LMFDB - Embedded newform 4003.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4003,2,Mod(1,4003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4003, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4003.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:	$31.9641159291$
Analytic rank:	$1$
Dimension:	$152$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59568 q^{2} +2.00123 q^{3} +4.73753 q^{4} -2.55331 q^{5} -5.19456 q^{6} +4.30357 q^{7} -7.10575 q^{8} +1.00494 q^{9} +O(q^{10})$	\(q-2.59568 q^{2} +2.00123 q^{3} +4.73753 q^{4} -2.55331 q^{5} -5.19456 q^{6} +4.30357 q^{7} -7.10575 q^{8} +1.00494 q^{9} +6.62756 q^{10} -0.721924 q^{11} +9.48091 q^{12} -0.206828 q^{13} -11.1707 q^{14} -5.10977 q^{15} +8.96915 q^{16} -7.08863 q^{17} -2.60850 q^{18} -1.94126 q^{19} -12.0964 q^{20} +8.61246 q^{21} +1.87388 q^{22} +2.09017 q^{23} -14.2203 q^{24} +1.51939 q^{25} +0.536857 q^{26} -3.99258 q^{27} +20.3883 q^{28} +8.47645 q^{29} +13.2633 q^{30} +6.08423 q^{31} -9.06951 q^{32} -1.44474 q^{33} +18.3998 q^{34} -10.9884 q^{35} +4.76093 q^{36} -6.39528 q^{37} +5.03888 q^{38} -0.413911 q^{39} +18.1432 q^{40} -7.05441 q^{41} -22.3551 q^{42} +3.62781 q^{43} -3.42014 q^{44} -2.56592 q^{45} -5.42540 q^{46} +5.44070 q^{47} +17.9494 q^{48} +11.5207 q^{49} -3.94385 q^{50} -14.1860 q^{51} -0.979853 q^{52} -9.83848 q^{53} +10.3635 q^{54} +1.84330 q^{55} -30.5801 q^{56} -3.88491 q^{57} -22.0021 q^{58} +0.691090 q^{59} -24.2077 q^{60} -6.96355 q^{61} -15.7927 q^{62} +4.32483 q^{63} +5.60321 q^{64} +0.528095 q^{65} +3.75007 q^{66} -8.86068 q^{67} -33.5826 q^{68} +4.18291 q^{69} +28.5222 q^{70} +9.39470 q^{71} -7.14084 q^{72} +5.11110 q^{73} +16.6001 q^{74} +3.04066 q^{75} -9.19677 q^{76} -3.10685 q^{77} +1.07438 q^{78} -4.80909 q^{79} -22.9010 q^{80} -11.0049 q^{81} +18.3110 q^{82} -17.1284 q^{83} +40.8018 q^{84} +18.0995 q^{85} -9.41661 q^{86} +16.9634 q^{87} +5.12981 q^{88} -2.32434 q^{89} +6.66030 q^{90} -0.890098 q^{91} +9.90224 q^{92} +12.1760 q^{93} -14.1223 q^{94} +4.95663 q^{95} -18.1502 q^{96} -13.8575 q^{97} -29.9041 q^{98} -0.725489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) $ 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.59568	−1.83542	−0.917710	−	0.397251i	$-0.869964\pi$
$2$	−2.59568	−1.83542	−0.917710	+	0.397251i	$0.869964\pi$
$3$	2.00123	1.15541	0.577707	−	0.816245i	$-0.303948\pi$
$3$	2.00123	1.15541	0.577707	+	0.816245i	$0.303948\pi$
$4$	4.73753	2.36877
$5$	−2.55331	−1.14187	−0.570937	−	0.820994i	$-0.693420\pi$
$5$	−2.55331	−1.14187	−0.570937	+	0.820994i	$0.693420\pi$
$6$	−5.19456	−2.12067
$7$	4.30357	1.62660	0.813299	−	0.581846i	$-0.197669\pi$
$7$	4.30357	1.62660	0.813299	+	0.581846i	$0.197669\pi$
$8$	−7.10575	−2.51226
$9$	1.00494	0.334980
$10$	6.62756	2.09582
$11$	−0.721924	−0.217668	−0.108834	−	0.994060i	$-0.534712\pi$
$11$	−0.721924	−0.217668	−0.108834	+	0.994060i	$0.534712\pi$
$12$	9.48091	2.73690
$13$	−0.206828	−0.0573637	−0.0286818	−	0.999589i	$-0.509131\pi$
$13$	−0.206828	−0.0573637	−0.0286818	+	0.999589i	$0.509131\pi$
$14$	−11.1707	−2.98549
$15$	−5.10977	−1.31934
$16$	8.96915	2.24229
$17$	−7.08863	−1.71925	−0.859623	−	0.510929i	$-0.829301\pi$
$17$	−7.08863	−1.71925	−0.859623	+	0.510929i	$0.829301\pi$
$18$	−2.60850	−0.614828
$19$	−1.94126	−0.445355	−0.222678	−	0.974892i	$-0.571480\pi$
$19$	−1.94126	−0.445355	−0.222678	+	0.974892i	$0.571480\pi$
$20$	−12.0964	−2.70483
$21$	8.61246	1.87939
$22$	1.87388	0.399513
$23$	2.09017	0.435830	0.217915	−	0.975968i	$-0.430074\pi$
$23$	2.09017	0.435830	0.217915	+	0.975968i	$0.430074\pi$
$24$	−14.2203	−2.90270
$25$	1.51939	0.303878
$26$	0.536857	0.105286
$27$	−3.99258	−0.768373
$28$	20.3883	3.85303
$29$	8.47645	1.57404	0.787019	−	0.616929i	$-0.211624\pi$
$29$	8.47645	1.57404	0.787019	+	0.616929i	$0.211624\pi$
$30$	13.2633	2.42154
$31$	6.08423	1.09276	0.546380	−	0.837537i	$-0.316005\pi$
$31$	6.08423	1.09276	0.546380	+	0.837537i	$0.316005\pi$
$32$	−9.06951	−1.60328
$33$	−1.44474	−0.251497
$34$	18.3998	3.15554
$35$	−10.9884	−1.85737
$36$	4.76093	0.793488
$37$	−6.39528	−1.05138	−0.525689	−	0.850677i	$-0.676192\pi$
$37$	−6.39528	−1.05138	−0.525689	+	0.850677i	$0.676192\pi$
$38$	5.03888	0.817414
$39$	−0.413911	−0.0662787
$40$	18.1432	2.86869
$41$	−7.05441	−1.10171	−0.550857	−	0.834600i	$-0.685699\pi$
$41$	−7.05441	−1.10171	−0.550857	+	0.834600i	$0.685699\pi$
$42$	−22.3551	−3.44947
$43$	3.62781	0.553236	0.276618	−	0.960980i	$-0.410786\pi$
$43$	3.62781	0.553236	0.276618	+	0.960980i	$0.410786\pi$
$44$	−3.42014	−0.515605
$45$	−2.56592	−0.382505
$46$	−5.42540	−0.799931
$47$	5.44070	0.793608	0.396804	−	0.917903i	$-0.370119\pi$
$47$	5.44070	0.793608	0.396804	+	0.917903i	$0.370119\pi$
$48$	17.9494	2.59077
$49$	11.5207	1.64582
$50$	−3.94385	−0.557744
$51$	−14.1860	−1.98644
$52$	−0.979853	−0.135881
$53$	−9.83848	−1.35142	−0.675709	−	0.737168i	$-0.736163\pi$
$53$	−9.83848	−1.35142	−0.675709	+	0.737168i	$0.736163\pi$
$54$	10.3635	1.41029
$55$	1.84330	0.248550
$56$	−30.5801	−4.08644
$57$	−3.88491	−0.514569
$58$	−22.0021	−2.88902
$59$	0.691090	0.0899722	0.0449861	−	0.998988i	$-0.485676\pi$
$59$	0.691090	0.0899722	0.0449861	+	0.998988i	$0.485676\pi$
$60$	−24.2077	−3.12520
$61$	−6.96355	−0.891591	−0.445795	−	0.895135i	$-0.647079\pi$
$61$	−6.96355	−0.891591	−0.445795	+	0.895135i	$0.647079\pi$
$62$	−15.7927	−2.00567
$63$	4.32483	0.544877
$64$	5.60321	0.700401
$65$	0.528095	0.0655021
$66$	3.75007	0.461602
$67$	−8.86068	−1.08250	−0.541252	−	0.840860i	$-0.682050\pi$
$67$	−8.86068	−1.08250	−0.541252	+	0.840860i	$0.682050\pi$
$68$	−33.5826	−4.07249
$69$	4.18291	0.503564
$70$	28.5222	3.40906
$71$	9.39470	1.11495	0.557473	−	0.830195i	$-0.311771\pi$
$71$	9.39470	1.11495	0.557473	+	0.830195i	$0.311771\pi$
$72$	−7.14084	−0.841556
$73$	5.11110	0.598209	0.299105	−	0.954220i	$-0.403312\pi$
$73$	5.11110	0.598209	0.299105	+	0.954220i	$0.403312\pi$
