LMFDB - Embedded newform 1003.2.a.i.1.4

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			1.4
Root			$-1.84714$ 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)

$f(q)$	$=$	$q-1.84714 q^{2} -2.22957 q^{3} +1.41194 q^{4} -0.984600 q^{5} +4.11833 q^{6} +2.90768 q^{7} +1.08623 q^{8} +1.97096 q^{9} +O(q^{10})$	\(q-1.84714 q^{2} -2.22957 q^{3} +1.41194 q^{4} -0.984600 q^{5} +4.11833 q^{6} +2.90768 q^{7} +1.08623 q^{8} +1.97096 q^{9} +1.81870 q^{10} +3.12652 q^{11} -3.14802 q^{12} -2.44065 q^{13} -5.37090 q^{14} +2.19523 q^{15} -4.83030 q^{16} +1.00000 q^{17} -3.64066 q^{18} +5.79028 q^{19} -1.39020 q^{20} -6.48286 q^{21} -5.77513 q^{22} +3.79490 q^{23} -2.42182 q^{24} -4.03056 q^{25} +4.50824 q^{26} +2.29430 q^{27} +4.10547 q^{28} -4.79696 q^{29} -4.05491 q^{30} -9.81687 q^{31} +6.74981 q^{32} -6.97078 q^{33} -1.84714 q^{34} -2.86290 q^{35} +2.78289 q^{36} -5.03447 q^{37} -10.6955 q^{38} +5.44160 q^{39} -1.06950 q^{40} +2.21163 q^{41} +11.9748 q^{42} -4.21354 q^{43} +4.41446 q^{44} -1.94061 q^{45} -7.00973 q^{46} +6.32958 q^{47} +10.7695 q^{48} +1.45460 q^{49} +7.44503 q^{50} -2.22957 q^{51} -3.44606 q^{52} +8.94914 q^{53} -4.23791 q^{54} -3.07837 q^{55} +3.15840 q^{56} -12.9098 q^{57} +8.86068 q^{58} -1.00000 q^{59} +3.09954 q^{60} +10.2111 q^{61} +18.1332 q^{62} +5.73093 q^{63} -2.80727 q^{64} +2.40307 q^{65} +12.8760 q^{66} +11.7143 q^{67} +1.41194 q^{68} -8.46099 q^{69} +5.28819 q^{70} +2.57692 q^{71} +2.14092 q^{72} +13.0734 q^{73} +9.29939 q^{74} +8.98640 q^{75} +8.17554 q^{76} +9.09091 q^{77} -10.0514 q^{78} -13.7238 q^{79} +4.75592 q^{80} -11.0282 q^{81} -4.08520 q^{82} -5.47691 q^{83} -9.15343 q^{84} -0.984600 q^{85} +7.78302 q^{86} +10.6951 q^{87} +3.39611 q^{88} +6.79697 q^{89} +3.58459 q^{90} -7.09663 q^{91} +5.35818 q^{92} +21.8874 q^{93} -11.6916 q^{94} -5.70111 q^{95} -15.0492 q^{96} -12.0607 q^{97} -2.68685 q^{98} +6.16226 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.84714	−1.30613	−0.653064	−	0.757303i	$-0.726517\pi$
$2$	−1.84714	−1.30613	−0.653064	+	0.757303i	$0.726517\pi$
$3$	−2.22957	−1.28724	−0.643620	−	0.765345i	$-0.722568\pi$
$3$	−2.22957	−1.28724	−0.643620	+	0.765345i	$0.722568\pi$
$4$	1.41194	0.705971
$5$	−0.984600	−0.440327	−0.220163	−	0.975463i	$-0.570659\pi$
$5$	−0.984600	−0.440327	−0.220163	+	0.975463i	$0.570659\pi$
$6$	4.11833	1.68130
$7$	2.90768	1.09900	0.549500	−	0.835494i	$-0.314818\pi$
$7$	2.90768	1.09900	0.549500	+	0.835494i	$0.314818\pi$
$8$	1.08623	0.384040
$9$	1.97096	0.656988
$10$	1.81870	0.575123
$11$	3.12652	0.942681	0.471340	−	0.881951i	$-0.343770\pi$
$11$	3.12652	0.942681	0.471340	+	0.881951i	$0.343770\pi$
$12$	−3.14802	−0.908754
$13$	−2.44065	−0.676915	−0.338458	−	0.940982i	$-0.609905\pi$
$13$	−2.44065	−0.676915	−0.338458	+	0.940982i	$0.609905\pi$
$14$	−5.37090	−1.43543
$15$	2.19523	0.566806
$16$	−4.83030	−1.20758
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.64066	−0.858111
$19$	5.79028	1.32838	0.664191	−	0.747563i	$-0.268776\pi$
$19$	5.79028	1.32838	0.664191	+	0.747563i	$0.268776\pi$
$20$	−1.39020	−0.310858
$21$	−6.48286	−1.41468
$22$	−5.77513	−1.23126
$23$	3.79490	0.791292	0.395646	−	0.918403i	$-0.370521\pi$
$23$	3.79490	0.791292	0.395646	+	0.918403i	$0.370521\pi$
$24$	−2.42182	−0.494351
$25$	−4.03056	−0.806112
$26$	4.50824	0.884138
$27$	2.29430	0.441539
$28$	4.10547	0.775862
$29$	−4.79696	−0.890773	−0.445387	−	0.895338i	$-0.646934\pi$
$29$	−4.79696	−0.890773	−0.445387	+	0.895338i	$0.646934\pi$
$30$	−4.05491	−0.740322
$31$	−9.81687	−1.76316	−0.881581	−	0.472034i	$-0.843520\pi$
$31$	−9.81687	−1.76316	−0.881581	+	0.472034i	$0.843520\pi$
$32$	6.74981	1.19321
$33$	−6.97078	−1.21346
$34$	−1.84714	−0.316783
$35$	−2.86290	−0.483919
$36$	2.78289	0.463815
$37$	−5.03447	−0.827661	−0.413831	−	0.910354i	$-0.635809\pi$
$37$	−5.03447	−0.827661	−0.413831	+	0.910354i	$0.635809\pi$
$38$	−10.6955	−1.73504
$39$	5.44160	0.871353
$40$	−1.06950	−0.169103
$41$	2.21163	0.345399	0.172699	−	0.984975i	$-0.444751\pi$
$41$	2.21163	0.345399	0.172699	+	0.984975i	$0.444751\pi$
$42$	11.9748	1.84775
$43$	−4.21354	−0.642559	−0.321280	−	0.946984i	$-0.604113\pi$
$43$	−4.21354	−0.642559	−0.321280	+	0.946984i	$0.604113\pi$
$44$	4.41446	0.665505
$45$	−1.94061	−0.289289
$46$	−7.00973	−1.03353
$47$	6.32958	0.923264	0.461632	−	0.887072i	$-0.347264\pi$
$47$	6.32958	0.923264	0.461632	+	0.887072i	$0.347264\pi$
$48$	10.7695	1.55444
$49$	1.45460	0.207800
$50$	7.44503	1.05289
$51$	−2.22957	−0.312202
$52$	−3.44606	−0.477882
$53$	8.94914	1.22926	0.614629	−	0.788816i	$-0.289306\pi$
$53$	8.94914	1.22926	0.614629	+	0.788816i	$0.289306\pi$
$54$	−4.23791	−0.576706
$55$	−3.07837	−0.415087
$56$	3.15840	0.422059
$57$	−12.9098	−1.70995
$58$	8.86068	1.16346
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	3.09954	0.400149
$61$	10.2111	1.30740	0.653700	−	0.756754i	$-0.273216\pi$
$61$	10.2111	1.30740	0.653700	+	0.756754i	$0.273216\pi$
$62$	18.1332	2.30291
$63$	5.73093	0.722030
$64$	−2.80727	−0.350909
$65$	2.40307	0.298064
$66$	12.8760	1.58493
$67$	11.7143	1.43113	0.715566	−	0.698545i	$-0.246169\pi$
$67$	11.7143	1.43113	0.715566	+	0.698545i	$0.246169\pi$
$68$	1.41194	0.171223
$69$	−8.46099	−1.01858
$70$	5.28819	0.632060
$71$	2.57692	0.305825	0.152912	−	0.988240i	$-0.451135\pi$
$71$	2.57692	0.305825	0.152912	+	0.988240i	$0.451135\pi$
$72$	2.14092	0.252310
$73$	13.0734	1.53013	0.765064	−	0.643954i	$-0.222707\pi$
$73$	13.0734	1.53013	0.765064	+	0.643954i	$0.222707\pi$
$74$	9.29939	1.08103
$75$	8.98640	1.03766
$76$	8.17554	0.937798
$77$	9.09091	1.03601
