LMFDB - Embedded newform 8003.2.a.a.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8003,2,Mod(1,8003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8003, 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("8003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8003 = 53 \cdot 151 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8003.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:	$63.9042767376$
Analytic rank:	$1$
Dimension:	$147$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.45879 q^{2} -0.163481 q^{3} +4.04563 q^{4} +2.51114 q^{5} +0.401964 q^{6} -0.639591 q^{7} -5.02975 q^{8} -2.97327 q^{9} +O(q^{10})$	\(q-2.45879 q^{2} -0.163481 q^{3} +4.04563 q^{4} +2.51114 q^{5} +0.401964 q^{6} -0.639591 q^{7} -5.02975 q^{8} -2.97327 q^{9} -6.17435 q^{10} -5.68804 q^{11} -0.661382 q^{12} +1.34521 q^{13} +1.57262 q^{14} -0.410523 q^{15} +4.27584 q^{16} +5.25063 q^{17} +7.31064 q^{18} +4.61965 q^{19} +10.1591 q^{20} +0.104561 q^{21} +13.9857 q^{22} -1.52444 q^{23} +0.822269 q^{24} +1.30582 q^{25} -3.30757 q^{26} +0.976516 q^{27} -2.58755 q^{28} -6.90771 q^{29} +1.00939 q^{30} -0.243204 q^{31} -0.453855 q^{32} +0.929885 q^{33} -12.9102 q^{34} -1.60610 q^{35} -12.0288 q^{36} +6.20290 q^{37} -11.3587 q^{38} -0.219915 q^{39} -12.6304 q^{40} +2.88149 q^{41} -0.257093 q^{42} -9.62667 q^{43} -23.0117 q^{44} -7.46630 q^{45} +3.74826 q^{46} +4.62806 q^{47} -0.699018 q^{48} -6.59092 q^{49} -3.21072 q^{50} -0.858378 q^{51} +5.44220 q^{52} +1.00000 q^{53} -2.40104 q^{54} -14.2834 q^{55} +3.21699 q^{56} -0.755224 q^{57} +16.9846 q^{58} +11.9108 q^{59} -1.66082 q^{60} -4.95631 q^{61} +0.597987 q^{62} +1.90168 q^{63} -7.43574 q^{64} +3.37800 q^{65} -2.28639 q^{66} +11.9291 q^{67} +21.2421 q^{68} +0.249216 q^{69} +3.94906 q^{70} +2.25567 q^{71} +14.9548 q^{72} -7.77529 q^{73} -15.2516 q^{74} -0.213476 q^{75} +18.6894 q^{76} +3.63802 q^{77} +0.540725 q^{78} -7.56905 q^{79} +10.7372 q^{80} +8.76018 q^{81} -7.08497 q^{82} +13.7979 q^{83} +0.423014 q^{84} +13.1851 q^{85} +23.6699 q^{86} +1.12928 q^{87} +28.6094 q^{88} -11.0125 q^{89} +18.3580 q^{90} -0.860382 q^{91} -6.16730 q^{92} +0.0397592 q^{93} -11.3794 q^{94} +11.6006 q^{95} +0.0741966 q^{96} +0.418269 q^{97} +16.2057 q^{98} +16.9121 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) $ 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * 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 $

$2$	−2.45879	−1.73862	−0.869312	−	0.494264i	$-0.835438\pi$
$2$	−2.45879	−1.73862	−0.869312	+	0.494264i	$0.835438\pi$
$3$	−0.163481	−0.0943857	−0.0471929	−	0.998886i	$-0.515028\pi$
$3$	−0.163481	−0.0943857	−0.0471929	+	0.998886i	$0.515028\pi$
$4$	4.04563	2.02281
$5$	2.51114	1.12302	0.561508	−	0.827472i	$-0.310222\pi$
$5$	2.51114	1.12302	0.561508	+	0.827472i	$0.310222\pi$
$6$	0.401964	0.164101
$7$	−0.639591	−0.241743	−0.120871	−	0.992668i	$-0.538569\pi$
$7$	−0.639591	−0.241743	−0.120871	+	0.992668i	$0.538569\pi$
$8$	−5.02975	−1.77829
$9$	−2.97327	−0.991091
$10$	−6.17435	−1.95250
$11$	−5.68804	−1.71501	−0.857504	−	0.514478i	$-0.827986\pi$
$11$	−5.68804	−1.71501	−0.857504	+	0.514478i	$0.827986\pi$
$12$	−0.661382	−0.190925
$13$	1.34521	0.373093	0.186546	−	0.982446i	$-0.440271\pi$
$13$	1.34521	0.373093	0.186546	+	0.982446i	$0.440271\pi$
$14$	1.57262	0.420300
$15$	−0.410523	−0.105997
$16$	4.27584	1.06896
$17$	5.25063	1.27347	0.636733	−	0.771084i	$-0.280285\pi$
$17$	5.25063	1.27347	0.636733	+	0.771084i	$0.280285\pi$
$18$	7.31064	1.72314
$19$	4.61965	1.05982	0.529910	−	0.848054i	$-0.322226\pi$
$19$	4.61965	1.05982	0.529910	+	0.848054i	$0.322226\pi$
$20$	10.1591	2.27165
$21$	0.104561	0.0228171
$22$	13.9857	2.98175
$23$	−1.52444	−0.317867	−0.158933	−	0.987289i	$-0.550806\pi$
$23$	−1.52444	−0.317867	−0.158933	+	0.987289i	$0.550806\pi$
$24$	0.822269	0.167845
$25$	1.30582	0.261163
$26$	−3.30757	−0.648668
$27$	0.976516	0.187931
$28$	−2.58755	−0.489000
$29$	−6.90771	−1.28273	−0.641365	−	0.767236i	$-0.721631\pi$
$29$	−6.90771	−1.28273	−0.641365	+	0.767236i	$0.721631\pi$
$30$	1.00939	0.184288
$31$	−0.243204	−0.0436807	−0.0218404	−	0.999761i	$-0.506953\pi$
$31$	−0.243204	−0.0436807	−0.0218404	+	0.999761i	$0.506953\pi$
$32$	−0.453855	−0.0802310
$33$	0.929885	0.161872
$34$	−12.9102	−2.21408
$35$	−1.60610	−0.271481
$36$	−12.0288	−2.00479
$37$	6.20290	1.01975	0.509875	−	0.860249i	$-0.329692\pi$
$37$	6.20290	1.01975	0.509875	+	0.860249i	$0.329692\pi$
$38$	−11.3587	−1.84263
$39$	−0.219915	−0.0352146
$40$	−12.6304	−1.99704
$41$	2.88149	0.450014	0.225007	−	0.974357i	$-0.427760\pi$
$41$	2.88149	0.450014	0.225007	+	0.974357i	$0.427760\pi$
$42$	−0.257093	−0.0396703
$43$	−9.62667	−1.46805	−0.734026	−	0.679121i	$-0.762361\pi$
$43$	−9.62667	−1.46805	−0.734026	+	0.679121i	$0.762361\pi$
$44$	−23.0117	−3.46914
$45$	−7.46630	−1.11301
$46$	3.74826	0.552651
$47$	4.62806	0.675072	0.337536	−	0.941313i	$-0.390406\pi$
$47$	4.62806	0.675072	0.337536	+	0.941313i	$0.390406\pi$
$48$	−0.699018	−0.100894
$49$	−6.59092	−0.941560
$50$	−3.21072	−0.454064
$51$	−0.858378	−0.120197
$52$	5.44220	0.754697
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−2.40104	−0.326741
$55$	−14.2834	−1.92598
$56$	3.21699	0.429888
$57$	−0.755224	−0.100032
$58$	16.9846	2.23018
$59$	11.9108	1.55066	0.775330	−	0.631556i	$-0.217584\pi$
$59$	11.9108	1.55066	0.775330	+	0.631556i	$0.217584\pi$
$60$	−1.66082	−0.214411
$61$	−4.95631	−0.634590	−0.317295	−	0.948327i	$-0.602775\pi$
$61$	−4.95631	−0.634590	−0.317295	+	0.948327i	$0.602775\pi$
$62$	0.597987	0.0759444
$63$	1.90168	0.239589
$64$	−7.43574	−0.929468
$65$	3.37800	0.418989
$66$	−2.28639	−0.281435
$67$	11.9291	1.45738	0.728689	−	0.684845i	$-0.240130\pi$
$67$	11.9291	1.45738	0.728689	+	0.684845i	$0.240130\pi$
$68$	21.2421	2.57598
$69$	0.249216	0.0300021
$70$	3.94906	0.472003
$71$	2.25567	0.267699	0.133850	−	0.991002i	$-0.457266\pi$
$71$	2.25567	0.267699	0.133850	+	0.991002i	$0.457266\pi$
