LMFDB - Embedded newform 8003.2.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.76716 q^{2} -2.20267 q^{3} +5.65717 q^{4} +0.836026 q^{5} +6.09513 q^{6} -1.25752 q^{7} -10.1200 q^{8} +1.85174 q^{9} +O(q^{10})$	\(q-2.76716 q^{2} -2.20267 q^{3} +5.65717 q^{4} +0.836026 q^{5} +6.09513 q^{6} -1.25752 q^{7} -10.1200 q^{8} +1.85174 q^{9} -2.31342 q^{10} +2.01948 q^{11} -12.4609 q^{12} +1.55975 q^{13} +3.47977 q^{14} -1.84149 q^{15} +16.6892 q^{16} -5.37995 q^{17} -5.12406 q^{18} -0.512919 q^{19} +4.72954 q^{20} +2.76991 q^{21} -5.58823 q^{22} -1.68892 q^{23} +22.2909 q^{24} -4.30106 q^{25} -4.31609 q^{26} +2.52923 q^{27} -7.11402 q^{28} +7.49751 q^{29} +5.09568 q^{30} +1.51211 q^{31} -25.9417 q^{32} -4.44825 q^{33} +14.8872 q^{34} -1.05132 q^{35} +10.4756 q^{36} -5.63090 q^{37} +1.41933 q^{38} -3.43562 q^{39} -8.46054 q^{40} +4.81590 q^{41} -7.66477 q^{42} -8.05951 q^{43} +11.4246 q^{44} +1.54810 q^{45} +4.67351 q^{46} +8.46642 q^{47} -36.7607 q^{48} -5.41863 q^{49} +11.9017 q^{50} +11.8502 q^{51} +8.82379 q^{52} +1.00000 q^{53} -6.99879 q^{54} +1.68834 q^{55} +12.7261 q^{56} +1.12979 q^{57} -20.7468 q^{58} -12.4594 q^{59} -10.4176 q^{60} +12.6988 q^{61} -4.18425 q^{62} -2.32861 q^{63} +38.4065 q^{64} +1.30400 q^{65} +12.3090 q^{66} +8.85499 q^{67} -30.4353 q^{68} +3.72013 q^{69} +2.90917 q^{70} +8.73207 q^{71} -18.7395 q^{72} -9.52821 q^{73} +15.5816 q^{74} +9.47380 q^{75} -2.90167 q^{76} -2.53955 q^{77} +9.50691 q^{78} -14.2457 q^{79} +13.9526 q^{80} -11.1263 q^{81} -13.3264 q^{82} +9.01721 q^{83} +15.6698 q^{84} -4.49778 q^{85} +22.3019 q^{86} -16.5145 q^{87} -20.4371 q^{88} +15.2276 q^{89} -4.28385 q^{90} -1.96143 q^{91} -9.55450 q^{92} -3.33068 q^{93} -23.4279 q^{94} -0.428813 q^{95} +57.1410 q^{96} +8.10162 q^{97} +14.9942 q^{98} +3.73956 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76716	−1.95668	−0.978338	−	0.207013i	$-0.933626\pi$
$2$	−2.76716	−1.95668	−0.978338	+	0.207013i	$0.933626\pi$
$3$	−2.20267	−1.27171	−0.635855	−	0.771808i	$-0.719352\pi$
$3$	−2.20267	−1.27171	−0.635855	+	0.771808i	$0.719352\pi$
$4$	5.65717	2.82858
$5$	0.836026	0.373882	0.186941	−	0.982371i	$-0.440143\pi$
$5$	0.836026	0.373882	0.186941	+	0.982371i	$0.440143\pi$
$6$	6.09513	2.48833
$7$	−1.25752	−0.475299	−0.237650	−	0.971351i	$-0.576377\pi$
$7$	−1.25752	−0.475299	−0.237650	+	0.971351i	$0.576377\pi$
$8$	−10.1200	−3.57795
$9$	1.85174	0.617247
$10$	−2.31342	−0.731566
$11$	2.01948	0.608898	0.304449	−	0.952529i	$-0.401528\pi$
$11$	2.01948	0.608898	0.304449	+	0.952529i	$0.401528\pi$
$12$	−12.4609	−3.59714
$13$	1.55975	0.432598	0.216299	−	0.976327i	$-0.430601\pi$
$13$	1.55975	0.432598	0.216299	+	0.976327i	$0.430601\pi$
$14$	3.47977	0.930007
$15$	−1.84149	−0.475470
$16$	16.6892	4.17230
$17$	−5.37995	−1.30483	−0.652415	−	0.757862i	$-0.726244\pi$
$17$	−5.37995	−1.30483	−0.652415	+	0.757862i	$0.726244\pi$