$78$	−10.0514	−1.13810
$79$	−13.7238	−1.54405	−0.772025	−	0.635593i	$-0.780756\pi$
$79$	−13.7238	−1.54405	−0.772025	+	0.635593i	$0.780756\pi$
$80$	4.75592	0.531728
$81$	−11.0282	−1.22535
$82$	−4.08520	−0.451135
$83$	−5.47691	−0.601169	−0.300584	−	0.953755i	$-0.597182\pi$
$83$	−5.47691	−0.601169	−0.300584	+	0.953755i	$0.597182\pi$
$84$	−9.15343	−0.998721
$85$	−0.984600	−0.106795
$86$	7.78302	0.839265
$87$	10.6951	1.14664
$88$	3.39611	0.362027
$89$	6.79697	0.720477	0.360238	−	0.932860i	$-0.382695\pi$
$89$	6.79697	0.720477	0.360238	+	0.932860i	$0.382695\pi$
$90$	3.58459	0.377849
$91$	−7.09663	−0.743929
$92$	5.35818	0.558629
$93$	21.8874	2.26961
$94$	−11.6916	−1.20590
$95$	−5.70111	−0.584922
$96$	−15.0492	−1.53595
$97$	−12.0607	−1.22458	−0.612289	−	0.790634i	$-0.709751\pi$
$97$	−12.0607	−1.22458	−0.612289	+	0.790634i	$0.709751\pi$
$98$	−2.68685	−0.271413
$99$	6.16226	0.619330
$100$	−5.69092	−0.569092
$101$	8.95875	0.891429	0.445715	−	0.895175i	$-0.352950\pi$
$101$	8.95875	0.891429	0.445715	+	0.895175i	$0.352950\pi$
$102$	4.11833	0.407775
$103$	−5.25835	−0.518120	−0.259060	−	0.965861i	$-0.583413\pi$
$103$	−5.25835	−0.518120	−0.259060	+	0.965861i	$0.583413\pi$
$104$	−2.65110	−0.259962
$105$	6.38303	0.622920
$106$	−16.5303	−1.60557
$107$	18.8255	1.81993	0.909966	−	0.414683i	$-0.136107\pi$
$107$	18.8255	1.81993	0.909966	+	0.414683i	$0.136107\pi$
$108$	3.23942	0.311713
$109$	15.0248	1.43911	0.719556	−	0.694434i	$-0.244345\pi$
$109$	15.0248	1.43911	0.719556	+	0.694434i	$0.244345\pi$
$110$	5.68620	0.542157
$111$	11.2247	1.06540
$112$	−14.0450	−1.32713
$113$	−1.10692	−0.104131	−0.0520653	−	0.998644i	$-0.516580\pi$
$113$	−1.10692	−0.104131	−0.0520653	+	0.998644i	$0.516580\pi$
$114$	23.8463	2.23341
$115$	−3.73646	−0.348427
$116$	−6.77303	−0.628860
$117$	−4.81044	−0.444725
$118$	1.84714	0.170043
$119$	2.90768	0.266546
$120$	2.38452	0.217676
$121$	−1.22488	−0.111353
$122$	−18.8614	−1.70763
$123$	−4.93098	−0.444611
$124$	−13.8608	−1.24474
$125$	8.89149	0.795279
$126$	−10.5859	−0.943063
$127$	4.94291	0.438612	0.219306	−	0.975656i	$-0.429621\pi$
$127$	4.94291	0.438612	0.219306	+	0.975656i	$0.429621\pi$
$128$	−8.31419	−0.734878
$129$	9.39437	0.827129
$130$	−4.43881	−0.389310
$131$	−15.4021	−1.34569	−0.672845	−	0.739784i	$-0.734928\pi$
$131$	−15.4021	−1.34569	−0.672845	+	0.739784i	$0.734928\pi$
$132$	−9.84234	−0.856665
$133$	16.8363	1.45989
$134$	−21.6380	−1.86924
$135$	−2.25897	−0.194421
$136$	1.08623	0.0931433
$137$	9.21256	0.787082	0.393541	−	0.919307i	$-0.371250\pi$
$137$	9.21256	0.787082	0.393541	+	0.919307i	$0.371250\pi$
$138$	15.6287	1.33040
$139$	15.5311	1.31733	0.658664	−	0.752437i	$-0.271122\pi$
$139$	15.5311	1.31733	0.658664	+	0.752437i	$0.271122\pi$
$140$	−4.04225	−0.341633
$141$	−14.1122	−1.18846
$142$	−4.75995	−0.399446
$143$	−7.63074	−0.638115
$144$	−9.52036	−0.793363
$145$	4.72309	0.392231
$146$	−24.1485	−1.99854
$147$	−3.24312	−0.267488
$148$	−7.10838	−0.584305
$149$	2.33892	0.191612	0.0958060	−	0.995400i	$-0.469457\pi$
$149$	2.33892	0.191612	0.0958060	+	0.995400i	$0.469457\pi$
$150$	−16.5992	−1.35532
$151$	−1.17197	−0.0953738	−0.0476869	−	0.998862i	$-0.515185\pi$
$151$	−1.17197	−0.0953738	−0.0476869	+	0.998862i	$0.515185\pi$
$152$	6.28956	0.510151
$153$	1.97096	0.159343
$154$	−16.7922	−1.35316
$155$	9.66569	0.776367
$156$	7.68322	0.615150
$157$	16.5237	1.31874	0.659368	−	0.751820i	$-0.270824\pi$
$157$	16.5237	1.31874	0.659368	+	0.751820i	$0.270824\pi$
$158$	25.3499	2.01673
$159$	−19.9527	−1.58235
$160$	−6.64587	−0.525402
$161$	11.0344	0.869629
$162$	20.3707	1.60047
$163$	−9.80497	−0.767985	−0.383992	−	0.923336i	$-0.625451\pi$
$163$	−9.80497	−0.767985	−0.383992	+	0.923336i	$0.625451\pi$
$164$	3.12270	0.243842
$165$	6.86343	0.534317
$166$	10.1166	0.785204
$167$	10.0308	0.776204	0.388102	−	0.921616i	$-0.373131\pi$
$167$	10.0308	0.776204	0.388102	+	0.921616i	$0.373131\pi$
$168$	−7.04187	−0.543292
$169$	−7.04322	−0.541786
$170$	1.81870	0.139488
$171$	11.4124	0.872731
$172$	−5.94928	−0.453628
$173$	15.1930	1.15511	0.577553	−	0.816353i	$-0.304008\pi$
$173$	15.1930	1.15511	0.577553	+	0.816353i	$0.304008\pi$
$174$	−19.7555	−1.49766
$175$	−11.7196	−0.885917
$176$	−15.1020	−1.13836
$177$	2.22957	0.167584
$178$	−12.5550	−0.941035
$179$	−1.86854	−0.139661	−0.0698304	−	0.997559i	$-0.522246\pi$
$179$	−1.86854	−0.139661	−0.0698304	+	0.997559i	$0.522246\pi$
$180$	−2.74003	−0.204230
$181$	−20.4786	−1.52216	−0.761082	−	0.648655i	$-0.775332\pi$
$181$	−20.4786	−1.52216	−0.761082	+	0.648655i	$0.775332\pi$
$182$	13.1085	0.971667
$183$	−22.7664	−1.68294
$184$	4.12213	0.303887
$185$	4.95694	0.364441
$186$	−40.4291	−2.96440
$187$	3.12652	0.228634
$188$	8.93700	0.651797
$189$	6.67109	0.485251
$190$	10.5308	0.763983
$191$	−20.0493	−1.45071	−0.725357	−	0.688373i	$-0.758325\pi$
$191$	−20.0493	−1.45071	−0.725357	+	0.688373i	$0.758325\pi$
$192$	6.25899	0.451704
$193$	2.19533	0.158023	0.0790116	−	0.996874i	$-0.474824\pi$
$193$	2.19533	0.158023	0.0790116	+	0.996874i	$0.474824\pi$
$194$	22.2779	1.59946
$195$	−5.35780	−0.383680
$196$	2.05381	0.146700
$197$	19.8148	1.41175	0.705875	−	0.708337i	$-0.250554\pi$
$197$	19.8148	1.41175	0.705875	+	0.708337i	$0.250554\pi$
$198$	−11.3826	−0.808925
$199$	20.1382	1.42756	0.713779	−	0.700371i	$-0.246982\pi$
$199$	20.1382	1.42756	0.713779	+	0.700371i	$0.246982\pi$
$200$	−4.37811	−0.309579
$201$	−26.1178	−1.84221
$202$	−16.5481	−1.16432
$203$	−13.9480	−0.978959
$204$	−3.14802	−0.220405
$205$	−2.17757	−0.152088
$206$	9.71292	0.676731
$207$	7.47962	0.519870