$72$	14.9548	1.76244
$73$	−7.77529	−0.910029	−0.455015	−	0.890484i	$-0.650366\pi$
$73$	−7.77529	−0.910029	−0.455015	+	0.890484i	$0.650366\pi$
$74$	−15.2516	−1.77296
$75$	−0.213476	−0.0246501
$76$	18.6894	2.14382
$77$	3.63802	0.414591
$78$	0.540725	0.0612250
$79$	−7.56905	−0.851585	−0.425792	−	0.904821i	$-0.640005\pi$
$79$	−7.56905	−0.851585	−0.425792	+	0.904821i	$0.640005\pi$
$80$	10.7372	1.20046
$81$	8.76018	0.973353
$82$	−7.08497	−0.782404
$83$	13.7979	1.51452	0.757260	−	0.653114i	$-0.226538\pi$
$83$	13.7979	1.51452	0.757260	+	0.653114i	$0.226538\pi$
$84$	0.423014	0.0461547
$85$	13.1851	1.43012
$86$	23.6699	2.55239
$87$	1.12928	0.121071
$88$	28.6094	3.04978
$89$	−11.0125	−1.16732	−0.583659	−	0.811999i	$-0.698380\pi$
$89$	−11.0125	−1.16732	−0.583659	+	0.811999i	$0.698380\pi$
$90$	18.3580	1.93511
$91$	−0.860382	−0.0901925
$92$	−6.16730	−0.642985
$93$	0.0397592	0.00412284
$94$	−11.3794	−1.17370
$95$	11.6006	1.19019
$96$	0.0741966	0.00757266
$97$	0.418269	0.0424687	0.0212344	−	0.999775i	$-0.493240\pi$
$97$	0.418269	0.0424687	0.0212344	+	0.999775i	$0.493240\pi$
$98$	16.2057	1.63702
$99$	16.9121	1.69973
$100$	5.28284	0.528284
$101$	6.94921	0.691473	0.345736	−	0.938332i	$-0.387629\pi$
$101$	6.94921	0.691473	0.345736	+	0.938332i	$0.387629\pi$
$102$	2.11057	0.208977
$103$	−13.7826	−1.35804	−0.679021	−	0.734119i	$-0.737595\pi$
$103$	−13.7826	−1.35804	−0.679021	+	0.734119i	$0.737595\pi$
$104$	−6.76606	−0.663466
$105$	0.262567	0.0256239
$106$	−2.45879	−0.238818
$107$	6.00385	0.580414	0.290207	−	0.956964i	$-0.406276\pi$
$107$	6.00385	0.580414	0.290207	+	0.956964i	$0.406276\pi$
$108$	3.95062	0.380148
$109$	−10.9865	−1.05232	−0.526159	−	0.850386i	$-0.676368\pi$
$109$	−10.9865	−1.05232	−0.526159	+	0.850386i	$0.676368\pi$
$110$	35.1199	3.34855
$111$	−1.01405	−0.0962498
$112$	−2.73479	−0.258413
$113$	19.2343	1.80941	0.904706	−	0.426036i	$-0.140090\pi$
$113$	19.2343	1.80941	0.904706	+	0.426036i	$0.140090\pi$
$114$	1.85693	0.173918
$115$	−3.82807	−0.356969
$116$	−27.9460	−2.59472
$117$	−3.99967	−0.369769
$118$	−29.2862	−2.69601
$119$	−3.35826	−0.307851
$120$	2.06483	0.188492
$121$	21.3538	1.94125
$122$	12.1865	1.10331
$123$	−0.471069	−0.0424749
$124$	−0.983912	−0.0883580
$125$	−9.27661	−0.829725
$126$	−4.67582	−0.416555
$127$	4.58335	0.406706	0.203353	−	0.979105i	$-0.434816\pi$
$127$	4.58335	0.406706	0.203353	+	0.979105i	$0.434816\pi$
$128$	19.1906	1.69623
$129$	1.57378	0.138563
$130$	−8.30577	−0.728464
$131$	−2.53601	−0.221572	−0.110786	−	0.993844i	$-0.535337\pi$
$131$	−2.53601	−0.221572	−0.110786	+	0.993844i	$0.535337\pi$
$132$	3.76197	0.327437
$133$	−2.95468	−0.256204
$134$	−29.3312	−2.53383
$135$	2.45217	0.211049
$136$	−26.4094	−2.26459
$137$	−19.9157	−1.70151	−0.850755	−	0.525562i	$-0.823855\pi$
$137$	−19.9157	−1.70151	−0.850755	+	0.525562i	$0.823855\pi$
$138$	−0.612769	−0.0521624
$139$	7.22358	0.612696	0.306348	−	0.951920i	$-0.400893\pi$
$139$	7.22358	0.612696	0.306348	+	0.951920i	$0.400893\pi$
$140$	−6.49769	−0.549155
$141$	−0.756600	−0.0637172
$142$	−5.54621	−0.465428
$143$	−7.65158	−0.639857
$144$	−12.7132	−1.05944
$145$	−17.3462	−1.44052
$146$	19.1178	1.58220
$147$	1.07749	0.0888699
$148$	25.0946	2.06276
$149$	−2.83142	−0.231959	−0.115980	−	0.993252i	$-0.537001\pi$
$149$	−2.83142	−0.231959	−0.115980	+	0.993252i	$0.537001\pi$
$150$	0.524891	0.0428572
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	−23.2357	−1.88466
$153$	−15.6116	−1.26212
$154$	−8.94511	−0.720817
$155$	−0.610719	−0.0490541
$156$	−0.889695	−0.0712326
$157$	−14.5132	−1.15828	−0.579139	−	0.815229i	$-0.696611\pi$
$157$	−14.5132	−1.15828	−0.579139	+	0.815229i	$0.696611\pi$
$158$	18.6107	1.48059
$159$	−0.163481	−0.0129649
$160$	−1.13969	−0.0901006
$161$	0.975016	0.0768420
$162$	−21.5394	−1.69230
$163$	1.27171	0.0996081	0.0498041	−	0.998759i	$-0.484140\pi$
$163$	1.27171	0.0996081	0.0498041	+	0.998759i	$0.484140\pi$
$164$	11.6574	0.910293
$165$	2.33507	0.181785
$166$	−33.9262	−2.63318
$167$	1.11890	0.0865827	0.0432914	−	0.999062i	$-0.486216\pi$
$167$	1.11890	0.0865827	0.0432914	+	0.999062i	$0.486216\pi$
$168$	−0.525916	−0.0405753
$169$	−11.1904	−0.860802
$170$	−32.4192	−2.48644
$171$	−13.7355	−1.05038
$172$	−38.9459	−2.96960
$173$	8.97934	0.682687	0.341343	−	0.939939i	$-0.389118\pi$
$173$	8.97934	0.682687	0.341343	+	0.939939i	$0.389118\pi$
$174$	−2.77665	−0.210497
$175$	−0.835188	−0.0631343
$176$	−24.3211	−1.83327
$177$	−1.94720	−0.146360
$178$	27.0773	2.02953
$179$	7.82325	0.584737	0.292368	−	0.956306i	$-0.405557\pi$
$179$	7.82325	0.584737	0.292368	+	0.956306i	$0.405557\pi$
$180$	−30.2059	−2.25141
$181$	−14.3433	−1.06613	−0.533065	−	0.846075i	$-0.678960\pi$
$181$	−14.3433	−1.06613	−0.533065	+	0.846075i	$0.678960\pi$
$182$	2.11549	0.156811
$183$	0.810262	0.0598963
$184$	7.66754	0.565259
$185$	15.5763	1.14519
$186$	−0.0977594	−0.00716806
$187$	−29.8658	−2.18400
$188$	18.7234	1.36555
$189$	−0.624571	−0.0454309
$190$	−28.5233	−2.06930
$191$	−13.8032	−0.998764	−0.499382	−	0.866382i	$-0.666440\pi$
$191$	−13.8032	−0.998764	−0.499382	+	0.866382i	$0.666440\pi$
$192$	1.21560	0.0877285
$193$	13.6730	0.984201	0.492101	−	0.870538i	$-0.336229\pi$
$193$	13.6730	0.984201	0.492101	+	0.870538i	$0.336229\pi$
$194$	−1.02843	−0.0738372
$195$	−0.552238	−0.0395466
$196$	−26.6644	−1.90460
$197$	−0.865649	−0.0616749	−0.0308375	−	0.999524i	$-0.509817\pi$
$197$	−0.865649	−0.0616749	−0.0308375	+	0.999524i	$0.509817\pi$
$198$	−41.5832	−2.95519
$199$	−14.6590	−1.03915	−0.519574	−	0.854425i	$-0.673909\pi$
$199$	−14.6590	−1.03915	−0.519574	+	0.854425i	$0.673909\pi$
$200$	−6.56793	−0.464423
$201$	−1.95019	−0.137556
$202$	−17.0866	−1.20221
$203$	4.41811	0.310090
$204$	−3.47268	−0.243136
$205$	7.23583	0.505372
$206$	33.8885	2.36112
$207$	4.53257	0.315035
$208$	5.75188	0.398821
$209$	−26.2767	−1.81760
$210$	−0.645596	−0.0445503
$211$	15.4335	1.06249	0.531243	−	0.847220i	$-0.321725\pi$
$211$	15.4335	1.06249	0.531243	+	0.847220i	$0.321725\pi$