$18$	−5.12406	−1.20775
$19$	−0.512919	−0.117672	−0.0588358	−	0.998268i	$-0.518739\pi$
$19$	−0.512919	−0.117672	−0.0588358	+	0.998268i	$0.518739\pi$
$20$	4.72954	1.05756
$21$	2.76991	0.604443
$22$	−5.58823	−1.19142
$23$	−1.68892	−0.352164	−0.176082	−	0.984375i	$-0.556342\pi$
$23$	−1.68892	−0.352164	−0.176082	+	0.984375i	$0.556342\pi$
$24$	22.2909	4.55011
$25$	−4.30106	−0.860212
$26$	−4.31609	−0.846455
$27$	2.52923	0.486751
$28$	−7.11402	−1.34442
$29$	7.49751	1.39225	0.696126	−	0.717919i	$-0.254905\pi$
$29$	7.49751	1.39225	0.696126	+	0.717919i	$0.254905\pi$
$30$	5.09568	0.930340
$31$	1.51211	0.271583	0.135792	−	0.990737i	$-0.456642\pi$
$31$	1.51211	0.271583	0.135792	+	0.990737i	$0.456642\pi$
$32$	−25.9417	−4.58590
$33$	−4.44825	−0.774341
$34$	14.8872	2.55313
$35$	−1.05132	−0.177706
$36$	10.4756	1.74593
$37$	−5.63090	−0.925714	−0.462857	−	0.886433i	$-0.653176\pi$
$37$	−5.63090	−0.925714	−0.462857	+	0.886433i	$0.653176\pi$
$38$	1.41933	0.230245
$39$	−3.43562	−0.550140
$40$	−8.46054	−1.33773
$41$	4.81590	0.752117	0.376059	−	0.926596i	$-0.377279\pi$
$41$	4.81590	0.752117	0.376059	+	0.926596i	$0.377279\pi$
$42$	−7.66477	−1.18270
$43$	−8.05951	−1.22906	−0.614532	−	0.788892i	$-0.710655\pi$
$43$	−8.05951	−1.22906	−0.614532	+	0.788892i	$0.710655\pi$
$44$	11.4246	1.72232
$45$	1.54810	0.230778
$46$	4.67351	0.689071
$47$	8.46642	1.23495	0.617477	−	0.786589i	$-0.288155\pi$
$47$	8.46642	1.23495	0.617477	+	0.786589i	$0.288155\pi$
$48$	−36.7607	−5.30596
$49$	−5.41863	−0.774091
$50$	11.9017	1.68316
$51$	11.8502	1.65936
$52$	8.82379	1.22364
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	−6.99879	−0.952414
$55$	1.68834	0.227656
$56$	12.7261	1.70060
$57$	1.12979	0.149644
$58$	−20.7468	−2.72419
$59$	−12.4594	−1.62208	−0.811041	−	0.584989i	$-0.801099\pi$
$59$	−12.4594	−1.62208	−0.811041	+	0.584989i	$0.801099\pi$
$60$	−10.4176	−1.34491
$61$	12.6988	1.62592	0.812960	−	0.582319i	$-0.197855\pi$
$61$	12.6988	1.62592	0.812960	+	0.582319i	$0.197855\pi$
$62$	−4.18425	−0.531401
$63$	−2.32861	−0.293377
$64$	38.4065	4.80081
$65$	1.30400	0.161741
$66$	12.3090	1.51514
$67$	8.85499	1.08181	0.540905	−	0.841084i	$-0.318082\pi$
$67$	8.85499	1.08181	0.540905	+	0.841084i	$0.318082\pi$
$68$	−30.4353	−3.69082
$69$	3.72013	0.447851
$70$	2.90917	0.347713
$71$	8.73207	1.03631	0.518153	−	0.855288i	$-0.326620\pi$
$71$	8.73207	1.03631	0.518153	+	0.855288i	$0.326620\pi$
$72$	−18.7395	−2.20848
$73$	−9.52821	−1.11519	−0.557597	−	0.830112i	$-0.688276\pi$
$73$	−9.52821	−1.11519	−0.557597	+	0.830112i	$0.688276\pi$
$74$	15.5816	1.81132
$75$	9.47380	1.09394
$76$	−2.90167	−0.332844
$77$	−2.53955	−0.289409
$78$	9.50691	1.07645
$79$	−14.2457	−1.60277	−0.801384	−	0.598150i	$-0.795903\pi$
$79$	−14.2457	−1.60277	−0.801384	+	0.598150i	$0.795903\pi$
$80$	13.9526	1.55995
$81$	−11.1263	−1.23625
