.473795
$276$	1.39395	0.0839058
$277$	−21.7776	−1.30849	−0.654245	−	0.756282i	$-0.727014\pi$
$277$	−21.7776	−1.30849	−0.654245	+	0.756282i	$0.727014\pi$
$278$	−24.9651	−1.49731
$279$	−1.94073	−0.116189
$280$	−12.5787	−0.751721
$281$	8.63709	0.515246	0.257623	−	0.966246i	$-0.417061\pi$
$281$	8.63709	0.515246	0.257623	+	0.966246i	$0.417061\pi$
$282$	−1.11123	−0.0661728
$283$	−7.56675	−0.449796	−0.224898	−	0.974382i	$-0.572205\pi$
$283$	−7.56675	−0.449796	−0.224898	+	0.974382i	$0.572205\pi$
$284$	0.758999	0.0450383
$285$	0.490300	0.0290429
$286$	24.9637	1.47614
$287$	−27.7916	−1.64048
$288$	0.221398	0.0130460
$289$	1.00000	0.0588235
$290$	−7.14974	−0.419847
$291$	−31.4547	−1.84391
$292$	0.637301	0.0372952
$293$	−7.12908	−0.416485	−0.208243	−	0.978077i	$-0.566774\pi$
$293$	−7.12908	−0.416485	−0.208243	+	0.978077i	$0.566774\pi$
$294$	2.84263	0.165785
$295$	1.77529	0.103361
$296$	−6.27975	−0.365003
$297$	−21.1394	−1.22663
$298$	20.1773	1.16884
$299$	−20.1434	−1.16492
$300$	−0.554799	−0.0320313
$301$	−26.1369	−1.50651
$302$	20.3613	1.17166
$303$	12.2426	0.703319
$304$	0.558668	0.0320418
$305$	23.7373	1.35919
$306$	0.318388	0.0182010
$307$	−18.4198	−1.05127	−0.525635	−	0.850710i	$-0.676172\pi$
$307$	−18.4198	−1.05127	−0.525635	+	0.850710i	$0.676172\pi$
$308$	1.71323	0.0976206
$309$	−30.2748	−1.72227
$310$	−19.8367	−1.12665
$311$	−18.1199	−1.02749	−0.513743	−	0.857944i	$-0.671741\pi$
$311$	−18.1199	−1.02749	−0.513743	+	0.857944i	$0.671741\pi$
$312$	−22.8885	−1.29581
$313$	−13.5682	−0.766919	−0.383459	−	0.923558i	$-0.625267\pi$
$313$	−13.5682	−0.766919	−0.383459	+	0.923558i	$0.625267\pi$
$314$	−19.9242	−1.12439
$315$	1.00824	0.0568081
$316$	0.764974	0.0430331
$317$	−24.1764	−1.35788	−0.678941	−	0.734193i	$-0.737561\pi$
$317$	−24.1764	−1.35788	−0.678941	+	0.734193i	$0.737561\pi$
$318$	20.5621	1.15307
$319$	12.6445	0.707954
$320$	15.1814	0.848664
$321$	−33.7511	−1.88380
$322$	15.1853	0.846244
$323$	−0.153548	−0.00854365
$324$	1.61043	0.0894682
$325$	8.01717	0.444712
$326$	27.2730	1.51051
$327$	23.8818	1.32067
$328$	33.7604	1.86411
$329$	1.10204	0.0607573
$330$	18.3776	1.01165
$331$	−34.3545	−1.88829	−0.944147	−	0.329525i	$-0.893111\pi$
$331$	−34.3545	−1.88829	−0.944147	+	0.329525i	$0.893111\pi$
$332$	−0.689670	−0.0378506
$333$	0.503353	0.0275836
$334$	26.4726	1.44852
$335$	−0.548887	−0.0299889
$336$	15.8049	0.862229
$337$	6.98574	0.380537	0.190269	−	0.981732i	$-0.439064\pi$
$337$	6.98574	0.380537	0.190269	+	0.981732i	$0.439064\pi$
$338$	7.87157	0.428157
$339$	23.2902	1.26495
$340$	−0.296262	−0.0160671
$341$	35.0817	1.89978
$342$	−0.0488878	−0.00264355
$343$	−19.7248	−1.06504
$344$	31.7504	1.71187
$345$	−14.8289	−0.798364
$346$	−11.0340	−0.593193
$347$	−4.17571	−0.224164	−0.112082	−	0.993699i	$-0.535752\pi$
$347$	−4.17571	−0.224164	−0.112082	+	0.993699i	$0.535752\pi$
$348$	−0.892851	−0.0478618
$349$	3.88405	0.207909	0.103954	−	0.994582i	$-0.466850\pi$
$349$	3.88405	0.207909	0.103954	+	0.994582i	$0.466850\pi$
$350$	−6.04383	−0.323057
$351$	−21.5703	−1.15134
$352$	−4.00210	−0.213313
$353$	3.46138	0.184231	0.0921154	−	0.995748i	$-0.470637\pi$
$353$	3.46138	0.184231	0.0921154	+	0.995748i	$0.470637\pi$
$354$	−2.43525	−0.129432
$355$	−8.07430	−0.428539
$356$	−1.76309	−0.0934434
$357$	−4.34393	−0.229905
$358$	4.57114	0.241592
$359$	−4.08123	−0.215399	−0.107699	−	0.994183i	$-0.534348\pi$
$359$	−4.08123	−0.215399	−0.107699	+	0.994183i	$0.534348\pi$
$360$	−1.22479	−0.0645520
$361$	−18.9764	−0.998759
$362$	6.91561	0.363476
$363$	−12.7159	−0.667412
$364$	1.74816	0.0916284
$365$	−6.77967	−0.354864
$366$	−32.5615	−1.70202
$367$	5.51644	0.287956	0.143978	−	0.989581i	$-0.454011\pi$
$367$	5.51644	0.287956	0.143978	+	0.989581i	$0.454011\pi$
$368$	−16.8967	−0.880802
$369$	−2.70607	−0.140872
$370$	5.14490	0.267471
$371$	−20.3920	−1.05870