$212$	4.04563	0.277855
$213$	−0.368759	−0.0252670
$214$	−14.7622	−1.00912
$215$	−24.1739	−1.64865
$216$	−4.91164	−0.334195
$217$	0.155551	0.0105595
$218$	27.0135	1.82959
$219$	1.27111	0.0858938
$220$	−57.7855	−3.89590
$221$	7.06318	0.475121
$222$	2.49334	0.167342
$223$	−5.18587	−0.347271	−0.173636	−	0.984810i	$-0.555552\pi$
$223$	−5.18587	−0.347271	−0.173636	+	0.984810i	$0.555552\pi$
$224$	0.290282	0.0193953
$225$	−3.88255	−0.258836
$226$	−47.2931	−3.14589
$227$	−0.224257	−0.0148845	−0.00744223	−	0.999972i	$-0.502369\pi$
$227$	−0.224257	−0.0148845	−0.00744223	+	0.999972i	$0.502369\pi$
$228$	−3.05535	−0.202346
$229$	6.21676	0.410815	0.205407	−	0.978677i	$-0.434148\pi$
$229$	6.21676	0.410815	0.205407	+	0.978677i	$0.434148\pi$
$230$	9.41240	0.620635
$231$	−0.594746	−0.0391314
$232$	34.7441	2.28106
$233$	−22.6049	−1.48090	−0.740449	−	0.672112i	$-0.765387\pi$
$233$	−22.6049	−1.48090	−0.740449	+	0.672112i	$0.765387\pi$
$234$	9.83432	0.642890
$235$	11.6217	0.758117
$236$	48.1868	3.13670
$237$	1.23740	0.0803775
$238$	8.25724	0.535237
$239$	−18.1955	−1.17697	−0.588485	−	0.808508i	$-0.700275\pi$
$239$	−18.1955	−1.17697	−0.588485	+	0.808508i	$0.700275\pi$
$240$	−1.75533	−0.113306
$241$	7.68324	0.494921	0.247461	−	0.968898i	$-0.420404\pi$
$241$	7.68324	0.494921	0.247461	+	0.968898i	$0.420404\pi$
$242$	−52.5043	−3.37511
$243$	−4.36167	−0.279801
$244$	−20.0514	−1.28366
$245$	−16.5507	−1.05739
$246$	1.15826	0.0738478
$247$	6.21437	0.395411
$248$	1.22326	0.0776769
$249$	−2.25570	−0.142949
$250$	22.8092	1.44258
$251$	−16.5928	−1.04733	−0.523664	−	0.851925i	$-0.675435\pi$
$251$	−16.5928	−1.04733	−0.523664	+	0.851925i	$0.675435\pi$
$252$	7.69348	0.484644
$253$	8.67105	0.545144
$254$	−11.2695	−0.707109
$255$	−2.15551	−0.134983
$256$	−32.3141	−2.01963
$257$	−14.2577	−0.889369	−0.444684	−	0.895687i	$-0.646684\pi$
$257$	−14.2577	−0.889369	−0.444684	+	0.895687i	$0.646684\pi$
$258$	−3.86958	−0.240909
$259$	−3.96732	−0.246517
$260$	13.6661	0.847536
$261$	20.5385	1.27130
$262$	6.23550	0.385231
$263$	−20.6720	−1.27469	−0.637344	−	0.770579i	$-0.719967\pi$
$263$	−20.6720	−1.27469	−0.637344	+	0.770579i	$0.719967\pi$
$264$	−4.67709	−0.287855
$265$	2.51114	0.154258
$266$	7.26494	0.445442
$267$	1.80033	0.110178
$268$	48.2609	2.94800
$269$	−6.79786	−0.414473	−0.207237	−	0.978291i	$-0.566447\pi$
$269$	−6.79786	−0.414473	−0.207237	+	0.978291i	$0.566447\pi$
$270$	−6.02935	−0.366935
$271$	7.46705	0.453591	0.226796	−	0.973942i	$-0.427175\pi$
$271$	7.46705	0.453591	0.226796	+	0.973942i	$0.427175\pi$
$272$	22.4509	1.36128
$273$	0.140656	0.00851289
$274$	48.9684	2.95829
$275$	−7.42752	−0.447897
$276$	1.00824	0.0606886
$277$	−11.1208	−0.668183	−0.334092	−	0.942541i	$-0.608429\pi$
$277$	−11.1208	−0.668183	−0.334092	+	0.942541i	$0.608429\pi$
$278$	−17.7612	−1.06525
$279$	0.723112	0.0432916
$280$	8.07830	0.482771
$281$	−26.3970	−1.57472	−0.787358	−	0.616496i	$-0.788552\pi$
$281$	−26.3970	−1.57472	−0.787358	+	0.616496i	$0.788552\pi$
$282$	1.86032	0.110780
$283$	25.4068	1.51028	0.755140	−	0.655564i	$-0.227569\pi$
$283$	25.4068	1.51028	0.755140	+	0.655564i	$0.227569\pi$
$284$	9.12560	0.541505
$285$	−1.89647	−0.112337
$286$	18.8136	1.11247
$287$	−1.84298	−0.108788
$288$	1.34943	0.0795162
$289$	10.5692	0.621715
$290$	42.6506	2.50453
$291$	−0.0683789	−0.00400844
$292$	−31.4559	−1.84082
$293$	−9.13894	−0.533903	−0.266951	−	0.963710i	$-0.586016\pi$
$293$	−9.13894	−0.533903	−0.266951	+	0.963710i	$0.586016\pi$
$294$	−2.64932	−0.154511
$295$	29.9098	1.74141
$296$	−31.1990	−1.81341
$297$	−5.55446	−0.322302
$298$	6.96186	0.403290
$299$	−2.05068	−0.118594
$300$	−0.863643	−0.0498625
$301$	6.15713	0.354891
$302$	−2.45879	−0.141487
$303$	−1.13606	−0.0652651
$304$	19.7529	1.13290
$305$	−12.4460	−0.712655
$306$	38.3855	2.19435
$307$	−6.31017	−0.360141	−0.180070	−	0.983654i	$-0.557633\pi$
$307$	−6.31017	−0.360141	−0.180070	+	0.983654i	$0.557633\pi$
$308$	14.7181	0.838639
$309$	2.25319	0.128180
$310$	1.50163	0.0852867
$311$	1.92242	0.109010	0.0545052	−	0.998513i	$-0.482642\pi$
$311$	1.92242	0.109010	0.0545052	+	0.998513i	$0.482642\pi$
$312$	1.10612	0.0626217
$313$	0.168129	0.00950319	0.00475159	−	0.999989i	$-0.498488\pi$
$313$	0.168129	0.00950319	0.00475159	+	0.999989i	$0.498488\pi$
$314$	35.6848	2.01381
$315$	4.77538	0.269062
$316$	−30.6216	−1.72260
$317$	10.8122	0.607271	0.303636	−	0.952788i	$-0.401799\pi$
$317$	10.8122	0.607271	0.303636	+	0.952788i	$0.401799\pi$
$318$	0.401964	0.0225410
$319$	39.2913	2.19989
$320$	−18.6722	−1.04381
$321$	−0.981515	−0.0547828
$322$	−2.39735	−0.133599
$323$	24.2561	1.34964
$324$	35.4404	1.96891
$325$	1.75659	0.0974381
$326$	−3.12687	−0.173181
$327$	1.79609	0.0993238
$328$	−14.4932	−0.800253
$329$	−2.96007	−0.163194
$330$	−5.74144	−0.316056
$331$	31.1262	1.71085	0.855425	−	0.517927i	$-0.173296\pi$
$331$	31.1262	1.71085	0.855425	+	0.517927i	$0.173296\pi$
$332$	55.8213	3.06359
$333$	−18.4429	−1.01067
$334$	−2.75112	−0.150535
$335$	29.9557	1.63666
$336$	0.447085	0.0243905
$337$	−14.7541	−0.803708	−0.401854	−	0.915704i	$-0.631634\pi$
$337$	−14.7541	−0.803708	−0.401854	+	0.915704i	$0.631634\pi$
$338$	27.5148	1.49661
$339$	−3.14444	−0.170783
$340$	53.3418	2.89287
$341$	1.38335	0.0749128
$342$	33.7726	1.82621
$343$	8.69263	0.469358
$344$	48.4198	2.61062
$345$	0.625816	0.0336928
$346$	−22.0783	−1.18694
$347$	6.55902	0.352107	0.176053	−	0.984381i	$-0.443667\pi$
$347$	6.55902	0.352107	0.176053	+	0.984381i	$0.443667\pi$
$348$	4.56864	0.244905
$349$	−33.4639	−1.79128	−0.895640	−	0.444781i	$-0.853282\pi$
$349$	−33.4639	−1.79128	−0.895640	+	0.444781i	$0.853282\pi$
$350$	2.05355	0.109767
$351$	1.31361	0.0701156
$352$	2.58154	0.137597
$353$	16.6139	0.884267	0.442134	−	0.896949i	$-0.354222\pi$
$353$	16.6139	0.884267	0.442134	+	0.896949i	$0.354222\pi$
$354$	4.78774	0.254465
$355$	5.66430	0.300630
$356$	−44.5523	−2.36127
$357$	0.549011	0.0290567