$208$	11.7891	0.817426
$209$	18.1034	1.25224
$210$	−11.7904	−0.813613
$211$	6.96801	0.479698	0.239849	−	0.970810i	$-0.422902\pi$
$211$	6.96801	0.479698	0.239849	+	0.970810i	$0.422902\pi$
$212$	12.6357	0.867821
$213$	−5.74542	−0.393670
$214$	−34.7735	−2.37706
$215$	4.14866	0.282936
$216$	2.49214	0.169568
$217$	−28.5443	−1.93771
$218$	−27.7529	−1.87967
$219$	−29.1480	−1.96964
$220$	−4.34648	−0.293040
$221$	−2.44065	−0.164176
$222$	−20.7336	−1.39155
$223$	−8.13514	−0.544769	−0.272385	−	0.962188i	$-0.587812\pi$
$223$	−8.13514	−0.544769	−0.272385	+	0.962188i	$0.587812\pi$
$224$	19.6263	1.31134
$225$	−7.94410	−0.529606
$226$	2.04465	0.136008
$227$	−15.0158	−0.996632	−0.498316	−	0.866996i	$-0.666048\pi$
$227$	−15.0158	−0.996632	−0.498316	+	0.866996i	$0.666048\pi$
$228$	−18.2279	−1.20717
$229$	20.6044	1.36158	0.680789	−	0.732480i	$-0.261637\pi$
$229$	20.6044	1.36158	0.680789	+	0.732480i	$0.261637\pi$
$230$	6.90179	0.455090
$231$	−20.2688	−1.33359
$232$	−5.21059	−0.342092
$233$	−8.78005	−0.575200	−0.287600	−	0.957751i	$-0.592857\pi$
$233$	−8.78005	−0.575200	−0.287600	+	0.957751i	$0.592857\pi$
$234$	8.88558	0.580868
$235$	−6.23210	−0.406538
$236$	−1.41194	−0.0919096
$237$	30.5981	1.98756
$238$	−5.37090	−0.348144
$239$	12.1261	0.784372	0.392186	−	0.919886i	$-0.371719\pi$
$239$	12.1261	0.784372	0.392186	+	0.919886i	$0.371719\pi$
$240$	−10.6036	−0.684462
$241$	−9.86364	−0.635373	−0.317686	−	0.948196i	$-0.602906\pi$
$241$	−9.86364	−0.635373	−0.317686	+	0.948196i	$0.602906\pi$
$242$	2.26254	0.145441
$243$	17.7052	1.13579
$244$	14.4175	0.922987
$245$	−1.43220	−0.0914997
$246$	9.10823	0.580719
$247$	−14.1321	−0.899201
$248$	−10.6634	−0.677124
$249$	12.2111	0.773849
$250$	−16.4239	−1.03874
$251$	−13.3608	−0.843323	−0.421662	−	0.906753i	$-0.638553\pi$
$251$	−13.3608	−0.843323	−0.421662	+	0.906753i	$0.638553\pi$
$252$	8.09174	0.509732
$253$	11.8648	0.745936
$254$	−9.13026	−0.572884
$255$	2.19523	0.137471
$256$	20.9721	1.31075
$257$	−12.4043	−0.773761	−0.386881	−	0.922130i	$-0.626447\pi$
$257$	−12.4043	−0.773761	−0.386881	+	0.922130i	$0.626447\pi$
$258$	−17.3528	−1.08034
$259$	−14.6386	−0.909599
$260$	3.39299	0.210424
$261$	−9.45464	−0.585228
$262$	28.4499	1.75764
$263$	32.0240	1.97469	0.987343	−	0.158598i	$-0.0506974\pi$
$263$	32.0240	1.97469	0.987343	+	0.158598i	$0.0506974\pi$
$264$	−7.57186	−0.466015
$265$	−8.81132	−0.541275
$266$	−31.0990	−1.90680
$267$	−15.1543	−0.927427
$268$	16.5399	1.01034
$269$	11.1585	0.680348	0.340174	−	0.940363i	$-0.389514\pi$
$269$	11.1585	0.680348	0.340174	+	0.940363i	$0.389514\pi$
$270$	4.17264	0.253939
$271$	6.93901	0.421515	0.210757	−	0.977538i	$-0.432407\pi$
$271$	6.93901	0.421515	0.210757	+	0.977538i	$0.432407\pi$
$272$	−4.83030	−0.292880
$273$	15.8224	0.957616
$274$	−17.0169	−1.02803
$275$	−12.6016	−0.759907
$276$	−11.9464	−0.719090
$277$	14.2373	0.855436	0.427718	−	0.903912i	$-0.359318\pi$
$277$	14.2373	0.855436	0.427718	+	0.903912i	$0.359318\pi$
$278$	−28.6881	−1.72060
$279$	−19.3487	−1.15838
$280$	−3.10976	−0.185844
$281$	−4.68197	−0.279303	−0.139651	−	0.990201i	$-0.544598\pi$
$281$	−4.68197	−0.279303	−0.139651	+	0.990201i	$0.544598\pi$
$282$	26.0673	1.55228
$283$	26.4357	1.57144	0.785719	−	0.618584i	$-0.212293\pi$
$283$	26.4357	1.57144	0.785719	+	0.618584i	$0.212293\pi$
$284$	3.63847	0.215903
$285$	12.7110	0.752935
$286$	14.0951	0.833460
$287$	6.43071	0.379593
$288$	13.3036	0.783925
$289$	1.00000	0.0588235
$290$	−8.72423	−0.512304
$291$	26.8901	1.57633
$292$	18.4589	1.08023
$293$	17.0942	0.998653	0.499326	−	0.866414i	$-0.333581\pi$
$293$	17.0942	0.998653	0.499326	+	0.866414i	$0.333581\pi$
$294$	5.99051	0.349374
$295$	0.984600	0.0573256
$296$	−5.46858	−0.317855
$297$	7.17318	0.416230
$298$	−4.32033	−0.250270
$299$	−9.26204	−0.535638
$300$	12.6883	0.732558
$301$	−12.2516	−0.706172
$302$	2.16480	0.124570
$303$	−19.9741	−1.14748
$304$	−27.9688	−1.60412
$305$	−10.0539	−0.575683
$306$	−3.64066	−0.208122
$307$	2.83047	0.161543	0.0807717	−	0.996733i	$-0.474262\pi$
$307$	2.83047	0.161543	0.0807717	+	0.996733i	$0.474262\pi$
$308$	12.8358	0.731390
$309$	11.7238	0.666945
$310$	−17.8539	−1.01403
$311$	27.6037	1.56526	0.782632	−	0.622484i	$-0.213876\pi$
$311$	27.6037	1.56526	0.782632	+	0.622484i	$0.213876\pi$
$312$	5.91081	0.334634
$313$	27.1578	1.53505	0.767526	−	0.641018i	$-0.221488\pi$
$313$	27.1578	1.53505	0.767526	+	0.641018i	$0.221488\pi$
$314$	−30.5217	−1.72244
$315$	−5.64268	−0.317929
$316$	−19.3772	−1.09005
$317$	18.5818	1.04366	0.521829	−	0.853050i	$-0.325250\pi$
$317$	18.5818	1.04366	0.521829	+	0.853050i	$0.325250\pi$
$318$	36.8555	2.06675
$319$	−14.9978	−0.839715
$320$	2.76404	0.154514
$321$	−41.9728	−2.34269
$322$	−20.3821	−1.13585
$323$	5.79028	0.322180
$324$	−15.5712	−0.865065
$325$	9.83720	0.545670
$326$	18.1112	1.00309
$327$	−33.4987	−1.85248
$328$	2.40234	0.132647
$329$	18.4044	1.01467
$330$	−12.6777	−0.697887
$331$	−17.5108	−0.962483	−0.481241	−	0.876588i	$-0.659814\pi$
$331$	−17.5108	−0.962483	−0.481241	+	0.876588i	$0.659814\pi$
$332$	−7.73308	−0.424408
$333$	−9.92276	−0.543764
$334$	−18.5283	−1.01382
$335$	−11.5339	−0.630165
$336$	31.3142	1.70833
$337$	−2.16246	−0.117797	−0.0588983	−	0.998264i	$-0.518759\pi$
$337$	−2.16246	−0.117797	−0.0588983	+	0.998264i	$0.518759\pi$
$338$	13.0098	0.707642
$339$	2.46796	0.134041
$340$	−1.39020	−0.0753941
$341$	−30.6926	−1.66210
$342$	−21.0804	−1.13990
$343$	−16.1243	−0.870628
$344$	−4.57687	−0.246768
$345$	8.33069	0.448509
$346$	−28.0637	−1.50872
$347$	20.2759	1.08847	0.544235	−	0.838933i	$-0.316820\pi$