$372$	−2.47719	−0.128436
$373$	9.25776	0.479349	0.239674	−	0.970853i	$-0.422959\pi$
$373$	9.25776	0.479349	0.239674	+	0.970853i	$0.422959\pi$
$374$	−5.75533	−0.297601
$375$	21.8677	1.12924
$376$	−1.33872	−0.0690395
$377$	12.9022	0.664498
$378$	16.2611	0.836379
$379$	9.46764	0.486320	0.243160	−	0.969986i	$-0.421816\pi$
$379$	9.46764	0.486320	0.243160	+	0.969986i	$0.421816\pi$
$380$	0.0454905	0.00233361
$381$	−21.1315	−1.08260
$382$	18.7669	0.960198
$383$	−16.4343	−0.839751	−0.419876	−	0.907582i	$-0.637926\pi$
$383$	−16.4343	−0.839751	−0.419876	+	0.907582i	$0.637926\pi$
$384$	−17.4382	−0.889888
$385$	−18.2255	−0.928859
$386$	8.13377	0.413998
$387$	−2.54495	−0.129367
$388$	−2.91839	−0.148159
$389$	−6.86143	−0.347889	−0.173944	−	0.984755i	$-0.555651\pi$
$389$	−6.86143	−0.347889	−0.173944	+	0.984755i	$0.555651\pi$
$390$	18.7522	0.949554
$391$	4.64401	0.234858
$392$	3.42458	0.172967
$393$	6.33609	0.319614
$394$	−22.7683	−1.14705
$395$	−8.13786	−0.409460
$396$	0.166818	0.00838290
$397$	36.5450	1.83414	0.917069	−	0.398727i	$-0.130548\pi$
$397$	36.5450	1.83414	0.917069	+	0.398727i	$0.130548\pi$
$398$	−24.8067	−1.24345
$399$	0.667003	0.0333919
$400$	6.72498	0.336249
$401$	−5.52387	−0.275849	−0.137924	−	0.990443i	$-0.544043\pi$
$401$	−5.52387	−0.275849	−0.137924	+	0.990443i	$0.544043\pi$
$402$	0.752934	0.0375529
$403$	35.7968	1.78317
$404$	1.13588	0.0565121
$405$	−17.1319	−0.851290
$406$	−9.72648	−0.482717
$407$	−9.09887	−0.451014
$408$	5.27689	0.261245
$409$	0.812397	0.0401704	0.0200852	−	0.999798i	$-0.493606\pi$
$409$	0.812397	0.0401704	0.0200852	+	0.999798i	$0.493606\pi$
$410$	−27.6594	−1.36600
$411$	16.2564	0.801868
$412$	−2.80892	−0.138386
$413$	2.41510	0.118839
$414$	1.47859	0.0726689
$415$	7.33677	0.360148
$416$	−4.08368	−0.200219
$417$	33.1654	1.62412
$418$	0.883721	0.0432242
$419$	−30.2247	−1.47657	−0.738286	−	0.674488i	$-0.764365\pi$
$419$	−30.2247	−1.47657	−0.738286	+	0.674488i	$0.764365\pi$
$420$	1.28694	0.0627963
$421$	34.7171	1.69201	0.846003	−	0.533178i	$-0.179002\pi$
$421$	34.7171	1.69201	0.846003	+	0.533178i	$0.179002\pi$
$422$	−3.28132	−0.159732
$423$	0.107305	0.00521737
$424$	24.7717	1.20302
$425$	−1.84834	−0.0896576
$426$	11.0759	0.536628
$427$	32.2922	1.56273
$428$	−3.13145	−0.151364
$429$	−33.1636	−1.60116
$430$	−26.0126	−1.25444
$431$	30.7553	1.48143	0.740714	−	0.671820i	$-0.234487\pi$
$431$	30.7553	1.48143	0.740714	+	0.671820i	$0.234487\pi$
$432$	−18.0937	−0.870533
$433$	2.81583	0.135320	0.0676602	−	0.997708i	$-0.478447\pi$
$433$	2.81583	0.135320	0.0676602	+	0.997708i	$0.478447\pi$
$434$	−26.9859	−1.29536
$435$	9.49823	0.455405
$436$	2.21577	0.106116
$437$	−0.713079	−0.0341112
$438$	9.29997	0.444370
$439$	17.9795	0.858117	0.429059	−	0.903277i	$-0.358845\pi$
$439$	17.9795	0.858117	0.429059	+	0.903277i	$0.358845\pi$
$440$	22.1399	1.05548
$441$	−0.274497	−0.0130713
$442$	−5.87266	−0.279334
$443$	−25.3827	−1.20597	−0.602985	−	0.797753i	$-0.706022\pi$
$443$	−25.3827	−1.20597	−0.602985	+	0.797753i	$0.706022\pi$
$444$	0.642490	0.0304912
$445$	18.7559	0.889114
$446$	22.3894	1.06017
$447$	−26.8050	−1.26783
$448$	20.6527	0.975748
$449$	−20.1400	−0.950465	−0.475233	−	0.879860i	$-0.657636\pi$
$449$	−20.1400	−0.950465	−0.475233	+	0.879860i	$0.657636\pi$
$450$	−0.588488	−0.0277416
$451$	48.9162	2.30337
$452$	2.16088	0.101639
$453$	−27.0495	−1.27089
$454$	−37.9150	−1.77944
$455$	−18.5971	−0.871844
$456$	−0.810257	−0.0379438
$457$	−15.1194	−0.707257	−0.353629	−	0.935386i	$-0.615052\pi$
$457$	−15.1194	−0.707257	−0.353629	+	0.935386i	$0.615052\pi$
$458$	0.786832	0.0367662
$459$	4.97299	0.232120
$460$	−1.37584	−0.0641490
$461$	1.71291	0.0797781	0.0398890	−	0.999204i	$-0.487300\pi$
$461$	1.71291	0.0797781	0.0398890	+	0.999204i	$0.487300\pi$
$462$	25.0008	1.16314
$463$	2.65162	0.123231	0.0616156	−	0.998100i	$-0.480375\pi$