$82$	−13.3264	−1.47165
$83$	9.01721	0.989767	0.494883	−	0.868959i	$-0.335211\pi$
$83$	9.01721	0.989767	0.494883	+	0.868959i	$0.335211\pi$
$84$	15.6698	1.70972
$85$	−4.49778	−0.487852
$86$	22.3019	2.40488
$87$	−16.5145	−1.77054
$88$	−20.4371	−2.17860
$89$	15.2276	1.61413	0.807064	−	0.590465i	$-0.201055\pi$
$89$	15.2276	1.61413	0.807064	+	0.590465i	$0.201055\pi$
$90$	−4.28385	−0.451557
$91$	−1.96143	−0.205614
$92$	−9.55450	−0.996125
$93$	−3.33068	−0.345375
$94$	−23.4279	−2.41641
$95$	−0.428813	−0.0439953
$96$	57.1410	5.83193
$97$	8.10162	0.822595	0.411298	−	0.911501i	$-0.365076\pi$
$97$	8.10162	0.822595	0.411298	+	0.911501i	$0.365076\pi$
$98$	14.9942	1.51464
$99$	3.73956	0.375840
$100$	−24.3318	−2.43318
$101$	7.05468	0.701967	0.350983	−	0.936382i	$-0.385847\pi$
$101$	7.05468	0.701967	0.350983	+	0.936382i	$0.385847\pi$
$102$	−32.7915	−3.24684
$103$	3.97067	0.391241	0.195621	−	0.980680i	$-0.437328\pi$
$103$	3.97067	0.391241	0.195621	+	0.980680i	$0.437328\pi$
$104$	−15.7847	−1.54781
$105$	2.31571	0.225990
$106$	−2.76716	−0.268770
$107$	11.5131	1.11302	0.556509	−	0.830842i	$-0.312140\pi$
$107$	11.5131	1.11302	0.556509	+	0.830842i	$0.312140\pi$
$108$	14.3083	1.37682
$109$	−7.99395	−0.765682	−0.382841	−	0.923814i	$-0.625054\pi$
$109$	−7.99395	−0.765682	−0.382841	+	0.923814i	$0.625054\pi$
$110$	−4.67191	−0.445449
$111$	12.4030	1.17724
$112$	−20.9871	−1.98309
$113$	−3.50779	−0.329985	−0.164992	−	0.986295i	$-0.552760\pi$
$113$	−3.50779	−0.329985	−0.164992	+	0.986295i	$0.552760\pi$
$114$	−3.12630	−0.292805
$115$	−1.41198	−0.131668
$116$	42.4147	3.93810
$117$	2.88826	0.267020
$118$	34.4773	3.17389
$119$	6.76541	0.620184
$120$	18.6358	1.70120
$121$	−6.92168	−0.629244
$122$	−35.1397	−3.18140
$123$	−10.6078	−0.956475
$124$	8.55427	0.768196
$125$	−7.77593	−0.695500
$126$	6.44363	0.574044
$127$	3.62026	0.321246	0.160623	−	0.987016i	$-0.448650\pi$
$127$	3.62026	0.321246	0.160623	+	0.987016i	$0.448650\pi$
$128$	−54.3934	−4.80774
$129$	17.7524	1.56301
$130$	−3.60836	−0.316474
$131$	2.23944	0.195661	0.0978304	−	0.995203i	$-0.468810\pi$
$131$	2.23944	0.195661	0.0978304	+	0.995203i	$0.468810\pi$
$132$	−25.1645	−2.19029
$133$	0.645007	0.0559292
$134$	−24.5032	−2.11675
$135$	2.11450	0.181987
$136$	54.4449	4.66861
$137$	−11.6931	−0.999007	−0.499504	−	0.866312i	$-0.666484\pi$
$137$	−11.6931	−0.999007	−0.499504	+	0.866312i	$0.666484\pi$
$138$	−10.2942	−0.876299
$139$	−15.0423	−1.27587	−0.637935	−	0.770090i	$-0.720211\pi$
$139$	−15.0423	−1.27587	−0.637935	+	0.770090i	$0.720211\pi$
$140$	−5.94750	−0.502656
$141$	−18.6487	−1.57050
$142$	−24.1630	−2.02772
$143$	3.14990	0.263408
$144$	30.9041	2.57534
$145$	6.26811	0.520538
$146$	26.3661	2.18207
$147$	11.9354	0.984419
$148$	−31.8549	−2.61846
$149$	0.202343	0.0165766	0.00828829	−	0.999966i	$-0.497362\pi$
$149$	0.202343	0.0165766	0.00828829	+	0.999966i	$0.497362\pi$