$347$	20.2759	1.08847	0.544235	+	0.838933i	$0.316820\pi$
$348$	15.1009	0.809494
$349$	−27.5373	−1.47404	−0.737020	−	0.675871i	$-0.763768\pi$
$349$	−27.5373	−1.47404	−0.737020	+	0.675871i	$0.763768\pi$
$350$	21.6478	1.15712
$351$	−5.59959	−0.298884
$352$	21.1034	1.12482
$353$	−7.95479	−0.423391	−0.211695	−	0.977336i	$-0.567898\pi$
$353$	−7.95479	−0.423391	−0.211695	+	0.977336i	$0.567898\pi$
$354$	−4.11833	−0.218887
$355$	−2.53724	−0.134663
$356$	9.59692	0.508636
$357$	−6.48286	−0.343109
$358$	3.45145	0.182415
$359$	22.8839	1.20777	0.603884	−	0.797072i	$-0.293619\pi$
$359$	22.8839	1.20777	0.603884	+	0.797072i	$0.293619\pi$
$360$	−2.10795	−0.111099
$361$	14.5273	0.764596
$362$	37.8270	1.98814
$363$	2.73096	0.143338
$364$	−10.0200	−0.525192
$365$	−12.8721	−0.673756
$366$	42.0528	2.19813
$367$	11.6278	0.606968	0.303484	−	0.952837i	$-0.401850\pi$
$367$	11.6278	0.606968	0.303484	+	0.952837i	$0.401850\pi$
$368$	−18.3305	−0.955545
$369$	4.35905	0.226923
$370$	−9.15618	−0.476007
$371$	26.0212	1.35095
$372$	30.9037	1.60228
$373$	26.6476	1.37976	0.689880	−	0.723924i	$-0.257663\pi$
$373$	26.6476	1.37976	0.689880	+	0.723924i	$0.257663\pi$
$374$	−5.77513	−0.298625
$375$	−19.8242	−1.02372
$376$	6.87536	0.354570
$377$	11.7077	0.602978
$378$	−12.3225	−0.633800
$379$	−24.2644	−1.24638	−0.623188	−	0.782072i	$-0.714163\pi$
$379$	−24.2644	−1.24638	−0.623188	+	0.782072i	$0.714163\pi$
$380$	−8.04964	−0.412938
$381$	−11.0205	−0.564599
$382$	37.0339	1.89482
$383$	−4.01972	−0.205398	−0.102699	−	0.994712i	$-0.532748\pi$
$383$	−4.01972	−0.205398	−0.102699	+	0.994712i	$0.532748\pi$
$384$	18.5370	0.945964
$385$	−8.95091	−0.456181
$386$	−4.05509	−0.206399
$387$	−8.30475	−0.422154
$388$	−17.0290	−0.864517
$389$	−36.8280	−1.86725	−0.933627	−	0.358246i	$-0.883375\pi$
$389$	−36.8280	−1.86725	−0.933627	+	0.358246i	$0.883375\pi$
$390$	9.89662	0.501135
$391$	3.79490	0.191917
$392$	1.58002	0.0798032
$393$	34.3400	1.73223
$394$	−36.6009	−1.84393
$395$	13.5125	0.679886
$396$	8.70075	0.437229
$397$	−20.5134	−1.02954	−0.514770	−	0.857328i	$-0.672123\pi$
$397$	−20.5134	−1.02954	−0.514770	+	0.857328i	$0.672123\pi$
$398$	−37.1981	−1.86457
$399$	−37.5376	−1.87923
$400$	19.4688	0.973442
$401$	10.1003	0.504385	0.252192	−	0.967677i	$-0.418848\pi$
$401$	10.1003	0.504385	0.252192	+	0.967677i	$0.418848\pi$
$402$	48.2434	2.40616
$403$	23.9596	1.19351
$404$	12.6492	0.629323
$405$	10.8584	0.539556
$406$	25.7640	1.27865
$407$	−15.7404	−0.780220
$408$	−2.42182	−0.119898
$409$	30.0799	1.48735	0.743677	−	0.668539i	$-0.233080\pi$
$409$	30.0799	1.48735	0.743677	+	0.668539i	$0.233080\pi$
$410$	4.02229	0.198647
$411$	−20.5400	−1.01316
$412$	−7.42448	−0.365778
$413$	−2.90768	−0.143078
$414$	−13.8159	−0.679016
$415$	5.39257	0.264711
$416$	−16.4739	−0.807702
$417$	−34.6275	−1.69572
$418$	−33.4396	−1.63559
$419$	35.1261	1.71602	0.858010	−	0.513632i	$-0.171700\pi$
$419$	35.1261	1.71602	0.858010	+	0.513632i	$0.171700\pi$
$420$	9.01247	0.439763
$421$	−4.81083	−0.234466	−0.117233	−	0.993104i	$-0.537402\pi$
$421$	−4.81083	−0.234466	−0.117233	+	0.993104i	$0.537402\pi$
$422$	−12.8709	−0.626547
$423$	12.4754	0.606573
$424$	9.72080	0.472084
$425$	−4.03056	−0.195511
$426$	10.6126	0.514183
$427$	29.6907	1.43683
$428$	26.5806	1.28482
$429$	17.0132	0.821407
$430$	−7.66317	−0.369551
$431$	5.92679	0.285483	0.142742	−	0.989760i	$-0.454408\pi$
$431$	5.92679	0.285483	0.142742	+	0.989760i	$0.454408\pi$
$432$	−11.0822	−0.533191
$433$	33.4568	1.60783	0.803917	−	0.594742i	$-0.202746\pi$
$433$	33.4568	1.60783	0.803917	+	0.594742i	$0.202746\pi$
$434$	52.7254	2.53090
$435$	−10.5304	−0.504896
$436$	21.2141	1.01597
$437$	21.9735	1.05114
$438$	53.8406	2.57261
$439$	27.4688	1.31102	0.655508	−	0.755188i	$-0.272454\pi$
$439$	27.4688	1.31102	0.655508	+	0.755188i	$0.272454\pi$
$440$	−3.34381	−0.159410
$441$	2.86696	0.136522
$442$	4.50824	0.214435
$443$	−13.6729	−0.649618	−0.324809	−	0.945780i	$-0.605300\pi$
$443$	−13.6729	−0.649618	−0.324809	+	0.945780i	$0.605300\pi$
$444$	15.8486	0.752141
$445$	−6.69229	−0.317245
$446$	15.0268	0.711538
$447$	−5.21478	−0.246651
$448$	−8.16264	−0.385648
$449$	−15.7217	−0.741952	−0.370976	−	0.928642i	$-0.620977\pi$
$449$	−15.7217	−0.741952	−0.370976	+	0.928642i	$0.620977\pi$
$450$	14.6739	0.691734
$451$	6.91471	0.325601
$452$	−1.56291	−0.0735132
$453$	2.61299	0.122769
$454$	27.7363	1.30173
$455$	6.98735	0.327572
$456$	−14.0230	−0.656687
$457$	−22.6741	−1.06065	−0.530325	−	0.847794i	$-0.677930\pi$
$457$	−22.6741	−1.06065	−0.530325	+	0.847794i	$0.677930\pi$
$458$	−38.0593	−1.77840
$459$	2.29430	0.107089
$460$	−5.27567	−0.245979
$461$	−18.3384	−0.854106	−0.427053	−	0.904227i	$-0.640448\pi$
$461$	−18.3384	−0.854106	−0.427053	+	0.904227i	$0.640448\pi$
$462$	37.4394	1.74184
$463$	−36.7040	−1.70578	−0.852890	−	0.522091i	$-0.825152\pi$
$463$	−36.7040	−1.70578	−0.852890	+	0.522091i	$0.825152\pi$
$464$	23.1708	1.07568
$465$	−21.5503	−0.999371
$466$	16.2180	0.751285
$467$	1.95154	0.0903066	0.0451533	−	0.998980i	$-0.485622\pi$
$467$	1.95154	0.0903066	0.0451533	+	0.998980i	$0.485622\pi$
$468$	−6.79206	−0.313963
$469$	34.0615	1.57281
$470$	11.5116	0.530990
$471$	−36.8407	−1.69753
$472$	−1.08623	−0.0499977
$473$	−13.1737	−0.605728
$474$	−56.5192	−2.59601
$475$	−23.3381	−1.07082
$476$	4.10547	0.188174
$477$	17.6384	0.807608
$478$	−22.3986	−1.02449
$479$	14.8397	0.678042	0.339021	−	0.940779i	$-0.389904\pi$
$479$	14.8397	0.678042	0.339021	+	0.940779i	$0.389904\pi$
$480$	14.8174	0.676319
$481$	12.2874	0.560257
$482$	18.2196	0.829878