$74$	16.6001	1.92972
$75$	3.04066	0.351105
$76$	−9.19677	−1.05494
$77$	−3.10685	−0.354059
$78$	1.07438	0.121649
$79$	−4.80909	−0.541065	−0.270533	−	0.962711i	$-0.587200\pi$
$79$	−4.80909	−0.541065	−0.270533	+	0.962711i	$0.587200\pi$
$80$	−22.9010	−2.56041
$81$	−11.0049	−1.22277
$82$	18.3110	2.02211
$83$	−17.1284	−1.88008	−0.940042	−	0.341060i	$-0.889214\pi$
$83$	−17.1284	−1.88008	−0.940042	+	0.341060i	$0.889214\pi$
$84$	40.8018	4.45184
$85$	18.0995	1.96316
$86$	−9.41661	−1.01542
$87$	16.9634	1.81866
$88$	5.12981	0.546840
$89$	−2.32434	−0.246379	−0.123190	−	0.992383i	$-0.539312\pi$
$89$	−2.32434	−0.246379	−0.123190	+	0.992383i	$0.539312\pi$
$90$	6.66030	0.702057
$91$	−0.890098	−0.0933076
$92$	9.90224	1.03238
$93$	12.1760	1.26259
$94$	−14.1223	−1.45660
$95$	4.95663	0.508540
$96$	−18.1502	−1.85245
$97$	−13.8575	−1.40701	−0.703506	−	0.710690i	$-0.748383\pi$
$97$	−13.8575	−1.40701	−0.703506	+	0.710690i	$0.748383\pi$
$98$	−29.9041	−3.02077
$99$	−0.725489	−0.0729144
$100$	7.19817	0.719817
$101$	−3.60538	−0.358749	−0.179375	−	0.983781i	$-0.557407\pi$
$101$	−3.60538	−0.358749	−0.179375	+	0.983781i	$0.557407\pi$
$102$	36.8223	3.64595
$103$	8.87257	0.874240	0.437120	−	0.899403i	$-0.355999\pi$
$103$	8.87257	0.874240	0.437120	+	0.899403i	$0.355999\pi$
$104$	1.46966	0.144112
$105$	−21.9903	−2.14603
$106$	25.5375	2.48042
$107$	16.8512	1.62906	0.814531	−	0.580120i	$-0.196994\pi$
$107$	16.8512	1.62906	0.814531	+	0.580120i	$0.196994\pi$
$108$	−18.9150	−1.82010
$109$	16.7958	1.60875	0.804375	−	0.594122i	$-0.202500\pi$
$109$	16.7958	1.60875	0.804375	+	0.594122i	$0.202500\pi$
$110$	−4.78460	−0.456194
$111$	−12.7985	−1.21478
$112$	38.5994	3.64730
$113$	−13.9405	−1.31141	−0.655705	−	0.755017i	$-0.727628\pi$
$113$	−13.9405	−1.31141	−0.655705	+	0.755017i	$0.727628\pi$
$114$	10.0840	0.944451
$115$	−5.33685	−0.497663
$116$	40.1575	3.72853
$117$	−0.207849	−0.0192157
$118$	−1.79385	−0.165137
$119$	−30.5064	−2.79652
$120$	36.3087	3.31452
$121$	−10.4788	−0.952621
$122$	18.0751	1.63644
$123$	−14.1175	−1.27293
$124$	28.8243	2.58849
$125$	8.88707	0.794884
$126$	−11.2258	−1.00008
$127$	−19.6273	−1.74164	−0.870821	−	0.491601i	$-0.836412\pi$
$127$	−19.6273	−1.74164	−0.870821	+	0.491601i	$0.836412\pi$
$128$	3.59490	0.317748
$129$	7.26009	0.639216
$130$	−1.37076	−0.120224
$131$	3.23261	0.282434	0.141217	−	0.989979i	$-0.454898\pi$
$131$	3.23261	0.282434	0.141217	+	0.989979i	$0.454898\pi$
$132$	−6.84450	−0.595737
$133$	−8.35434	−0.724414
$134$	22.9995	1.98685
$135$	10.1943	0.877386
$136$	50.3700	4.31919
$137$	−18.0969	−1.54612	−0.773059	−	0.634334i	$-0.781274\pi$
$137$	−18.0969	−1.54612	−0.773059	+	0.634334i	$0.781274\pi$
$138$	−10.8575	−0.924251
$139$	−13.6873	−1.16094	−0.580471	−	0.814281i	$-0.697132\pi$
$139$	−13.6873	−1.16094	−0.580471	+	0.814281i	$0.697132\pi$
$140$	−52.0577	−4.39968
$141$	10.8881	0.916945
$142$	−24.3856	−2.04639
$143$	0.149314	0.0124862
$144$	9.01345	0.751121
$145$	−21.6430	−1.79735
$146$	−13.2668	−1.09797
$147$	23.0557	1.90160
$148$	−30.2979	−2.49047
$149$	−23.1111	−1.89334	−0.946669	−	0.322209i	$-0.895575\pi$
$149$	−23.1111	−1.89334	−0.946669	+	0.322209i	$0.895575\pi$
$150$	−7.89256	−0.644425
$151$	−12.3167	−1.00232	−0.501160	−	0.865355i	$-0.667093\pi$
$151$	−12.3167	−1.00232	−0.501160	+	0.865355i	$0.667093\pi$
$152$	13.7941	1.11885
$153$	−7.12364	−0.575912
$154$	8.06438	0.649846
$155$	−15.5349	−1.24780
$156$	−1.96091	−0.156999
$157$	13.6451	1.08900	0.544499	−	0.838761i	$-0.316720\pi$
$157$	13.6451	1.08900	0.544499	+	0.838761i	$0.316720\pi$
$158$	12.4828	0.993082
$159$	−19.6891	−1.56145
$160$	23.1573	1.83074
$161$	8.99519	0.708920
$162$	28.5652	2.24429
$163$	8.61674	0.674915	0.337458	−	0.941341i	$-0.390433\pi$
$163$	8.61674	0.674915	0.337458	+	0.941341i	$0.390433\pi$
$164$	−33.4205	−2.60970
$165$	3.68887	0.287178
$166$	44.4597	3.45074
$167$	6.94325	0.537285	0.268643	−	0.963240i	$-0.413425\pi$
$167$	6.94325	0.537285	0.268643	+	0.963240i	$0.413425\pi$
$168$	−61.1979	−4.72152
$169$	−12.9572	−0.996709
$170$	−46.9804	−3.60323
$171$	−1.95085	−0.149185
$172$	17.1869	1.31049
$173$	7.86537	0.597993	0.298996	−	0.954254i	$-0.403348\pi$
$173$	7.86537	0.597993	0.298996	+	0.954254i	$0.403348\pi$
$174$	−44.0314	−3.33801
$175$	6.53881	0.494288
$176$	−6.47504	−0.488075
$177$	1.38303	0.103955
$178$	6.03323	0.452210
$179$	2.97368	0.222264	0.111132	−	0.993806i	$-0.464552\pi$
$179$	2.97368	0.222264	0.111132	+	0.993806i	$0.464552\pi$
$180$	−12.1561	−0.906065
$181$	−5.08216	−0.377754	−0.188877	−	0.982001i	$-0.560485\pi$
$181$	−5.08216	−0.377754	−0.188877	+	0.982001i	$0.560485\pi$
$182$	2.31040	0.171259
$183$	−13.9357	−1.03016
$184$	−14.8522	−1.09492
$185$	16.3291	1.20054
$186$	−31.6049	−2.31738
$187$	5.11745	0.374225
$188$	25.7755	1.87987
$189$	−17.1824	−1.24983
$190$	−12.8658	−0.933384
$191$	5.12984	0.371182	0.185591	−	0.982627i	$-0.440580\pi$
$191$	5.12984	0.371182	0.185591	+	0.982627i	$0.440580\pi$
$192$	11.2133	0.809253
$193$	0.0765360	0.00550918	0.00275459	−	0.999996i	$-0.499123\pi$
$193$	0.0765360	0.00550918	0.00275459	+	0.999996i	$0.499123\pi$
$194$	35.9695	2.58246
$195$	1.05684	0.0756820
$196$	54.5799	3.89856
$197$	−3.04659	−0.217060	−0.108530	−	0.994093i	$-0.534614\pi$
$197$	−3.04659	−0.217060	−0.108530	+	0.994093i	$0.534614\pi$
$198$	1.88314	0.133829
$199$	−7.88995	−0.559304	−0.279652	−	0.960101i	$-0.590219\pi$
$199$	−7.88995	−0.559304	−0.279652	+	0.960101i	$0.590219\pi$
$200$	−10.7964	−0.763422
$201$	−17.7323	−1.25074
$202$	9.35841	0.658455
$203$	36.4790	2.56033
$204$	−67.2067	−4.70541
$205$	18.0121	1.25802
$206$	−23.0303	−1.60460
$207$	2.10049	0.145994
$208$	−1.85507	−0.128626
$209$	1.40144	0.0969397
$210$	57.0796	3.93887
$211$	−6.42169	−0.442087	−0.221044	−	0.975264i	$-0.570946\pi$
$211$	−6.42169	−0.442087	−0.221044	+	0.975264i	$0.570946\pi$
$212$	−46.6101	−3.20120
$213$	18.8010	1.28822