$463$	2.65162	0.123231	0.0616156	+	0.998100i	$0.480375\pi$
$464$	10.8227	0.502430
$465$	26.3526	1.22207
$466$	−23.2899	−1.07888
$467$	1.03816	0.0480403	0.0240202	−	0.999711i	$-0.492353\pi$
$467$	1.03816	0.0480403	0.0240202	+	0.999711i	$0.492353\pi$
$468$	0.170218	0.00786834
$469$	−0.746705	−0.0344796
$470$	1.09680	0.0505914
$471$	26.4687	1.21961
$472$	−2.93380	−0.135039
$473$	46.0039	2.11526
$474$	11.1631	0.512737
$475$	0.283809	0.0130221
$476$	−0.403034	−0.0184730
$477$	−1.98557	−0.0909131
$478$	24.3189	1.11232
$479$	−14.0429	−0.641637	−0.320819	−	0.947141i	$-0.603958\pi$
$479$	−14.0429	−0.641637	−0.320819	+	0.947141i	$0.603958\pi$
$480$	−3.00628	−0.137217
$481$	−9.28435	−0.423330
$482$	31.4974	1.43467
$483$	−20.1733	−0.917915
$484$	−1.17979	−0.0536269
$485$	31.0461	1.40973
$486$	3.30135	0.149752
$487$	32.7289	1.48309	0.741543	−	0.670905i	$-0.234094\pi$
$487$	32.7289	1.48309	0.741543	+	0.670905i	$0.234094\pi$
$488$	−39.2276	−1.77575
$489$	−36.2314	−1.63844
$490$	−2.80570	−0.126749
$491$	−32.3226	−1.45870	−0.729349	−	0.684142i	$-0.760177\pi$
$491$	−32.3226	−1.45870	−0.729349	+	0.684142i	$0.760177\pi$
$492$	−3.45407	−0.155722
$493$	−2.97458	−0.133968
$494$	0.901736	0.0405710
$495$	−1.77462	−0.0797633
$496$	30.0272	1.34826
$497$	−10.9843	−0.492711
$498$	−10.0642	−0.450987
$499$	32.6182	1.46019	0.730097	−	0.683344i	$-0.239475\pi$
$499$	32.6182	1.46019	0.730097	+	0.683344i	$0.239475\pi$
$500$	2.02890	0.0907353
$501$	−35.1681	−1.57119
$502$	18.4912	0.825303
$503$	11.0741	0.493771	0.246886	−	0.969045i	$-0.420593\pi$
$503$	11.0741	0.493771	0.246886	+	0.969045i	$0.420593\pi$
$504$	−1.66620	−0.0742183
$505$	−12.0836	−0.537712
$506$	−26.7278	−1.18820
$507$	−10.4572	−0.464419
$508$	−1.96060	−0.0869876
$509$	6.22486	0.275912	0.137956	−	0.990438i	$-0.455947\pi$
$509$	6.22486	0.275912	0.137956	+	0.990438i	$0.455947\pi$
$510$	−4.32328	−0.191438
$511$	−9.22304	−0.408003
$512$	−24.7741	−1.09487
$513$	−0.763594	−0.0337135
$514$	−6.27309	−0.276694
$515$	29.8815	1.31674
$516$	−3.24843	−0.143004
$517$	−1.93971	−0.0853082
$518$	6.99911	0.307523
$519$	14.6584	0.643432
$520$	22.5912	0.990690
$521$	−17.8717	−0.782974	−0.391487	−	0.920184i	$-0.628039\pi$
$521$	−17.8717	−0.782974	−0.391487	+	0.920184i	$0.628039\pi$
$522$	−0.947068	−0.0414520
$523$	−3.17004	−0.138616	−0.0693081	−	0.997595i	$-0.522079\pi$
$523$	−3.17004	−0.138616	−0.0693081	+	0.997595i	$0.522079\pi$
$524$	0.587868	0.0256811
$525$	8.02906	0.350417
$526$	29.8664	1.30224
$527$	−8.25288	−0.359501
$528$	−27.8184	−1.21064
$529$	−1.43320	−0.0623128
$530$	−20.2950	−0.881560
$531$	0.235159	0.0102050
$532$	0.0618851	0.00268306
$533$	49.9134	2.16199
$534$	−25.7283	−1.11337
$535$	33.3127	1.44023
$536$	0.907077	0.0391797
$537$	−6.07264	−0.262054
$538$	−34.4744	−1.48630
$539$	4.96194	0.213726
$540$	−1.47331	−0.0634011
$541$	24.6280	1.05884	0.529420	−	0.848360i	$-0.322409\pi$
$541$	24.6280	1.05884	0.529420	+	0.848360i	$0.322409\pi$
$542$	−10.8830	−0.467465
$543$	−9.18719	−0.394260
$544$	0.941483	0.0403658
$545$	−23.5716	−1.00970
$546$	25.5104	1.09175
$547$	7.80827	0.333857	0.166929	−	0.985969i	$-0.446615\pi$
$547$	7.80827	0.333857	0.166929	+	0.985969i	$0.446615\pi$
$548$	1.50828	0.0644305
$549$	3.14429	0.134195
$550$	10.6378	0.453598
$551$	0.456741	0.0194578
$552$	24.5059	1.04304
$553$	−11.0707	−0.470775
$554$	−29.4853	−1.25271
$555$	−6.83486	−0.290124
$556$	3.07711	0.130499
$557$	6.21629	0.263393	0.131696	−	0.991290i	$-0.457958\pi$
$557$	6.21629	0.263393	0.131696	+	0.991290i	$0.457958\pi$
$558$	−2.62761	−0.111236
$559$	46.9416	1.98542
$560$	−15.5996	−0.659205
$561$	7.64580	0.322806
$562$	11.6940	0.493281
$563$	−27.0875	−1.14160	−0.570802	−	0.821088i	$-0.693367\pi$
$563$	−27.0875	−1.14160	−0.570802	+	0.821088i	$0.693367\pi$
$564$	0.136967	0.00576734
$565$	−22.9877	−0.967098
$566$	−10.2448	−0.430622