$483$	−24.6018	−1.11942
$484$	−1.72946	−0.0786120
$485$	11.8750	0.539215
$486$	−32.7040	−1.48348
$487$	−17.9056	−0.811381	−0.405691	−	0.914010i	$-0.632969\pi$
$487$	−17.9056	−0.811381	−0.405691	+	0.914010i	$0.632969\pi$
$488$	11.0916	0.502094
$489$	21.8608	0.988581
$490$	2.64547	0.119510
$491$	−16.8269	−0.759389	−0.379694	−	0.925112i	$-0.623971\pi$
$491$	−16.8269	−0.759389	−0.379694	+	0.925112i	$0.623971\pi$
$492$	−6.96225	−0.313883
$493$	−4.79696	−0.216044
$494$	26.1039	1.17447
$495$	−6.06736	−0.272708
$496$	47.4184	2.12915
$497$	7.49287	0.336101
$498$	−22.5557	−1.01075
$499$	0.351800	0.0157487	0.00787436	−	0.999969i	$-0.497493\pi$
$499$	0.351800	0.0157487	0.00787436	+	0.999969i	$0.497493\pi$
$500$	12.5543	0.561444
$501$	−22.3643	−0.999161
$502$	24.6792	1.10149
$503$	12.0850	0.538845	0.269422	−	0.963022i	$-0.413167\pi$
$503$	12.0850	0.538845	0.269422	+	0.963022i	$0.413167\pi$
$504$	6.22510	0.277288
$505$	−8.82079	−0.392520
$506$	−21.9161	−0.974288
$507$	15.7033	0.697409
$508$	6.97910	0.309647
$509$	9.36168	0.414949	0.207475	−	0.978240i	$-0.433476\pi$
$509$	9.36168	0.414949	0.207475	+	0.978240i	$0.433476\pi$
$510$	−4.05491	−0.179554
$511$	38.0133	1.68161
$512$	−22.1100	−0.977134
$513$	13.2846	0.586532
$514$	22.9126	1.01063
$515$	5.17737	0.228142
$516$	13.2643	0.583929
$517$	19.7895	0.870343
$518$	27.0396	1.18805
$519$	−33.8739	−1.48690
$520$	2.61028	0.114468
$521$	−5.86177	−0.256809	−0.128404	−	0.991722i	$-0.540986\pi$
$521$	−5.86177	−0.256809	−0.128404	+	0.991722i	$0.540986\pi$
$522$	17.4641	0.764382
$523$	16.4661	0.720011	0.360006	−	0.932950i	$-0.382775\pi$
$523$	16.4661	0.720011	0.360006	+	0.932950i	$0.382775\pi$
$524$	−21.7469	−0.950018
$525$	26.1296	1.14039
$526$	−59.1530	−2.57919
$527$	−9.81687	−0.427629
$528$	33.6710	1.46534
$529$	−8.59871	−0.373857
$530$	16.2758	0.706975
$531$	−1.97096	−0.0855326
$532$	23.7718	1.03064
$533$	−5.39782	−0.233806
$534$	27.9921	1.21134
$535$	−18.5356	−0.801365
$536$	12.7244	0.549611
$537$	4.16602	0.179777
$538$	−20.6114	−0.888621
$539$	4.54782	0.195889
$540$	−3.18954	−0.137256
$541$	30.2119	1.29891	0.649455	−	0.760400i	$-0.274997\pi$
$541$	30.2119	1.29891	0.649455	+	0.760400i	$0.274997\pi$
$542$	−12.8173	−0.550552
$543$	45.6585	1.95939
$544$	6.74981	0.289396
$545$	−14.7934	−0.633680
$546$	−29.2263	−1.25077
$547$	−14.4798	−0.619112	−0.309556	−	0.950881i	$-0.600180\pi$
$547$	−14.4798	−0.619112	−0.309556	+	0.950881i	$0.600180\pi$
$548$	13.0076	0.555657
$549$	20.1258	0.858947
$550$	23.2770	0.992536
$551$	−27.7757	−1.18329
$552$	−9.19056	−0.391176
$553$	−39.9044	−1.69691
$554$	−26.2983	−1.11731
$555$	−11.0518	−0.469124
$556$	21.9290	0.929995
$557$	38.0899	1.61392	0.806961	−	0.590604i	$-0.201111\pi$
$557$	38.0899	1.61392	0.806961	+	0.590604i	$0.201111\pi$
$558$	35.7398	1.51299
$559$	10.2838	0.434958
$560$	13.8287	0.584369
$561$	−6.97078	−0.294307
$562$	8.64827	0.364805
$563$	−30.6460	−1.29158	−0.645788	−	0.763516i	$-0.723471\pi$
$563$	−30.6460	−1.29158	−0.645788	+	0.763516i	$0.723471\pi$
$564$	−19.9256	−0.839020
$565$	1.08988	0.0458515
$566$	−48.8305	−2.05250
$567$	−32.0664	−1.34666
$568$	2.79913	0.117449
$569$	−5.77440	−0.242076	−0.121038	−	0.992648i	$-0.538622\pi$
$569$	−5.77440	−0.242076	−0.121038	+	0.992648i	$0.538622\pi$
$570$	−23.4791	−0.983429
$571$	20.7142	0.866861	0.433430	−	0.901187i	$-0.357303\pi$
$571$	20.7142	0.866861	0.433430	+	0.901187i	$0.357303\pi$
$572$	−10.7742	−0.450491
$573$	44.7011	1.86742
$574$	−11.8785	−0.495797
$575$	−15.2956	−0.637870
$576$	−5.53303	−0.230543
$577$	−33.0811	−1.37718	−0.688591	−	0.725150i	$-0.741770\pi$
$577$	−33.0811	−1.37718	−0.688591	+	0.725150i	$0.741770\pi$
$578$	−1.84714	−0.0768311
$579$	−4.89463	−0.203414
$580$	6.66873	0.276904
$581$	−15.9251	−0.660684
$582$	−49.6700	−2.05889
$583$	27.9796	1.15880
$584$	14.2007	0.587630
$585$	4.73636	0.195824
$586$	−31.5754	−1.30437
$587$	−21.6837	−0.894981	−0.447491	−	0.894289i	$-0.647682\pi$
$587$	−21.6837	−0.894981	−0.447491	+	0.894289i	$0.647682\pi$
$588$	−4.57910	−0.188839
$589$	−56.8424	−2.34215
$590$	−1.81870	−0.0748746
$591$	−44.1785	−1.81726
$592$	24.3180	0.999464
$593$	33.9994	1.39619	0.698094	−	0.716006i	$-0.254032\pi$
$593$	33.9994	1.39619	0.698094	+	0.716006i	$0.254032\pi$
$594$	−13.2499	−0.543650
$595$	−2.86290	−0.117368
$596$	3.30242	0.135272
$597$	−44.8994	−1.83761
$598$	17.1083	0.699611
$599$	−33.9720	−1.38806	−0.694030	−	0.719946i	$-0.744166\pi$
$599$	−33.9720	−1.38806	−0.694030	+	0.719946i	$0.744166\pi$
$600$	9.76128	0.398503
$601$	35.7728	1.45920	0.729601	−	0.683873i	$-0.239706\pi$
$601$	35.7728	1.45920	0.729601	+	0.683873i	$0.239706\pi$
$602$	22.6305	0.922352
$603$	23.0885	0.940237
$604$	−1.65476	−0.0673311
$605$	1.20602	0.0490317
$606$	36.8951	1.49876
$607$	−3.87291	−0.157196	−0.0785982	−	0.996906i	$-0.525044\pi$
$607$	−3.87291	−0.157196	−0.0785982	+	0.996906i	$0.525044\pi$
$608$	39.0833	1.58504
$609$	31.0980	1.26016
$610$	18.5710	0.751916
$611$	−15.4483	−0.624971
$612$	2.78289	0.112492
$613$	−30.2063	−1.22002	−0.610011	−	0.792393i	$-0.708835\pi$
$613$	−30.2063	−1.22002	−0.610011	+	0.792393i	$0.708835\pi$
$614$	−5.22829	−0.210996
$615$	4.85504	0.195774
$616$	9.87480	0.397867
$617$	−39.9456	−1.60815	−0.804075	−	0.594528i	$-0.797339\pi$
$617$	−39.9456	−1.60815	−0.804075	+	0.594528i	$0.797339\pi$
$618$	−21.6556	−0.871116
$619$	35.1527	1.41291	0.706454	−	0.707759i	$-0.250294\pi$
$619$	35.1527	1.41291	0.706454	+	0.707759i	$0.250294\pi$
$620$	13.6474	0.548092
$621$	8.70665	0.349386
$622$	−50.9881	−2.04444
$623$	19.7634	0.791804
$624$	−26.2846	−1.05222