$214$	−43.7401	−2.99001
$215$	−9.26292	−0.631726
$216$	28.3703	1.93035
$217$	26.1839	1.77748
$218$	−43.5965	−2.95273
$219$	10.2285	0.691179
$220$	8.73267	0.588757
$221$	1.46612	0.0986222
$222$	33.2206	2.22962
$223$	13.6758	0.915802	0.457901	−	0.889003i	$-0.348601\pi$
$223$	13.6758	0.915802	0.457901	+	0.889003i	$0.348601\pi$
$224$	−39.0313	−2.60789
$225$	1.52690	0.101793
$226$	36.1850	2.40699
$227$	−19.9865	−1.32655	−0.663275	−	0.748376i	$-0.730834\pi$
$227$	−19.9865	−1.32655	−0.663275	+	0.748376i	$0.730834\pi$
$228$	−18.4049	−1.21889
$229$	11.7776	0.778287	0.389143	−	0.921177i	$-0.372771\pi$
$229$	11.7776	0.778287	0.389143	+	0.921177i	$0.372771\pi$
$230$	13.8527	0.913421
$231$	−6.21754	−0.409084
$232$	−60.2315	−3.95439
$233$	15.8305	1.03709	0.518546	−	0.855050i	$-0.326474\pi$
$233$	15.8305	1.03709	0.518546	+	0.855050i	$0.326474\pi$
$234$	0.539509	0.0352688
$235$	−13.8918	−0.906201
$236$	3.27406	0.213123
$237$	−9.62412	−0.625154
$238$	79.1848	5.13279
$239$	6.92240	0.447773	0.223886	−	0.974615i	$-0.428126\pi$
$239$	6.92240	0.447773	0.223886	+	0.974615i	$0.428126\pi$
$240$	−45.8303	−2.95833
$241$	0.325562	0.0209713	0.0104857	−	0.999945i	$-0.496662\pi$
$241$	0.325562	0.0209713	0.0104857	+	0.999945i	$0.496662\pi$
$242$	27.1996	1.74846
$243$	−10.0457	−0.644429
$244$	−32.9900	−2.11197
$245$	−29.4160	−1.87932
$246$	36.6445	2.33637
$247$	0.401506	0.0255472
$248$	−43.2330	−2.74530
$249$	−34.2779	−2.17227
$250$	−23.0680	−1.45895
$251$	−21.4115	−1.35148	−0.675742	−	0.737139i	$-0.736176\pi$
$251$	−21.4115	−1.35148	−0.675742	+	0.737139i	$0.736176\pi$
$252$	20.4890	1.29069
$253$	−1.50894	−0.0948664
$254$	50.9461	3.19664
$255$	36.2213	2.26826
$256$	−20.5376	−1.28360
$257$	−10.5944	−0.660859	−0.330429	−	0.943831i	$-0.607194\pi$
$257$	−10.5944	−0.660859	−0.330429	+	0.943831i	$0.607194\pi$
$258$	−18.8449	−1.17323
$259$	−27.5226	−1.71017
$260$	2.50187	0.155159
$261$	8.51831	0.527270
$262$	−8.39080	−0.518385
$263$	17.4834	1.07807	0.539036	−	0.842283i	$-0.318789\pi$
$263$	17.4834	1.07807	0.539036	+	0.842283i	$0.318789\pi$
$264$	10.2660	0.631826
$265$	25.1207	1.54315
$266$	21.6852	1.32960
$267$	−4.65155	−0.284670
$268$	−41.9778	−2.56420
$269$	−26.6456	−1.62461	−0.812304	−	0.583234i	$-0.801787\pi$
$269$	−26.6456	−1.62461	−0.812304	+	0.583234i	$0.801787\pi$
$270$	−26.4611	−1.61037
$271$	20.5733	1.24974	0.624869	−	0.780729i	$-0.285152\pi$
$271$	20.5733	1.24974	0.624869	+	0.780729i	$0.285152\pi$
$272$	−63.5790	−3.85504
$273$	−1.78129	−0.107809
$274$	46.9736	2.83778
$275$	−1.09689	−0.0661447
$276$	19.8167	1.19282
$277$	−3.76363	−0.226135	−0.113067	−	0.993587i	$-0.536068\pi$
$277$	−3.76363	−0.226135	−0.113067	+	0.993587i	$0.536068\pi$
$278$	35.5278	2.13082
$279$	6.11428	0.366053
$280$	78.0805	4.66620
$281$	−11.3890	−0.679410	−0.339705	−	0.940532i	$-0.610327\pi$
$281$	−11.3890	−0.679410	−0.339705	+	0.940532i	$0.610327\pi$
$282$	−28.2620	−1.68298
$283$	0.567111	0.0337112	0.0168556	−	0.999858i	$-0.494634\pi$
$283$	0.567111	0.0337112	0.0168556	+	0.999858i	$0.494634\pi$
$284$	44.5077	2.64105
$285$	9.91938	0.587574
$286$	−0.387570	−0.0229175
$287$	−30.3592	−1.79204
$288$	−9.11430	−0.537066
$289$	33.2487	1.95580
$290$	56.1782	3.29890
$291$	−27.7320	−1.62568
$292$	24.2140	1.41702
$293$	2.61408	0.152716	0.0763580	−	0.997080i	$-0.475671\pi$
$293$	2.61408	0.152716	0.0763580	+	0.997080i	$0.475671\pi$
$294$	−59.8451	−3.49024
$295$	−1.76457	−0.102737
$296$	45.4432	2.64134
$297$	2.88234	0.167250
$298$	59.9890	3.47507
$299$	−0.432304	−0.0250008
$300$	14.4052	0.831686
$301$	15.6125	0.899892
$302$	31.9702	1.83968
$303$	−7.21522	−0.414503
$304$	−17.4114	−0.998614
$305$	17.7801	1.01809
$306$	18.4907	1.05704
$307$	−8.62811	−0.492432	−0.246216	−	0.969215i	$-0.579187\pi$
$307$	−8.62811	−0.492432	−0.246216	+	0.969215i	$0.579187\pi$
$308$	−14.7188	−0.838682
$309$	17.7561	1.01011
$310$	40.3236	2.29023
$311$	21.7248	1.23190	0.615950	−	0.787785i	$-0.288772\pi$
$311$	21.7248	1.23190	0.615950	+	0.787785i	$0.288772\pi$
$312$	2.94114	0.166509
$313$	10.7355	0.606808	0.303404	−	0.952862i	$-0.401877\pi$
$313$	10.7355	0.606808	0.303404	+	0.952862i	$0.401877\pi$
$314$	−35.4183	−1.99877
$315$	−11.0426	−0.622181
$316$	−22.7832	−1.28166
$317$	18.6947	1.05000	0.524999	−	0.851103i	$-0.324066\pi$
$317$	18.6947	1.05000	0.524999	+	0.851103i	$0.324066\pi$
$318$	51.1065	2.86591
$319$	−6.11935	−0.342618
$320$	−14.3067	−0.799771
$321$	33.7231	1.88224
$322$	−23.3486	−1.30117
$323$	13.7609	0.765675
$324$	−52.1361	−2.89645
$325$	−0.314252	−0.0174316
$326$	−22.3663	−1.23875
$327$	33.6124	1.85877
$328$	50.1269	2.76779
$329$	23.4144	1.29088
$330$	−9.57510	−0.527092
$331$	−4.93993	−0.271523	−0.135762	−	0.990742i	$-0.543348\pi$
$331$	−4.93993	−0.271523	−0.135762	+	0.990742i	$0.543348\pi$
$332$	−81.1462	−4.45348
$333$	−6.42687	−0.352190
$334$	−18.0224	−0.986144
$335$	22.6241	1.23608
$336$	77.2464	4.21414
$337$	−7.88706	−0.429635	−0.214818	−	0.976654i	$-0.568916\pi$
$337$	−7.88706	−0.429635	−0.214818	+	0.976654i	$0.568916\pi$
$338$	33.6327	1.82938
$339$	−27.8982	−1.51522
$340$	85.7468	4.65027
$341$	−4.39235	−0.237859
$342$	5.06376	0.273817
$343$	19.4553	1.05049
$344$	−25.7783	−1.38987
$345$	−10.6803	−0.575007
$346$	−20.4159	−1.09757
$347$	−9.17487	−0.492533	−0.246266	−	0.969202i	$-0.579204\pi$
$347$	−9.17487	−0.492533	−0.246266	+	0.969202i	$0.579204\pi$
$348$	80.3645	4.30799
$349$	16.9457	0.907081	0.453541	−	0.891236i	$-0.350161\pi$
$349$	16.9457	0.907081	0.453541	+	0.891236i	$0.350161\pi$
$350$	−16.9726	−0.907225
$351$	0.825777	0.0440767
$352$	6.54750	0.348983
$353$	−29.5867	−1.57474	−0.787371	−	0.616480i	$-0.788558\pi$
$353$	−29.5867	−1.57474	−0.787371	+	0.616480i	$0.788558\pi$
$354$	−3.58991	−0.190801
$355$	−23.9876	−1.27313
$356$	−11.0116	−0.583615
$357$	−61.0505	−3.23114
$358$	−7.71872	−0.407947
$359$	10.3798	0.547826	0.273913	−	0.961754i	$-0.411682\pi$