$358$	−19.2357	−1.01664
$359$	26.9513	1.42243	0.711217	−	0.702973i	$-0.248144\pi$
$359$	26.9513	1.42243	0.711217	+	0.702973i	$0.248144\pi$
$360$	37.5537	1.97925
$361$	2.34113	0.123217
$362$	35.2671	1.85360
$363$	−3.49093	−0.183226
$364$	−3.48078	−0.182443
$365$	−19.5248	−1.02198
$366$	−1.99226	−0.104137
$367$	−35.2853	−1.84188	−0.920938	−	0.389709i	$-0.872575\pi$
$367$	−35.2853	−1.84188	−0.920938	+	0.389709i	$0.872575\pi$
$368$	−6.51824	−0.339787
$369$	−8.56747	−0.446005
$370$	−38.2988	−1.99106
$371$	−0.639591	−0.0332059
$372$	0.160851	0.00833973
$373$	0.543384	0.0281354	0.0140677	−	0.999901i	$-0.495522\pi$
$373$	0.543384	0.0281354	0.0140677	+	0.999901i	$0.495522\pi$
$374$	73.4336	3.79716
$375$	1.51655	0.0783142
$376$	−23.2780	−1.20047
$377$	−9.29229	−0.478577
$378$	1.53569	0.0789872
$379$	20.8184	1.06937	0.534684	−	0.845052i	$-0.320431\pi$
$379$	20.8184	1.06937	0.534684	+	0.845052i	$0.320431\pi$
$380$	46.9316	2.40754
$381$	−0.749289	−0.0383873
$382$	33.9391	1.73648
$383$	27.6078	1.41069	0.705346	−	0.708863i	$-0.250792\pi$
$383$	27.6078	1.41069	0.705346	+	0.708863i	$0.250792\pi$
$384$	−3.13730	−0.160099
$385$	9.13557	0.465592
$386$	−33.6189	−1.71116
$387$	28.6227	1.45497
$388$	1.69216	0.0859063
$389$	−16.8728	−0.855487	−0.427744	−	0.903900i	$-0.640691\pi$
$389$	−16.8728	−0.855487	−0.427744	+	0.903900i	$0.640691\pi$
$390$	1.35783	0.0687566
$391$	−8.00426	−0.404793
$392$	33.1507	1.67436
$393$	0.414589	0.0209133
$394$	2.12844	0.107230
$395$	−19.0069	−0.956343
$396$	68.4200	3.43823
$397$	−22.9779	−1.15323	−0.576614	−	0.817017i	$-0.695626\pi$
$397$	−22.9779	−1.15323	−0.576614	+	0.817017i	$0.695626\pi$
$398$	36.0433	1.80669
$399$	0.483034	0.0241820
$400$	5.58345	0.279173
$401$	20.0975	1.00362	0.501810	−	0.864978i	$-0.332668\pi$
$401$	20.0975	1.00362	0.501810	+	0.864978i	$0.332668\pi$
$402$	4.79509	0.239157
$403$	−0.327159	−0.0162970
$404$	28.1139	1.39872
$405$	21.9980	1.09309
$406$	−10.8632	−0.539131
$407$	−35.2823	−1.74888
$408$	4.31743	0.213745
$409$	−6.79876	−0.336177	−0.168089	−	0.985772i	$-0.553759\pi$
$409$	−6.79876	−0.336177	−0.168089	+	0.985772i	$0.553759\pi$
$410$	−17.7913	−0.878652
$411$	3.25583	0.160598
$412$	−55.7593	−2.74706
$413$	−7.61807	−0.374861
$414$	−11.1446	−0.547728
$415$	34.6485	1.70083
$416$	−0.610528	−0.0299336
$417$	−1.18092	−0.0578298
$418$	64.6088	3.16012
$419$	11.8466	0.578746	0.289373	−	0.957216i	$-0.406553\pi$
$419$	11.8466	0.578746	0.289373	+	0.957216i	$0.406553\pi$
$420$	1.06225	0.0518324
$421$	−0.360762	−0.0175824	−0.00879122	−	0.999961i	$-0.502798\pi$
$421$	−0.360762	−0.0175824	−0.00879122	+	0.999961i	$0.502798\pi$
$422$	−37.9476	−1.84726
$423$	−13.7605	−0.669058
$424$	−5.02975	−0.244266
$425$	6.85636	0.332582
$426$	0.906700	0.0439297
$427$	3.17001	0.153408
$428$	24.2893	1.17407
$429$	1.25089	0.0603934
$430$	59.4384	2.86637
$431$	−16.0832	−0.774699	−0.387349	−	0.921933i	$-0.626609\pi$
$431$	−16.0832	−0.774699	−0.387349	+	0.921933i	$0.626609\pi$
$432$	4.17542	0.200890
$433$	−38.8189	−1.86552	−0.932758	−	0.360503i	$-0.882605\pi$
$433$	−38.8189	−1.86552	−0.932758	+	0.360503i	$0.882605\pi$
$434$	−0.382467	−0.0183590
$435$	2.83577	0.135965
$436$	−44.4474	−2.12864
$437$	−7.04236	−0.336882
$438$	−3.12539	−0.149337
$439$	−9.95558	−0.475154	−0.237577	−	0.971369i	$-0.576353\pi$
$439$	−9.95558	−0.475154	−0.237577	+	0.971369i	$0.576353\pi$
$440$	71.8422	3.42494
$441$	19.5966	0.933172
$442$	−17.3668	−0.826057
$443$	−10.8454	−0.515280	−0.257640	−	0.966241i	$-0.582945\pi$
$443$	−10.8454	−0.515280	−0.257640	+	0.966241i	$0.582945\pi$
$444$	−4.10249	−0.194695
$445$	−27.6538	−1.31092
$446$	12.7509	0.603774
$447$	0.462884	0.0218936
$448$	4.75583	0.224692
$449$	24.8980	1.17501	0.587505	−	0.809220i	$-0.300110\pi$
$449$	24.8980	1.17501	0.587505	+	0.809220i	$0.300110\pi$
$450$	9.54635	0.450019
$451$	−16.3900	−0.771777
$452$	77.8148	3.66010
$453$	−0.163481	−0.00768100
$454$	0.551400	0.0258785
$455$	−2.16054	−0.101288
$456$	3.79859	0.177885
$457$	−29.4961	−1.37977	−0.689884	−	0.723920i	$-0.742339\pi$
$457$	−29.4961	−1.37977	−0.689884	+	0.723920i	$0.742339\pi$
$458$	−15.2857	−0.714252
$459$	5.12733	0.239323
$460$	−15.4869	−0.722082
$461$	−3.68421	−0.171591	−0.0857953	−	0.996313i	$-0.527343\pi$
$461$	−3.68421	−0.171591	−0.0857953	+	0.996313i	$0.527343\pi$
$462$	1.46235	0.0680349
$463$	4.98360	0.231608	0.115804	−	0.993272i	$-0.463056\pi$
$463$	4.98360	0.231608	0.115804	+	0.993272i	$0.463056\pi$
$464$	−29.5362	−1.37118
$465$	0.0998409	0.00463001
$466$	55.5807	2.57473
$467$	40.2120	1.86079	0.930394	−	0.366561i	$-0.119465\pi$
$467$	40.2120	1.86079	0.930394	+	0.366561i	$0.119465\pi$
$468$	−16.1811	−0.747974
$469$	−7.62978	−0.352310
$470$	−28.5753	−1.31808
$471$	2.37263	0.109325
$472$	−59.9086	−2.75752
$473$	54.7568	2.51772
$474$	−3.04249	−0.139746
$475$	6.03240	0.276786
$476$	−13.5863	−0.622725
$477$	−2.97327	−0.136137
$478$	44.7389	2.04631
$479$	−5.04285	−0.230414	−0.115207	−	0.993342i	$-0.536753\pi$
$479$	−5.04285	−0.230414	−0.115207	+	0.993342i	$0.536753\pi$
$480$	0.186318	0.00850421
$481$	8.34417	0.380461
$482$	−18.8914	−0.860482
$483$	−0.159396	−0.00725279
$484$	86.3893	3.92679
$485$	1.05033	0.0476930
$486$	10.7244	0.486469
$487$	−27.2879	−1.23653	−0.618267	−	0.785968i	$-0.712165\pi$
$487$	−27.2879	−1.23653	−0.618267	+	0.785968i	$0.712165\pi$
$488$	24.9290	1.12848
$489$	−0.207900	−0.00940159
$490$	40.6947	1.83840
$491$	−2.66863	−0.120434	−0.0602168	−	0.998185i	$-0.519179\pi$
$491$	−2.66863	−0.120434	−0.0602168	+	0.998185i	$0.519179\pi$
$492$	−1.90577	−0.0859187
$493$	−36.2698	−1.63351
$494$	−15.2798	−0.687471
$495$	42.4686	1.90882
$496$	−1.03990	−0.0466929
$497$	−1.44271	−0.0647143
$498$	5.54628	0.248535
$499$	−31.7130	−1.41967	−0.709834	−	0.704369i	$-0.751230\pi$
$499$	−31.7130	−1.41967	−0.709834	+	0.704369i	$0.751230\pi$
$500$	−37.5297	−1.67838
$501$	−0.182918	−0.00817218
$502$	40.7981	1.82091
$503$	−38.0888	−1.69830	−0.849148	−	0.528155i	$-0.822884\pi$