$625$	11.3982	0.455930
$626$	−50.1644	−2.00497
$627$	−40.3628	−1.61193
$628$	23.3305	0.930990
$629$	−5.03447	−0.200737
$630$	10.4228	0.415256
$631$	−43.6475	−1.73758	−0.868790	−	0.495182i	$-0.835102\pi$
$631$	−43.6475	−1.73758	−0.868790	+	0.495182i	$0.835102\pi$
$632$	−14.9072	−0.592976
$633$	−15.5356	−0.617486
$634$	−34.3232	−1.36315
$635$	−4.86679	−0.193133
$636$	−28.1720	−1.11709
$637$	−3.55016	−0.140663
$638$	27.7031	1.09678
$639$	5.07903	0.200923
$640$	8.18616	0.323586
$641$	−8.30308	−0.327952	−0.163976	−	0.986464i	$-0.552432\pi$
$641$	−8.30308	−0.327952	−0.163976	+	0.986464i	$0.552432\pi$
$642$	77.5297	3.05985
$643$	−28.4058	−1.12022	−0.560109	−	0.828419i	$-0.689241\pi$
$643$	−28.4058	−1.12022	−0.560109	+	0.828419i	$0.689241\pi$
$644$	15.5799	0.613933
$645$	−9.24970	−0.364207
$646$	−10.6955	−0.420808
$647$	−3.35509	−0.131902	−0.0659510	−	0.997823i	$-0.521008\pi$
$647$	−3.35509	−0.131902	−0.0659510	+	0.997823i	$0.521008\pi$
$648$	−11.9791	−0.470585
$649$	−3.12652	−0.122727
$650$	−18.1707	−0.712715
$651$	63.6414	2.49430
$652$	−13.8440	−0.542175
$653$	17.1269	0.670225	0.335113	−	0.942178i	$-0.391226\pi$
$653$	17.1269	0.670225	0.335113	+	0.942178i	$0.391226\pi$
$654$	61.8770	2.41958
$655$	15.1649	0.592543
$656$	−10.6829	−0.417095
$657$	25.7672	1.00528
$658$	−33.9955	−1.32528
$659$	−8.52832	−0.332216	−0.166108	−	0.986108i	$-0.553120\pi$
$659$	−8.52832	−0.332216	−0.166108	+	0.986108i	$0.553120\pi$
$660$	9.69077	0.377213
$661$	−19.0371	−0.740456	−0.370228	−	0.928941i	$-0.620720\pi$
$661$	−19.0371	−0.740456	−0.370228	+	0.928941i	$0.620720\pi$
$662$	32.3450	1.25713
$663$	5.44160	0.211334
$664$	−5.94917	−0.230873
$665$	−16.5770	−0.642828
$666$	18.3288	0.710225
$667$	−18.2040	−0.704862
$668$	14.1629	0.547977
$669$	18.1378	0.701249
$670$	21.3048	0.823077
$671$	31.9253	1.23246
$672$	−43.7581	−1.68801
$673$	3.03849	0.117125	0.0585626	−	0.998284i	$-0.481348\pi$
$673$	3.03849	0.117125	0.0585626	+	0.998284i	$0.481348\pi$
$674$	3.99437	0.153858
$675$	−9.24733	−0.355930
$676$	−9.94461	−0.382485
$677$	−3.64377	−0.140041	−0.0700207	−	0.997546i	$-0.522307\pi$
$677$	−3.64377	−0.140041	−0.0700207	+	0.997546i	$0.522307\pi$
$678$	−4.55868	−0.175075
$679$	−35.0687	−1.34581
$680$	−1.06950	−0.0410135
$681$	33.4786	1.28290
$682$	56.6937	2.17091
$683$	21.8213	0.834968	0.417484	−	0.908684i	$-0.362912\pi$
$683$	21.8213	0.834968	0.417484	+	0.908684i	$0.362912\pi$
$684$	16.1137	0.616123
$685$	−9.07069	−0.346573
$686$	29.7838	1.13715
$687$	−45.9389	−1.75268
$688$	20.3527	0.775939
$689$	−21.8417	−0.832104
$690$	−15.3880	−0.585811
$691$	12.4467	0.473494	0.236747	−	0.971571i	$-0.423919\pi$
$691$	12.4467	0.473494	0.236747	+	0.971571i	$0.423919\pi$
$692$	21.4517	0.815471
$693$	17.9179	0.680643
$694$	−37.4526	−1.42168
$695$	−15.2919	−0.580054
$696$	11.6174	0.440355
$697$	2.21163	0.0837715
$698$	50.8654	1.92529
$699$	19.5757	0.740421
$700$	−16.5474	−0.625432
$701$	−8.73056	−0.329749	−0.164874	−	0.986315i	$-0.552722\pi$
$701$	−8.73056	−0.329749	−0.164874	+	0.986315i	$0.552722\pi$
$702$	10.3433	0.390381
$703$	−29.1510	−1.09945
$704$	−8.77698	−0.330795
$705$	13.8949	0.523312
$706$	14.6936	0.553002
$707$	26.0492	0.979680
$708$	3.14802	0.118310
$709$	21.2731	0.798930	0.399465	−	0.916749i	$-0.369196\pi$
$709$	21.2731	0.798930	0.399465	+	0.916749i	$0.369196\pi$
$710$	4.68665	0.175887
$711$	−27.0491	−1.01442
$712$	7.38305	0.276692
$713$	−37.2541	−1.39518
$714$	11.9748	0.448145
$715$	7.51323	0.280979
$716$	−2.63826	−0.0985965
$717$	−27.0359	−1.00967
$718$	−42.2699	−1.57750
$719$	28.1520	1.04989	0.524947	−	0.851135i	$-0.324085\pi$
$719$	28.1520	1.04989	0.524947	+	0.851135i	$0.324085\pi$
$720$	9.37375	0.349339
$721$	−15.2896	−0.569414
$722$	−26.8341	−0.998661
$723$	21.9916	0.817877
$724$	−28.9146	−1.07460
$725$	19.3345	0.718064
$726$	−5.04447	−0.187218
$727$	11.2686	0.417931	0.208966	−	0.977923i	$-0.432990\pi$
$727$	11.2686	0.417931	0.208966	+	0.977923i	$0.432990\pi$
$728$	−7.70856	−0.285698
$729$	−6.39028	−0.236677
$730$	23.7766	0.880012
$731$	−4.21354	−0.155844
$732$	−32.1448	−1.18811
$733$	−5.34171	−0.197301	−0.0986503	−	0.995122i	$-0.531453\pi$
$733$	−5.34171	−0.197301	−0.0986503	+	0.995122i	$0.531453\pi$
$734$	−21.4783	−0.792778
$735$	3.19318	0.117782
$736$	25.6149	0.944177
$737$	36.6250	1.34910
$738$	−8.05179	−0.296390
$739$	−9.21167	−0.338857	−0.169428	−	0.985542i	$-0.554192\pi$
$739$	−9.21167	−0.338857	−0.169428	+	0.985542i	$0.554192\pi$
$740$	6.99891	0.257285
$741$	31.5084	1.15749
$742$	−48.0649	−1.76452
$743$	−34.3887	−1.26160	−0.630800	−	0.775945i	$-0.717273\pi$
$743$	−34.3887	−1.26160	−0.630800	+	0.775945i	$0.717273\pi$
$744$	23.7747	0.871621
$745$	−2.30290	−0.0843719
$746$	−49.2219	−1.80214
$747$	−10.7948	−0.394961
$748$	4.41446	0.161409
$749$	54.7386	2.00010
$750$	36.6181	1.33710
$751$	−31.1622	−1.13713	−0.568563	−	0.822640i	$-0.692500\pi$
$751$	−31.1622	−1.13713	−0.568563	+	0.822640i	$0.692500\pi$
$752$	−30.5738	−1.11491
$753$	29.7887	1.08556
$754$	−21.6258	−0.787567
$755$	1.15392	0.0419956
$756$	9.41920	0.342573
$757$	7.66737	0.278675	0.139338	−	0.990245i	$-0.455503\pi$
$757$	7.66737	0.278675	0.139338	+	0.990245i	$0.455503\pi$
$758$	44.8198	1.62793
$759$	−26.4534	−0.960199
$760$	−6.19271	−0.224633
$761$	−17.2943	−0.626917	−0.313458	−	0.949602i	$-0.601488\pi$
$761$	−17.2943	−0.626917	−0.313458	+	0.949602i	$0.601488\pi$
$762$	20.3565	0.737439
$763$	43.6872	1.58158
$764$	−28.3084	−1.02416
$765$	−1.94061	−0.0701630
$766$	7.42501	0.268277
$767$	2.44065	0.0881268
$768$	−46.7586	−1.68725
