LMFDB - Embedded newform 1003.2.a.i.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.8
Root			$-0.149899$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.149899 q^{2} -2.07180 q^{3} -1.97753 q^{4} +4.08629 q^{5} +0.310561 q^{6} +5.08021 q^{7} +0.596228 q^{8} +1.29235 q^{9} +O(q^{10})$	\(q-0.149899 q^{2} -2.07180 q^{3} -1.97753 q^{4} +4.08629 q^{5} +0.310561 q^{6} +5.08021 q^{7} +0.596228 q^{8} +1.29235 q^{9} -0.612531 q^{10} +6.60568 q^{11} +4.09704 q^{12} -2.12783 q^{13} -0.761519 q^{14} -8.46596 q^{15} +3.86569 q^{16} +1.00000 q^{17} -0.193722 q^{18} -4.59660 q^{19} -8.08076 q^{20} -10.5252 q^{21} -0.990185 q^{22} -5.10850 q^{23} -1.23526 q^{24} +11.6977 q^{25} +0.318961 q^{26} +3.53791 q^{27} -10.0463 q^{28} -4.00448 q^{29} +1.26904 q^{30} -1.51654 q^{31} -1.77192 q^{32} -13.6856 q^{33} -0.149899 q^{34} +20.7592 q^{35} -2.55565 q^{36} +2.41581 q^{37} +0.689027 q^{38} +4.40844 q^{39} +2.43636 q^{40} +1.14518 q^{41} +1.57771 q^{42} +7.94203 q^{43} -13.0629 q^{44} +5.28090 q^{45} +0.765760 q^{46} -0.669492 q^{47} -8.00892 q^{48} +18.8086 q^{49} -1.75348 q^{50} -2.07180 q^{51} +4.20786 q^{52} +0.270789 q^{53} -0.530330 q^{54} +26.9927 q^{55} +3.02897 q^{56} +9.52324 q^{57} +0.600268 q^{58} -1.00000 q^{59} +16.7417 q^{60} +3.88583 q^{61} +0.227328 q^{62} +6.56539 q^{63} -7.46576 q^{64} -8.69495 q^{65} +2.05146 q^{66} -13.6595 q^{67} -1.97753 q^{68} +10.5838 q^{69} -3.11179 q^{70} -7.63076 q^{71} +0.770533 q^{72} -10.2193 q^{73} -0.362127 q^{74} -24.2354 q^{75} +9.08992 q^{76} +33.5582 q^{77} -0.660822 q^{78} -4.89550 q^{79} +15.7963 q^{80} -11.2069 q^{81} -0.171662 q^{82} -3.63584 q^{83} +20.8139 q^{84} +4.08629 q^{85} -1.19050 q^{86} +8.29647 q^{87} +3.93849 q^{88} +7.06524 q^{89} -0.791602 q^{90} -10.8099 q^{91} +10.1022 q^{92} +3.14197 q^{93} +0.100356 q^{94} -18.7830 q^{95} +3.67106 q^{96} +13.5650 q^{97} -2.81939 q^{98} +8.53682 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.149899	−0.105995	−0.0529973	−	0.998595i	$-0.516877\pi$
$2$	−0.149899	−0.105995	−0.0529973	+	0.998595i	$0.516877\pi$
$3$	−2.07180	−1.19615	−0.598077	−	0.801439i	$-0.704068\pi$
$3$	−2.07180	−1.19615	−0.598077	+	0.801439i	$0.704068\pi$
$4$	−1.97753	−0.988765
$5$	4.08629	1.82744	0.913722	−	0.406341i	$-0.133195\pi$
$5$	4.08629	1.82744	0.913722	+	0.406341i	$0.133195\pi$
$6$	0.310561	0.126786
$7$	5.08021	1.92014	0.960070	−	0.279760i	$-0.0902548\pi$
$7$	5.08021	1.92014	0.960070	+	0.279760i	$0.0902548\pi$
$8$	0.596228	0.210799
$9$	1.29235	0.430782
$10$	−0.612531	−0.193699
$11$	6.60568	1.99169	0.995843	−	0.0910828i	$-0.0290328\pi$
$11$	6.60568	1.99169	0.995843	+	0.0910828i	$0.0290328\pi$
$12$	4.09704	1.18271
$13$	−2.12783	−0.590155	−0.295078	−	0.955473i	$-0.595346\pi$
$13$	−2.12783	−0.590155	−0.295078	+	0.955473i	$0.595346\pi$
$14$	−0.761519	−0.203525
$15$	−8.46596	−2.18590
$16$	3.86569	0.966422
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.193722	−0.0456606
$19$	−4.59660	−1.05453	−0.527267	−	0.849700i	$-0.676783\pi$
$19$	−4.59660	−1.05453	−0.527267	+	0.849700i	$0.676783\pi$
$20$	−8.08076	−1.80691
$21$	−10.5252	−2.29678
$22$	−0.990185	−0.211108
$23$	−5.10850	−1.06520	−0.532598	−	0.846368i	$-0.678784\pi$
$23$	−5.10850	−1.06520	−0.532598	+	0.846368i	$0.678784\pi$
$24$	−1.23526	−0.252147
$25$	11.6977	2.33955
$26$	0.318961	0.0625533
$27$	3.53791	0.680872
$28$	−10.0463	−1.89857
$29$	−4.00448	−0.743613	−0.371807	−	0.928310i	$-0.621262\pi$
$29$	−4.00448	−0.743613	−0.371807	+	0.928310i	$0.621262\pi$
$30$	1.26904	0.231694
$31$	−1.51654	−0.272379	−0.136189	−	0.990683i	$-0.543486\pi$
$31$	−1.51654	−0.272379	−0.136189	+	0.990683i	$0.543486\pi$
$32$	−1.77192	−0.313234
$33$	−13.6856	−2.38236
$34$	−0.149899	−0.0257075
$35$	20.7592	3.50895
$36$	−2.55565	−0.425942
$37$	2.41581	0.397156	0.198578	−	0.980085i	$-0.436368\pi$
$37$	2.41581	0.397156	0.198578	+	0.980085i	$0.436368\pi$
$38$	0.689027	0.111775
$39$	4.40844	0.705916
$40$	2.43636	0.385222
$41$	1.14518	0.178848	0.0894238	−	0.995994i	$-0.471497\pi$
$41$	1.14518	0.178848	0.0894238	+	0.995994i	$0.471497\pi$
$42$	1.57771	0.243447
$43$	7.94203	1.21115	0.605574	−	0.795789i	$-0.292944\pi$
$43$	7.94203	1.21115	0.605574	+	0.795789i	$0.292944\pi$
$44$	−13.0629	−1.96931
$45$	5.28090	0.787230
$46$	0.765760	0.112905
$47$	−0.669492	−0.0976554	−0.0488277	−	0.998807i	$-0.515549\pi$
$47$	−0.669492	−0.0976554	−0.0488277	+	0.998807i	$0.515549\pi$
$48$	−8.00892	−1.15599
$49$	18.8086	2.68694
$50$	−1.75348	−0.247980
$51$	−2.07180	−0.290110
$52$	4.20786	0.583525
$53$	0.270789	0.0371958	0.0185979	−	0.999827i	$-0.494080\pi$
$53$	0.270789	0.0371958	0.0185979	+	0.999827i	$0.494080\pi$
$54$	−0.530330	−0.0721688
$55$	26.9927	3.63969
$56$	3.02897	0.404763
$57$	9.52324	1.26138
$58$	0.600268	0.0788190
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	16.7417	2.16134
$61$	3.88583	0.497529	0.248765	−	0.968564i	$-0.419975\pi$
$61$	3.88583	0.497529	0.248765	+	0.968564i	$0.419975\pi$
$62$	0.227328	0.0288707
$63$	6.56539	0.827162
$64$	−7.46576	−0.933220
$65$	−8.69495	−1.07848
$66$	2.05146	0.252518
$67$	−13.6595	−1.66878	−0.834388	−	0.551177i	$-0.814179\pi$
$67$	−13.6595	−1.66878	−0.834388	+	0.551177i	$0.814179\pi$
$68$	−1.97753	−0.239811
$69$	10.5838	1.27414
$70$	−3.11179	−0.371930
$71$	−7.63076	−0.905604	−0.452802	−	0.891611i	$-0.649576\pi$
$71$	−7.63076	−0.905604	−0.452802	+	0.891611i	$0.649576\pi$
$72$	0.770533	0.0908082
$73$	−10.2193	−1.19607	−0.598037	−	0.801468i	$-0.704053\pi$
$73$	−10.2193	−1.19607	−0.598037	+	0.801468i	$0.704053\pi$
$74$	−0.362127	−0.0420964
$75$	−24.2354	−2.79846
$76$	9.08992	1.04269
$77$	33.5582	3.82432
$78$	−0.660822	−0.0748233
$79$	−4.89550	−0.550787	−0.275394	−	0.961332i	$-0.588808\pi$
$79$	−4.89550	−0.550787	−0.275394	+	0.961332i	$0.588808\pi$
$80$	15.7963	1.76608
$81$	−11.2069	−1.24521
$82$	−0.171662	−0.0189569