$503$	−38.0888	−1.69830	−0.849148	+	0.528155i	$0.822884\pi$
$504$	−9.56498	−0.426058
$505$	17.4504	0.776534
$506$	−21.3202	−0.947801
$507$	1.82942	0.0812474
$508$	18.5425	0.822691
$509$	−10.8313	−0.480088	−0.240044	−	0.970762i	$-0.577162\pi$
$509$	−10.8313	−0.480088	−0.240044	+	0.970762i	$0.577162\pi$
$510$	5.29993	0.234685
$511$	4.97301	0.219993
$512$	41.0722	1.81515
$513$	4.51116	0.199173
$514$	35.0565	1.54628
$515$	−34.6100	−1.52510
$516$	6.36691	0.280287
$517$	−26.3246	−1.15775
$518$	9.75478	0.428601
$519$	−1.46795	−0.0644359
$520$	−16.9905	−0.745083
$521$	18.6624	0.817613	0.408807	−	0.912621i	$-0.365945\pi$
$521$	18.6624	0.817613	0.408807	+	0.912621i	$0.365945\pi$
$522$	−50.4998	−2.21032
$523$	−13.5208	−0.591224	−0.295612	−	0.955308i	$-0.595524\pi$
$523$	−13.5208	−0.591224	−0.295612	+	0.955308i	$0.595524\pi$
$524$	−10.2597	−0.448199
$525$	0.136537	0.00595897
$526$	50.8279	2.21620
$527$	−1.27698	−0.0556259
$528$	3.97604	0.173035
$529$	−20.6761	−0.898961
$530$	−6.17435	−0.268197
$531$	−35.4142	−1.53685
$532$	−11.9535	−0.518252
$533$	3.87620	0.167897
$534$	−4.42662	−0.191558
$535$	15.0765	0.651814
$536$	−60.0007	−2.59163
$537$	−1.27895	−0.0551908
$538$	16.7145	0.720613
$539$	37.4894	1.61478
$540$	9.92055	0.426912
$541$	−0.00922763	−0.000396727 0	−0.000198363	−	1.00000i	$-0.500063\pi$
$541$	−0.00922763	−0.000396727 0	−0.000198363		1.00000i	$0.500063\pi$
$542$	−18.3599	−0.788624
$543$	2.34486	0.100627
$544$	−2.38303	−0.102171
$545$	−27.5887	−1.18177
$546$	−0.345843	−0.0148007
$547$	−20.6713	−0.883843	−0.441921	−	0.897054i	$-0.645703\pi$
$547$	−20.6713	−0.883843	−0.441921	+	0.897054i	$0.645703\pi$
$548$	−80.5714	−3.44184
$549$	14.7365	0.628937
$550$	18.2627	0.778724
$551$	−31.9112	−1.35946
$552$	−1.25350	−0.0533523
$553$	4.84110	0.205864
$554$	27.3436	1.16172
$555$	−2.54643	−0.108090
$556$	29.2239	1.23937
$557$	25.7183	1.08972	0.544860	−	0.838527i	$-0.316583\pi$
$557$	25.7183	1.08972	0.544860	+	0.838527i	$0.316583\pi$
$558$	−1.77798	−0.0752678
$559$	−12.9498	−0.547720
$560$	−6.86743	−0.290202
$561$	4.88249	0.206139
$562$	64.9047	2.73784
$563$	−28.0553	−1.18239	−0.591196	−	0.806528i	$-0.701344\pi$
$563$	−28.0553	−1.18239	−0.591196	+	0.806528i	$0.701344\pi$
$564$	−3.06092	−0.128888
$565$	48.3000	2.03200
$566$	−62.4700	−2.62581
$567$	−5.60293	−0.235301
$568$	−11.3455	−0.476046
$569$	7.89047	0.330786	0.165393	−	0.986228i	$-0.447111\pi$
$569$	7.89047	0.330786	0.165393	+	0.986228i	$0.447111\pi$
$570$	4.66302	0.195312
$571$	4.73324	0.198080	0.0990399	−	0.995083i	$-0.468423\pi$
$571$	4.73324	0.198080	0.0990399	+	0.995083i	$0.468423\pi$
$572$	−30.9554	−1.29431
$573$	2.25656	0.0942691
$574$	4.53149	0.189141
$575$	−1.99063	−0.0830151
$576$	22.1085	0.921187
$577$	13.9850	0.582205	0.291103	−	0.956692i	$-0.405978\pi$
$577$	13.9850	0.582205	0.291103	+	0.956692i	$0.405978\pi$
$578$	−25.9873	−1.08093
$579$	−2.23527	−0.0928946
$580$	−70.1763	−2.91391
$581$	−8.82504	−0.366124
$582$	0.168129	0.00696918
$583$	−5.68804	−0.235574
$584$	39.1078	1.61829
$585$	−10.0437	−0.415256
$586$	22.4707	0.928256
$587$	23.9255	0.987509	0.493755	−	0.869601i	$-0.335624\pi$
$587$	23.9255	0.987509	0.493755	+	0.869601i	$0.335624\pi$
$588$	4.35912	0.179767
$589$	−1.12352	−0.0462937
$590$	−73.5417	−3.02767
$591$	0.141517	0.00582123
$592$	26.5226	1.09007
$593$	−0.0384772	−0.00158007	−0.000790035	−	1.00000i	$-0.500251\pi$
$593$	−0.0384772	−0.00158007	−0.000790035		1.00000i	$0.500251\pi$
$594$	13.6572	0.560363
$595$	−8.43305	−0.345721
$596$	−11.4549	−0.469210
$597$	2.39647	0.0980808
$598$	5.04218	0.206190
$599$	−23.7995	−0.972421	−0.486211	−	0.873842i	$-0.661621\pi$
$599$	−23.7995	−0.972421	−0.486211	+	0.873842i	$0.661621\pi$
$600$	1.07373	0.0438349
$601$	20.3267	0.829141	0.414571	−	0.910017i	$-0.363932\pi$
$601$	20.3267	0.829141	0.414571	+	0.910017i	$0.363932\pi$
$602$	−15.1391	−0.617022
$603$	−35.4686	−1.44439
$604$	4.04563	0.164614
$605$	53.6223	2.18005
$606$	2.79334	0.113472
$607$	−33.6688	−1.36657	−0.683287	−	0.730150i	$-0.739450\pi$
$607$	−33.6688	−1.36657	−0.683287	+	0.730150i	$0.739450\pi$
$608$	−2.09665	−0.0850303
$609$	−0.722276	−0.0292681
$610$	30.6020	1.23904
$611$	6.22570	0.251865
$612$	−63.1586	−2.55303
$613$	−48.4627	−1.95739	−0.978695	−	0.205321i	$-0.934176\pi$
$613$	−48.4627	−1.95739	−0.978695	+	0.205321i	$0.934176\pi$
$614$	15.5154	0.626149
$615$	−1.18292	−0.0476999
$616$	−18.2983	−0.737261
$617$	30.9970	1.24789	0.623946	−	0.781467i	$-0.285529\pi$
$617$	30.9970	1.24789	0.623946	+	0.781467i	$0.285529\pi$
$618$	−5.54012	−0.222856
$619$	13.8299	0.555869	0.277935	−	0.960600i	$-0.410350\pi$
$619$	13.8299	0.555869	0.277935	+	0.960600i	$0.410350\pi$
$620$	−2.47074	−0.0992273
$621$	−1.48864	−0.0597369
$622$	−4.72682	−0.189528
$623$	7.04347	0.282191
$624$	−0.940322	−0.0376430
$625$	−29.8239	−1.19296
$626$	−0.413392	−0.0165225
$627$	4.29574	0.171555
$628$	−58.7149	−2.34298
$629$	32.5691	1.29862
$630$	−11.7416	−0.467798
$631$	13.1121	0.521986	0.260993	−	0.965341i	$-0.415950\pi$
$631$	13.1121	0.521986	0.260993	+	0.965341i	$0.415950\pi$
$632$	38.0705	1.51436
$633$	−2.52308	−0.100283
$634$	−26.5848	−1.05582
$635$	11.5094	0.456737
$636$	−0.661382	−0.0262255
$637$	−8.86615	−0.351290
$638$	−96.6089	−3.82478
$639$	−6.70673	−0.265314
$640$	48.1903	1.90489
$641$	−15.8363	−0.625497	−0.312749	−	0.949836i	$-0.601250\pi$
$641$	−15.8363	−0.625497	−0.312749	+	0.949836i	$0.601250\pi$
$642$	2.41333	0.0952467
$643$	−18.6222	−0.734387	−0.367193	−	0.930145i	$-0.619681\pi$
$643$	−18.6222	−0.734387	−0.367193	+	0.930145i	$0.619681\pi$
$644$	3.94455	0.155437
$645$	3.95197	0.155609
$646$	−59.6405	−2.34652
$647$	38.8142	1.52594	0.762972	−	0.646431i	$-0.223739\pi$
$647$	38.8142	1.52594	0.762972	+	0.646431i	$0.223739\pi$
$648$	−44.0616	−1.73090
$649$	−67.7493	−2.65939
$650$	−4.31908	−0.169408
$651$	−0.0254296	−0.000996666 0
$652$	5.14487	0.201489