$567$	−23.3062	−0.978767
$568$	13.3434	0.559875
$569$	−10.0351	−0.420692	−0.210346	−	0.977627i	$-0.567459\pi$
$569$	−10.0351	−0.420692	−0.210346	+	0.977627i	$0.567459\pi$
$570$	0.663831	0.0278048
$571$	24.9847	1.04558	0.522788	−	0.852463i	$-0.324892\pi$
$571$	24.9847	1.04558	0.522788	+	0.852463i	$0.324892\pi$
$572$	−3.07695	−0.128654
$573$	−24.9313	−1.04152
$574$	−37.6278	−1.57055
$575$	−8.58370	−0.357965
$576$	2.01095	0.0837897
$577$	−35.9940	−1.49845	−0.749225	−	0.662316i	$-0.769574\pi$
$577$	−35.9940	−1.49845	−0.749225	+	0.662316i	$0.769574\pi$
$578$	1.35393	0.0563160
$579$	−10.8055	−0.449061
$580$	0.881253	0.0365921
$581$	9.98093	0.414079
$582$	−42.5874	−1.76530
$583$	35.8922	1.48650
$584$	11.2039	0.463620
$585$	−1.81080	−0.0748672
$586$	−9.65225	−0.398731
$587$	−25.9681	−1.07182	−0.535909	−	0.844276i	$-0.680031\pi$
$587$	−25.9681	−1.07182	−0.535909	+	0.844276i	$0.680031\pi$
$588$	−0.350373	−0.0144491
$589$	1.26721	0.0522146
$590$	2.40362	0.0989553
$591$	30.2471	1.24420
$592$	−7.78792	−0.320081
$593$	−35.2982	−1.44952	−0.724761	−	0.689000i	$-0.758050\pi$
$593$	−35.2982	−1.44952	−0.724761	+	0.689000i	$0.758050\pi$
$594$	−28.6212	−1.17434
$595$	4.28751	0.175771
$596$	−2.48699	−0.101871
$597$	32.9549	1.34876
$598$	−27.2727	−1.11526
$599$	36.0624	1.47347	0.736735	−	0.676182i	$-0.236367\pi$
$599$	36.0624	1.47347	0.736735	+	0.676182i	$0.236367\pi$
$600$	−9.75349	−0.398184
$601$	−1.63317	−0.0666186	−0.0333093	−	0.999445i	$-0.510605\pi$
$601$	−1.63317	−0.0666186	−0.0333093	+	0.999445i	$0.510605\pi$
$602$	−35.3875	−1.44229
$603$	−0.0727067	−0.00296084
$604$	−2.50967	−0.102117
$605$	12.5507	0.510260
$606$	16.5756	0.673337
$607$	−17.0222	−0.690910	−0.345455	−	0.938435i	$-0.612275\pi$
$607$	−17.0222	−0.690910	−0.345455	+	0.938435i	$0.612275\pi$
$608$	−0.144563	−0.00586280
$609$	12.9214	0.523600
$610$	32.1386	1.30125
$611$	−1.97925	−0.0800718
$612$	−0.0392434	−0.00158632
$613$	27.9571	1.12918	0.564589	−	0.825372i	$-0.309035\pi$
$613$	27.9571	1.12918	0.564589	+	0.825372i	$0.309035\pi$
$614$	−24.9390	−1.00646
$615$	36.7447	1.48169
$616$	30.1190	1.21353
$617$	−4.60023	−0.185198	−0.0925992	−	0.995703i	$-0.529518\pi$
$617$	−4.60023	−0.185198	−0.0925992	+	0.995703i	$0.529518\pi$
$618$	−40.9899	−1.64885
$619$	−7.43277	−0.298748	−0.149374	−	0.988781i	$-0.547726\pi$
$619$	−7.43277	−0.298748	−0.149374	+	0.988781i	$0.547726\pi$
$620$	2.44501	0.0981941
$621$	23.0946	0.926755
$622$	−24.5330	−0.983685
$623$	25.5154	1.02225
$624$	−28.3855	−1.13633
$625$	−12.3419	−0.493678
$626$	−18.3703	−0.734226
$627$	−1.17400	−0.0468850
$628$	2.45579	0.0979966
$629$	2.14049	0.0853467
$630$	1.36509	0.0543865
$631$	−13.8706	−0.552180	−0.276090	−	0.961132i	$-0.589039\pi$
$631$	−13.8706	−0.552180	−0.276090	+	0.961132i	$0.589039\pi$
$632$	13.4484	0.534949
$633$	4.35915	0.173261
$634$	−32.7331	−1.30000
$635$	20.8570	0.827687
$636$	−2.53442	−0.100496
$637$	5.06309	0.200607
$638$	17.1197	0.677774
$639$	−1.06954	−0.0423102
$640$	17.2117	0.680350
$641$	10.5968	0.418549	0.209275	−	0.977857i	$-0.432890\pi$
$641$	10.5968	0.418549	0.209275	+	0.977857i	$0.432890\pi$
$642$	−45.6965	−1.80350
$643$	−44.1301	−1.74032	−0.870160	−	0.492770i	$-0.835984\pi$
$643$	−44.1301	−1.74032	−0.870160	+	0.492770i	$0.835984\pi$
$644$	−1.87169	−0.0737550
$645$	34.5570	1.36068
$646$	−0.207893	−0.00817944
$647$	28.3371	1.11405	0.557023	−	0.830497i	$-0.311944\pi$
$647$	28.3371	1.11405	0.557023	+	0.830497i	$0.311944\pi$
$648$	28.3117	1.11219
$649$	−4.25084	−0.166860
$650$	10.8547	0.425755
$651$	35.8499	1.40507
$652$	−3.36158	−0.131650
$653$	−43.3531	−1.69654	−0.848268	−	0.529567i	$-0.822354\pi$
$653$	−43.3531	−1.69654	−0.848268	+	0.529567i	$0.822354\pi$
$654$	32.3342	1.26437
$655$	−6.25379	−0.244356
$656$	41.8685	1.63469
$657$	−0.898047	−0.0350362
$658$	1.49208	0.0581673