$83$	−3.63584	−0.399086	−0.199543	−	0.979889i	$-0.563946\pi$
$83$	−3.63584	−0.399086	−0.199543	+	0.979889i	$0.563946\pi$
$84$	20.8139	2.27098
$85$	4.08629	0.443220
$86$	−1.19050	−0.128375
$87$	8.29647	0.889475
$88$	3.93849	0.419845
$89$	7.06524	0.748914	0.374457	−	0.927244i	$-0.377829\pi$
$89$	7.06524	0.748914	0.374457	+	0.927244i	$0.377829\pi$
$90$	−0.791602	−0.0834422
$91$	−10.8099	−1.13318
$92$	10.1022	1.05323
$93$	3.14197	0.325807
$94$	0.100356	0.0103510
$95$	−18.7830	−1.92710
$96$	3.67106	0.374676
$97$	13.5650	1.37732	0.688660	−	0.725084i	$-0.258199\pi$
$97$	13.5650	1.37732	0.688660	+	0.725084i	$0.258199\pi$
$98$	−2.81939	−0.284801
$99$	8.53682	0.857983
$100$	−23.1326	−2.31326
$101$	−1.87295	−0.186365	−0.0931825	−	0.995649i	$-0.529704\pi$
$101$	−1.87295	−0.186365	−0.0931825	+	0.995649i	$0.529704\pi$
$102$	0.310561	0.0307501
$103$	11.9970	1.18210	0.591048	−	0.806637i	$-0.298715\pi$
$103$	11.9970	1.18210	0.591048	+	0.806637i	$0.298715\pi$
$104$	−1.26868	−0.124404
$105$	−43.0089	−4.19724
$106$	−0.0405911	−0.00394255
$107$	−1.16800	−0.112915	−0.0564573	−	0.998405i	$-0.517980\pi$
$107$	−1.16800	−0.112915	−0.0564573	+	0.998405i	$0.517980\pi$
$108$	−6.99633	−0.673222
$109$	8.94465	0.856742	0.428371	−	0.903603i	$-0.359088\pi$
$109$	8.94465	0.856742	0.428371	+	0.903603i	$0.359088\pi$
$110$	−4.04618	−0.385788
$111$	−5.00506	−0.475060
$112$	19.6385	1.85566
$113$	12.2756	1.15479	0.577397	−	0.816464i	$-0.304069\pi$
$113$	12.2756	1.15479	0.577397	+	0.816464i	$0.304069\pi$
$114$	−1.42752	−0.133700
$115$	−20.8748	−1.94659
$116$	7.91898	0.735259
$117$	−2.74990	−0.254228
$118$	0.149899	0.0137993
$119$	5.08021	0.465702
$120$	−5.04765	−0.460785
$121$	32.6350	2.96682
$122$	−0.582482	−0.0527354
$123$	−2.37259	−0.213929
$124$	2.99900	0.269319
$125$	27.3689	2.44795
$126$	−0.984147	−0.0876748
$127$	−16.9940	−1.50797	−0.753985	−	0.656892i	$-0.771871\pi$
$127$	−16.9940	−1.50797	−0.753985	+	0.656892i	$0.771871\pi$
$128$	4.66295	0.412150
$129$	−16.4543	−1.44872
$130$	1.30336	0.114313
$131$	−7.91793	−0.691793	−0.345896	−	0.938273i	$-0.612425\pi$
$131$	−7.91793	−0.691793	−0.345896	+	0.938273i	$0.612425\pi$
$132$	27.0637	2.35560
$133$	−23.3517	−2.02485
$134$	2.04755	0.176881
$135$	14.4569	1.24425
$136$	0.596228	0.0511261
$137$	−1.42323	−0.121595	−0.0607975	−	0.998150i	$-0.519364\pi$
$137$	−1.42323	−0.121595	−0.0607975	+	0.998150i	$0.519364\pi$
$138$	−1.58650	−0.135052
$139$	5.22072	0.442815	0.221408	−	0.975181i	$-0.428935\pi$
$139$	5.22072	0.442815	0.221408	+	0.975181i	$0.428935\pi$
$140$	−41.0520	−3.46952
$141$	1.38705	0.116811
$142$	1.14384	0.0959892
$143$	−14.0558	−1.17540
$144$	4.99581	0.416317
$145$	−16.3635	−1.35891
$146$	1.53186	0.126778
$147$	−38.9675	−3.21399
$148$	−4.77733	−0.392694
$149$	4.45485	0.364956	0.182478	−	0.983210i	$-0.441588\pi$
$149$	4.45485	0.364956	0.182478	+	0.983210i	$0.441588\pi$
$150$	3.63286	0.296622
$151$	11.5879	0.943006	0.471503	−	0.881864i	$-0.343712\pi$
$151$	11.5879	0.943006	0.471503	+	0.881864i	$0.343712\pi$
$152$	−2.74063	−0.222294
$153$	1.29235	0.104480
$154$	−5.03035	−0.405357
$155$	−6.19702	−0.497757
$156$	−8.71783	−0.697985
$157$	6.25393	0.499118	0.249559	−	0.968360i	$-0.419714\pi$
$157$	6.25393	0.499118	0.249559	+	0.968360i	$0.419714\pi$
$158$	0.733831	0.0583805
$159$	−0.561020	−0.0444918
$160$	−7.24057	−0.572417
$161$	−25.9523	−2.04533
$162$	1.67990	0.131986
$163$	−12.9166	−1.01171	−0.505855	−	0.862619i	$-0.668823\pi$
$163$	−12.9166	−1.01171	−0.505855	+	0.862619i	$0.668823\pi$
$164$	−2.26463	−0.176838
$165$	−55.9234	−4.35363
$166$	0.545009	0.0423009
$167$	−6.72846	−0.520664	−0.260332	−	0.965519i	$-0.583832\pi$
$167$	−6.72846	−0.520664	−0.260332	+	0.965519i	$0.583832\pi$
$168$	−6.27541	−0.484158
$169$	−8.47232	−0.651717
$170$	−0.612531	−0.0469790
$171$	−5.94040	−0.454274
$172$	−15.7056	−1.19754
$173$	7.16826	0.544993	0.272496	−	0.962157i	$-0.412151\pi$
$173$	7.16826	0.544993	0.272496	+	0.962157i	$0.412151\pi$
$174$	−1.24363	−0.0942796
$175$	59.4270	4.49226
$176$	25.5355	1.92481
$177$	2.07180	0.155726
$178$	−1.05907	−0.0793809
$179$	−8.26829	−0.618001	−0.309000	−	0.951062i	$-0.599994\pi$
$179$	−8.26829	−0.618001	−0.309000	+	0.951062i	$0.599994\pi$
$180$	−10.4431	−0.778385
$181$	14.9781	1.11331	0.556657	−	0.830743i	$-0.312084\pi$
$181$	14.9781	1.11331	0.556657	+	0.830743i	$0.312084\pi$
$182$	1.62039	0.120111
$183$	−8.05065	−0.595121
$184$	−3.04583	−0.224542
$185$	9.87168	0.725780
$186$	−0.470978	−0.0345338
$187$	6.60568	0.483055
$188$	1.32394	0.0965582
$189$	17.9734	1.30737
$190$	2.81556	0.204262
$191$	−20.5741	−1.48869	−0.744344	−	0.667796i	$-0.767238\pi$
$191$	−20.5741	−1.48869	−0.744344	+	0.667796i	$0.767238\pi$
$192$	15.4676	1.11627
$193$	−13.2340	−0.952602	−0.476301	−	0.879282i	$-0.658023\pi$
$193$	−13.2340	−0.952602	−0.476301	+	0.879282i	$0.658023\pi$
$194$	−2.03339	−0.145989
$195$	18.0142	1.29002
$196$	−37.1945	−2.65675
$197$	−3.22632	−0.229865	−0.114933	−	0.993373i	$-0.536665\pi$
$197$	−3.22632	−0.229865	−0.114933	+	0.993373i	$0.536665\pi$
$198$	−1.27966	−0.0909416
$199$	−10.2046	−0.723386	−0.361693	−	0.932297i	$-0.617801\pi$
$199$	−10.2046	−0.723386	−0.361693	+	0.932297i	$0.617801\pi$
$200$	6.97453	0.493173
$201$	28.2998	1.99611
$202$	0.280753	0.0197537
$203$	−20.3436	−1.42784
$204$	4.09704	0.286850
$205$	4.67955	0.326834
$206$	−1.79833	−0.125296
$207$	−6.60195	−0.458867
$208$	−8.22554	−0.570339
$209$	−30.3637	−2.10030
$210$	6.44699	0.444885
$211$	−7.29336	−0.502096	−0.251048	−	0.967975i	$-0.580775\pi$
$211$	−7.29336	−0.502096	−0.251048	+	0.967975i	$0.580775\pi$
$212$	−0.535494	−0.0367779
$213$	15.8094	1.08324
$214$	0.175082	0.0119683
$215$	32.4534	2.21330
$216$	2.10940	0.143527
$217$	−7.70435	−0.523005
$218$	−1.34079	−0.0908101
$219$	21.1723	1.43069
$220$	−53.3789	−3.59880
$221$	−2.12783	−0.143134
$222$	0.750254	0.0503538