$653$	−31.2728	−1.22380	−0.611900	−	0.790935i	$-0.709595\pi$
$653$	−31.2728	−1.22380	−0.611900	+	0.790935i	$0.709595\pi$
$654$	−4.41619	−0.172687
$655$	−6.36827	−0.248829
$656$	12.3208	0.481046
$657$	23.1181	0.901922
$658$	7.27817	0.283733
$659$	10.4368	0.406562	0.203281	−	0.979120i	$-0.434840\pi$
$659$	10.4368	0.406562	0.203281	+	0.979120i	$0.434840\pi$
$660$	9.44682	0.367717
$661$	−12.6031	−0.490204	−0.245102	−	0.969497i	$-0.578821\pi$
$661$	−12.6031	−0.490204	−0.245102	+	0.969497i	$0.578821\pi$
$662$	−76.5326	−2.97452
$663$	−1.15470	−0.0448446
$664$	−69.4002	−2.69325
$665$	−7.41962	−0.287721
$666$	45.3472	1.75717
$667$	10.5304	0.407737
$668$	4.52663	0.175141
$669$	0.847790	0.0327775
$670$	−73.6547	−2.84553
$671$	28.1917	1.08833
$672$	−0.0474555	−0.00183064
$673$	−30.2203	−1.16491	−0.582453	−	0.812864i	$-0.697907\pi$
$673$	−30.2203	−1.16491	−0.582453	+	0.812864i	$0.697907\pi$
$674$	36.2772	1.39735
$675$	1.27515	0.0490805
$676$	−45.2723	−1.74124
$677$	−13.2206	−0.508109	−0.254055	−	0.967190i	$-0.581764\pi$
$677$	−13.2206	−0.508109	−0.254055	+	0.967190i	$0.581764\pi$
$678$	7.73151	0.296927
$679$	−0.267521	−0.0102665
$680$	−66.3177	−2.54317
$681$	0.0366617	0.00140488
$682$	−3.40137	−0.130245
$683$	12.0167	0.459806	0.229903	−	0.973214i	$-0.426159\pi$
$683$	12.0167	0.459806	0.229903	+	0.973214i	$0.426159\pi$
$684$	−55.5686	−2.12472
$685$	−50.0110	−1.91082
$686$	−21.3733	−0.816037
$687$	−1.01632	−0.0387750
$688$	−41.1621	−1.56929
$689$	1.34521	0.0512483
$690$	−1.53875	−0.0585791
$691$	−20.7646	−0.789922	−0.394961	−	0.918698i	$-0.629242\pi$
$691$	−20.7646	−0.789922	−0.394961	+	0.918698i	$0.629242\pi$
$692$	36.3271	1.38095
$693$	−10.8168	−0.410897
$694$	−16.1272	−0.612181
$695$	18.1394	0.688067
$696$	−5.67999	−0.215300
$697$	15.1297	0.573077
$698$	82.2804	3.11436
$699$	3.69547	0.139776
$700$	−3.37886	−0.127709
$701$	−48.6980	−1.83930	−0.919649	−	0.392742i	$-0.871527\pi$
$701$	−48.6980	−1.83930	−0.919649	+	0.392742i	$0.871527\pi$
$702$	−3.22990	−0.121905
$703$	28.6552	1.08075
$704$	42.2948	1.59404
$705$	−1.89993	−0.0715554
$706$	−40.8499	−1.53741
$707$	−4.44466	−0.167158
$708$	−7.87762	−0.296059
$709$	−21.7735	−0.817720	−0.408860	−	0.912597i	$-0.634074\pi$
$709$	−21.7735	−0.817720	−0.408860	+	0.912597i	$0.634074\pi$
$710$	−13.9273	−0.522683
$711$	22.5049	0.843998
$712$	55.3900	2.07583
$713$	0.370749	0.0138847
$714$	−1.34990	−0.0505188
$715$	−19.2142	−0.718569
$716$	31.6499	1.18281
$717$	2.97462	0.111089
$718$	−66.2674	−2.47308
$719$	−9.61340	−0.358519	−0.179260	−	0.983802i	$-0.557370\pi$
$719$	−9.61340	−0.358519	−0.179260	+	0.983802i	$0.557370\pi$
$720$	−31.9247	−1.18976
$721$	8.81524	0.328297
$722$	−5.75633	−0.214228
$723$	−1.25606	−0.0467135
$724$	−58.0276	−2.15658
$725$	−9.02019	−0.335001
$726$	8.58345	0.318562
$727$	34.9634	1.29672	0.648361	−	0.761333i	$-0.275455\pi$
$727$	34.9634	1.29672	0.648361	+	0.761333i	$0.275455\pi$
$728$	4.32751	0.160388
$729$	−25.5675	−0.946944
$730$	48.0074	1.77683
$731$	−50.5461	−1.86951
$732$	3.27802	0.121159
$733$	−28.6767	−1.05920	−0.529600	−	0.848248i	$-0.677658\pi$
$733$	−28.6767	−1.05920	−0.529600	+	0.848248i	$0.677658\pi$
$734$	86.7589	3.20233
$735$	2.70573	0.0998022
$736$	0.691873	0.0255028
$737$	−67.8534	−2.49941
$738$	21.0656	0.775434
$739$	13.9540	0.513306	0.256653	−	0.966504i	$-0.417380\pi$
$739$	13.9540	0.513306	0.256653	+	0.966504i	$0.417380\pi$
$740$	63.0160	2.31651
$741$	−1.01593	−0.0373212
$742$	1.57262	0.0577326
$743$	−25.1203	−0.921573	−0.460786	−	0.887511i	$-0.652433\pi$
$743$	−25.1203	−0.921573	−0.460786	+	0.887511i	$0.652433\pi$
$744$	−0.199979	−0.00733159
$745$	−7.11010	−0.260494
$746$	−1.33607	−0.0489168
$747$	−41.0250	−1.50103
$748$	−120.826	−4.41783
$749$	−3.84001	−0.140311
$750$	−3.72887	−0.136159
$751$	−14.8991	−0.543674	−0.271837	−	0.962343i	$-0.587631\pi$
$751$	−14.8991	−0.543674	−0.271837	+	0.962343i	$0.587631\pi$
$752$	19.7888	0.721625
$753$	2.71260	0.0988527
$754$	22.8477	0.832066
$755$	2.51114	0.0913897
$756$	−2.52678	−0.0918981
$757$	34.1401	1.24084	0.620421	−	0.784269i	$-0.286962\pi$
$757$	34.1401	1.24084	0.620421	+	0.784269i	$0.286962\pi$
$758$	−51.1879	−1.85923
$759$	−1.41755	−0.0514538
$760$	−58.3480	−2.11651
$761$	32.3120	1.17131	0.585655	−	0.810560i	$-0.300837\pi$
$761$	32.3120	1.17131	0.585655	+	0.810560i	$0.300837\pi$
$762$	1.84234	0.0667410
$763$	7.02688	0.254390
$764$	−55.8426	−2.02031
$765$	−39.2028	−1.41738
$766$	−67.8816	−2.45266
$767$	16.0225	0.578540
$768$	5.28274	0.190624
$769$	−1.28773	−0.0464366	−0.0232183	−	0.999730i	$-0.507391\pi$
$769$	−1.28773	−0.0464366	−0.0232183	+	0.999730i	$0.507391\pi$
$770$	−22.4624	−0.809489
$771$	2.33086	0.0839437
$772$	55.3157	1.99086
$773$	6.66112	0.239584	0.119792	−	0.992799i	$-0.461777\pi$
$773$	6.66112	0.239584	0.119792	+	0.992799i	$0.461777\pi$
$774$	−70.3771	−2.52965
$775$	−0.317579	−0.0114078
$776$	−2.10379	−0.0755216
$777$	0.648580	0.0232677
$778$	41.4867	1.48737
$779$	13.3115	0.476933
$780$	−2.23415	−0.0799953
$781$	−12.8303	−0.459106
$782$	19.6807	0.703782
$783$	−6.74549	−0.241064
$784$	−28.1817	−1.00649
$785$	−36.4446	−1.30076
$786$	−1.01939	−0.0363603
$787$	2.94829	0.105095	0.0525477	−	0.998618i	$-0.483266\pi$
$787$	2.94829	0.105095	0.0525477	+	0.998618i	$0.483266\pi$
$788$	−3.50209	−0.124757
$789$	3.37947	0.120312
$790$	46.7340	1.66272
$791$	−12.3021	−0.437412
$792$	−85.0637	−3.02261
$793$	−6.66726	−0.236761
$794$	56.4978	2.00503
$795$	−0.410523	−0.0145598
$796$	−59.3048	−2.10200
$797$	−47.2794	−1.67472	−0.837361	−	0.546651i	$-0.815903\pi$
$797$	−47.2794	−1.67472	−0.837361	+	0.546651i	$0.815903\pi$
$798$	−1.18768	−0.0420433
$799$	24.3003	0.859682
$800$	−0.592651	−0.0209534
$801$	32.7431	1.15692
$802$	−49.4154	−1.74492
$803$	44.2262	1.56071
$804$	−7.88973	−0.278249
$805$	2.44840	0.0862947
$806$	0.804415	0.0283343
$807$	1.11132	0.0391203
$808$	−34.9528	−1.22964
$809$	44.9676	1.58098	0.790488	−	0.612477i	$-0.209827\pi$