$659$	−8.61752	−0.335691	−0.167845	−	0.985813i	$-0.553681\pi$
$659$	−8.61752	−0.335691	−0.167845	+	0.985813i	$0.553681\pi$
$660$	−2.26516	−0.0881712
$661$	−36.1230	−1.40502	−0.702511	−	0.711672i	$-0.747938\pi$
$661$	−36.1230	−1.40502	−0.702511	+	0.711672i	$0.747938\pi$
$662$	−46.5135	−1.80780
$663$	7.80166	0.302991
$664$	−12.1246	−0.470524
$665$	−0.658339	−0.0255293
$666$	0.681504	0.0264077
$667$	−13.8139	−0.534878
$668$	−3.26292	−0.126246
$669$	−29.7436	−1.14996
$670$	−0.743154	−0.0287105
$671$	−56.8377	−2.19420
$672$	−4.08974	−0.157765
$673$	46.9177	1.80854	0.904271	−	0.426958i	$-0.140415\pi$
$673$	46.9177	1.80854	0.904271	+	0.426958i	$0.140415\pi$
$674$	9.45818	0.364316
$675$	−9.19178	−0.353792
$676$	−0.970224	−0.0373163
$677$	−16.4894	−0.633740	−0.316870	−	0.948469i	$-0.602632\pi$
$677$	−16.4894	−0.633740	−0.316870	+	0.948469i	$0.602632\pi$
$678$	31.5332	1.21103
$679$	42.2350	1.62083
$680$	−5.20835	−0.199731
$681$	50.3690	1.93015
$682$	47.4981	1.81879
$683$	−39.5108	−1.51184	−0.755919	−	0.654665i	$-0.772810\pi$
$683$	−39.5108	−1.51184	−0.755919	+	0.654665i	$0.772810\pi$
$684$	0.00602576	0.000230401 0
$685$	−16.0452	−0.613056
$686$	−26.7060	−1.01964
$687$	−1.04528	−0.0398801
$688$	39.3757	1.50118
$689$	36.6238	1.39526
$690$	−20.0773	−0.764331
$691$	−44.5788	−1.69586	−0.847929	−	0.530110i	$-0.822151\pi$
$691$	−44.5788	−1.69586	−0.847929	+	0.530110i	$0.822151\pi$
$692$	1.36002	0.0517002
$693$	−2.41419	−0.0917075
$694$	−5.65361	−0.214608
$695$	−32.7346	−1.24169
$696$	−15.6965	−0.594975
$697$	−11.5074	−0.435874
$698$	5.25873	0.199046
$699$	30.9400	1.17026
$700$	0.744943	0.0281562
$701$	15.9761	0.603408	0.301704	−	0.953402i	$-0.402445\pi$
$701$	15.9761	0.603408	0.301704	+	0.953402i	$0.402445\pi$
$702$	−29.2047	−1.10226
$703$	−0.328668	−0.0123959
$704$	−36.3510	−1.37003
$705$	−1.45706	−0.0548762
$706$	4.68646	0.176377
$707$	−16.4385	−0.618232
$708$	0.300161	0.0112807
$709$	−50.8419	−1.90941	−0.954705	−	0.297555i	$-0.903829\pi$
$709$	−50.8419	−1.90941	−0.954705	+	0.297555i	$0.903829\pi$
$710$	−10.9320	−0.410271
$711$	−1.07796	−0.0404265
$712$	−30.9954	−1.16160
$713$	−38.3264	−1.43534
$714$	−5.88137	−0.220105
$715$	32.7329	1.22414
$716$	−0.563424	−0.0210562
$717$	−32.3070	−1.20653
$718$	−5.52568	−0.206217
$719$	−47.3464	−1.76572	−0.882862	−	0.469633i	$-0.844386\pi$
$719$	−47.3464	−1.76572	−0.882862	+	0.469633i	$0.844386\pi$
$720$	−1.51894	−0.0566074
$721$	40.6508	1.51391
$722$	−25.6927	−0.956183
$723$	−41.8434	−1.55617
$724$	−0.852396	−0.0316790
$725$	5.49802	0.204192
$726$	−17.2164	−0.638961
$727$	31.3479	1.16263	0.581314	−	0.813679i	$-0.302539\pi$
$727$	31.3479	1.16263	0.581314	+	0.813679i	$0.302539\pi$
$728$	30.7330	1.13904
$729$	24.5648	0.909807
$730$	−9.17917	−0.339736
$731$	−10.8223	−0.400277
$732$	4.01343	0.148341
$733$	−20.8271	−0.769267	−0.384633	−	0.923069i	$-0.625672\pi$
$733$	−20.8271	−0.769267	−0.384633	+	0.923069i	$0.625672\pi$
$734$	7.46886	0.275681
$735$	3.72730	0.137483
$736$	4.37225	0.161163
$737$	1.31428	0.0484122
$738$	−3.66382	−0.134867
$739$	0.941756	0.0346431	0.0173215	−	0.999850i	$-0.494486\pi$
$739$	0.941756	0.0346431	0.0173215	+	0.999850i	$0.494486\pi$
$740$	−0.634144	−0.0233116
$741$	−1.19793	−0.0440071
$742$	−27.6093	−1.01357
$743$	8.86837	0.325349	0.162674	−	0.986680i	$-0.447988\pi$
$743$	8.86837	0.325349	0.162674	+	0.986680i	$0.447988\pi$
$744$	−43.5495	−1.59660
$745$	26.4568	0.969304
$746$	12.5343	0.458915
$747$	0.971843	0.0355579
$748$	0.709384	0.0259376
$749$	45.3184	1.65590
$750$	29.6073	1.08110
$751$	24.2181	0.883731	0.441866	−	0.897081i	$-0.354317\pi$
$751$	24.2181	0.883731	0.441866	+	0.897081i	$0.354317\pi$
$752$	−1.66024	−0.0605426
$753$	−24.5650	−0.895200
$754$	17.4687	0.636171
$755$	26.6981	0.971644
$756$	−2.00429	−0.0728952
$757$	−8.96517	−0.325845	−0.162922	−	0.986639i	$-0.552092\pi$