$223$	22.7424	1.52294	0.761472	−	0.648198i	$-0.224477\pi$
$223$	22.7424	1.52294	0.761472	+	0.648198i	$0.224477\pi$
$224$	−9.00173	−0.601453
$225$	15.1175	1.00784
$226$	−1.84010	−0.122402
$227$	13.4338	0.891631	0.445815	−	0.895125i	$-0.352914\pi$
$227$	13.4338	0.891631	0.445815	+	0.895125i	$0.352914\pi$
$228$	−18.8325	−1.24721
$229$	−10.2134	−0.674924	−0.337462	−	0.941339i	$-0.609568\pi$
$229$	−10.2134	−0.674924	−0.337462	+	0.941339i	$0.609568\pi$
$230$	3.12911	0.206328
$231$	−69.5259	−4.57447
$232$	−2.38758	−0.156753
$233$	2.32044	0.152017	0.0760085	−	0.997107i	$-0.475782\pi$
$233$	2.32044	0.152017	0.0760085	+	0.997107i	$0.475782\pi$
$234$	0.412207	0.0269468
$235$	−2.73574	−0.178460
$236$	1.97753	0.128726
$237$	10.1425	0.658826
$238$	−0.761519	−0.0493620
$239$	18.6717	1.20777	0.603885	−	0.797071i	$-0.293619\pi$
$239$	18.6717	1.20777	0.603885	+	0.797071i	$0.293619\pi$
$240$	−32.7268	−2.11250
$241$	−29.2196	−1.88220	−0.941099	−	0.338131i	$-0.890205\pi$
$241$	−29.2196	−1.88220	−0.941099	+	0.338131i	$0.890205\pi$
$242$	−4.89195	−0.314467
$243$	12.6046	0.808589
$244$	−7.68434	−0.491940
$245$	76.8572	4.91023
$246$	0.355649	0.0226753
$247$	9.78082	0.622338
$248$	−0.904204	−0.0574170
$249$	7.53273	0.477367
$250$	−4.10258	−0.259470
$251$	9.15802	0.578049	0.289024	−	0.957322i	$-0.406669\pi$
$251$	9.15802	0.578049	0.289024	+	0.957322i	$0.406669\pi$
$252$	−12.9833	−0.817869
$253$	−33.7451	−2.12154
$254$	2.54738	0.159837
$255$	−8.46596	−0.530159
$256$	14.2326	0.889535
$257$	−3.48071	−0.217121	−0.108560	−	0.994090i	$-0.534624\pi$
$257$	−3.48071	−0.217121	−0.108560	+	0.994090i	$0.534624\pi$
$258$	2.46648	0.153556
$259$	12.2728	0.762595
$260$	17.1945	1.06636
$261$	−5.17517	−0.320335
$262$	1.18689	0.0733264
$263$	5.44026	0.335461	0.167730	−	0.985833i	$-0.446356\pi$
$263$	5.44026	0.335461	0.167730	+	0.985833i	$0.446356\pi$
$264$	−8.15976	−0.502198
$265$	1.10652	0.0679731
$266$	3.50040	0.214624
$267$	−14.6378	−0.895816
$268$	27.0121	1.65003
$269$	−4.85862	−0.296235	−0.148118	−	0.988970i	$-0.547321\pi$
$269$	−4.85862	−0.296235	−0.148118	+	0.988970i	$0.547321\pi$
$270$	−2.16708	−0.131884
$271$	−22.1008	−1.34253	−0.671263	−	0.741219i	$-0.734248\pi$
$271$	−22.1008	−1.34253	−0.671263	+	0.741219i	$0.734248\pi$
$272$	3.86569	0.234392
$273$	22.3958	1.35546
$274$	0.213341	0.0128884
$275$	77.2715	4.65965
$276$	−20.9297	−1.25982
$277$	1.14089	0.0685491	0.0342746	−	0.999412i	$-0.489088\pi$
$277$	1.14089	0.0685491	0.0342746	+	0.999412i	$0.489088\pi$
$278$	−0.782581	−0.0469361
$279$	−1.95990	−0.117336
$280$	12.3772	0.739681
$281$	−0.00789805	−0.000471158 0	−0.000235579	−	1.00000i	$-0.500075\pi$
$281$	−0.00789805	−0.000471158 0	−0.000235579		1.00000i	$0.500075\pi$
$282$	−0.207918	−0.0123813
$283$	−11.4040	−0.677897	−0.338949	−	0.940805i	$-0.610071\pi$
$283$	−11.4040	−0.677897	−0.338949	+	0.940805i	$0.610071\pi$
$284$	15.0901	0.895430
$285$	38.9147	2.30511
$286$	2.10695	0.124587
$287$	5.81778	0.343412
$288$	−2.28993	−0.134936
$289$	1.00000	0.0588235
$290$	2.45287	0.144037
$291$	−28.1040	−1.64749
$292$	20.2089	1.18264
$293$	23.4881	1.37219	0.686096	−	0.727511i	$-0.259323\pi$
$293$	23.4881	1.37219	0.686096	+	0.727511i	$0.259323\pi$
$294$	5.84120	0.340666
$295$	−4.08629	−0.237913
$296$	1.44037	0.0837199
$297$	23.3703	1.35608
$298$	−0.667778	−0.0386833
$299$	10.8700	0.628631
$300$	47.9262	2.76702
$301$	40.3472	2.32557
$302$	−1.73701	−0.0999537
$303$	3.88036	0.222921
$304$	−17.7690	−1.01912
$305$	15.8786	0.909207
$306$	−0.193722	−0.0110743
$307$	−22.1729	−1.26547	−0.632736	−	0.774368i	$-0.718068\pi$
$307$	−22.1729	−1.26547	−0.632736	+	0.774368i	$0.718068\pi$
$308$	−66.3625	−3.78135
$309$	−24.8553	−1.41397
$310$	0.928928	0.0527596
$311$	9.65728	0.547614	0.273807	−	0.961785i	$-0.411717\pi$
$311$	9.65728	0.547614	0.273807	+	0.961785i	$0.411717\pi$
$312$	2.62844	0.148806
$313$	−6.97936	−0.394497	−0.197248	−	0.980354i	$-0.563201\pi$
$313$	−6.97936	−0.394497	−0.197248	+	0.980354i	$0.563201\pi$
$314$	−0.937458	−0.0529038
$315$	26.8281	1.51159
$316$	9.68100	0.544599
$317$	−1.77872	−0.0999027	−0.0499513	−	0.998752i	$-0.515907\pi$
$317$	−1.77872	−0.0999027	−0.0499513	+	0.998752i	$0.515907\pi$
$318$	0.0840965	0.00471590
$319$	−26.4523	−1.48104
$320$	−30.5073	−1.70541
$321$	2.41985	0.135063
$322$	3.89022	0.216794
$323$	−4.59660	−0.255762
$324$	22.1619	1.23122
$325$	−24.8909	−1.38070
$326$	1.93619	0.107236
$327$	−18.5315	−1.02479
$328$	0.682791	0.0377008
$329$	−3.40116	−0.187512
$330$	8.38287	0.461462
$331$	11.6046	0.637847	0.318924	−	0.947780i	$-0.396679\pi$
$331$	11.6046	0.637847	0.318924	+	0.947780i	$0.396679\pi$
$332$	7.18999	0.394602
$333$	3.12206	0.171088
$334$	1.00859	0.0551876
$335$	−55.8168	−3.04960
$336$	−40.6870	−2.21966
$337$	−6.46296	−0.352060	−0.176030	−	0.984385i	$-0.556326\pi$
$337$	−6.46296	−0.352060	−0.176030	+	0.984385i	$0.556326\pi$
$338$	1.26999	0.0690785
$339$	−25.4326	−1.38131
$340$	−8.08076	−0.438241
$341$	−10.0178	−0.542493
$342$	0.890461	0.0481506
$343$	59.9900	3.23916
$344$	4.73526	0.255308
$345$	43.2484	2.32841
$346$	−1.07452	−0.0577663
$347$	−16.2606	−0.872917	−0.436459	−	0.899724i	$-0.643767\pi$
$347$	−16.2606	−0.872917	−0.436459	+	0.899724i	$0.643767\pi$
$348$	−16.4065	−0.879482
$349$	−24.8546	−1.33044	−0.665218	−	0.746649i	$-0.731662\pi$
$349$	−24.8546	−1.33044	−0.665218	+	0.746649i	$0.731662\pi$
$350$	−8.90806	−0.476156
$351$	−7.52810	−0.401820
$352$	−11.7047	−0.623864
$353$	30.2666	1.61093	0.805466	−	0.592643i	$-0.201915\pi$
$353$	30.2666	1.61093	0.805466	+	0.592643i	$0.201915\pi$
$354$	−0.310561	−0.0165061
$355$	−31.1815	−1.65494
$356$	−13.9717	−0.740500
$357$	−10.5252	−0.557051
$358$	1.23941	0.0655048
$359$	−25.5406	−1.34798	−0.673991	−	0.738740i	$-0.735421\pi$
$359$	−25.5406	−1.34798	−0.673991	+	0.738740i	$0.735421\pi$
$360$	3.14862	0.165947
$361$	2.12877	0.112041
$362$	−2.24520	−0.118005