$809$	44.9676	1.58098	0.790488	+	0.612477i	$0.209827\pi$
$810$	−54.0884	−1.90047
$811$	49.6009	1.74172	0.870862	−	0.491527i	$-0.163561\pi$
$811$	49.6009	1.74172	0.870862	+	0.491527i	$0.163561\pi$
$812$	17.8740	0.627255
$813$	−1.22072	−0.0428125
$814$	86.7516	3.04064
$815$	3.19344	0.111861
$816$	−3.67028	−0.128486
$817$	−44.4718	−1.55587
$818$	16.7167	0.584485
$819$	2.55815	0.0893890
$820$	29.2735	1.02227
$821$	−1.00503	−0.0350759	−0.0175380	−	0.999846i	$-0.505583\pi$
$821$	−1.00503	−0.0350759	−0.0175380	+	0.999846i	$0.505583\pi$
$822$	−8.00539	−0.279220
$823$	−17.4716	−0.609021	−0.304510	−	0.952509i	$-0.598493\pi$
$823$	−17.4716	−0.609021	−0.304510	+	0.952509i	$0.598493\pi$
$824$	69.3232	2.41499
$825$	1.21426	0.0422750
$826$	18.7312	0.651742
$827$	40.0966	1.39430	0.697148	−	0.716927i	$-0.254452\pi$
$827$	40.0966	1.39430	0.697148	+	0.716927i	$0.254452\pi$
$828$	18.3371	0.637257
$829$	21.7491	0.755378	0.377689	−	0.925933i	$-0.376719\pi$
$829$	21.7491	0.755378	0.377689	+	0.925933i	$0.376719\pi$
$830$	−85.1933	−2.95710
$831$	1.81804	0.0630669
$832$	−10.0026	−0.346778
$833$	−34.6065	−1.19904
$834$	2.90362	0.100544
$835$	2.80970	0.0972337
$836$	−106.306	−3.67666
$837$	−0.237493	−0.00820895
$838$	−29.1284	−1.00622
$839$	−25.1982	−0.869940	−0.434970	−	0.900445i	$-0.643241\pi$
$839$	−25.1982	−0.869940	−0.434970	+	0.900445i	$0.643241\pi$
$840$	−1.32065	−0.0455667
$841$	18.7164	0.645394
$842$	0.887036	0.0305693
$843$	4.31541	0.148631
$844$	62.4381	2.14921
$845$	−28.1007	−0.966693
$846$	33.8341	1.16324
$847$	−13.6577	−0.469283
$848$	4.27584	0.146833
$849$	−4.15353	−0.142549
$850$	−16.8583	−0.578235
$851$	−9.45592	−0.324145
$852$	−1.49186	−0.0511103
$853$	12.3059	0.421347	0.210673	−	0.977557i	$-0.432434\pi$
$853$	12.3059	0.421347	0.210673	+	0.977557i	$0.432434\pi$
$854$	−7.79438	−0.266718
$855$	−34.4917	−1.17959
$856$	−30.1979	−1.03214
$857$	−15.5544	−0.531329	−0.265664	−	0.964066i	$-0.585591\pi$
$857$	−15.5544	−0.531329	−0.265664	+	0.964066i	$0.585591\pi$
$858$	−3.07566	−0.105001
$859$	12.1487	0.414507	0.207254	−	0.978287i	$-0.433547\pi$
$859$	12.1487	0.414507	0.207254	+	0.978287i	$0.433547\pi$
$860$	−97.7985	−3.33490
$861$	0.301292	0.0102680
$862$	39.5451	1.34691
$863$	40.5411	1.38003	0.690017	−	0.723793i	$-0.257603\pi$
$863$	40.5411	1.38003	0.690017	+	0.723793i	$0.257603\pi$
$864$	−0.443197	−0.0150779
$865$	22.5484	0.766668
$866$	95.4473	3.24343
$867$	−1.72785	−0.0586810
$868$	0.629302	0.0213599
$869$	43.0530	1.46047
$870$	−6.97256	−0.236392
$871$	16.0472	0.543737
$872$	55.2595	1.87132
$873$	−1.24363	−0.0420904
$874$	17.3156	0.585710
$875$	5.93324	0.200580
$876$	5.14244	0.173747
$877$	18.9678	0.640497	0.320249	−	0.947334i	$-0.396234\pi$
$877$	18.9678	0.640497	0.320249	+	0.947334i	$0.396234\pi$
$878$	24.4786	0.826114
$879$	1.49404	0.0503928
$880$	−61.0737	−2.05879
$881$	43.8717	1.47808	0.739038	−	0.673664i	$-0.235280\pi$
$881$	43.8717	1.47808	0.739038	+	0.673664i	$0.235280\pi$
$882$	−48.1839	−1.62244
$883$	−26.7940	−0.901689	−0.450844	−	0.892603i	$-0.648877\pi$
$883$	−26.7940	−0.901689	−0.450844	+	0.892603i	$0.648877\pi$
$884$	28.5750	0.961081
$885$	−4.88968	−0.164365
$886$	26.6665	0.895877
$887$	−43.4056	−1.45742	−0.728709	−	0.684823i	$-0.759879\pi$
$887$	−43.4056	−1.45742	−0.728709	+	0.684823i	$0.759879\pi$
$888$	5.10045	0.171160
$889$	−2.93147	−0.0983183
$890$	67.9948	2.27919
$891$	−49.8282	−1.66931
$892$	−20.9801	−0.702465
$893$	21.3800	0.715455
$894$	−1.13813	−0.0380648
$895$	19.6453	0.656668
$896$	−12.2741	−0.410050
$897$	0.335247	0.0111936
$898$	−61.2189	−2.04290
$899$	1.67998	0.0560305
$900$	−15.7073	−0.523578
$901$	5.25063	0.174924
$902$	40.2996	1.34183
$903$	−1.00657	−0.0334967
$904$	−96.7439	−3.21765
$905$	−36.0180	−1.19728
$906$	0.401964	0.0133544
$907$	−42.3701	−1.40687	−0.703437	−	0.710757i	$-0.748352\pi$
$907$	−42.3701	−1.40687	−0.703437	+	0.710757i	$0.748352\pi$
$908$	−0.907260	−0.0301085
$909$	−20.6619	−0.685312
$910$	5.31230	0.176101
$911$	40.4960	1.34169	0.670846	−	0.741596i	$-0.265931\pi$
$911$	40.4960	1.34169	0.670846	+	0.741596i	$0.265931\pi$
$912$	−3.22921	−0.106930
$913$	−78.4832	−2.59741
$914$	72.5245	2.39890
$915$	2.03468	0.0672644
$916$	25.1507	0.831001
$917$	1.62201	0.0535635
$918$	−12.6070	−0.416093
$919$	20.5223	0.676969	0.338484	−	0.940972i	$-0.390086\pi$
$919$	20.5223	0.676969	0.338484	+	0.940972i	$0.390086\pi$
$920$	19.2543	0.634794
$921$	1.03159	0.0339921
$922$	9.05867	0.298331
$923$	3.03434	0.0998766
$924$	−2.40612	−0.0791556
$925$	8.09983	0.266321
$926$	−12.2536	−0.402678
$927$	40.9795	1.34594
$928$	3.13510	0.102915
$929$	−46.0654	−1.51136	−0.755679	−	0.654942i	$-0.772693\pi$
$929$	−46.0654	−1.51136	−0.755679	+	0.654942i	$0.772693\pi$
$930$	−0.245487	−0.00804984
$931$	−30.4477	−0.997884
$932$	−91.4511	−2.99558
$933$	−0.314279	−0.0102890
$934$	−98.8726	−3.23521
$935$	−74.9971	−2.45267
$936$	20.1173	0.657556
$937$	50.9733	1.66522	0.832612	−	0.553857i	$-0.186845\pi$
$937$	50.9733	1.66522	0.832612	+	0.553857i	$0.186845\pi$
$938$	18.7600	0.612535
$939$	−0.0274858	−0.000896965 0
$940$	47.0171	1.53353
$941$	15.3560	0.500590	0.250295	−	0.968170i	$-0.419472\pi$
$941$	15.3560	0.500590	0.250295	+	0.968170i	$0.419472\pi$
$942$	−5.83379	−0.190075
$943$	−4.39265	−0.143044
$944$	50.9288	1.65759
$945$	−1.56838	−0.0510195
$946$	−134.635	−4.37737
$947$	−14.2940	−0.464492	−0.232246	−	0.972657i	$-0.574607\pi$
$947$	−14.2940	−0.464492	−0.232246	+	0.972657i	$0.574607\pi$
$948$	5.00604	0.162589
$949$	−10.4594	−0.339526
$950$	−14.8324	−0.481226
$951$	−1.76758	−0.0573177
$952$	16.8912	0.547448
$953$	42.2914	1.36995	0.684977	−	0.728565i	$-0.259812\pi$
$953$	42.2914	1.36995	0.684977	+	0.728565i	$0.259812\pi$
$954$	7.31064	0.236691
$955$	−34.6617	−1.12163
$956$	−73.6122	−2.38079
$957$	−6.42337	−0.207638
$958$	12.3993	0.400603
$959$	12.7379	0.411328
$960$	3.05254	0.0985204
$961$	−30.9409	−0.998092
$962$	−20.5165	−0.661479
$963$	−17.8511	−0.575243