$359$	10.3798	0.547826	0.273913	+	0.961754i	$0.411682\pi$
$360$	18.2328	0.960952
$361$	−15.2315	−0.801659
$362$	13.1916	0.693337
$363$	−20.9706	−1.10067
$364$	−4.21687	−0.221024
$365$	−13.0502	−0.683080
$366$	36.1725	1.89077
$367$	−13.6717	−0.713656	−0.356828	−	0.934170i	$-0.616142\pi$
$367$	−13.6717	−0.713656	−0.356828	+	0.934170i	$0.616142\pi$
$368$	18.7470	0.977256
$369$	−7.08925	−0.369052
$370$	−42.3851	−2.20350
$371$	−42.3406	−2.19821
$372$	57.6841	2.99078
$373$	−35.9774	−1.86284	−0.931421	−	0.363944i	$-0.881430\pi$
$373$	−35.9774	−1.86284	−0.931421	+	0.363944i	$0.881430\pi$
$374$	−13.2832	−0.686860
$375$	17.7851	0.918419
$376$	−38.6602	−1.99375
$377$	−1.75316	−0.0902925
$378$	44.5999	2.29397
$379$	−0.840472	−0.0431721	−0.0215861	−	0.999767i	$-0.506872\pi$
$379$	−0.840472	−0.0431721	−0.0215861	+	0.999767i	$0.506872\pi$
$380$	23.4822	1.20461
$381$	−39.2788	−2.01232
$382$	−13.3154	−0.681275
$383$	12.6758	0.647701	0.323851	−	0.946108i	$-0.395022\pi$
$383$	12.6758	0.647701	0.323851	+	0.946108i	$0.395022\pi$
$384$	7.19425	0.367130
$385$	7.93276	0.404291
$386$	−0.198663	−0.0101117
$387$	3.64573	0.185323
$388$	−65.6501	−3.33288
$389$	28.9552	1.46809	0.734044	−	0.679102i	$-0.237631\pi$
$389$	28.9552	1.46809	0.734044	+	0.679102i	$0.237631\pi$
$390$	−2.74322	−0.138908
$391$	−14.8164	−0.749299
$392$	−81.8634	−4.13473
$393$	6.46920	0.326328
$394$	7.90795	0.398397
$395$	12.2791	0.617829
$396$	−3.43703	−0.172717
$397$	−14.1889	−0.712122	−0.356061	−	0.934463i	$-0.615880\pi$
$397$	−14.1889	−0.712122	−0.356061	+	0.934463i	$0.615880\pi$
$398$	20.4797	1.02656
$399$	−16.7190	−0.836997
$400$	13.6276	0.681382
$401$	19.1715	0.957377	0.478689	−	0.877985i	$-0.341112\pi$
$401$	19.1715	0.957377	0.478689	+	0.877985i	$0.341112\pi$
$402$	46.0273	2.29563
$403$	−1.25839	−0.0626847
$404$	−17.0806	−0.849793
$405$	28.0990	1.39625
$406$	−94.6877	−4.69927
$407$	4.61691	0.228852
$408$	100.802	4.99045
$409$	−0.791300	−0.0391273	−0.0195636	−	0.999809i	$-0.506228\pi$
$409$	−0.791300	−0.0391273	−0.0195636	+	0.999809i	$0.506228\pi$
$410$	−46.7536	−2.30899
$411$	−36.2160	−1.78641
$412$	42.0341	2.07087
$413$	2.97416	0.146349
$414$	−5.45219	−0.267961
$415$	43.7340	2.14682
$416$	1.87583	0.0919699
$417$	−27.3915	−1.34137
$418$	−3.63769	−0.177925
$419$	−11.7406	−0.573566	−0.286783	−	0.957996i	$-0.592586\pi$
$419$	−11.7406	−0.573566	−0.286783	+	0.957996i	$0.592586\pi$
$420$	−104.180	−5.08345
$421$	−4.31636	−0.210366	−0.105183	−	0.994453i	$-0.533543\pi$
$421$	−4.31636	−0.210366	−0.105183	+	0.994453i	$0.533543\pi$
$422$	16.6686	0.811416
$423$	5.46757	0.265842
$424$	69.9097	3.39512
$425$	−10.7704	−0.522441
$426$	−48.8013	−2.36443
$427$	−29.9681	−1.45026
$428$	79.8329	3.85887
$429$	0.298812	0.0144268
$430$	24.0435	1.15948
$431$	−10.8071	−0.520558	−0.260279	−	0.965533i	$-0.583815\pi$
$431$	−10.8071	−0.520558	−0.260279	+	0.965533i	$0.583815\pi$
$432$	−35.8101	−1.72291
$433$	−3.33623	−0.160329	−0.0801644	−	0.996782i	$-0.525545\pi$
$433$	−3.33623	−0.160329	−0.0801644	+	0.996782i	$0.525545\pi$
$434$	−67.9650	−3.26243
$435$	−43.3127	−2.07669
$436$	79.5708	3.81075
$437$	−4.05755	−0.194099
$438$	−26.5499	−1.26860
$439$	−22.6093	−1.07908	−0.539541	−	0.841960i	$-0.681402\pi$
$439$	−22.6093	−1.07908	−0.539541	+	0.841960i	$0.681402\pi$
$440$	−13.0980	−0.624422
$441$	11.5776	0.551316
$442$	−3.80558	−0.181013
$443$	−41.8565	−1.98866	−0.994331	−	0.106331i	$-0.966090\pi$
$443$	−41.8565	−1.98866	−0.994331	+	0.106331i	$0.966090\pi$
$444$	−60.6331	−2.87752
$445$	5.93476	0.281334
$446$	−35.4980	−1.68088
$447$	−46.2508	−2.18759
$448$	24.1138	1.13927
$449$	27.2518	1.28609	0.643045	−	0.765828i	$-0.277671\pi$
$449$	27.2518	1.28609	0.643045	+	0.765828i	$0.277671\pi$
$450$	−3.96333	−0.186833
$451$	5.09275	0.239808
$452$	−66.0435	−3.10642
$453$	−24.6486	−1.15809
$454$	51.8785	2.43478
$455$	2.27270	0.106546
$456$	27.6052	1.29273
$457$	10.6382	0.497633	0.248817	−	0.968551i	$-0.419958\pi$
$457$	10.6382	0.497633	0.248817	+	0.968551i	$0.419958\pi$
$458$	−30.5709	−1.42848
$459$	28.3020	1.32102
$460$	−25.2835	−1.17885
$461$	18.9352	0.881900	0.440950	−	0.897532i	$-0.354642\pi$
$461$	18.9352	0.881900	0.440950	+	0.897532i	$0.354642\pi$
$462$	16.1387	0.750841
$463$	−27.1296	−1.26082	−0.630409	−	0.776263i	$-0.717113\pi$
$463$	−27.1296	−1.26082	−0.630409	+	0.776263i	$0.717113\pi$
$464$	76.0266	3.52944
$465$	−31.0890	−1.44172
$466$	−41.0909	−1.90350
$467$	−17.9118	−0.828858	−0.414429	−	0.910082i	$-0.636019\pi$
$467$	−17.9118	−0.828858	−0.414429	+	0.910082i	$0.636019\pi$
$468$	−0.984692	−0.0455174
$469$	−38.1326	−1.76080
$470$	36.0586	1.66326
$471$	27.3071	1.25824
$472$	−4.91071	−0.226034
$473$	−2.61900	−0.120422
$474$	24.9811	1.14742
$475$	−2.94953	−0.135334
$476$	−144.525	−6.62430
$477$	−9.88707	−0.452698
$478$	−17.9683	−0.821851
$479$	7.51390	0.343319	0.171659	−	0.985156i	$-0.445087\pi$
$479$	7.51390	0.343319	0.171659	+	0.985156i	$0.445087\pi$
$480$	46.3431	2.11526
$481$	1.32272	0.0603109
$482$	−0.845054	−0.0384911
$483$	18.0015	0.819096
$484$	−49.6438	−2.25654
$485$	35.3824	1.60663
$486$	26.0753	1.18280
$487$	−35.4930	−1.60834	−0.804171	−	0.594398i	$-0.797390\pi$
$487$	−35.4930	−1.60834	−0.804171	+	0.594398i	$0.797390\pi$
$488$	49.4812	2.23991
$489$	17.2441	0.779806
$490$	76.3544	3.44934
$491$	−16.9482	−0.764862	−0.382431	−	0.923984i	$-0.624913\pi$
$491$	−16.9482	−0.764862	−0.382431	+	0.923984i	$0.624913\pi$
$492$	−66.8822	−3.01528
$493$	−60.0864	−2.70616
$494$	−1.04218	−0.0468898
$495$	1.85240	0.0832592
$496$	54.5704	2.45028
$497$	40.4308	1.81357
$498$	88.9743	3.98703
$499$	−2.64920	−0.118594	−0.0592972	−	0.998240i	$-0.518886\pi$
$499$	−2.64920	−0.118594	−0.0592972	+	0.998240i	$0.518886\pi$
$500$	42.1028	1.88289
$501$	13.8951	0.620786
$502$	55.5774	2.48054
$503$	−4.63993	−0.206884	−0.103442	−	0.994635i	$-0.532986\pi$