$363$	−67.6131	−3.54877
$364$	21.3768	1.12045
$365$	−41.7589	−2.18576
$366$	1.20679	0.0630797
$367$	25.7623	1.34478	0.672391	−	0.740197i	$-0.265268\pi$
$367$	25.7623	1.34478	0.672391	+	0.740197i	$0.265268\pi$
$368$	−19.7479	−1.02943
$369$	1.47997	0.0770443
$370$	−1.47976	−0.0769289
$371$	1.37567	0.0714211
$372$	−6.21333	−0.322146
$373$	6.63829	0.343718	0.171859	−	0.985122i	$-0.445023\pi$
$373$	6.63829	0.343718	0.171859	+	0.985122i	$0.445023\pi$
$374$	−0.990185	−0.0512013
$375$	−56.7029	−2.92812
$376$	−0.399170	−0.0205856
$377$	8.52087	0.438847
$378$	−2.69419	−0.138574
$379$	0.599995	0.0308197	0.0154098	−	0.999881i	$-0.495095\pi$
$379$	0.599995	0.0308197	0.0154098	+	0.999881i	$0.495095\pi$
$380$	37.1440	1.90545
$381$	35.2080	1.80376
$382$	3.08404	0.157793
$383$	−25.6842	−1.31240	−0.656200	−	0.754587i	$-0.727837\pi$
$383$	−25.6842	−1.31240	−0.656200	+	0.754587i	$0.727837\pi$
$384$	−9.66069	−0.492995
$385$	137.129	6.98872
$386$	1.98376	0.100971
$387$	10.2638	0.521741
$388$	−26.8253	−1.36185
$389$	8.96237	0.454410	0.227205	−	0.973847i	$-0.427041\pi$
$389$	8.96237	0.454410	0.227205	+	0.973847i	$0.427041\pi$
$390$	−2.70031	−0.136735
$391$	−5.10850	−0.258348
$392$	11.2142	0.566403
$393$	16.4044	0.827490
$394$	0.483622	0.0243645
$395$	−20.0044	−1.00653
$396$	−16.8818	−0.848344
$397$	0.681719	0.0342145	0.0171072	−	0.999854i	$-0.494554\pi$
$397$	0.681719	0.0342145	0.0171072	+	0.999854i	$0.494554\pi$
$398$	1.52966	0.0766751
$399$	48.3801	2.42203
$400$	45.2198	2.26099
$401$	12.0985	0.604173	0.302086	−	0.953281i	$-0.402317\pi$
$401$	12.0985	0.604173	0.302086	+	0.953281i	$0.402317\pi$
$402$	−4.24211	−0.211577
$403$	3.22695	0.160746
$404$	3.70381	0.184271
$405$	−45.7945	−2.27555
$406$	3.04949	0.151344
$407$	15.9580	0.791011
$408$	−1.23526	−0.0611547
$409$	−30.5143	−1.50884	−0.754419	−	0.656394i	$-0.772081\pi$
$409$	−30.5143	−1.50884	−0.754419	+	0.656394i	$0.772081\pi$
$410$	−0.701460	−0.0346426
$411$	2.94865	0.145446
$412$	−23.7243	−1.16881
$413$	−5.08021	−0.249981
$414$	0.989627	0.0486375
$415$	−14.8571	−0.729306
$416$	3.77035	0.184857
$417$	−10.8163	−0.529675
$418$	4.55149	0.222621
$419$	12.6964	0.620259	0.310130	−	0.950694i	$-0.399628\pi$
$419$	12.6964	0.620259	0.310130	+	0.950694i	$0.399628\pi$
$420$	85.0514	4.15008
$421$	−5.56869	−0.271401	−0.135701	−	0.990750i	$-0.543329\pi$
$421$	−5.56869	−0.271401	−0.135701	+	0.990750i	$0.543329\pi$
$422$	1.09327	0.0532195
$423$	−0.865215	−0.0420682
$424$	0.161452	0.00784081
$425$	11.6977	0.567424
$426$	−2.36981	−0.114818
$427$	19.7408	0.955326
$428$	2.30975	0.111646
$429$	29.1208	1.40596
$430$	−4.86474	−0.234598
$431$	9.48862	0.457051	0.228525	−	0.973538i	$-0.426610\pi$
$431$	9.48862	0.457051	0.228525	+	0.973538i	$0.426610\pi$
$432$	13.6765	0.658009
$433$	−0.147709	−0.00709845	−0.00354923	−	0.999994i	$-0.501130\pi$
$433$	−0.147709	−0.00709845	−0.00354923	+	0.999994i	$0.501130\pi$
$434$	1.15488	0.0554358
$435$	33.9018	1.62547
$436$	−17.6883	−0.847117
$437$	23.4818	1.12328
$438$	−3.17370	−0.151645
$439$	−31.8245	−1.51890	−0.759450	−	0.650566i	$-0.774532\pi$
$439$	−31.8245	−1.51890	−0.759450	+	0.650566i	$0.774532\pi$
$440$	16.0938	0.767242
$441$	24.3072	1.15748
$442$	0.318961	0.0151714
$443$	18.9816	0.901845	0.450923	−	0.892563i	$-0.351095\pi$
$443$	18.9816	0.901845	0.450923	+	0.892563i	$0.351095\pi$
$444$	9.89766	0.469722
$445$	28.8706	1.36860
$446$	−3.40906	−0.161424
$447$	−9.22955	−0.436543
$448$	−37.9277	−1.79191
$449$	−34.9239	−1.64816	−0.824080	−	0.566474i	$-0.808307\pi$
$449$	−34.9239	−1.64816	−0.824080	+	0.566474i	$0.808307\pi$
$450$	−2.26611	−0.106825
$451$	7.56471	0.356208
$452$	−24.2754	−1.14182
$453$	−24.0077	−1.12798
$454$	−2.01371	−0.0945081
$455$	−44.1722	−2.07082
$456$	5.67802	0.265898
$457$	20.4519	0.956701	0.478351	−	0.878169i	$-0.341235\pi$
$457$	20.4519	0.956701	0.478351	+	0.878169i	$0.341235\pi$
$458$	1.53099	0.0715383
$459$	3.53791	0.165136
$460$	41.2806	1.92472
$461$	24.1918	1.12673	0.563363	−	0.826210i	$-0.309507\pi$
$461$	24.1918	1.12673	0.563363	+	0.826210i	$0.309507\pi$
$462$	10.4219	0.484869
$463$	−2.97547	−0.138282	−0.0691410	−	0.997607i	$-0.522026\pi$
$463$	−2.97547	−0.138282	−0.0691410	+	0.997607i	$0.522026\pi$
$464$	−15.4801	−0.718644
$465$	12.8390	0.595393
$466$	−0.347832	−0.0161130
$467$	19.2108	0.888968	0.444484	−	0.895787i	$-0.353387\pi$
$467$	19.2108	0.888968	0.444484	+	0.895787i	$0.353387\pi$
$468$	5.43801	0.251372
$469$	−69.3933	−3.20429
$470$	0.410084	0.0189158
$471$	−12.9569	−0.597021
$472$	−0.596228	−0.0274436
$473$	52.4625	2.41223
$474$	−1.52035	−0.0698320
$475$	−53.7699	−2.46713
$476$	−10.0463	−0.460470
$477$	0.349953	0.0160233
$478$	−2.79887	−0.128017
$479$	−22.9938	−1.05061	−0.525306	−	0.850914i	$-0.676049\pi$
$479$	−22.9938	−1.05061	−0.525306	+	0.850914i	$0.676049\pi$
$480$	15.0010	0.684699
$481$	−5.14044	−0.234384
$482$	4.37999	0.199503
$483$	53.7679	2.44652
$484$	−64.5366	−2.93348
$485$	55.4306	2.51697
$486$	−1.88943	−0.0857061
$487$	−42.3789	−1.92037	−0.960186	−	0.279361i	$-0.909877\pi$
$487$	−42.3789	−1.92037	−0.960186	+	0.279361i	$0.909877\pi$
$488$	2.31684	0.104878
$489$	26.7607	1.21016
$490$	−11.5208	−0.520458
$491$	0.120943	0.00545810	0.00272905	−	0.999996i	$-0.499131\pi$
$491$	0.120943	0.00545810	0.00272905	+	0.999996i	$0.499131\pi$
$492$	4.69186	0.211526
$493$	−4.00448	−0.180353
$494$	−1.46614	−0.0659646
$495$	34.8839	1.56792
$496$	−5.86247	−0.263233
$497$	−38.7659	−1.73889
$498$	−1.12915	−0.0505984
$499$	3.46624	0.155170	0.0775850	−	0.996986i	$-0.475279\pi$
$499$	3.46624	0.155170	0.0775850	+	0.996986i	$0.475279\pi$
$500$	−54.1229	−2.42045
$501$	13.9400	0.622794
$502$	−1.37278	−0.0612701
$503$	−19.4597	−0.867665	−0.433832	−	0.900994i	$-0.642839\pi$
$503$	−19.4597	−0.867665	−0.433832	+	0.900994i	$0.642839\pi$
$504$	3.91447	0.174365
$505$	−7.65339	−0.340571
$506$	5.05836	0.224872