$757$	−8.96517	−0.325845	−0.162922	+	0.986639i	$0.552092\pi$
$758$	12.8185	0.465589
$759$	35.5072	1.28883
$760$	0.799733	0.0290093
$761$	−48.0735	−1.74266	−0.871331	−	0.490696i	$-0.836743\pi$
$761$	−48.0735	−1.74266	−0.871331	+	0.490696i	$0.836743\pi$
$762$	−28.6106	−1.03645
$763$	−32.0667	−1.16089
$764$	−2.31315	−0.0836867
$765$	0.417475	0.0150938
$766$	−22.2508	−0.803954
$767$	−4.33750	−0.156618
$768$	7.15231	0.258087
$769$	−16.5302	−0.596096	−0.298048	−	0.954551i	$-0.596335\pi$
$769$	−16.5302	−0.596096	−0.298048	+	0.954551i	$0.596335\pi$
$770$	−24.6761	−0.889263
$771$	8.33362	0.300128
$772$	−1.00254	−0.0360823
$773$	30.2099	1.08658	0.543288	−	0.839547i	$-0.317179\pi$
$773$	30.2099	1.08658	0.543288	+	0.839547i	$0.317179\pi$
$774$	−3.44568	−0.123852
$775$	15.2541	0.547944
$776$	−51.3060	−1.84178
$777$	−9.29813	−0.333568
$778$	−9.28988	−0.333058
$779$	1.76694	0.0633073
$780$	−2.31133	−0.0827590
$781$	19.3335	0.691807
$782$	6.28765	0.224846
$783$	−14.7925	−0.528643
$784$	4.24703	0.151680
$785$	−26.1249	−0.932437
$786$	8.57861	0.305989
$787$	−21.4101	−0.763189	−0.381595	−	0.924330i	$-0.624625\pi$
$787$	−21.4101	−0.763189	−0.381595	+	0.924330i	$0.624625\pi$
$788$	2.80635	0.0999720
$789$	−39.6767	−1.41253
$790$	−11.0181	−0.392005
$791$	−31.2724	−1.11192
$792$	2.93269	0.104209
$793$	−57.9964	−2.05951
$794$	49.4792	1.75595
$795$	26.9614	0.956222
$796$	3.05759	0.108373
$797$	23.7008	0.839524	0.419762	−	0.907634i	$-0.362114\pi$
$797$	23.7008	0.839524	0.419762	+	0.907634i	$0.362114\pi$
$798$	0.903074	0.0319685
$799$	0.456311	0.0161431
$800$	−1.74018	−0.0615247
$801$	2.48444	0.0877833
$802$	−7.47891	−0.264090
$803$	16.2336	0.572870
$804$	−0.0928042	−0.00327295
$805$	19.9112	0.701779
$806$	48.4663	1.70715
$807$	45.7982	1.61217
$808$	19.9690	0.702507
$809$	−5.29172	−0.186047	−0.0930234	−	0.995664i	$-0.529653\pi$
$809$	−5.29172	−0.186047	−0.0930234	+	0.995664i	$0.529653\pi$
$810$	−23.1953	−0.815000
$811$	2.41372	0.0847572	0.0423786	−	0.999102i	$-0.486506\pi$
$811$	2.41372	0.0847572	0.0423786	+	0.999102i	$0.486506\pi$
$812$	1.19885	0.0420715
$813$	14.4578	0.507056
$814$	−12.3192	−0.431788
$815$	35.7608	1.25265
$816$	6.54421	0.229093
$817$	1.66174	0.0581370
$818$	1.09993	0.0384580
$819$	−2.46340	−0.0860782
$820$	3.40921	0.119055
$821$	22.3406	0.779691	0.389845	−	0.920880i	$-0.372528\pi$
$821$	22.3406	0.779691	0.389845	+	0.920880i	$0.372528\pi$
$822$	22.0099	0.767685
$823$	−11.5909	−0.404035	−0.202017	−	0.979382i	$-0.564750\pi$
$823$	−11.5909	−0.404035	−0.202017	+	0.979382i	$0.564750\pi$
$824$	−49.3814	−1.72028
$825$	−14.1320	−0.492014
$826$	3.26987	0.113773
$827$	−5.69589	−0.198065	−0.0990327	−	0.995084i	$-0.531575\pi$
$827$	−5.69589	−0.198065	−0.0990327	+	0.995084i	$0.531575\pi$
$828$	−0.182247	−0.00633351
$829$	−20.6184	−0.716106	−0.358053	−	0.933701i	$-0.616559\pi$
$829$	−20.6184	−0.716106	−0.358053	+	0.933701i	$0.616559\pi$
$830$	9.93346	0.344795
$831$	39.1704	1.35881
$832$	−37.0920	−1.28593
$833$	−1.16728	−0.0404440
$834$	44.9036	1.55488
$835$	34.7113	1.20123
$836$	−0.108925	−0.00376724
$837$	−41.0415	−1.41860
$838$	−40.9220	−1.41363
$839$	−11.8695	−0.409781	−0.204890	−	0.978785i	$-0.565684\pi$
$839$	−11.8695	−0.409781	−0.204890	+	0.978785i	$0.565684\pi$
$840$	22.6247	0.780627
$841$	−20.1519	−0.694893
$842$	47.0044	1.61988
$843$	−15.5351	−0.535059
$844$	0.404445	0.0139216
$845$	10.3213	0.355064
$846$	0.145284	0.00499496
$847$	17.0740	0.586669
$848$	30.7209	1.05496
$849$	13.6100	0.467093
$850$	−2.50252	−0.0858356
$851$	9.94043	0.340754
$852$	−1.36518	−0.0467702
$853$	18.8268	0.644617	0.322309	−	0.946635i	$-0.395541\pi$
$853$	18.8268	0.644617	0.322309	+	0.946635i	$0.395541\pi$
$854$	43.7212	1.49611
$855$	−0.0641025	−0.00219226
$856$	−55.0516	−1.88162
$857$	6.74435	0.230383	0.115191	−	0.993343i	$-0.463252\pi$
$857$	6.74435	0.230383	0.115191	+	0.993343i	$0.463252\pi$