$150$	−26.2155	−2.14049
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	5.19072	0.421023
$153$	−9.96227	−0.805402
$154$	7.02734	0.566279
$155$	1.26416	0.101540
$156$	−19.4359	−1.55612
$157$	−4.16597	−0.332480	−0.166240	−	0.986085i	$-0.553163\pi$
$157$	−4.16597	−0.332480	−0.166240	+	0.986085i	$0.553163\pi$
$158$	39.4201	3.13610
$159$	−2.20267	−0.174683
$160$	−21.6880	−1.71458
$161$	2.12386	0.167383
$162$	30.7882	2.41895
$163$	−14.0201	−1.09814	−0.549069	−	0.835777i	$-0.685018\pi$
$163$	−14.0201	−1.09814	−0.549069	+	0.835777i	$0.685018\pi$
$164$	27.2444	2.12743
$165$	−3.71885	−0.289512
$166$	−24.9520	−1.93665
$167$	−10.0203	−0.775397	−0.387698	−	0.921786i	$-0.626730\pi$
$167$	−10.0203	−0.775397	−0.387698	+	0.921786i	$0.626730\pi$
$168$	−28.0313	−2.16266
$169$	−10.5672	−0.812859
$170$	12.4461	0.954569
$171$	−0.949792	−0.0726324
$172$	−45.5940	−3.47651
$173$	−14.7103	−1.11840	−0.559201	−	0.829032i	$-0.688892\pi$
$173$	−14.7103	−1.11840	−0.559201	+	0.829032i	$0.688892\pi$
$174$	45.6983	3.46438
$175$	5.40869	0.408858
$176$	33.7036	2.54050
$177$	27.4440	2.06282
$178$	−42.1373	−3.15832
$179$	0.646156	0.0482960	0.0241480	−	0.999708i	$-0.492313\pi$
$179$	0.646156	0.0482960	0.0241480	+	0.999708i	$0.492313\pi$
$180$	8.75788	0.652774
$181$	18.3720	1.36558	0.682791	−	0.730613i	$-0.260766\pi$
$181$	18.3720	1.36558	0.682791	+	0.730613i	$0.260766\pi$
$182$	5.42758	0.402319
$183$	−27.9713	−2.06770
$184$	17.0918	1.26002
$185$	−4.70757	−0.346108
$186$	9.21652	0.675788
$187$	−10.8647	−0.794507
$188$	47.8959	3.49317
$189$	−3.18057	−0.231352
$190$	1.18659	0.0860846
$191$	−11.9915	−0.867676	−0.433838	−	0.900991i	$-0.642841\pi$
$191$	−11.9915	−0.867676	−0.433838	+	0.900991i	$0.642841\pi$
$192$	−84.5967	−6.10524
$193$	11.2819	0.812091	0.406046	−	0.913853i	$-0.366907\pi$
$193$	11.2819	0.812091	0.406046	+	0.913853i	$0.366907\pi$
$194$	−22.4185	−1.60955
$195$	−2.87227	−0.205687
$196$	−30.6541	−2.18958
$197$	16.1462	1.15037	0.575185	−	0.818023i	$-0.304930\pi$
$197$	16.1462	1.15037	0.575185	+	0.818023i	$0.304930\pi$
$198$	−10.3480	−0.735398
$199$	−17.0964	−1.21193	−0.605967	−	0.795490i	$-0.707214\pi$
$199$	−17.0964	−1.21193	−0.605967	+	0.795490i	$0.707214\pi$
$200$	43.5266	3.07779
$201$	−19.5046	−1.37575
$202$	−19.5214	−1.37352
$203$	−9.42830	−0.661737
$204$	67.0388	4.69365
$205$	4.02622	0.281203
$206$	−10.9875	−0.765533
$207$	−3.12744	−0.217372
$208$	26.0311	1.80493
$209$	−1.03583	−0.0716499
$210$	−6.40794	−0.442190
$211$	15.3673	1.05793	0.528966	−	0.848643i	$-0.322580\pi$
$211$	15.3673	1.05793	0.528966	+	0.848643i	$0.322580\pi$
$212$	5.65717	0.388536
$213$	−19.2338	−1.31788
$214$	−31.8587	−2.17782
$215$	−6.73795	−0.459525
$216$	−25.5957	−1.74157
$217$	−1.90152	−0.129083
$218$	22.1205	1.49819
$219$	20.9875	1.41820
$220$	9.55122	0.643943
$221$	−8.39140	−0.564467
$222$	−34.3210	−2.30348