$507$	17.5529	0.779553
$508$	33.6061	1.49103
$509$	−19.7458	−0.875216	−0.437608	−	0.899166i	$-0.644174\pi$
$509$	−19.7458	−0.875216	−0.437608	+	0.899166i	$0.644174\pi$
$510$	1.26904	0.0561940
$511$	−51.9160	−2.29663
$512$	−11.4593	−0.506436
$513$	−16.2624	−0.718002
$514$	0.521756	0.0230137
$515$	49.0230	2.16021
$516$	32.5388	1.43244
$517$	−4.42245	−0.194499
$518$	−1.83968	−0.0808311
$519$	−14.8512	−0.651895
$520$	−5.18417	−0.227341
$521$	−30.3592	−1.33006	−0.665030	−	0.746817i	$-0.731581\pi$
$521$	−30.3592	−1.33006	−0.665030	+	0.746817i	$0.731581\pi$
$522$	0.775754	0.0339538
$523$	−8.76375	−0.383212	−0.191606	−	0.981472i	$-0.561370\pi$
$523$	−8.76375	−0.383212	−0.191606	+	0.981472i	$0.561370\pi$
$524$	15.6579	0.684021
$525$	−123.121	−5.37343
$526$	−0.815490	−0.0355570
$527$	−1.51654	−0.0660615
$528$	−52.9043	−2.30237
$529$	3.09678	0.134643
$530$	−0.165867	−0.00720479
$531$	−1.29235	−0.0560831
$532$	46.1788	2.00210
$533$	−2.43676	−0.105548
$534$	2.19419	0.0949517
$535$	−4.77277	−0.206345
$536$	−8.14420	−0.351776
$537$	17.1302	0.739223
$538$	0.728303	0.0313994
$539$	124.243	5.35154
$540$	−28.5890	−1.23028
$541$	32.7384	1.40753	0.703767	−	0.710431i	$-0.251500\pi$
$541$	32.7384	1.40753	0.703767	+	0.710431i	$0.251500\pi$
$542$	3.31289	0.142301
$543$	−31.0316	−1.33169
$544$	−1.77192	−0.0759704
$545$	36.5504	1.56565
$546$	−3.35712	−0.143671
$547$	2.79045	0.119311	0.0596556	−	0.998219i	$-0.481000\pi$
$547$	2.79045	0.119311	0.0596556	+	0.998219i	$0.481000\pi$
$548$	2.81448	0.120229
$549$	5.02183	0.214327
$550$	−11.5829	−0.493898
$551$	18.4070	0.784165
$552$	6.31035	0.268586
$553$	−24.8702	−1.05759
$554$	−0.171018	−0.00726584
$555$	−20.4521	−0.868144
$556$	−10.3241	−0.437840
$557$	−11.7867	−0.499420	−0.249710	−	0.968321i	$-0.580335\pi$
$557$	−11.7867	−0.499420	−0.249710	+	0.968321i	$0.580335\pi$
$558$	0.293787	0.0124370
$559$	−16.8993	−0.714765
$560$	80.2486	3.39112
$561$	−13.6856	−0.577808
$562$	0.00118391	4.99403e−5 0
$563$	25.5045	1.07489	0.537444	−	0.843299i	$-0.319390\pi$
$563$	25.5045	1.07489	0.537444	+	0.843299i	$0.319390\pi$
$564$	−2.74294	−0.115498
$565$	50.1617	2.11032
$566$	1.70945	0.0718535
$567$	−56.9333	−2.39098
$568$	−4.54967	−0.190900
$569$	19.3869	0.812743	0.406371	−	0.913708i	$-0.366794\pi$
$569$	19.3869	0.812743	0.406371	+	0.913708i	$0.366794\pi$
$570$	−5.83328	−0.244329
$571$	−29.1693	−1.22070	−0.610349	−	0.792133i	$-0.708971\pi$
$571$	−29.1693	−1.22070	−0.610349	+	0.792133i	$0.708971\pi$
$572$	27.7958	1.16220
$573$	42.6253	1.78070
$574$	−0.872079	−0.0363999
$575$	−59.7579	−2.49208
$576$	−9.64835	−0.402015
$577$	13.1135	0.545922	0.272961	−	0.962025i	$-0.411997\pi$
$577$	13.1135	0.545922	0.272961	+	0.962025i	$0.411997\pi$
$578$	−0.149899	−0.00623498
$579$	27.4181	1.13946
$580$	32.3592	1.34364
$581$	−18.4709	−0.766300
$582$	4.21276	0.174625
$583$	1.78875	0.0740823
$584$	−6.09301	−0.252131
$585$	−11.2369	−0.464588
$586$	−3.52085	−0.145445
$587$	−15.4022	−0.635718	−0.317859	−	0.948138i	$-0.602964\pi$
$587$	−15.4022	−0.635718	−0.317859	+	0.948138i	$0.602964\pi$
$588$	77.0595	3.17788
$589$	6.97094	0.287232
$590$	0.612531	0.0252175
$591$	6.68427	0.274954
$592$	9.33875	0.383820
$593$	22.4096	0.920250	0.460125	−	0.887854i	$-0.347805\pi$
$593$	22.4096	0.920250	0.460125	+	0.887854i	$0.347805\pi$
$594$	−3.50319	−0.143738
$595$	20.7592	0.851045
$596$	−8.80960	−0.360855
$597$	21.1419	0.865281
$598$	−1.62941	−0.0666315
$599$	−26.7752	−1.09400	−0.547002	−	0.837131i	$-0.684231\pi$
$599$	−26.7752	−1.09400	−0.547002	+	0.837131i	$0.684231\pi$
$600$	−14.4498	−0.589911
$601$	−33.5188	−1.36726	−0.683630	−	0.729829i	$-0.739600\pi$
$601$	−33.5188	−1.36726	−0.683630	+	0.729829i	$0.739600\pi$
$602$	−6.04801	−0.246498
$603$	−17.6528	−0.718879
$604$	−22.9153	−0.932412
$605$	133.356	5.42169
$606$	−0.581663	−0.0236284
$607$	20.8148	0.844846	0.422423	−	0.906399i	$-0.361180\pi$
$607$	20.8148	0.844846	0.422423	+	0.906399i	$0.361180\pi$
$608$	8.14481	0.330316
$609$	42.1478	1.70792
$610$	−2.38019	−0.0963710
$611$	1.42457	0.0576318
$612$	−2.55565	−0.103306
$613$	−35.4269	−1.43088	−0.715440	−	0.698674i	$-0.753774\pi$
$613$	−35.4269	−1.43088	−0.715440	+	0.698674i	$0.753774\pi$
$614$	3.32369	0.134133
$615$	−9.69508	−0.390943
$616$	20.0084	0.806160
$617$	19.8081	0.797446	0.398723	−	0.917071i	$-0.369453\pi$
$617$	19.8081	0.797446	0.398723	+	0.917071i	$0.369453\pi$
$618$	3.72578	0.149873
$619$	−32.6096	−1.31069	−0.655345	−	0.755329i	$-0.727477\pi$
$619$	−32.6096	−1.31069	−0.655345	+	0.755329i	$0.727477\pi$
$620$	12.2548	0.492164
$621$	−18.0734	−0.725262
$622$	−1.44762	−0.0580442
$623$	35.8929	1.43802
$624$	17.0417	0.682212
$625$	53.3485	2.13394
$626$	1.04620	0.0418146
$627$	62.9074	2.51228
$628$	−12.3673	−0.493510
$629$	2.41581	0.0963245
$630$	−4.02151	−0.160221
$631$	1.31670	0.0524169	0.0262085	−	0.999656i	$-0.491657\pi$
$631$	1.31670	0.0524169	0.0262085	+	0.999656i	$0.491657\pi$
$632$	−2.91884	−0.116105
$633$	15.1104	0.600583
$634$	0.266628	0.0105892
$635$	−69.4422	−2.75573
$636$	1.10943	0.0439920
$637$	−40.0215	−1.58571
$638$	3.96518	0.156983
$639$	−9.86158	−0.390118
$640$	19.0542	0.753182
$641$	12.7181	0.502334	0.251167	−	0.967944i	$-0.419186\pi$
$641$	12.7181	0.502334	0.251167	+	0.967944i	$0.419186\pi$
$642$	−0.362734	−0.0143160
$643$	−37.8467	−1.49253	−0.746265	−	0.665649i	$-0.768155\pi$
$643$	−37.8467	−1.49253	−0.746265	+	0.665649i	$0.768155\pi$
$644$	51.3214	2.02235
$645$	−67.2369	−2.64745
$646$	0.689027	0.0271094
$647$	0.0711931	0.00279889	0.00139944	−	0.999999i	$-0.499555\pi$
$647$	0.0711931	0.00279889	0.00139944	+	0.999999i	$0.499555\pi$
$648$	−6.68186	−0.262488
$649$	−6.60568	−0.259296
$650$	3.73112	0.146347
$651$	15.9619	0.625594
$652$	25.5431	1.00034
$653$	3.76552	0.147356	0.0736780	−	0.997282i	$-0.476526\pi$
$653$	3.76552	0.147356	0.0736780	+	0.997282i	$0.476526\pi$