$858$	−44.9011	−1.53290
$859$	22.1459	0.755609	0.377804	−	0.925885i	$-0.376679\pi$
$859$	22.1459	0.755609	0.377804	+	0.925885i	$0.376679\pi$
$860$	3.20623	0.109332
$861$	49.9874	1.70357
$862$	41.6404	1.41828
$863$	17.8331	0.607045	0.303523	−	0.952824i	$-0.401837\pi$
$863$	17.8331	0.607045	0.303523	+	0.952824i	$0.401837\pi$
$864$	4.68199	0.159285
$865$	−14.4680	−0.491927
$866$	3.81244	0.129552
$867$	−1.79865	−0.0610855
$868$	3.32619	0.112898
$869$	19.4857	0.661007
$870$	12.8599	0.435992
$871$	1.34107	0.0454406
$872$	38.9538	1.31914
$873$	4.11243	0.139185
$874$	−0.965457	−0.0326571
$875$	−29.3623	−0.992628
$876$	−1.14628	−0.0387294
$877$	21.8493	0.737800	0.368900	−	0.929469i	$-0.379735\pi$
$877$	21.8493	0.737800	0.368900	+	0.929469i	$0.379735\pi$
$878$	24.3430	0.821537
$879$	12.8227	0.432500
$880$	27.4571	0.925577
$881$	−29.4534	−0.992311	−0.496155	−	0.868234i	$-0.665255\pi$
$881$	−29.4534	−0.992311	−0.496155	+	0.868234i	$0.665255\pi$
$882$	−0.371649	−0.0125141
$883$	55.8091	1.87813	0.939063	−	0.343746i	$-0.111696\pi$
$883$	55.8091	1.87813	0.939063	+	0.343746i	$0.111696\pi$
$884$	0.723844	0.0243455
$885$	−3.19314	−0.107336
$886$	−34.3664	−1.15456
$887$	−44.5696	−1.49650	−0.748251	−	0.663416i	$-0.769106\pi$
$887$	−44.5696	−1.49650	−0.748251	+	0.663416i	$0.769106\pi$
$888$	11.2951	0.379039
$889$	28.3739	0.951629
$890$	25.3941	0.851212
$891$	41.0214	1.37427
$892$	−2.75964	−0.0923996
$893$	−0.0700657	−0.00234466
$894$	−36.2920	−1.21379
$895$	5.99376	0.200349
$896$	23.4147	0.782230
$897$	36.2310	1.20972
$898$	−27.2681	−0.909948
$899$	24.5488	0.818748
$900$	0.0725352	0.00241784
$901$	−8.44354	−0.281295
$902$	66.2290	2.20518
$903$	47.0113	1.56444
$904$	37.9888	1.26349
$905$	9.06786	0.301426
$906$	−36.6230	−1.21672
$907$	38.8734	1.29077	0.645386	−	0.763857i	$-0.276697\pi$
$907$	38.8734	1.29077	0.645386	+	0.763857i	$0.276697\pi$
$908$	4.67328	0.155088
$909$	−1.60061	−0.0530890
$910$	−25.1791	−0.834678
$911$	8.47877	0.280914	0.140457	−	0.990087i	$-0.455143\pi$
$911$	8.47877	0.280914	0.140457	+	0.990087i	$0.455143\pi$
$912$	−1.00485	−0.0332739
$913$	−17.5675	−0.581400
$914$	−20.4706	−0.677108
$915$	−42.6952	−1.41146
$916$	−0.0969823	−0.00320439
$917$	−8.50764	−0.280947
$918$	6.73307	0.222225
$919$	8.70739	0.287230	0.143615	−	0.989634i	$-0.454127\pi$
$919$	8.70739	0.287230	0.143615	+	0.989634i	$0.454127\pi$
$920$	−24.1876	−0.797442
$921$	33.1308	1.09170
$922$	2.31915	0.0763772
$923$	19.7276	0.649342
$924$	−3.08152	−0.101374
$925$	−3.95634	−0.130084
$926$	3.59010	0.117978
$927$	3.95817	0.130003
$928$	−2.80051	−0.0919313
$929$	21.3309	0.699845	0.349922	−	0.936779i	$-0.386208\pi$
$929$	21.3309	0.699845	0.349922	+	0.936779i	$0.386208\pi$
$930$	35.6795	1.16998
$931$	0.179234	0.00587417
$932$	2.87064	0.0940308
$933$	32.5915	1.06700
$934$	1.40559	0.0459924
$935$	−7.54649	−0.246797
$936$	2.99247	0.0978120
$937$	4.23868	0.138472	0.0692358	−	0.997600i	$-0.477944\pi$
$937$	4.23868	0.138472	0.0692358	+	0.997600i	$0.477944\pi$
$938$	−1.01098	−0.0330098
$939$	24.4045	0.796410
$940$	−0.135188	−0.00440933
$941$	18.0268	0.587657	0.293829	−	0.955858i	$-0.405071\pi$
$941$	18.0268	0.587657	0.293829	+	0.955858i	$0.405071\pi$
$942$	35.8367	1.16762
$943$	−53.4405	−1.74026
$944$	−3.63839	−0.118419
$945$	21.3218	0.693597
$946$	62.2859	2.02509
$947$	−28.5595	−0.928058	−0.464029	−	0.885820i	$-0.653597\pi$
$947$	−28.5595	−0.928058	−0.464029	+	0.885820i	$0.653597\pi$
$948$	−1.37592	−0.0446879
$949$	16.5645	0.537706
$950$	0.384257	0.0124669
$951$	43.4850	1.41010
$952$	−7.08542	−0.229640
$953$	12.9902	0.420794	0.210397	−	0.977616i	$-0.432524\pi$
$953$	12.9902	0.420794	0.210397	+	0.977616i	$0.432524\pi$
$954$	−2.68832	−0.0870376
$955$	24.6075	0.796279
$956$	−2.99747	−0.0969452
$957$	−22.7430	−0.735177
$958$	−19.0131	−0.614285
$959$	−21.8279	−0.704858