$769$	−17.3569	−0.625905	−0.312953	−	0.949769i	$-0.601318\pi$
$769$	−17.3569	−0.625905	−0.312953	+	0.949769i	$0.601318\pi$
$770$	16.5336	0.595831
$771$	27.6563	0.996017
$772$	3.09968	0.111560
$773$	15.5444	0.559093	0.279547	−	0.960132i	$-0.409816\pi$
$773$	15.5444	0.559093	0.279547	+	0.960132i	$0.409816\pi$
$774$	15.3401	0.551387
$775$	39.5675	1.42131
$776$	−13.1007	−0.470287
$777$	32.6378	1.17087
$778$	68.0267	2.43887
$779$	12.8060	0.458821
$780$	−7.56490	−0.270867
$781$	8.05680	0.288295
$782$	−7.00973	−0.250668
$783$	−11.0057	−0.393311
$784$	−7.02614	−0.250934
$785$	−16.2693	−0.580675
$786$	−63.4310	−2.26251
$787$	−7.37730	−0.262973	−0.131486	−	0.991318i	$-0.541975\pi$
$787$	−7.37730	−0.262973	−0.131486	+	0.991318i	$0.541975\pi$
$788$	27.9774	0.996654
$789$	−71.3997	−2.54190
$790$	−24.9595	−0.888018
$791$	−3.21858	−0.114439
$792$	6.69362	0.237847
$793$	−24.9218	−0.884999
$794$	37.8913	1.34471
$795$	19.6454	0.696751
$796$	28.4340	1.00781
$797$	−2.94753	−0.104407	−0.0522035	−	0.998636i	$-0.516624\pi$
$797$	−2.94753	−0.104407	−0.0522035	+	0.998636i	$0.516624\pi$
$798$	69.3373	2.45451
$799$	6.32958	0.223924
$800$	−27.2055	−0.961861
$801$	13.3966	0.473345
$802$	−18.6567	−0.658791
$803$	40.8743	1.44242
$804$	−36.8769	−1.30055
$805$	−10.8644	−0.382921
$806$	−44.2568	−1.55888
$807$	−24.8787	−0.875771
$808$	9.73125	0.342344
$809$	2.56071	0.0900299	0.0450150	−	0.998986i	$-0.485666\pi$
$809$	2.56071	0.0900299	0.0450150	+	0.998986i	$0.485666\pi$
$810$	−20.0570	−0.704730
$811$	16.2257	0.569761	0.284881	−	0.958563i	$-0.408046\pi$
$811$	16.2257	0.569761	0.284881	+	0.958563i	$0.408046\pi$
$812$	−19.6938	−0.691117
$813$	−15.4710	−0.542591
$814$	29.0747	1.01907
$815$	9.65398	0.338164
$816$	10.7695	0.377007
$817$	−24.3976	−0.853564
$818$	−55.5619	−1.94268
$819$	−13.9872	−0.488753
$820$	−3.07461	−0.107370
$821$	27.7646	0.968992	0.484496	−	0.874793i	$-0.339003\pi$
$821$	27.7646	0.968992	0.484496	+	0.874793i	$0.339003\pi$
$822$	37.9404	1.32332
$823$	−13.2688	−0.462520	−0.231260	−	0.972892i	$-0.574285\pi$
$823$	−13.2688	−0.462520	−0.231260	+	0.972892i	$0.574285\pi$
$824$	−5.71176	−0.198979
$825$	28.0962	0.978183
$826$	5.37090	0.186878
$827$	−22.2443	−0.773511	−0.386756	−	0.922182i	$-0.626404\pi$
$827$	−22.2443	−0.773511	−0.386756	+	0.922182i	$0.626404\pi$
$828$	10.5608	0.367013
$829$	26.0468	0.904643	0.452322	−	0.891855i	$-0.350596\pi$
$829$	26.0468	0.904643	0.452322	+	0.891855i	$0.350596\pi$
$830$	−9.96085	−0.345746
$831$	−31.7430	−1.10115
$832$	6.85157	0.237535
$833$	1.45460	0.0503988
$834$	63.9621	2.21482
$835$	−9.87629	−0.341783
$836$	25.5610	0.884045
$837$	−22.5229	−0.778504
$838$	−64.8829	−2.24134
$839$	19.7074	0.680375	0.340188	−	0.940358i	$-0.389509\pi$
$839$	19.7074	0.680375	0.340188	+	0.940358i	$0.389509\pi$
$840$	6.93342	0.239226
$841$	−5.98916	−0.206523
$842$	8.88630	0.306242
$843$	10.4388	0.359530
$844$	9.83843	0.338653
$845$	6.93475	0.238563
$846$	−23.0438	−0.792263
$847$	−3.56157	−0.122377
$848$	−43.2270	−1.48442
$849$	−58.9401	−2.02282
$850$	7.44503	0.255362
$851$	−19.1053	−0.654922
$852$	−8.11220	−0.277920
$853$	34.8664	1.19380	0.596902	−	0.802314i	$-0.296398\pi$
$853$	34.8664	1.19380	0.596902	+	0.802314i	$0.296398\pi$
$854$	−54.8430	−1.87669
$855$	−11.2367	−0.384287
$856$	20.4488	0.698926
$857$	46.2316	1.57924	0.789621	−	0.613595i	$-0.210277\pi$
$857$	46.2316	1.57924	0.789621	+	0.613595i	$0.210277\pi$
$858$	−31.4259	−1.07286
$859$	15.9358	0.543722	0.271861	−	0.962337i	$-0.412361\pi$
$859$	15.9358	0.543722	0.271861	+	0.962337i	$0.412361\pi$
$860$	5.85766	0.199745
$861$	−14.3377	−0.488628
$862$	−10.9476	−0.372878
$863$	12.9885	0.442134	0.221067	−	0.975259i	$-0.429046\pi$
$863$	12.9885	0.442134	0.221067	+	0.975259i	$0.429046\pi$
$864$	15.4861	0.526848
$865$	−14.9591	−0.508624
$866$	−61.7996	−2.10004
$867$	−2.22957	−0.0757200
$868$	−40.3029	−1.36797
$869$	−42.9077	−1.45555
$870$	19.4512	0.659459
$871$	−28.5906	−0.968755
$872$	16.3203	0.552676
$873$	−23.7712	−0.804534
$874$	−40.5883	−1.37292
$875$	25.8536	0.874012
$876$	−41.1553	−1.39051
$877$	−4.24824	−0.143453	−0.0717265	−	0.997424i	$-0.522851\pi$
$877$	−4.24824	−0.143453	−0.0717265	+	0.997424i	$0.522851\pi$
$878$	−50.7389	−1.71236
$879$	−38.1126	−1.28551
$880$	14.8695	0.501250
$881$	42.8887	1.44496	0.722479	−	0.691393i	$-0.243003\pi$
$881$	42.8887	1.44496	0.722479	+	0.691393i	$0.243003\pi$
$882$	−5.29569	−0.178315
$883$	−12.5884	−0.423633	−0.211816	−	0.977309i	$-0.567938\pi$
$883$	−12.5884	−0.423633	−0.211816	+	0.977309i	$0.567938\pi$
$884$	−3.44606	−0.115904
$885$	−2.19523	−0.0737919
$886$	25.2558	0.848484
$887$	−37.0996	−1.24568	−0.622842	−	0.782348i	$-0.714022\pi$
$887$	−37.0996	−1.24568	−0.622842	+	0.782348i	$0.714022\pi$
$888$	12.1926	0.409155
$889$	14.3724	0.482035
$890$	12.3616	0.414363
$891$	−34.4798	−1.15512
$892$	−11.4863	−0.384591
$893$	36.6500	1.22645
$894$	9.63245	0.322157
$895$	1.83976	0.0614964
$896$	−24.1750	−0.807630
$897$	20.6503	0.689494
$898$	29.0402	0.969085
$899$	47.0911	1.57058
$900$	−11.2166	−0.373887
$901$	8.94914	0.298139
$902$	−12.7725	−0.425276
$903$	27.3158	0.909014
$904$	−1.20237	−0.0399903
$905$	20.1633	0.670250
$906$	−4.82657	−0.160352
$907$	−48.2816	−1.60316	−0.801582	−	0.597885i	$-0.796008\pi$
$907$	−48.2816	−1.60316	−0.801582	+	0.597885i	$0.796008\pi$
$908$	−21.2014	−0.703593
$909$	17.6574	0.585658
$910$	−12.9066	−0.427851
$911$	−43.4280	−1.43883	−0.719416	−	0.694579i	$-0.755591\pi$
$911$	−43.4280	−1.43883	−0.719416	+	0.694579i	$0.755591\pi$
$912$	62.3583	2.06489
$913$	−17.1237	−0.566710