$654$	2.77786	0.108623
$655$	−32.3549	−1.26421
$656$	4.42692	0.172842
$657$	−13.2068	−0.515247
$658$	0.509831	0.0198753
$659$	45.6920	1.77991	0.889954	−	0.456050i	$-0.150736\pi$
$659$	45.6920	1.77991	0.889954	+	0.456050i	$0.150736\pi$
$660$	110.590	4.30472
$661$	−38.0042	−1.47819	−0.739097	−	0.673599i	$-0.764747\pi$
$661$	−38.0042	−1.47819	−0.739097	+	0.673599i	$0.764747\pi$
$662$	−1.73952	−0.0676084
$663$	4.40844	0.171210
$664$	−2.16779	−0.0841266
$665$	−95.4219	−3.70030
$666$	−0.467994	−0.0181344
$667$	20.4569	0.792094
$668$	13.3057	0.514815
$669$	−47.1176	−1.82167
$670$	8.36688	0.323241
$671$	25.6685	0.990922
$672$	18.6498	0.719430
$673$	−39.6861	−1.52979	−0.764893	−	0.644157i	$-0.777208\pi$
$673$	−39.6861	−1.52979	−0.764893	+	0.644157i	$0.777208\pi$
$674$	0.968793	0.0373165
$675$	41.3856	1.59293
$676$	16.7543	0.644395
$677$	1.47460	0.0566733	0.0283367	−	0.999598i	$-0.490979\pi$
$677$	1.47460	0.0566733	0.0283367	+	0.999598i	$0.490979\pi$
$678$	3.81233	0.146411
$679$	68.9132	2.64465
$680$	2.43636	0.0934301
$681$	−27.8321	−1.06653
$682$	1.50166	0.0575014
$683$	31.9921	1.22414	0.612072	−	0.790802i	$-0.290336\pi$
$683$	31.9921	1.22414	0.612072	+	0.790802i	$0.290336\pi$
$684$	11.7473	0.449170
$685$	−5.81573	−0.222208
$686$	−8.99245	−0.343333
$687$	21.1602	0.807312
$688$	30.7014	1.17048
$689$	−0.576195	−0.0219513
$690$	−6.48289	−0.246800
$691$	−19.8948	−0.756834	−0.378417	−	0.925635i	$-0.623531\pi$
$691$	−19.8948	−0.756834	−0.378417	+	0.925635i	$0.623531\pi$
$692$	−14.1755	−0.538870
$693$	43.3689	1.64745
$694$	2.43746	0.0925246
$695$	21.3333	0.809220
$696$	4.94659	0.187500
$697$	1.14518	0.0433769
$698$	3.72568	0.141019
$699$	−4.80748	−0.181836
$700$	−117.519	−4.44179
$701$	−49.0588	−1.85293	−0.926464	−	0.376385i	$-0.877167\pi$
$701$	−49.0588	−1.85293	−0.926464	+	0.376385i	$0.877167\pi$
$702$	1.12845	0.0425908
$703$	−11.1045	−0.418814
$704$	−49.3164	−1.85868
$705$	5.66789	0.213465
$706$	−4.53694	−0.170750
$707$	−9.51496	−0.357847
$708$	−4.09704	−0.153976
$709$	9.83165	0.369235	0.184618	−	0.982810i	$-0.440895\pi$
$709$	9.83165	0.369235	0.184618	+	0.982810i	$0.440895\pi$
$710$	4.67407	0.175415
$711$	−6.32668	−0.237269
$712$	4.21250	0.157870
$713$	7.74725	0.290137
$714$	1.57771	0.0590445
$715$	−57.4360	−2.14798
$716$	16.3508	0.611057
$717$	−38.6839	−1.44468
$718$	3.82851	0.142879
$719$	35.3055	1.31667	0.658337	−	0.752724i	$-0.271260\pi$
$719$	35.3055	1.31667	0.658337	+	0.752724i	$0.271260\pi$
$720$	20.4143	0.760796
$721$	60.9471	2.26979
$722$	−0.319101	−0.0118757
$723$	60.5371	2.25140
$724$	−29.6197	−1.10081
$725$	−46.8434	−1.73972
$726$	10.1351	0.376150
$727$	4.55419	0.168906	0.0844528	−	0.996427i	$-0.473086\pi$
$727$	4.55419	0.168906	0.0844528	+	0.996427i	$0.473086\pi$
$728$	−6.44514	−0.238873
$729$	7.50635	0.278013
$730$	6.25962	0.231679
$731$	7.94203	0.293746
$732$	15.9204	0.588435
$733$	48.2068	1.78056	0.890280	−	0.455414i	$-0.150509\pi$
$733$	48.2068	1.78056	0.890280	+	0.455414i	$0.150509\pi$
$734$	−3.86175	−0.142540
$735$	−159.233	−5.87338
$736$	9.05185	0.333656
$737$	−90.2304	−3.32368
$738$	−0.221847	−0.00816629
$739$	15.2916	0.562511	0.281256	−	0.959633i	$-0.409249\pi$
$739$	15.2916	0.562511	0.281256	+	0.959633i	$0.409249\pi$
$740$	−19.5215	−0.717626
$741$	−20.2639	−0.744412
$742$	−0.206211	−0.00757025
$743$	−16.2719	−0.596958	−0.298479	−	0.954416i	$-0.596479\pi$
$743$	−16.2719	−0.596958	−0.298479	+	0.954416i	$0.596479\pi$
$744$	1.87333	0.0686795
$745$	18.2038	0.666936
$746$	−0.995074	−0.0364323
$747$	−4.69877	−0.171919
$748$	−13.0629	−0.477628
$749$	−5.93367	−0.216812
$750$	8.49971	0.310365
$751$	4.80309	0.175267	0.0876337	−	0.996153i	$-0.472070\pi$
$751$	4.80309	0.175267	0.0876337	+	0.996153i	$0.472070\pi$
$752$	−2.58804	−0.0943763
$753$	−18.9736	−0.691435
$754$	−1.27727	−0.0465155
$755$	47.3513	1.72329
$756$	−35.5429	−1.29268
$757$	−18.8397	−0.684740	−0.342370	−	0.939565i	$-0.611230\pi$
$757$	−18.8397	−0.684740	−0.342370	+	0.939565i	$0.611230\pi$
$758$	−0.0899387	−0.00326672
$759$	69.9130	2.53768
$760$	−11.1990	−0.406230
$761$	−20.3223	−0.736682	−0.368341	−	0.929691i	$-0.620074\pi$
$761$	−20.3223	−0.736682	−0.368341	+	0.929691i	$0.620074\pi$
$762$	−5.27765	−0.191189
$763$	45.4407	1.64506
$764$	40.6859	1.47196
$765$	5.28090	0.190931
$766$	3.85003	0.139107
$767$	2.12783	0.0768317
$768$	−29.4870	−1.06402
$769$	−0.252234	−0.00909580	−0.00454790	−	0.999990i	$-0.501448\pi$
$769$	−0.252234	−0.00909580	−0.00454790	+	0.999990i	$0.501448\pi$
$770$	−20.5555	−0.740767
$771$	7.21134	0.259710
$772$	26.1706	0.941899
$773$	51.2621	1.84377	0.921884	−	0.387466i	$-0.126649\pi$
$773$	51.2621	1.84377	0.921884	+	0.387466i	$0.126649\pi$
$774$	−1.53854	−0.0553017
$775$	−17.7401	−0.637243
$776$	8.08785	0.290337
$777$	−25.4268	−0.912181
$778$	−1.34345	−0.0481651
$779$	−5.26395	−0.188601
$780$	−35.6236	−1.27553
$781$	−50.4063	−1.80368
$782$	0.765760	0.0273835
$783$	−14.1675	−0.506305
$784$	72.7080	2.59672
$785$	25.5553	0.912109
$786$	−2.45900	−0.0877095
$787$	−0.278652	−0.00993287	−0.00496644	−	0.999988i	$-0.501581\pi$
$787$	−0.278652	−0.00993287	−0.00496644	+	0.999988i	$0.501581\pi$
$788$	6.38014	0.227283
$789$	−11.2711	−0.401262
$790$	2.99865	0.106687
$791$	62.3628	2.21737
$792$	5.08989	0.180862
$793$	−8.26840	−0.293619
$794$	−0.102189	−0.00362655
$795$	−2.29249	−0.0813063
$796$	20.1799	0.715259
$797$	−46.6815	−1.65354	−0.826772	−	0.562537i	$-0.809825\pi$
$797$	−46.6815	−1.65354	−0.826772	+	0.562537i	$0.809825\pi$
$798$	−7.25213	−0.256723
$799$	−0.669492	−0.0236849
$800$	−20.7275	−0.732826
$801$	9.13074	0.322619
$802$	−1.81356	−0.0640391
$803$	−67.5052	−2.38221
$804$	−55.9637	−1.97369
$805$	−106.048	−3.73772
$806$	−0.483717	−0.0170382
$807$	10.0661	0.354343
$808$	−1.11670	−0.0392855
$809$	−37.5786	−1.32119	−0.660597	−	0.750741i	$-0.729697\pi$
$809$	−37.5786	−1.32119	−0.660597	+	0.750741i	$0.729697\pi$