$503$	−4.63993	−0.206884	−0.103442	+	0.994635i	$0.532986\pi$
$504$	−30.7311	−1.36887
$505$	9.20566	0.409647
$506$	3.91672	0.174120
$507$	−25.9304	−1.15161
$508$	−92.9850	−4.12554
$509$	16.2144	0.718691	0.359346	−	0.933205i	$-0.383000\pi$
$509$	16.2144	0.718691	0.359346	+	0.933205i	$0.383000\pi$
$510$	−94.0187	−4.16322
$511$	21.9960	0.973046
$512$	46.1192	2.03820
$513$	7.75064	0.342199
$514$	27.4995	1.21295
$515$	−22.6544	−0.998273
$516$	34.3949	1.51415
$517$	−3.92777	−0.172743
$518$	71.4396	3.13888
$519$	15.7404	0.690929
$520$	−3.75251	−0.164558
$521$	11.5085	0.504195	0.252098	−	0.967702i	$-0.418880\pi$
$521$	11.5085	0.504195	0.252098	+	0.967702i	$0.418880\pi$
$522$	−22.1108	−0.967763
$523$	−27.8895	−1.21952	−0.609760	−	0.792586i	$-0.708734\pi$
$523$	−27.8895	−1.21952	−0.609760	+	0.792586i	$0.708734\pi$
$524$	15.3146	0.669021
$525$	13.0857	0.571106
$526$	−45.3812	−1.97871
$527$	−43.1289	−1.87872
$528$	−12.9581	−0.563928
$529$	−18.6312	−0.810052
$530$	−65.2052	−2.83233
$531$	0.694503	0.0301389
$532$	−39.5790	−1.71597
$533$	1.45905	0.0631983
$534$	12.0739	0.522489
$535$	−43.0262	−1.86019
$536$	62.9618	2.71953
$537$	5.95104	0.256806
$538$	69.1632	2.98184
$539$	−8.31710	−0.358243
$540$	48.2959	2.07832
$541$	38.3438	1.64853	0.824264	−	0.566206i	$-0.191589\pi$
$541$	38.3438	1.64853	0.824264	+	0.566206i	$0.191589\pi$
$542$	−53.4016	−2.29379
$543$	−10.1706	−0.436462
$544$	64.2904	2.75643
$545$	−42.8850	−1.83699
$546$	4.62366	0.197874
$547$	−13.2293	−0.565646	−0.282823	−	0.959172i	$-0.591271\pi$
$547$	−13.2293	−0.565646	−0.282823	+	0.959172i	$0.591271\pi$
$548$	−85.7344	−3.66239
$549$	−6.99794	−0.298665
$550$	2.84716	0.121403
$551$	−16.4550	−0.701006
$552$	−29.7227	−1.26508
$553$	−20.6963	−0.880095
$554$	9.76917	0.415052
$555$	32.6784	1.38712
$556$	−64.8441	−2.75000
$557$	12.6579	0.536334	0.268167	−	0.963372i	$-0.413582\pi$
$557$	12.6579	0.536334	0.268167	+	0.963372i	$0.413582\pi$
$558$	−15.8707	−0.671860
$559$	−0.750331	−0.0317356
$560$	−98.5562	−4.16476
$561$	10.2412	0.432385
$562$	29.5621	1.24700
$563$	36.0539	1.51949	0.759745	−	0.650221i	$-0.225324\pi$
$563$	36.0539	1.51949	0.759745	+	0.650221i	$0.225324\pi$
$564$	51.5828	2.17203
$565$	35.5944	1.49747
$566$	−1.47204	−0.0618743
$567$	−47.3604	−1.98895
$568$	−66.7564	−2.80103
$569$	−23.3823	−0.980238	−0.490119	−	0.871656i	$-0.663047\pi$
$569$	−23.3823	−0.980238	−0.490119	+	0.871656i	$0.663047\pi$
$570$	−25.7475	−1.07844
$571$	−24.1559	−1.01089	−0.505447	−	0.862858i	$-0.668672\pi$
$571$	−24.1559	−1.01089	−0.505447	+	0.862858i	$0.668672\pi$
$572$	0.707379	0.0295770
$573$	10.2660	0.428869
$574$	78.8026	3.28915
$575$	3.17578	0.132439
$576$	5.63088	0.234620
$577$	43.2095	1.79883	0.899417	−	0.437092i	$-0.143992\pi$
$577$	43.2095	1.79883	0.899417	+	0.437092i	$0.143992\pi$
$578$	−86.3028	−3.58972
$579$	0.153166	0.00636538
$580$	−102.534	−4.25751
$581$	−73.7132	−3.05814
$582$	71.9833	2.98380
$583$	7.10263	0.294161
$584$	−36.3182	−1.50286
$585$	0.530703	0.0219419
$586$	−6.78529	−0.280298
$587$	−34.1105	−1.40789	−0.703945	−	0.710254i	$-0.748580\pi$
$587$	−34.1105	−1.40789	−0.703945	+	0.710254i	$0.748580\pi$
$588$	109.227	4.50445
$589$	−11.8111	−0.486667
$590$	4.58024	0.188566
$591$	−6.09693	−0.250794
$592$	−57.3602	−2.35749
$593$	15.7197	0.645529	0.322764	−	0.946479i	$-0.395388\pi$
$593$	15.7197	0.645529	0.322764	+	0.946479i	$0.395388\pi$
$594$	−7.48163	−0.306975
$595$	77.8924	3.19328
$596$	−109.490	−4.48487
$597$	−15.7896	−0.646227
$598$	1.12212	0.0458870
$599$	−19.6085	−0.801183	−0.400591	−	0.916257i	$-0.631195\pi$
$599$	−19.6085	−0.801183	−0.400591	+	0.916257i	$0.631195\pi$
$600$	−21.6061	−0.882067
$601$	−1.73398	−0.0707305	−0.0353653	−	0.999374i	$-0.511259\pi$
$601$	−1.73398	−0.0707305	−0.0353653	+	0.999374i	$0.511259\pi$
$602$	−40.5251	−1.65168
$603$	−8.90444	−0.362617
$604$	−58.3509	−2.37426
$605$	26.7557	1.08777
$606$	18.7284	0.760788
$607$	12.5419	0.509060	0.254530	−	0.967065i	$-0.418079\pi$
$607$	12.5419	0.509060	0.254530	+	0.967065i	$0.418079\pi$
$608$	17.6063	0.714028
$609$	73.0031	2.95823
$610$	−46.1514	−1.86861
$611$	−1.12529	−0.0455242
$612$	−33.7485	−1.36420
$613$	−32.5981	−1.31662	−0.658312	−	0.752746i	$-0.728729\pi$
$613$	−32.5981	−1.31662	−0.658312	+	0.752746i	$0.728729\pi$
$614$	22.3958	0.903820
$615$	36.0464	1.45353
$616$	22.0765	0.889488
$617$	2.35505	0.0948106	0.0474053	−	0.998876i	$-0.484905\pi$
$617$	2.35505	0.0948106	0.0474053	+	0.998876i	$0.484905\pi$
$618$	−46.0890	−1.85397
$619$	28.2721	1.13635	0.568177	−	0.822907i	$-0.307649\pi$
$619$	28.2721	1.13635	0.568177	+	0.822907i	$0.307649\pi$
$620$	−73.5972	−2.95574
$621$	−8.34517	−0.334880
$622$	−56.3905	−2.26105
$623$	−10.0030	−0.400760
$624$	−3.71243	−0.148616
$625$	−30.2884	−1.21154
$626$	−27.8660	−1.11375
$627$	2.80461	0.112005
$628$	64.6442	2.57958
$629$	45.3338	1.80758
$630$	28.6631	1.14196
$631$	13.6288	0.542555	0.271278	−	0.962501i	$-0.412554\pi$
$631$	13.6288	0.542555	0.271278	+	0.962501i	$0.412554\pi$
$632$	34.1722	1.35930
$633$	−12.8513	−0.510794
$634$	−48.5254	−1.92719
$635$	50.1146	1.98874
$636$	−93.2778	−3.69870
$637$	−2.38281	−0.0944102
$638$	15.8839	0.628848
$639$	9.44110	0.373484
$640$	−9.17891	−0.362828
$641$	35.7660	1.41267	0.706336	−	0.707877i	$-0.250347\pi$
$641$	35.7660	1.41267	0.706336	+	0.707877i	$0.250347\pi$
$642$	−87.5342	−3.45470
$643$	−18.8023	−0.741492	−0.370746	−	0.928734i	$-0.620898\pi$
$643$	−18.8023	−0.741492	−0.370746	+	0.928734i	$0.620898\pi$
$644$	42.6150	1.67927
$645$	−18.5373	−0.729904
$646$	−35.7187	−1.40533
$647$	−48.5078	−1.90704	−0.953519	−	0.301333i	$-0.902568\pi$
$647$	−48.5078	−1.90704	−0.953519	+	0.301333i	$0.902568\pi$
$648$	78.1981	3.07191
$649$	−0.498914	−0.0195841
$650$	0.815697	0.0319943
$651$	52.4002	2.05373
$652$	40.8221	1.59872
$653$	−30.1179	−1.17861	−0.589303	−	0.807912i	$-0.700598\pi$
$653$	−30.1179	−1.17861	−0.589303	+	0.807912i	$0.700598\pi$