$223$	−16.1756	−1.08320	−0.541598	−	0.840637i	$-0.682181\pi$
$223$	−16.1756	−1.08320	−0.541598	+	0.840637i	$0.682181\pi$
$224$	32.6224	2.17967
$225$	−7.96445	−0.530963
$226$	9.70661	0.645674
$227$	−8.72599	−0.579164	−0.289582	−	0.957153i	$-0.593516\pi$
$227$	−8.72599	−0.579164	−0.289582	+	0.957153i	$0.593516\pi$
$228$	6.39140	0.423281
$229$	2.60900	0.172408	0.0862039	−	0.996278i	$-0.472526\pi$
$229$	2.60900	0.172408	0.0862039	+	0.996278i	$0.472526\pi$
$230$	3.90717	0.257631
$231$	5.59378	0.368044
$232$	−75.8745	−4.98140
$233$	16.0784	1.05333	0.526664	−	0.850074i	$-0.323443\pi$
$233$	16.0784	1.05333	0.526664	+	0.850074i	$0.323443\pi$
$234$	−7.99228	−0.522472
$235$	7.07814	0.461727
$236$	−70.4852	−4.58819
$237$	31.3786	2.03826
$238$	−18.7210	−1.21350
$239$	23.4859	1.51917	0.759587	−	0.650405i	$-0.225401\pi$
$239$	23.4859	1.51917	0.759587	+	0.650405i	$0.225401\pi$
$240$	−30.7329	−1.98380
$241$	−22.9382	−1.47758	−0.738790	−	0.673936i	$-0.764603\pi$
$241$	−22.9382	−1.47758	−0.738790	+	0.673936i	$0.764603\pi$
$242$	19.1534	1.23123
$243$	16.9198	1.08540
$244$	71.8395	4.59905
$245$	−4.53012	−0.289419
$246$	29.3535	1.87151
$247$	−0.800027	−0.0509045
$248$	−15.3025	−0.971710
$249$	−19.8619	−1.25870
$250$	21.5172	1.36087
$251$	30.7198	1.93901	0.969507	−	0.245062i	$-0.0788084\pi$
$251$	30.7198	1.93901	0.969507	+	0.245062i	$0.0788084\pi$
$252$	−13.1733	−0.829841
$253$	−3.41075	−0.214432
$254$	−10.0178	−0.628575
$255$	9.90710	0.620407
$256$	73.7022	4.60639
$257$	−18.4756	−1.15248	−0.576238	−	0.817282i	$-0.695480\pi$
$257$	−18.4756	−1.15248	−0.576238	+	0.817282i	$0.695480\pi$
$258$	−49.1237	−3.05831
$259$	7.08098	0.439991
$260$	7.37692	0.457497
$261$	13.8834	0.859364
$262$	−6.19688	−0.382845
$263$	−1.78242	−0.109908	−0.0549542	−	0.998489i	$-0.517501\pi$
$263$	−1.78242	−0.109908	−0.0549542	+	0.998489i	$0.517501\pi$
$264$	45.0161	2.77055
$265$	0.836026	0.0513566
$266$	−1.78484	−0.109435
$267$	−33.5414	−2.05270
$268$	50.0942	3.05999
$269$	−24.3946	−1.48737	−0.743683	−	0.668532i	$-0.766923\pi$
$269$	−24.3946	−1.48737	−0.743683	+	0.668532i	$0.766923\pi$
$270$	−5.85116	−0.356090
$271$	14.6331	0.888897	0.444448	−	0.895804i	$-0.353400\pi$
$271$	14.6331	0.888897	0.444448	+	0.895804i	$0.353400\pi$
$272$	−89.7870	−5.44414
$273$	4.32037	0.261481
$274$	32.3566	1.95473
$275$	−8.68593	−0.523781
$276$	21.0454	1.26678
$277$	29.2349	1.75655	0.878276	−	0.478154i	$-0.158694\pi$
$277$	29.2349	1.75655	0.878276	+	0.478154i	$0.158694\pi$
$278$	41.6244	2.49647
$279$	2.80004	0.167634
$280$	10.6393	0.635822
$281$	−10.7288	−0.640026	−0.320013	−	0.947413i	$-0.603687\pi$
$281$	−10.7288	−0.640026	−0.320013	+	0.947413i	$0.603687\pi$
$282$	51.6039	3.07297
$283$	24.3095	1.44505	0.722526	−	0.691344i	$-0.242981\pi$
$283$	24.3095	1.44505	0.722526	+	0.691344i	$0.242981\pi$
$284$	49.3988	2.93128