$810$	6.86456	0.241196
$811$	20.0715	0.704807	0.352403	−	0.935848i	$-0.385365\pi$
$811$	20.0715	0.704807	0.352403	+	0.935848i	$0.385365\pi$
$812$	40.2301	1.41180
$813$	45.7883	1.60587
$814$	−2.39210	−0.0838429
$815$	−52.7811	−1.84884
$816$	−8.00892	−0.280368
$817$	−36.5064	−1.27720
$818$	4.57407	0.159929
$819$	−13.9701	−0.488154
$820$	−9.25395	−0.323162
$821$	−21.5071	−0.750602	−0.375301	−	0.926903i	$-0.622461\pi$
$821$	−21.5071	−0.750602	−0.375301	+	0.926903i	$0.622461\pi$
$822$	−0.442000	−0.0154165
$823$	28.8193	1.00458	0.502289	−	0.864700i	$-0.332491\pi$
$823$	28.8193	1.00458	0.502289	+	0.864700i	$0.332491\pi$
$824$	7.15292	0.249184
$825$	−160.091	−5.57365
$826$	0.761519	0.0264966
$827$	−23.9255	−0.831973	−0.415986	−	0.909371i	$-0.636564\pi$
$827$	−23.9255	−0.831973	−0.415986	+	0.909371i	$0.636564\pi$
$828$	13.0556	0.453712
$829$	22.5719	0.783955	0.391978	−	0.919975i	$-0.371791\pi$
$829$	22.5719	0.783955	0.391978	+	0.919975i	$0.371791\pi$
$830$	2.22707	0.0773026
$831$	−2.36368	−0.0819953
$832$	15.8859	0.550745
$833$	18.8086	0.651678
$834$	1.62135	0.0561427
$835$	−27.4944	−0.951484
$836$	60.0451	2.07670
$837$	−5.36539	−0.185455
$838$	−1.90318	−0.0657442
$839$	−37.9076	−1.30872	−0.654358	−	0.756185i	$-0.727061\pi$
$839$	−37.9076	−1.30872	−0.654358	+	0.756185i	$0.727061\pi$
$840$	−25.6431	−0.884772
$841$	−12.9641	−0.447039
$842$	0.834742	0.0287671
$843$	0.0163632	0.000563577 0
$844$	14.4228	0.496455
$845$	−34.6203	−1.19098
$846$	0.129695	0.00445900
$847$	165.793	5.69670
$848$	1.04679	0.0359468
$849$	23.6268	0.810869
$850$	−1.75348	−0.0601439
$851$	−12.3412	−0.423049
$852$	−31.2635	−1.07107
$853$	18.1315	0.620810	0.310405	−	0.950604i	$-0.399535\pi$
$853$	18.1315	0.620810	0.310405	+	0.950604i	$0.399535\pi$
$854$	−2.95913	−0.101259
$855$	−24.2742	−0.830160
$856$	−0.696393	−0.0238022
$857$	28.3037	0.966837	0.483418	−	0.875389i	$-0.339395\pi$
$857$	28.3037	0.966837	0.483418	+	0.875389i	$0.339395\pi$
$858$	−4.36518	−0.149025
$859$	−41.9748	−1.43216	−0.716081	−	0.698017i	$-0.754066\pi$
$859$	−41.9748	−1.43216	−0.716081	+	0.698017i	$0.754066\pi$
$860$	−64.1776	−2.18844
$861$	−12.0533	−0.410774
$862$	−1.42234	−0.0484449
$863$	2.72900	0.0928963	0.0464482	−	0.998921i	$-0.485210\pi$
$863$	2.72900	0.0928963	0.0464482	+	0.998921i	$0.485210\pi$
$864$	−6.26890	−0.213272
$865$	29.2916	0.995943
$866$	0.0221415	0.000752398 0
$867$	−2.07180	−0.0703619
$868$	15.2356	0.517129
$869$	−32.3381	−1.09700
$870$	−5.08184	−0.172291
$871$	29.0652	0.984837
$872$	5.33305	0.180600
$873$	17.5307	0.593325
$874$	−3.51989	−0.119062
$875$	139.040	4.70041
$876$	−41.8688	−1.41461
$877$	36.7073	1.23952	0.619759	−	0.784792i	$-0.287230\pi$
$877$	36.7073	1.23952	0.619759	+	0.784792i	$0.287230\pi$
$878$	4.77046	0.160995
$879$	−48.6627	−1.64135
$880$	104.345	3.51748
$881$	−30.4784	−1.02684	−0.513422	−	0.858136i	$-0.671622\pi$
$881$	−30.4784	−1.02684	−0.513422	+	0.858136i	$0.671622\pi$
$882$	−3.64362	−0.122687
$883$	21.5609	0.725584	0.362792	−	0.931870i	$-0.381824\pi$
$883$	21.5609	0.725584	0.362792	+	0.931870i	$0.381824\pi$
$884$	4.20786	0.141526
$885$	8.46596	0.284580
$886$	−2.84533	−0.0955908
$887$	47.7601	1.60363	0.801813	−	0.597574i	$-0.203869\pi$
$887$	47.7601	1.60363	0.801813	+	0.597574i	$0.203869\pi$
$888$	−2.98416	−0.100142
$889$	−86.3329	−2.89551
$890$	−4.32768	−0.145064
$891$	−74.0290	−2.48007
$892$	−44.9738	−1.50583
$893$	3.07739	0.102981
$894$	1.38350	0.0462712
$895$	−33.7866	−1.12936
$896$	23.6888	0.791387
$897$	−22.5205	−0.751939
$898$	5.23506	0.174696
$899$	6.07296	0.202544
$900$	−29.8954	−0.996513
$901$	0.270789	0.00902130
$902$	−1.13394	−0.0377562
$903$	−83.5912	−2.78174
$904$	7.31907	0.243429
$905$	61.2048	2.03452
$906$	3.59873	0.119560
$907$	−31.2119	−1.03637	−0.518187	−	0.855267i	$-0.673393\pi$
$907$	−31.2119	−1.03637	−0.518187	+	0.855267i	$0.673393\pi$
$908$	−26.5657	−0.881613
$909$	−2.42049	−0.0802827
$910$	6.62137	0.219496
$911$	−16.6869	−0.552861	−0.276430	−	0.961034i	$-0.589152\pi$
$911$	−16.6869	−0.552861	−0.276430	+	0.961034i	$0.589152\pi$
$912$	36.8138	1.21903
$913$	−24.0172	−0.794853
$914$	−3.06573	−0.101405
$915$	−32.8973	−1.08755
$916$	20.1974	0.667341
$917$	−40.2248	−1.32834
$918$	−0.530330	−0.0175035
$919$	−24.9073	−0.821617	−0.410808	−	0.911722i	$-0.634753\pi$
$919$	−24.9073	−0.821617	−0.410808	+	0.911722i	$0.634753\pi$
$920$	−12.4461	−0.410337
$921$	45.9377	1.51370
$922$	−3.62633	−0.119427
$923$	16.2370	0.534447
$924$	137.490	4.52308
$925$	28.2595	0.929166
$926$	0.446021	0.0146572
$927$	15.5042	0.509225
$928$	7.09561	0.232925
$929$	22.3531	0.733380	0.366690	−	0.930343i	$-0.380491\pi$
$929$	22.3531	0.733380	0.366690	+	0.930343i	$0.380491\pi$
$930$	−1.92455	−0.0631085
$931$	−86.4555	−2.83347
$932$	−4.58874	−0.150309
$933$	−20.0079	−0.655030
$934$	−2.87968	−0.0942259
$935$	26.9927	0.882756
$936$	−1.63957	−0.0535909
$937$	36.0925	1.17909	0.589545	−	0.807736i	$-0.299307\pi$
$937$	36.0925	1.17909	0.589545	+	0.807736i	$0.299307\pi$
$938$	10.4020	0.339637
$939$	14.4598	0.471879
$940$	5.41000	0.176455
$941$	24.3593	0.794091	0.397046	−	0.917799i	$-0.370035\pi$
$941$	24.3593	0.794091	0.397046	+	0.917799i	$0.370035\pi$
$942$	1.94222	0.0632811
$943$	−5.85017	−0.190508
$944$	−3.86569	−0.125817
$945$	73.4443	2.38914
$946$	−7.86408	−0.255683
$947$	−22.2055	−0.721581	−0.360791	−	0.932647i	$-0.617493\pi$
$947$	−22.2055	−0.721581	−0.360791	+	0.932647i	$0.617493\pi$
$948$	−20.0571	−0.651424
$949$	21.7449	0.705870
$950$	8.06006	0.261503
$951$	3.68514	0.119499
$952$	3.02897	0.0981694
$953$	−24.8691	−0.805591	−0.402795	−	0.915290i	$-0.631961\pi$
$953$	−24.8691	−0.805591	−0.402795	+	0.915290i	$0.631961\pi$
$954$	−0.0524577	−0.00169838
$955$	−84.0716	−2.72049
$956$	−36.9238	−1.19420
$957$	54.8038	1.77156
$958$	3.44674	0.111359
$959$	−7.23032	−0.233479