$654$	−87.2469	−3.41162
$655$	−8.25385	−0.322505
$656$	−63.2721	−2.47036
$657$	5.13635	0.200388
$658$	−60.7763	−2.36931
$659$	−15.3081	−0.596320	−0.298160	−	0.954516i	$-0.596373\pi$
$659$	−15.3081	−0.596320	−0.298160	+	0.954516i	$0.596373\pi$
$660$	17.4761	0.680257
$661$	−30.7490	−1.19600	−0.597998	−	0.801498i	$-0.704037\pi$
$661$	−30.7490	−1.19600	−0.597998	+	0.801498i	$0.704037\pi$
$662$	12.8225	0.498359
$663$	2.93406	0.113949
$664$	121.710	4.72326
$665$	21.3312	0.827190
$666$	16.6821	0.646417
$667$	17.7172	0.686013
$668$	32.8939	1.27270
$669$	27.3685	1.05813
$670$	−58.7247	−2.26873
$671$	5.02715	0.194071
$672$	−78.1108	−3.01319
$673$	−1.94981	−0.0751598	−0.0375799	−	0.999294i	$-0.511965\pi$
$673$	−1.94981	−0.0751598	−0.0375799	+	0.999294i	$0.511965\pi$
$674$	20.4722	0.788561
$675$	−6.06630	−0.233492
$676$	−61.3853	−2.36097
$677$	4.93627	0.189716	0.0948581	−	0.995491i	$-0.469760\pi$
$677$	4.93627	0.189716	0.0948581	+	0.995491i	$0.469760\pi$
$678$	72.4146	2.78107
$679$	−59.6366	−2.28864
$680$	−128.610	−4.93198
$681$	−39.9977	−1.53271
$682$	11.4011	0.436572
$683$	19.1081	0.731152	0.365576	−	0.930781i	$-0.380872\pi$
$683$	19.1081	0.731152	0.365576	+	0.930781i	$0.380872\pi$
$684$	−9.24220	−0.353384
$685$	46.2069	1.76547
$686$	−50.4997	−1.92809
$687$	23.5698	0.899243
$688$	32.5384	1.24051
$689$	2.03487	0.0775223
$690$	27.7225	1.05538
$691$	−14.4910	−0.551262	−0.275631	−	0.961263i	$-0.588887\pi$
$691$	−14.4910	−0.551262	−0.275631	+	0.961263i	$0.588887\pi$
$692$	37.2624	1.41650
$693$	−3.12220	−0.118602
$694$	23.8150	0.904004
$695$	34.9479	1.32565
$696$	−120.537	−4.56896
$697$	50.0061	1.89412
$698$	−43.9855	−1.66487
$699$	31.6806	1.19827
$700$	30.9778	1.17085
$701$	−0.379290	−0.0143256	−0.00716280	−	0.999974i	$-0.502280\pi$
$701$	−0.379290	−0.0143256	−0.00716280	+	0.999974i	$0.502280\pi$
$702$	−2.14345	−0.0808993
$703$	12.4149	0.468236
$704$	−4.04509	−0.152455
$705$	−27.8007	−1.04704
$706$	76.7975	2.89031
$707$	−15.5160	−0.583540
$708$	6.55216	0.246245
$709$	−46.3790	−1.74180	−0.870900	−	0.491461i	$-0.836463\pi$
$709$	−46.3790	−1.74180	−0.870900	+	0.491461i	$0.836463\pi$
$710$	62.2640	2.33673
$711$	−4.83284	−0.181246
$712$	16.5162	0.618969
$713$	12.7171	0.476258
$714$	158.467	5.93049
$715$	−0.381244	−0.0142577
$716$	14.0879	0.526491
$717$	13.8533	0.517363
$718$	−26.9427	−1.00549
$719$	−19.0781	−0.711494	−0.355747	−	0.934582i	$-0.615774\pi$
$719$	−19.0781	−0.711494	−0.355747	+	0.934582i	$0.615774\pi$
$720$	−23.0141	−0.857686
$721$	38.1837	1.42204
$722$	39.5361	1.47138
$723$	0.651526	0.0242305
$724$	−24.0769	−0.894811
$725$	12.8790	0.478316
$726$	54.4328	2.02019
$727$	50.2047	1.86199	0.930994	−	0.365033i	$-0.118942\pi$
$727$	50.2047	1.86199	0.930994	+	0.365033i	$0.118942\pi$
$728$	6.32481	0.234413
$729$	12.9110	0.478186
$730$	33.8742	1.25374
$731$	−25.7162	−0.951148
$732$	−66.0208	−2.44020
$733$	9.20267	0.339908	0.169954	−	0.985452i	$-0.445638\pi$
$733$	9.20267	0.339908	0.169954	+	0.985452i	$0.445638\pi$
$734$	35.4873	1.30986
$735$	−58.8683	−2.17139
$736$	−18.9568	−0.698757
$737$	6.39674	0.235627
$738$	18.4014	0.677365
$739$	3.35181	0.123298	0.0616491	−	0.998098i	$-0.480364\pi$
$739$	3.35181	0.123298	0.0616491	+	0.998098i	$0.480364\pi$
$740$	77.3598	2.84380
$741$	0.803507	0.0295176
$742$	109.902	4.03465
$743$	38.5447	1.41407	0.707035	−	0.707179i	$-0.250032\pi$
$743$	38.5447	1.41407	0.707035	+	0.707179i	$0.250032\pi$
$744$	−86.5194	−3.17196
$745$	59.0099	2.16195
$746$	93.3858	3.41910
$747$	−17.2130	−0.629790
$748$	24.2441	0.886452
$749$	72.5202	2.64983
$750$	−46.1644	−1.68569
$751$	12.7559	0.465470	0.232735	−	0.972540i	$-0.425233\pi$
$751$	12.7559	0.465470	0.232735	+	0.972540i	$0.425233\pi$
$752$	48.7985	1.77950
$753$	−42.8495	−1.56152
$754$	4.55065	0.165725
$755$	31.4484	1.14452
$756$	−81.4021	−2.96056
$757$	39.9523	1.45209	0.726045	−	0.687647i	$-0.241356\pi$
$757$	39.9523	1.45209	0.726045	+	0.687647i	$0.241356\pi$
$758$	2.18159	0.0792390
$759$	−3.01975	−0.109610
$760$	−35.2206	−1.27758
$761$	47.2255	1.71192	0.855962	−	0.517038i	$-0.172966\pi$
$761$	47.2255	1.71192	0.855962	+	0.517038i	$0.172966\pi$
$762$	101.955	3.69344
$763$	72.2821	2.61679
$764$	24.3028	0.879244
$765$	18.1889	0.657620
$766$	−32.9022	−1.18880
$767$	−0.142936	−0.00516114
$768$	−41.1006	−1.48309
$769$	30.7500	1.10887	0.554437	−	0.832226i	$-0.312934\pi$
$769$	30.7500	1.10887	0.554437	+	0.832226i	$0.312934\pi$
$770$	−20.5909	−0.742043
$771$	−21.2018	−0.763565
$772$	0.362592	0.0130500
$773$	−38.1154	−1.37091	−0.685457	−	0.728113i	$-0.740398\pi$
$773$	−38.1154	−1.37091	−0.685457	+	0.728113i	$0.740398\pi$
$774$	−9.46312	−0.340145
$775$	9.24433	0.332066
$776$	98.4675	3.53478
$777$	−55.0791	−1.97595
$778$	−75.1584	−2.69456
$779$	13.6944	0.490654
$780$	5.00682	0.179273
$781$	−6.78226	−0.242688
$782$	38.4586	1.37528
$783$	−33.8429	−1.20945
$784$	103.331	3.69040
$785$	−34.8402	−1.24350
$786$	−16.7920	−0.598949
$787$	−10.3292	−0.368197	−0.184099	−	0.982908i	$-0.558937\pi$
$787$	−10.3292	−0.368197	−0.184099	+	0.982908i	$0.558937\pi$
$788$	−14.4333	−0.514165
$789$	34.9883	1.24562
$790$	−31.8726	−1.13398
$791$	−59.9939	−2.13314
$792$	5.15514	0.183180
$793$	1.44025	0.0511449
$794$	36.8299	1.30704
$795$	50.2724	1.78298
$796$	−37.3789	−1.32486
$797$	30.1903	1.06940	0.534698	−	0.845043i	$-0.320425\pi$
$797$	30.1903	1.06940	0.534698	+	0.845043i	$0.320425\pi$
$798$	43.3971	1.53624
$799$	−38.5671	−1.36441
$800$	−13.7801	−0.487201
$801$	−2.33582	−0.0825321
$802$	−49.7629	−1.75719
$803$	−3.68983	−0.130211
$804$	−84.0073	−2.96271
$805$	−22.9675	−0.809498
$806$	3.26637	0.115053
$807$	−53.3240	−1.87709
$808$	25.6189	0.901271
$809$	−32.6664	−1.14849	−0.574244	−	0.818684i	$-0.694704\pi$
$809$	−32.6664	−1.14849	−0.574244	+	0.818684i	$0.694704\pi$
$810$	−72.9358	−2.56270
$811$	−36.5632	−1.28391	−0.641954	−	0.766743i	$-0.721876\pi$