$960$	−27.3060	−0.881299
$961$	37.1100	1.19710
$962$	−12.5703	−0.405284
$963$	4.41266	0.142196
$964$	−3.88227	−0.125039
$965$	10.6651	0.343323
$966$	−27.3131	−0.878786
$967$	−19.7658	−0.635626	−0.317813	−	0.948153i	$-0.602948\pi$
$967$	−19.7658	−0.635626	−0.317813	+	0.948153i	$0.602948\pi$
$968$	−20.7410	−0.666641
$969$	0.276180	0.00887218
$970$	42.0342	1.34964
$971$	10.4679	0.335930	0.167965	−	0.985793i	$-0.446280\pi$
$971$	10.4679	0.335930	0.167965	+	0.985793i	$0.446280\pi$
$972$	−0.406913	−0.0130518
$973$	−44.5321	−1.42763
$974$	44.3125	1.41986
$975$	−14.4201	−0.461813
$976$	−48.6487	−1.55721
$977$	−23.4487	−0.750191	−0.375095	−	0.926986i	$-0.622390\pi$
$977$	−23.4487	−0.750191	−0.375095	+	0.926986i	$0.622390\pi$
$978$	−49.0547	−1.56860
$979$	−44.9100	−1.43533
$980$	0.345822	0.0110469
$981$	−3.12234	−0.0996886
$982$	−43.7624	−1.39652
$983$	−26.3985	−0.841982	−0.420991	−	0.907065i	$-0.638318\pi$
$983$	−26.3985	−0.841982	−0.420991	+	0.907065i	$0.638318\pi$
$984$	−60.7234	−1.93579
$985$	−29.8542	−0.951233
$986$	−4.02736	−0.128257
$987$	−1.98218	−0.0630936
$988$	−0.111145	−0.00353599
$989$	−50.2588	−1.59814
$990$	−2.40271	−0.0763631
$991$	18.8846	0.599888	0.299944	−	0.953957i	$-0.403032\pi$
$991$	18.8846	0.599888	0.299944	+	0.953957i	$0.403032\pi$
$992$	−7.76994	−0.246696
$993$	61.7919	1.96091
$994$	−14.8719	−0.471707
$995$	−32.5269	−1.03117
$996$	1.24048	0.0393061
$997$	−11.0977	−0.351466	−0.175733	−	0.984438i	$-0.556230\pi$
$997$	−11.0977	−0.351466	−0.175733	+	0.984438i	$0.556230\pi$
$998$	44.1627	1.39795
$999$	10.6446	0.336781

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.h.1.13	✓	16
3.2	odd	2		9027.2.a.n.1.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.h.1.13	✓	16	1.1	even	1	trivial
9027.2.a.n.1.4		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)

\(f(q)\)	\(=\)	\(q+1.35393 q^{2} -1.79865 q^{3} -0.166881 q^{4} +1.77529 q^{5} -2.43525 q^{6} +2.41510 q^{7} -2.93380 q^{8} +0.235159 q^{9} +O(q^{10})\)	\(q+1.35393 q^{2} -1.79865 q^{3} -0.166881 q^{4} +1.77529 q^{5} -2.43525 q^{6} +2.41510 q^{7} -2.93380 q^{8} +0.235159 q^{9} +2.40362 q^{10} -4.25084 q^{11} +0.300161 q^{12} -4.33750 q^{13} +3.26987 q^{14} -3.19314 q^{15} -3.63839 q^{16} +1.00000 q^{17} +0.318388 q^{18} -0.153548 q^{19} -0.296262 q^{20} -4.34393 q^{21} -5.75533 q^{22} +4.64401 q^{23} +5.27689 q^{24} -1.84834 q^{25} -5.87266 q^{26} +4.97299 q^{27} -0.403034 q^{28} -2.97458 q^{29} -4.32328 q^{30} -8.25288 q^{31} +0.941483 q^{32} +7.64580 q^{33} +1.35393 q^{34} +4.28751 q^{35} -0.0392434 q^{36} +2.14049 q^{37} -0.207893 q^{38} +7.80166 q^{39} -5.20835 q^{40} -11.5074 q^{41} -5.88137 q^{42} -10.8223 q^{43} +0.709384 q^{44} +0.417475 q^{45} +6.28765 q^{46} +0.456311 q^{47} +6.54421 q^{48} -1.16728 q^{49} -2.50252 q^{50} -1.79865 q^{51} +0.723844 q^{52} -8.44354 q^{53} +6.73307 q^{54} -7.54649 q^{55} -7.08542 q^{56} +0.276180 q^{57} -4.02736 q^{58} +1.00000 q^{59} +0.532873 q^{60} +13.3709 q^{61} -11.1738 q^{62} +0.567932 q^{63} +8.55148 q^{64} -7.70032 q^{65} +10.3519 q^{66} -0.309182 q^{67} -0.166881 q^{68} -8.35297 q^{69} +5.80498 q^{70} -4.54815 q^{71} -0.689908 q^{72} -3.81890 q^{73} +2.89806 q^{74} +3.32452 q^{75} +0.0256242 q^{76} -10.2662 q^{77} +10.5629 q^{78} -4.58396 q^{79} -6.45920 q^{80} -9.65018 q^{81} -15.5802 q^{82} +4.13272 q^{83} +0.724919 q^{84} +1.77529 q^{85} -14.6526 q^{86} +5.35023 q^{87} +12.4711 q^{88} +10.5650 q^{89} +0.565231 q^{90} -10.4755 q^{91} -0.774995 q^{92} +14.8441 q^{93} +0.617812 q^{94} -0.272593 q^{95} -1.69340 q^{96} +17.4879 q^{97} -1.58042 q^{98} -0.999622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 7 q^{3} + 14 q^{4} - 21 q^{5} - 5 q^{6} - 11 q^{7} - 12 q^{8} + 17 q^{9}+O(q^{10}) \) 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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