$285$	0.944532	0.0559493
$286$	−8.71628	−0.515404
$287$	−6.05611	−0.357481
$288$	−48.0374	−2.83063
$289$	11.9439	0.702580
$290$	−17.3449	−1.01852
$291$	−17.8452	−1.04610
$292$	−53.9027	−3.15442
$293$	5.53938	0.323614	0.161807	−	0.986822i	$-0.448268\pi$
$293$	5.53938	0.323614	0.161807	+	0.986822i	$0.448268\pi$
$294$	−33.0273	−1.92619
$295$	−10.4164	−0.606467
$296$	56.9844	3.31215
$297$	5.10774	0.296381
$298$	−0.559915	−0.0324350
$299$	−2.63430	−0.152346
$300$	53.5949	3.09430
$301$	10.1350	0.584173
$302$	−2.76716	−0.159232
$303$	−15.5391	−0.892698
$304$	−8.56020	−0.490961
$305$	10.6166	0.607902
$306$	27.5672	1.57591
$307$	25.5743	1.45960	0.729801	−	0.683659i	$-0.239613\pi$
$307$	25.5743	1.45960	0.729801	+	0.683659i	$0.239613\pi$
$308$	−14.3667	−0.818616
$309$	−8.74605	−0.497546
$310$	−3.49814	−0.198681
$311$	−17.8564	−1.01255	−0.506273	−	0.862374i	$-0.668977\pi$
$311$	−17.8564	−1.01255	−0.506273	+	0.862374i	$0.668977\pi$
$312$	34.7683	1.96837
$313$	25.5821	1.44599	0.722993	−	0.690855i	$-0.242766\pi$
$313$	25.5821	1.44599	0.722993	+	0.690855i	$0.242766\pi$
$314$	11.5279	0.650557
$315$	−1.94678	−0.109688
$316$	−80.5904	−4.53356
$317$	8.81138	0.494896	0.247448	−	0.968901i	$-0.420408\pi$
$317$	8.81138	0.494896	0.247448	+	0.968901i	$0.420408\pi$
$318$	6.09513	0.341798
$319$	15.1411	0.847739
$320$	32.1088	1.79494
$321$	−25.3596	−1.41544
$322$	−5.87705	−0.327515
$323$	2.75948	0.153541
$324$	−62.9432	−3.49684
$325$	−6.70860	−0.372126
$326$	38.7958	2.14870
$327$	17.6080	0.973725
$328$	−48.7367	−2.69103
$329$	−10.6467	−0.586973
$330$	10.2907	0.566482
$331$	25.8056	1.41840	0.709201	−	0.705006i	$-0.249056\pi$
$331$	25.8056	1.41840	0.709201	+	0.705006i	$0.249056\pi$
$332$	51.0118	2.79964
$333$	−10.4270	−0.571394
$334$	27.7278	1.51720
$335$	7.40300	0.404469
$336$	46.2275	2.52192
$337$	−22.4906	−1.22514	−0.612569	−	0.790417i	$-0.709864\pi$
$337$	−22.4906	−1.22514	−0.612569	+	0.790417i	$0.709864\pi$
$338$	29.2410	1.59050
$339$	7.72649	0.419645
$340$	−25.4447	−1.37993
$341$	3.05369	0.165366
$342$	2.62823	0.142118
$343$	15.6167	0.843224
$344$	81.5619	4.39752
$345$	3.11012	0.167443
$346$	40.7057	2.18835
$347$	18.9788	1.01884	0.509418	−	0.860519i	$-0.329861\pi$
$347$	18.9788	1.01884	0.509418	+	0.860519i	$0.329861\pi$
$348$	−93.4254	−5.00813
$349$	1.13316	0.0606569	0.0303284	−	0.999540i	$-0.490345\pi$
$349$	1.13316	0.0606569	0.0303284	+	0.999540i	$0.490345\pi$
$350$	−14.9667	−0.800003
$351$	3.94498	0.210568
$352$	−52.3889	−2.79234
$353$	−11.1008	−0.590833	−0.295417	−	0.955368i	$-0.595458\pi$
$353$	−11.1008	−0.590833	−0.295417	+	0.955368i	$0.595458\pi$
$354$	−75.9419	−4.03627
$355$	7.30023	0.387456
$356$	86.1453	4.56569
$357$	−14.9020	−0.788695
$358$	−1.78802	−0.0944996
$359$	−1.75314	−0.0925273	−0.0462636	−	0.998929i	$-0.514731\pi$
$359$	−1.75314	−0.0925273	−0.0462636	+	0.998929i	$0.514731\pi$