$811$	−36.5632	−1.28391	−0.641954	+	0.766743i	$0.721876\pi$
$812$	172.821	6.06481
$813$	41.1720	1.44396
$814$	−11.9840	−0.420039
$815$	−22.0012	−0.770669
$816$	−127.236	−4.45417
$817$	−7.04251	−0.246386
$818$	2.05396	0.0718149
$819$	−0.894494	−0.0312561
$820$	85.3329	2.97995
$821$	9.65378	0.336919	0.168460	−	0.985709i	$-0.446121\pi$
$821$	9.65378	0.336919	0.168460	+	0.985709i	$0.446121\pi$
$822$	94.0051	3.27880
$823$	−4.01032	−0.139791	−0.0698954	−	0.997554i	$-0.522267\pi$
$823$	−4.01032	−0.139791	−0.0698954	+	0.997554i	$0.522267\pi$
$824$	−63.0462	−2.19632
$825$	−2.19512	−0.0764244
$826$	−7.71994	−0.268611
$827$	−4.10677	−0.142806	−0.0714032	−	0.997448i	$-0.522748\pi$
$827$	−4.10677	−0.142806	−0.0714032	+	0.997448i	$0.522748\pi$
$828$	9.95114	0.345826
$829$	28.6597	0.995393	0.497697	−	0.867351i	$-0.334179\pi$
$829$	28.6597	0.995393	0.497697	+	0.867351i	$0.334179\pi$
$830$	−113.519	−3.94032
$831$	−7.53191	−0.261279
$832$	−1.15890	−0.0401776
$833$	−81.6662	−2.82957
$834$	71.0995	2.46197
$835$	−17.7283	−0.613512
$836$	6.63937	0.229627
$837$	−24.2918	−0.839648
$838$	30.4748	1.05273
$839$	−30.7012	−1.05992	−0.529962	−	0.848021i	$-0.677794\pi$
$839$	−30.7012	−1.05992	−0.529962	+	0.848021i	$0.677794\pi$
$840$	156.257	5.39139
$841$	42.8502	1.47759
$842$	11.2039	0.386111
$843$	−22.7920	−0.784999
$844$	−30.4230	−1.04720
$845$	33.0838	1.13812
$846$	−14.1920	−0.487932
$847$	−45.0964	−1.54953
$848$	−88.2428	−3.03027
$849$	1.13492	0.0389504
$850$	27.9565	0.958899
$851$	−13.3672	−0.458222
$852$	89.0703	3.05150
$853$	51.4675	1.76221	0.881107	−	0.472917i	$-0.156799\pi$
$853$	51.4675	1.76221	0.881107	+	0.472917i	$0.156799\pi$
$854$	77.7876	2.66184
$855$	4.98111	0.170350
$856$	−119.740	−4.09263
$857$	4.72225	0.161309	0.0806545	−	0.996742i	$-0.474299\pi$
$857$	4.72225	0.161309	0.0806545	+	0.996742i	$0.474299\pi$
$858$	−0.775619	−0.0264792
$859$	21.5474	0.735187	0.367594	−	0.929987i	$-0.380182\pi$
$859$	21.5474	0.735187	0.367594	+	0.929987i	$0.380182\pi$
$860$	−43.8834	−1.49641
$861$	−60.7558	−2.07055
$862$	28.0516	0.955442
$863$	45.4434	1.54691	0.773455	−	0.633851i	$-0.218527\pi$
$863$	45.4434	1.54691	0.773455	+	0.633851i	$0.218527\pi$
$864$	36.2108	1.23192
$865$	−20.0827	−0.682833
$866$	8.65977	0.294271
$867$	66.5384	2.25976
$868$	124.047	4.21044
$869$	3.47180	0.117773
$870$	112.426	3.81159
$871$	1.83263	0.0620964
$872$	−119.347	−4.04160
$873$	−13.9259	−0.471320
$874$	10.5321	0.356253
$875$	38.2462	1.29296
$876$	48.4579	1.63724
$877$	−24.3662	−0.822787	−0.411393	−	0.911458i	$-0.634958\pi$
$877$	−24.3662	−0.822787	−0.411393	+	0.911458i	$0.634958\pi$
$878$	58.6863	1.98057
$879$	5.23138	0.176450
$880$	16.5328	0.557320
$881$	4.79543	0.161562	0.0807811	−	0.996732i	$-0.474259\pi$
$881$	4.79543	0.161562	0.0807811	+	0.996732i	$0.474259\pi$
$882$	−30.0518	−1.01190
$883$	29.3529	0.987804	0.493902	−	0.869518i	$-0.335570\pi$
$883$	29.3529	0.987804	0.493902	+	0.869518i	$0.335570\pi$
$884$	6.94581	0.233613
$885$	−3.53131	−0.118704
$886$	108.646	3.65003
$887$	16.3611	0.549353	0.274677	−	0.961537i	$-0.411429\pi$
$887$	16.3611	0.549353	0.274677	+	0.961537i	$0.411429\pi$
$888$	90.9426	3.05183
$889$	−84.4675	−2.83295
$890$	−15.4047	−0.516367
$891$	7.94471	0.266158
$892$	64.7897	2.16932
$893$	−10.5618	−0.353437
$894$	120.052	4.01514
$895$	−7.59274	−0.253797
$896$	15.4709	0.516848
$897$	−0.865142	−0.0288863
$898$	−70.7367	−2.36052
$899$	51.5727	1.72005
$900$	7.23372	0.241124
$901$	69.7413	2.32342
$902$	−13.2191	−0.440149
$903$	31.2443	1.03975
$904$	99.0575	3.29460
$905$	12.9763	0.431348
$906$	63.9799	2.12559
$907$	−40.7918	−1.35447	−0.677235	−	0.735767i	$-0.736822\pi$
$907$	−40.7918	−1.35447	−0.677235	+	0.735767i	$0.736822\pi$
$908$	−94.6867	−3.14229
$909$	−3.62319	−0.120174
$910$	−5.89918	−0.195556
$911$	−32.1532	−1.06528	−0.532642	−	0.846341i	$-0.678801\pi$
$911$	−32.1532	−1.06528	−0.532642	+	0.846341i	$0.678801\pi$
$912$	−34.8444	−1.15381
$913$	12.3654	0.409234
$914$	−27.6133	−0.913366
$915$	35.5821	1.17631
$916$	55.7969	1.84358
$917$	13.9118	0.459407
$918$	−73.4627	−2.42463
$919$	−40.1221	−1.32351	−0.661753	−	0.749722i	$-0.730187\pi$
$919$	−40.1221	−1.32351	−0.661753	+	0.749722i	$0.730187\pi$
$920$	37.9223	1.25026
$921$	−17.2669	−0.568963
$922$	−49.1496	−1.61866
$923$	−1.94308	−0.0639574
$924$	−29.4558	−0.969025
$925$	−9.71693	−0.319491
$926$	70.4196	2.31413
$927$	8.91639	0.292853
$928$	−76.8773	−2.52362
$929$	57.9228	1.90039	0.950193	−	0.311661i	$-0.100885\pi$
$929$	57.9228	1.90039	0.950193	+	0.311661i	$0.100885\pi$
$930$	80.6971	2.64616
$931$	−22.3647	−0.732974
$932$	74.9976	2.45663
$933$	43.4764	1.42335
$934$	46.4932	1.52130
$935$	−13.0664	−0.427318
$936$	1.47692	0.0482747
$937$	−9.48324	−0.309804	−0.154902	−	0.987930i	$-0.549506\pi$
$937$	−9.48324	−0.309804	−0.154902	+	0.987930i	$0.549506\pi$
$938$	98.9798	3.23181
$939$	21.4843	0.701114
$940$	−65.8128	−2.14658
$941$	20.6449	0.673006	0.336503	−	0.941682i	$-0.390756\pi$
$941$	20.6449	0.673006	0.336503	+	0.941682i	$0.390756\pi$
$942$	−70.8803	−2.30941
$943$	−14.7449	−0.480160
$944$	6.19849	0.201744
$945$	43.8719	1.42715
$946$	6.79808	0.221025
$947$	33.4884	1.08823	0.544113	−	0.839012i	$-0.316866\pi$
$947$	33.4884	1.08823	0.544113	+	0.839012i	$0.316866\pi$
$948$	−45.5946	−1.48084
$949$	−1.05712	−0.0343155
$950$	7.65603	0.248394
$951$	37.4125	1.21318
$952$	216.771	7.02559
$953$	−11.7983	−0.382184	−0.191092	−	0.981572i	$-0.561203\pi$
$953$	−11.7983	−0.382184	−0.191092	+	0.981572i	$0.561203\pi$
$954$	25.6636	0.830891
$955$	−13.0981	−0.423844
$956$	32.7951	1.06067
$957$	−12.2463	−0.395865
$958$	−19.5037	−0.630134
$959$	−77.8811	−2.51491
$960$	−28.6311	−0.924066
$961$	6.01789	0.194126
$962$	−3.43335	−0.110696
$963$	16.9344	0.545703
$964$	1.54236	0.0496761
$965$	−0.195420	−0.00629080
$966$	−46.7260	−1.50338