$964$	31.0835	1.00113
$965$	34.3347	1.10527
$966$	0.391922	0.0126099
$967$	−47.6505	−1.53234	−0.766168	−	0.642640i	$-0.777839\pi$
$967$	−47.6505	−1.53234	−0.766168	+	0.642640i	$0.777839\pi$
$968$	−107.404	−3.45210
$969$	−3.96540	−0.127387
$970$	−2.58254	−0.0829203
$971$	−6.46639	−0.207516	−0.103758	−	0.994603i	$-0.533087\pi$
$971$	−6.46639	−0.207516	−0.103758	+	0.994603i	$0.533087\pi$
$972$	−17.6457	−0.565986
$973$	−4.62014	−0.148115
$974$	67.0952	2.14987
$975$	−0.287169	−0.00919676
$976$	−21.1924	−0.678351
$977$	24.4285	0.781538	0.390769	−	0.920489i	$-0.372209\pi$
$977$	24.4285	0.781538	0.390769	+	0.920489i	$0.372209\pi$
$978$	0.511183	0.0163458
$979$	62.6393	2.00196
$980$	−66.9580	−2.13890
$981$	32.6660	1.04294
$982$	6.56159	0.209389
$983$	26.6715	0.850687	0.425344	−	0.905032i	$-0.360153\pi$
$983$	26.6715	0.850687	0.425344	+	0.905032i	$0.360153\pi$
$984$	2.36936	0.0755325
$985$	−2.17376	−0.0692619
$986$	89.1798	2.84006
$987$	0.483915	0.0154032
$988$	25.1410	0.799843
$989$	14.6752	0.466645
$990$	−104.421	−3.31872
$991$	−3.36156	−0.106784	−0.0533918	−	0.998574i	$-0.517003\pi$
$991$	−3.36156	−0.106784	−0.0533918	+	0.998574i	$0.517003\pi$
$992$	0.110379	0.00350455
$993$	−5.08853	−0.161480
$994$	3.54731	0.112514
$995$	−36.8108	−1.16698
$996$	−9.12571	−0.289159
$997$	41.8167	1.32435	0.662175	−	0.749349i	$-0.269634\pi$
$997$	41.8167	1.32435	0.662175	+	0.749349i	$0.269634\pi$
$998$	77.9754	2.46827
$999$	6.05723	0.191642

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.a.1.11	✓	147

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.11	✓	147	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:	\( N \)	\(=\)	\( 8003 = 53 \cdot 151 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8003.a (trivial)

\(f(q)\)	\(=\)	\(q-2.45879 q^{2} -0.163481 q^{3} +4.04563 q^{4} +2.51114 q^{5} +0.401964 q^{6} -0.639591 q^{7} -5.02975 q^{8} -2.97327 q^{9} +O(q^{10})\)	\(q-2.45879 q^{2} -0.163481 q^{3} +4.04563 q^{4} +2.51114 q^{5} +0.401964 q^{6} -0.639591 q^{7} -5.02975 q^{8} -2.97327 q^{9} -6.17435 q^{10} -5.68804 q^{11} -0.661382 q^{12} +1.34521 q^{13} +1.57262 q^{14} -0.410523 q^{15} +4.27584 q^{16} +5.25063 q^{17} +7.31064 q^{18} +4.61965 q^{19} +10.1591 q^{20} +0.104561 q^{21} +13.9857 q^{22} -1.52444 q^{23} +0.822269 q^{24} +1.30582 q^{25} -3.30757 q^{26} +0.976516 q^{27} -2.58755 q^{28} -6.90771 q^{29} +1.00939 q^{30} -0.243204 q^{31} -0.453855 q^{32} +0.929885 q^{33} -12.9102 q^{34} -1.60610 q^{35} -12.0288 q^{36} +6.20290 q^{37} -11.3587 q^{38} -0.219915 q^{39} -12.6304 q^{40} +2.88149 q^{41} -0.257093 q^{42} -9.62667 q^{43} -23.0117 q^{44} -7.46630 q^{45} +3.74826 q^{46} +4.62806 q^{47} -0.699018 q^{48} -6.59092 q^{49} -3.21072 q^{50} -0.858378 q^{51} +5.44220 q^{52} +1.00000 q^{53} -2.40104 q^{54} -14.2834 q^{55} +3.21699 q^{56} -0.755224 q^{57} +16.9846 q^{58} +11.9108 q^{59} -1.66082 q^{60} -4.95631 q^{61} +0.597987 q^{62} +1.90168 q^{63} -7.43574 q^{64} +3.37800 q^{65} -2.28639 q^{66} +11.9291 q^{67} +21.2421 q^{68} +0.249216 q^{69} +3.94906 q^{70} +2.25567 q^{71} +14.9548 q^{72} -7.77529 q^{73} -15.2516 q^{74} -0.213476 q^{75} +18.6894 q^{76} +3.63802 q^{77} +0.540725 q^{78} -7.56905 q^{79} +10.7372 q^{80} +8.76018 q^{81} -7.08497 q^{82} +13.7979 q^{83} +0.423014 q^{84} +13.1851 q^{85} +23.6699 q^{86} +1.12928 q^{87} +28.6094 q^{88} -11.0125 q^{89} +18.3580 q^{90} -0.860382 q^{91} -6.16730 q^{92} +0.0397592 q^{93} -11.3794 q^{94} +11.6006 q^{95} +0.0741966 q^{96} +0.418269 q^{97} +16.2057 q^{98} +16.9121 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9} - 24 q^{10} - 13 q^{11} - 52 q^{12} - 119 q^{13} - 6 q^{14} - 22 q^{15} + 100 q^{16} - 42 q^{17} - 6 q^{18} - 31 q^{19} - 50 q^{20} - 44 q^{21} - 38 q^{22} - 16 q^{23} - 30 q^{24} + 80 q^{25} - 18 q^{26} - 68 q^{27} - 72 q^{28} - 40 q^{29} - 3 q^{30} - 44 q^{31} - 41 q^{32} - 71 q^{33} - 55 q^{34} - 24 q^{35} + 108 q^{36} - 145 q^{37} - 39 q^{38} + 28 q^{39} - 81 q^{40} - 28 q^{41} - 54 q^{42} - 47 q^{43} - 33 q^{44} - 89 q^{45} - 43 q^{46} - 65 q^{47} - 82 q^{48} + 52 q^{49} - 43 q^{50} + 7 q^{51} - 215 q^{52} + 147 q^{53} - 88 q^{54} - 48 q^{55} + 19 q^{56} - 66 q^{57} - 110 q^{58} - 66 q^{59} - 118 q^{60} - 80 q^{61} - 41 q^{62} - 52 q^{63} + 33 q^{64} - 17 q^{65} - 86 q^{66} - 114 q^{67} - 77 q^{68} - 49 q^{69} - 56 q^{70} + 10 q^{71} + 5 q^{72} - 143 q^{73} - 30 q^{74} - 97 q^{75} - 104 q^{76} - 116 q^{77} - 33 q^{78} - 31 q^{79} - 83 q^{80} - q^{81} - 72 q^{82} - 70 q^{83} - 64 q^{84} - 85 q^{85} - 43 q^{87} - 149 q^{88} - 130 q^{89} + 42 q^{90} - 35 q^{91} - 31 q^{92} - 149 q^{93} - 94 q^{94} - 9 q^{95} + 6 q^{96} - 211 q^{97} - 18 q^{98} - 19 q^{99}+O(q^{100}) \) 147 * q - 6 * q^2 - 23 * q^3 + 130 * q^4 - 25 * q^5 - 18 * q^6 - 33 * q^7 - 15 * q^8 + 114 * q^9 - 24 * q^10 - 13 * q^11 - 52 * q^12 - 119 * q^13 - 6 * q^14 - 22 * q^15 + 100 * q^16 - 42 * q^17 - 6 * q^18 - 31 * q^19 - 50 * q^20 - 44 * q^21 - 38 * q^22 - 16 * q^23 - 30 * q^24 + 80 * q^25 - 18 * q^26 - 68 * q^27 - 72 * q^28 - 40 * q^29 - 3 * q^30 - 44 * q^31 - 41 * q^32 - 71 * q^33 - 55 * q^34 - 24 * q^35 + 108 * q^36 - 145 * q^37 - 39 * q^38 + 28 * q^39 - 81 * q^40 - 28 * q^41 - 54 * q^42 - 47 * q^43 - 33 * q^44 - 89 * q^45 - 43 * q^46 - 65 * q^47 - 82 * q^48 + 52 * q^49 - 43 * q^50 + 7 * q^51 - 215 * q^52 + 147 * q^53 - 88 * q^54 - 48 * q^55 + 19 * q^56 - 66 * q^57 - 110 * q^58 - 66 * q^59 - 118 * q^60 - 80 * q^61 - 41 * q^62 - 52 * q^63 + 33 * q^64 - 17 * q^65 - 86 * q^66 - 114 * q^67 - 77 * q^68 - 49 * q^69 - 56 * q^70 + 10 * q^71 + 5 * q^72 - 143 * q^73 - 30 * q^74 - 97 * q^75 - 104 * q^76 - 116 * q^77 - 33 * q^78 - 31 * q^79 - 83 * q^80 - q^81 - 72 * q^82 - 70 * q^83 - 64 * q^84 - 85 * q^85 - 43 * q^87 - 149 * q^88 - 130 * q^89 + 42 * q^90 - 35 * q^91 - 31 * q^92 - 149 * q^93 - 94 * q^94 - 9 * q^95 + 6 * q^96 - 211 * q^97 - 18 * q^98 - 19 * q^99

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