$360$	−15.6667	−0.825710
$361$	−18.7369	−0.986153
$362$	−50.8383	−2.67200
$363$	15.2462	0.800216
$364$	−11.0961	−0.581595
$365$	−7.96583	−0.416951
$366$	77.4011	4.04582
$367$	26.1091	1.36288	0.681441	−	0.731873i	$-0.261353\pi$
$367$	26.1091	1.36288	0.681441	+	0.731873i	$0.261353\pi$
$368$	−28.1867	−1.46933
$369$	8.91780	0.464242
$370$	13.0266	0.677221
$371$	−1.25752	−0.0652874
$372$	−18.8422	−0.976923
$373$	−13.0910	−0.677827	−0.338913	−	0.940818i	$-0.610059\pi$
$373$	−13.0910	−0.677827	−0.338913	+	0.940818i	$0.610059\pi$
$374$	30.0644	1.55459
$375$	17.1278	0.884474
$376$	−85.6798	−4.41860
$377$	11.6943	0.602286
$378$	8.80114	0.452682
$379$	−34.3918	−1.76659	−0.883294	−	0.468819i	$-0.844680\pi$
$379$	−34.3918	−1.76659	−0.883294	+	0.468819i	$0.844680\pi$
$380$	−2.42587	−0.124444
$381$	−7.97423	−0.408532
$382$	33.1825	1.69776
$383$	28.6169	1.46225	0.731127	−	0.682241i	$-0.238995\pi$
$383$	28.6169	1.46225	0.731127	+	0.682241i	$0.238995\pi$
$384$	119.811	6.11406
$385$	−2.12313	−0.108205
$386$	−31.2189	−1.58900
$387$	−14.9241	−0.758636
$388$	45.8322	2.32678
$389$	21.2985	1.07988	0.539938	−	0.841705i	$-0.318448\pi$
$389$	21.2985	1.07988	0.539938	+	0.841705i	$0.318448\pi$
$390$	7.94802	0.402463
$391$	9.08630	0.459514
$392$	54.8364	2.76965
$393$	−4.93274	−0.248824
$394$	−44.6791	−2.25090
$395$	−11.9098	−0.599246
$396$	21.1553	1.06310
$397$	1.04920	0.0526577	0.0263288	−	0.999653i	$-0.491618\pi$
$397$	1.04920	0.0526577	0.0263288	+	0.999653i	$0.491618\pi$
$398$	47.3086	2.37136
$399$	−1.42074	−0.0711258
$400$	−71.7813	−3.58906
$401$	−2.14930	−0.107331	−0.0536654	−	0.998559i	$-0.517090\pi$
$401$	−2.14930	−0.107331	−0.0536654	+	0.998559i	$0.517090\pi$
$402$	53.9723	2.69189
$403$	2.35852	0.117486
$404$	39.9095	1.98557
$405$	−9.30185	−0.462213
$406$	26.0896	1.29480
$407$	−11.3715	−0.563665
$408$	−119.924	−5.93712
$409$	−15.4805	−0.765461	−0.382731	−	0.923860i	$-0.625016\pi$
$409$	−15.4805	−0.765461	−0.382731	+	0.923860i	$0.625016\pi$
$410$	−11.1412	−0.550224
$411$	25.7560	1.27045
$412$	22.4627	1.10666
$413$	15.6681	0.770974
$414$	8.65413	0.425327
$415$	7.53861	0.370056
$416$	−40.4628	−1.98385
$417$	33.1331	1.62254
$418$	2.86631	0.140196
$419$	23.7805	1.16175	0.580876	−	0.813992i	$-0.302710\pi$
$419$	23.7805	1.16175	0.580876	+	0.813992i	$0.302710\pi$
$420$	13.1004	0.639233
$421$	−25.3133	−1.23369	−0.616847	−	0.787083i	$-0.711590\pi$
$421$	−25.3133	−1.23369	−0.616847	+	0.787083i	$0.711590\pi$
$422$	−42.5239	−2.07003
$423$	15.6776	0.762272
$424$	−10.1200	−0.491469
$425$	23.1395	1.12243
$426$	53.2231	2.57867
$427$	−15.9691	−0.772799
$428$	65.1318	3.14826
$429$	−6.93818	−0.334979
$430$	18.6450	0.899141
$431$	−38.4818	−1.85360	−0.926802	−	0.375551i	$-0.877453\pi$
$431$	−38.4818	−1.85360	−0.926802	+	0.375551i	$0.877453\pi$
$432$	42.2108	2.03087
$433$	−24.5568	−1.18012	−0.590062	−	0.807358i	$-0.700897\pi$