$960$	63.2049	2.03993
$961$	−28.7001	−0.925810
$962$	0.770547	0.0248434
$963$	−1.50946	−0.0486415
$964$	57.7826	1.86105
$965$	−54.0778	−1.74083
$966$	−8.05976	−0.259318
$967$	−10.2864	−0.330788	−0.165394	−	0.986228i	$-0.552890\pi$
$967$	−10.2864	−0.330788	−0.165394	+	0.986228i	$0.552890\pi$
$968$	19.4579	0.625400
$969$	9.52324	0.305930
$970$	−8.30900	−0.266786
$971$	12.6425	0.405718	0.202859	−	0.979208i	$-0.434977\pi$
$971$	12.6425	0.405718	0.202859	+	0.979208i	$0.434977\pi$
$972$	−24.9261	−0.799504
$973$	26.5224	0.850268
$974$	6.35256	0.203549
$975$	51.5689	1.65153
$976$	15.0214	0.480823
$977$	−56.1063	−1.79500	−0.897500	−	0.441014i	$-0.854619\pi$
$977$	−56.1063	−1.79500	−0.897500	+	0.441014i	$0.854619\pi$
$978$	−4.01140	−0.128270
$979$	46.6707	1.49160
$980$	−151.987	−4.85506
$981$	11.5596	0.369069
$982$	−0.0181293	−0.000578529 0
$983$	24.8351	0.792117	0.396058	−	0.918225i	$-0.370378\pi$
$983$	24.8351	0.792117	0.396058	+	0.918225i	$0.370378\pi$
$984$	−1.41460	−0.0450959
$985$	−13.1837	−0.420066
$986$	0.600268	0.0191164
$987$	7.04652	0.224293
$988$	−19.3419	−0.615347
$989$	−40.5719	−1.29011
$990$	−5.22907	−0.166191
$991$	−43.9779	−1.39700	−0.698502	−	0.715608i	$-0.746150\pi$
$991$	−43.9779	−1.39700	−0.698502	+	0.715608i	$0.746150\pi$
$992$	2.68719	0.0853183
$993$	−24.0424	−0.762963
$994$	5.81097	0.184313
$995$	−41.6990	−1.32195
$996$	−14.8962	−0.472004
$997$	15.9262	0.504389	0.252194	−	0.967677i	$-0.418848\pi$
$997$	15.9262	0.504389	0.252194	+	0.967677i	$0.418848\pi$
$998$	−0.519586	−0.0164472
$999$	8.54691	0.270412

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.8	✓	18
3.2	odd	2		9027.2.a.q.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.8	✓	18	1.1	even	1	trivial
9027.2.a.q.1.11		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.149899 q^{2} -2.07180 q^{3} -1.97753 q^{4} +4.08629 q^{5} +0.310561 q^{6} +5.08021 q^{7} +0.596228 q^{8} +1.29235 q^{9} +O(q^{10})\)	\(q-0.149899 q^{2} -2.07180 q^{3} -1.97753 q^{4} +4.08629 q^{5} +0.310561 q^{6} +5.08021 q^{7} +0.596228 q^{8} +1.29235 q^{9} -0.612531 q^{10} +6.60568 q^{11} +4.09704 q^{12} -2.12783 q^{13} -0.761519 q^{14} -8.46596 q^{15} +3.86569 q^{16} +1.00000 q^{17} -0.193722 q^{18} -4.59660 q^{19} -8.08076 q^{20} -10.5252 q^{21} -0.990185 q^{22} -5.10850 q^{23} -1.23526 q^{24} +11.6977 q^{25} +0.318961 q^{26} +3.53791 q^{27} -10.0463 q^{28} -4.00448 q^{29} +1.26904 q^{30} -1.51654 q^{31} -1.77192 q^{32} -13.6856 q^{33} -0.149899 q^{34} +20.7592 q^{35} -2.55565 q^{36} +2.41581 q^{37} +0.689027 q^{38} +4.40844 q^{39} +2.43636 q^{40} +1.14518 q^{41} +1.57771 q^{42} +7.94203 q^{43} -13.0629 q^{44} +5.28090 q^{45} +0.765760 q^{46} -0.669492 q^{47} -8.00892 q^{48} +18.8086 q^{49} -1.75348 q^{50} -2.07180 q^{51} +4.20786 q^{52} +0.270789 q^{53} -0.530330 q^{54} +26.9927 q^{55} +3.02897 q^{56} +9.52324 q^{57} +0.600268 q^{58} -1.00000 q^{59} +16.7417 q^{60} +3.88583 q^{61} +0.227328 q^{62} +6.56539 q^{63} -7.46576 q^{64} -8.69495 q^{65} +2.05146 q^{66} -13.6595 q^{67} -1.97753 q^{68} +10.5838 q^{69} -3.11179 q^{70} -7.63076 q^{71} +0.770533 q^{72} -10.2193 q^{73} -0.362127 q^{74} -24.2354 q^{75} +9.08992 q^{76} +33.5582 q^{77} -0.660822 q^{78} -4.89550 q^{79} +15.7963 q^{80} -11.2069 q^{81} -0.171662 q^{82} -3.63584 q^{83} +20.8139 q^{84} +4.08629 q^{85} -1.19050 q^{86} +8.29647 q^{87} +3.93849 q^{88} +7.06524 q^{89} -0.791602 q^{90} -10.8099 q^{91} +10.1022 q^{92} +3.14197 q^{93} +0.100356 q^{94} -18.7830 q^{95} +3.67106 q^{96} +13.5650 q^{97} -2.81939 q^{98} +8.53682 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 6 q^{11} + 20 q^{12} + 12 q^{13} + 9 q^{14} - q^{15} + 19 q^{16} + 18 q^{17} + 10 q^{18} - 14 q^{19} + 17 q^{20} - 14 q^{21} - 4 q^{22} + 7 q^{23} - 3 q^{24} + 35 q^{25} + 3 q^{26} + 13 q^{27} + q^{28} + 23 q^{29} + 17 q^{30} - q^{31} + 13 q^{32} + 7 q^{33} + 5 q^{34} + 5 q^{35} - 16 q^{36} + 36 q^{37} - 19 q^{38} + 8 q^{39} - 4 q^{40} + 37 q^{41} + 9 q^{42} - 15 q^{43} - 9 q^{44} + 17 q^{45} + q^{46} + 23 q^{47} + 17 q^{48} + 15 q^{49} + 32 q^{50} + q^{51} - 11 q^{52} + 35 q^{53} - 17 q^{54} - 6 q^{55} + 37 q^{56} - 16 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 39 q^{61} - q^{62} + 15 q^{63} + 5 q^{64} + 15 q^{65} - 36 q^{66} + 14 q^{67} + 21 q^{68} + 16 q^{69} - 45 q^{70} + 3 q^{71} - 71 q^{72} + 56 q^{73} - 27 q^{74} + 16 q^{75} - q^{76} + 39 q^{77} - 71 q^{78} - 22 q^{79} + 45 q^{80} - 18 q^{81} + 5 q^{82} + 12 q^{83} + 2 q^{84} + 21 q^{85} + 4 q^{86} + 8 q^{87} - 18 q^{88} + 34 q^{89} + 48 q^{90} + 3 q^{91} + 67 q^{92} - 19 q^{93} - 38 q^{94} - 72 q^{95} + 6 q^{96} + 31 q^{97} + 19 q^{98} + 44 q^{99}+O(q^{100}) \) 18 * q + 5 * q^2 + q^3 + 21 * q^4 + 21 * q^5 + 5 * q^6 - q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 6 * q^11 + 20 * q^12 + 12 * q^13 + 9 * q^14 - q^15 + 19 * q^16 + 18 * q^17 + 10 * q^18 - 14 * q^19 + 17 * q^20 - 14 * q^21 - 4 * q^22 + 7 * q^23 - 3 * q^24 + 35 * q^25 + 3 * q^26 + 13 * q^27 + q^28 + 23 * q^29 + 17 * q^30 - q^31 + 13 * q^32 + 7 * q^33 + 5 * q^34 + 5 * q^35 - 16 * q^36 + 36 * q^37 - 19 * q^38 + 8 * q^39 - 4 * q^40 + 37 * q^41 + 9 * q^42 - 15 * q^43 - 9 * q^44 + 17 * q^45 + q^46 + 23 * q^47 + 17 * q^48 + 15 * q^49 + 32 * q^50 + q^51 - 11 * q^52 + 35 * q^53 - 17 * q^54 - 6 * q^55 + 37 * q^56 - 16 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 39 * q^61 - q^62 + 15 * q^63 + 5 * q^64 + 15 * q^65 - 36 * q^66 + 14 * q^67 + 21 * q^68 + 16 * q^69 - 45 * q^70 + 3 * q^71 - 71 * q^72 + 56 * q^73 - 27 * q^74 + 16 * q^75 - q^76 + 39 * q^77 - 71 * q^78 - 22 * q^79 + 45 * q^80 - 18 * q^81 + 5 * q^82 + 12 * q^83 + 2 * q^84 + 21 * q^85 + 4 * q^86 + 8 * q^87 - 18 * q^88 + 34 * q^89 + 48 * q^90 + 3 * q^91 + 67 * q^92 - 19 * q^93 - 38 * q^94 - 72 * q^95 + 6 * q^96 + 31 * q^97 + 19 * q^98 + 44 * q^99

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