$967$	35.3563	1.13698	0.568491	−	0.822689i	$-0.307527\pi$
$967$	35.3563	1.13698	0.568491	+	0.822689i	$0.307527\pi$
$968$	74.4599	2.39323
$969$	27.5387	0.884671
$970$	−91.8412	−2.94884
$971$	−24.9563	−0.800885	−0.400442	−	0.916322i	$-0.631144\pi$
$971$	−24.9563	−0.800885	−0.400442	+	0.916322i	$0.631144\pi$
$972$	−47.5916	−1.52650
$973$	−58.9043	−1.88839
$974$	92.1283	2.95198
$975$	−0.628892	−0.0201407
$976$	−62.4571	−1.99920
$977$	−41.5705	−1.32996	−0.664980	−	0.746861i	$-0.731560\pi$
$977$	−41.5705	−1.32996	−0.664980	+	0.746861i	$0.731560\pi$
$978$	−44.7601	−1.43127
$979$	1.67800	0.0536290
$980$	−139.359	−4.45167
$981$	16.8788	0.538898
$982$	43.9920	1.40384
$983$	7.32015	0.233477	0.116738	−	0.993163i	$-0.462756\pi$
$983$	7.32015	0.233477	0.116738	+	0.993163i	$0.462756\pi$
$984$	100.316	3.19794
$985$	7.77888	0.247856
$986$	155.965	4.96693
$987$	46.8578	1.49150
$988$	1.90215	0.0605154
$989$	7.58273	0.241117
$990$	−4.80823	−0.152816
$991$	15.4030	0.489292	0.244646	−	0.969613i	$-0.421328\pi$
$991$	15.4030	0.489292	0.244646	+	0.969613i	$0.421328\pi$
$992$	−55.1810	−1.75200
$993$	−9.88597	−0.313722
$994$	−104.945	−3.32866
$995$	20.1455	0.638655
$996$	−162.393	−5.14561
$997$	−16.6711	−0.527979	−0.263990	−	0.964526i	$-0.585038\pi$
$997$	−16.6711	−0.527979	−0.263990	+	0.964526i	$0.585038\pi$
$998$	6.87646	0.217671
$999$	25.5337	0.807851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4003.2.a.b.1.10	✓	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4003.2.a.b.1.10	✓	152	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59568 q^{2} +2.00123 q^{3} +4.73753 q^{4} -2.55331 q^{5} -5.19456 q^{6} +4.30357 q^{7} -7.10575 q^{8} +1.00494 q^{9} +O(q^{10})\)	\(q-2.59568 q^{2} +2.00123 q^{3} +4.73753 q^{4} -2.55331 q^{5} -5.19456 q^{6} +4.30357 q^{7} -7.10575 q^{8} +1.00494 q^{9} +6.62756 q^{10} -0.721924 q^{11} +9.48091 q^{12} -0.206828 q^{13} -11.1707 q^{14} -5.10977 q^{15} +8.96915 q^{16} -7.08863 q^{17} -2.60850 q^{18} -1.94126 q^{19} -12.0964 q^{20} +8.61246 q^{21} +1.87388 q^{22} +2.09017 q^{23} -14.2203 q^{24} +1.51939 q^{25} +0.536857 q^{26} -3.99258 q^{27} +20.3883 q^{28} +8.47645 q^{29} +13.2633 q^{30} +6.08423 q^{31} -9.06951 q^{32} -1.44474 q^{33} +18.3998 q^{34} -10.9884 q^{35} +4.76093 q^{36} -6.39528 q^{37} +5.03888 q^{38} -0.413911 q^{39} +18.1432 q^{40} -7.05441 q^{41} -22.3551 q^{42} +3.62781 q^{43} -3.42014 q^{44} -2.56592 q^{45} -5.42540 q^{46} +5.44070 q^{47} +17.9494 q^{48} +11.5207 q^{49} -3.94385 q^{50} -14.1860 q^{51} -0.979853 q^{52} -9.83848 q^{53} +10.3635 q^{54} +1.84330 q^{55} -30.5801 q^{56} -3.88491 q^{57} -22.0021 q^{58} +0.691090 q^{59} -24.2077 q^{60} -6.96355 q^{61} -15.7927 q^{62} +4.32483 q^{63} +5.60321 q^{64} +0.528095 q^{65} +3.75007 q^{66} -8.86068 q^{67} -33.5826 q^{68} +4.18291 q^{69} +28.5222 q^{70} +9.39470 q^{71} -7.14084 q^{72} +5.11110 q^{73} +16.6001 q^{74} +3.04066 q^{75} -9.19677 q^{76} -3.10685 q^{77} +1.07438 q^{78} -4.80909 q^{79} -22.9010 q^{80} -11.0049 q^{81} +18.3110 q^{82} -17.1284 q^{83} +40.8018 q^{84} +18.0995 q^{85} -9.41661 q^{86} +16.9634 q^{87} +5.12981 q^{88} -2.32434 q^{89} +6.66030 q^{90} -0.890098 q^{91} +9.90224 q^{92} +12.1760 q^{93} -14.1223 q^{94} +4.95663 q^{95} -18.1502 q^{96} -13.8575 q^{97} -29.9041 q^{98} -0.725489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9}+O(q^{10}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9	\( 152 q - 22 q^{2} - 18 q^{3} + 138 q^{4} - 59 q^{5} - 17 q^{6} - 19 q^{7} - 66 q^{8} + 106 q^{9} - 15 q^{10} - 40 q^{11} - 53 q^{12} - 59 q^{13} - 36 q^{14} - 40 q^{15} + 118 q^{16} - 93 q^{17} - 59 q^{18} - 16 q^{19} - 108 q^{20} - 62 q^{21} - 37 q^{22} - 107 q^{23} - 31 q^{24} + 101 q^{25} - 64 q^{26} - 63 q^{27} - 53 q^{28} - 124 q^{29} - 68 q^{30} - 15 q^{31} - 129 q^{32} - 49 q^{33} - 76 q^{35} + 45 q^{36} - 98 q^{37} - 125 q^{38} - 47 q^{39} - 7 q^{40} - 56 q^{41} - 84 q^{42} - 62 q^{43} - 114 q^{44} - 142 q^{45} - 3 q^{46} - 111 q^{47} - 92 q^{48} + 117 q^{49} - 64 q^{50} - 21 q^{51} - 85 q^{52} - 347 q^{53} + 3 q^{54} - 16 q^{55} - 73 q^{56} - 115 q^{57} - 29 q^{58} - 50 q^{59} - 54 q^{60} - 62 q^{61} - 55 q^{62} - 70 q^{63} + 64 q^{64} - 147 q^{65} + 34 q^{66} - 86 q^{67} - 174 q^{68} - 104 q^{69} - 7 q^{70} - 86 q^{71} - 139 q^{72} - 27 q^{73} - 52 q^{74} - 49 q^{75} - 11 q^{76} - 346 q^{77} - 59 q^{78} - 17 q^{79} - 149 q^{80} - 8 q^{81} - 31 q^{82} - 106 q^{83} - 51 q^{84} - 69 q^{85} - 85 q^{86} - 32 q^{87} - 113 q^{88} - 59 q^{89} + 10 q^{90} - 9 q^{91} - 314 q^{92} - 230 q^{93} + 7 q^{94} - 74 q^{95} - 54 q^{96} - 60 q^{97} - 77 q^{98} - 96 q^{99}+O(q^{100}) \) 152 * q - 22 * q^2 - 18 * q^3 + 138 * q^4 - 59 * q^5 - 17 * q^6 - 19 * q^7 - 66 * q^8 + 106 * q^9 - 15 * q^10 - 40 * q^11 - 53 * q^12 - 59 * q^13 - 36 * q^14 - 40 * q^15 + 118 * q^16 - 93 * q^17 - 59 * q^18 - 16 * q^19 - 108 * q^20 - 62 * q^21 - 37 * q^22 - 107 * q^23 - 31 * q^24 + 101 * q^25 - 64 * q^26 - 63 * q^27 - 53 * q^28 - 124 * q^29 - 68 * q^30 - 15 * q^31 - 129 * q^32 - 49 * q^33 - 76 * q^35 + 45 * q^36 - 98 * q^37 - 125 * q^38 - 47 * q^39 - 7 * q^40 - 56 * q^41 - 84 * q^42 - 62 * q^43 - 114 * q^44 - 142 * q^45 - 3 * q^46 - 111 * q^47 - 92 * q^48 + 117 * q^49 - 64 * q^50 - 21 * q^51 - 85 * q^52 - 347 * q^53 + 3 * q^54 - 16 * q^55 - 73 * q^56 - 115 * q^57 - 29 * q^58 - 50 * q^59 - 54 * q^60 - 62 * q^61 - 55 * q^62 - 70 * q^63 + 64 * q^64 - 147 * q^65 + 34 * q^66 - 86 * q^67 - 174 * q^68 - 104 * q^69 - 7 * q^70 - 86 * q^71 - 139 * q^72 - 27 * q^73 - 52 * q^74 - 49 * q^75 - 11 * q^76 - 346 * q^77 - 59 * q^78 - 17 * q^79 - 149 * q^80 - 8 * q^81 - 31 * q^82 - 106 * q^83 - 51 * q^84 - 69 * q^85 - 85 * q^86 - 32 * q^87 - 113 * q^88 - 59 * q^89 + 10 * q^90 - 9 * q^91 - 314 * q^92 - 230 * q^93 + 7 * q^94 - 74 * q^95 - 54 * q^96 - 60 * q^97 - 77 * q^98 - 96 * q^99

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