$914$	41.8824	1.38535
$915$	22.4158	0.741043
$916$	29.0922	0.961234
$917$	−44.7844	−1.47891
$918$	−4.23791	−0.139872
$919$	−48.2745	−1.59243	−0.796215	−	0.605014i	$-0.793168\pi$
$919$	−48.2745	−1.59243	−0.796215	+	0.605014i	$0.793168\pi$
$920$	−4.05865	−0.133810
$921$	−6.31072	−0.207945
$922$	33.8737	1.11557
$923$	−6.28938	−0.207017
$924$	−28.6184	−0.941475
$925$	20.2917	0.667188
$926$	67.7976	2.22797
$927$	−10.3640	−0.340399
$928$	−32.3786	−1.06288
$929$	−15.8006	−0.518400	−0.259200	−	0.965824i	$-0.583459\pi$
$929$	−15.8006	−0.518400	−0.259200	+	0.965824i	$0.583459\pi$
$930$	39.8065	1.30531
$931$	8.42252	0.276037
$932$	−12.3969	−0.406075
$933$	−61.5444	−2.01487
$934$	−3.60478	−0.117952
$935$	−3.07837	−0.100673
$936$	−5.22523	−0.170792
$937$	23.6389	0.772250	0.386125	−	0.922447i	$-0.373813\pi$
$937$	23.6389	0.772250	0.386125	+	0.922447i	$0.373813\pi$
$938$	−62.9164	−2.05429
$939$	−60.5502	−1.97598
$940$	−8.79937	−0.287004
$941$	−50.7784	−1.65533	−0.827664	−	0.561224i	$-0.810331\pi$
$941$	−50.7784	−1.65533	−0.827664	+	0.561224i	$0.810331\pi$
$942$	68.0502	2.21719
$943$	8.39293	0.273311
$944$	4.83030	0.157213
$945$	−6.56836	−0.213669
$946$	24.3338	0.791159
$947$	−17.3591	−0.564094	−0.282047	−	0.959401i	$-0.591013\pi$
$947$	−17.3591	−0.564094	−0.282047	+	0.959401i	$0.591013\pi$
$948$	43.2028	1.40316
$949$	−31.9077	−1.03577
$950$	43.1088	1.39863
$951$	−41.4293	−1.34344
$952$	3.15840	0.102364
$953$	−34.6956	−1.12390	−0.561950	−	0.827171i	$-0.689949\pi$
$953$	−34.6956	−1.12390	−0.561950	+	0.827171i	$0.689949\pi$
$954$	−32.5807	−1.05484
$955$	19.7405	0.638788
$956$	17.1213	0.553744
$957$	33.4386	1.08092
$958$	−27.4110	−0.885610
$959$	26.7872	0.865003
$960$	−6.16261	−0.198897
$961$	65.3709	2.10874
$962$	−22.6966	−0.731767
$963$	37.1044	1.19567
$964$	−13.9269	−0.448555
$965$	−2.16152	−0.0695818
$966$	45.4431	1.46211
$967$	34.7635	1.11792	0.558959	−	0.829196i	$-0.311201\pi$
$967$	34.7635	1.11792	0.558959	+	0.829196i	$0.311201\pi$
$968$	−1.33050	−0.0427640
$969$	−12.9098	−0.414723
$970$	−21.9348	−0.704284
$971$	−21.8759	−0.702033	−0.351016	−	0.936369i	$-0.614164\pi$
$971$	−21.8759	−0.702033	−0.351016	+	0.936369i	$0.614164\pi$
$972$	24.9987	0.801833
$973$	45.1593	1.44774
$974$	33.0743	1.05977
$975$	−21.9327	−0.702408
$976$	−49.3228	−1.57879
$977$	−15.0502	−0.481499	−0.240749	−	0.970587i	$-0.577393\pi$
$977$	−15.0502	−0.481499	−0.240749	+	0.970587i	$0.577393\pi$
$978$	−40.3801	−1.29121
$979$	21.2508	0.679180
$980$	−2.02218	−0.0645961
$981$	29.6133	0.945480
$982$	31.0818	0.991859
$983$	−15.4111	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$983$	−15.4111	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$984$	−5.35617	−0.170748
$985$	−19.5097	−0.621631
$986$	8.86068	0.282182
$987$	−41.0338	−1.30612
$988$	−19.9536	−0.634810
$989$	−15.9900	−0.508452
$990$	11.2073	0.356191
$991$	−22.2264	−0.706046	−0.353023	−	0.935615i	$-0.614846\pi$
$991$	−22.2264	−0.706046	−0.353023	+	0.935615i	$0.614846\pi$
$992$	−66.2620	−2.10382
$993$	39.0416	1.23895
$994$	−13.8404	−0.438991
$995$	−19.8281	−0.628592
$996$	17.2414	0.546315
$997$	−37.5266	−1.18848	−0.594240	−	0.804288i	$-0.702547\pi$
$997$	−37.5266	−1.18848	−0.594240	+	0.804288i	$0.702547\pi$
$998$	−0.649825	−0.0205698
$999$	−11.5506	−0.365444

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.i.1.4	✓	18
3.2	odd	2		9027.2.a.q.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.i.1.4	✓	18	1.1	even	1	trivial
9027.2.a.q.1.15		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)

\(f(q)\)	\(=\)	\(q-1.84714 q^{2} -2.22957 q^{3} +1.41194 q^{4} -0.984600 q^{5} +4.11833 q^{6} +2.90768 q^{7} +1.08623 q^{8} +1.97096 q^{9} +O(q^{10})\)	\(q-1.84714 q^{2} -2.22957 q^{3} +1.41194 q^{4} -0.984600 q^{5} +4.11833 q^{6} +2.90768 q^{7} +1.08623 q^{8} +1.97096 q^{9} +1.81870 q^{10} +3.12652 q^{11} -3.14802 q^{12} -2.44065 q^{13} -5.37090 q^{14} +2.19523 q^{15} -4.83030 q^{16} +1.00000 q^{17} -3.64066 q^{18} +5.79028 q^{19} -1.39020 q^{20} -6.48286 q^{21} -5.77513 q^{22} +3.79490 q^{23} -2.42182 q^{24} -4.03056 q^{25} +4.50824 q^{26} +2.29430 q^{27} +4.10547 q^{28} -4.79696 q^{29} -4.05491 q^{30} -9.81687 q^{31} +6.74981 q^{32} -6.97078 q^{33} -1.84714 q^{34} -2.86290 q^{35} +2.78289 q^{36} -5.03447 q^{37} -10.6955 q^{38} +5.44160 q^{39} -1.06950 q^{40} +2.21163 q^{41} +11.9748 q^{42} -4.21354 q^{43} +4.41446 q^{44} -1.94061 q^{45} -7.00973 q^{46} +6.32958 q^{47} +10.7695 q^{48} +1.45460 q^{49} +7.44503 q^{50} -2.22957 q^{51} -3.44606 q^{52} +8.94914 q^{53} -4.23791 q^{54} -3.07837 q^{55} +3.15840 q^{56} -12.9098 q^{57} +8.86068 q^{58} -1.00000 q^{59} +3.09954 q^{60} +10.2111 q^{61} +18.1332 q^{62} +5.73093 q^{63} -2.80727 q^{64} +2.40307 q^{65} +12.8760 q^{66} +11.7143 q^{67} +1.41194 q^{68} -8.46099 q^{69} +5.28819 q^{70} +2.57692 q^{71} +2.14092 q^{72} +13.0734 q^{73} +9.29939 q^{74} +8.98640 q^{75} +8.17554 q^{76} +9.09091 q^{77} -10.0514 q^{78} -13.7238 q^{79} +4.75592 q^{80} -11.0282 q^{81} -4.08520 q^{82} -5.47691 q^{83} -9.15343 q^{84} -0.984600 q^{85} +7.78302 q^{86} +10.6951 q^{87} +3.39611 q^{88} +6.79697 q^{89} +3.58459 q^{90} -7.09663 q^{91} +5.35818 q^{92} +21.8874 q^{93} -11.6916 q^{94} -5.70111 q^{95} -15.0492 q^{96} -12.0607 q^{97} -2.68685 q^{98} +6.16226 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 5 q^{2} + q^{3} + 21 q^{4} + 21 q^{5} + 5 q^{6} - q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 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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