$433$	−24.5568	−1.18012	−0.590062	+	0.807358i	$0.700897\pi$
$434$	5.26180	0.252574
$435$	−13.8066	−0.661974
$436$	−45.2231	−2.16579
$437$	0.866278	0.0414397
$438$	−58.0757	−2.77496
$439$	−11.5353	−0.550548	−0.275274	−	0.961366i	$-0.588769\pi$
$439$	−11.5353	−0.550548	−0.275274	+	0.961366i	$0.588769\pi$
$440$	−17.0859	−0.814540
$441$	−10.0339	−0.477805
$442$	23.2203	1.10448
$443$	−27.1619	−1.29050	−0.645251	−	0.763971i	$-0.723247\pi$
$443$	−27.1619	−1.29050	−0.645251	+	0.763971i	$0.723247\pi$
$444$	70.1658	3.32992
$445$	12.7307	0.603493
$446$	44.7604	2.11947
$447$	−0.445694	−0.0210806
$448$	−48.2971	−2.28182
$449$	0.105246	0.00496684	0.00248342	−	0.999997i	$-0.499210\pi$
$449$	0.105246	0.00496684	0.00248342	+	0.999997i	$0.499210\pi$
$450$	22.0389	1.03892
$451$	9.72564	0.457962
$452$	−19.8441	−0.933390
$453$	−2.20267	−0.103490
$454$	24.1462	1.13324
$455$	−1.63980	−0.0768752
$456$	−11.4334	−0.535419
$457$	8.51227	0.398187	0.199094	−	0.979980i	$-0.436200\pi$
$457$	8.51227	0.398187	0.199094	+	0.979980i	$0.436200\pi$
$458$	−7.21952	−0.337346
$459$	−13.6071	−0.635127
$460$	−7.98780	−0.372433
$461$	36.5177	1.70080	0.850400	−	0.526136i	$-0.176360\pi$
$461$	36.5177	1.70080	0.850400	+	0.526136i	$0.176360\pi$
$462$	−15.4789	−0.720143
$463$	−2.63295	−0.122364	−0.0611818	−	0.998127i	$-0.519487\pi$
$463$	−2.63295	−0.122364	−0.0611818	+	0.998127i	$0.519487\pi$
$464$	125.127	5.80890
$465$	−2.78453	−0.129130
$466$	−44.4914	−2.06102
$467$	12.2573	0.567198	0.283599	−	0.958943i	$-0.408472\pi$
$467$	12.2573	0.567198	0.283599	+	0.958943i	$0.408472\pi$
$468$	16.3394	0.755288
$469$	−11.1354	−0.514183
$470$	−19.5863	−0.903451
$471$	9.17624	0.422819
$472$	126.089	5.80372
$473$	−16.2760	−0.748373
$474$	−86.8294	−3.98821
$475$	2.20609	0.101223
$476$	38.2731	1.75424
$477$	1.85174	0.0847854
$478$	−64.9891	−2.97253
$479$	35.4731	1.62081	0.810404	−	0.585871i	$-0.199248\pi$
$479$	35.4731	1.62081	0.810404	+	0.585871i	$0.199248\pi$
$480$	47.7713	2.18045
$481$	−8.78282	−0.400462
$482$	63.4737	2.89115
$483$	−4.67815	−0.212863
$484$	−39.1571	−1.77987
$485$	6.77316	0.307554
$486$	−46.8197	−2.12379
$487$	25.6237	1.16112	0.580561	−	0.814217i	$-0.302833\pi$
$487$	25.6237	1.16112	0.580561	+	0.814217i	$0.302833\pi$
$488$	−128.512	−5.81745
$489$	30.8816	1.39651
$490$	12.5356	0.566298
$491$	33.2061	1.49857	0.749286	−	0.662246i	$-0.230397\pi$
$491$	33.2061	1.49857	0.749286	+	0.662246i	$0.230397\pi$
$492$	−60.0102	−2.70547
$493$	−40.3362	−1.81665
$494$	2.21380	0.0996037
$495$	3.12637	0.140520
$496$	25.2359	1.13313
$497$	−10.9808	−0.492555
$498$	54.9610	2.46286
$499$	8.08393	0.361887	0.180943	−	0.983494i	$-0.442085\pi$
$499$	8.08393	0.361887	0.180943	+	0.983494i	$0.442085\pi$
$500$	−43.9897	−1.96728
$501$	22.0715	0.986080
$502$	−85.0065	−3.79402
$503$	−20.9998	−0.936335	−0.468167	−	0.883640i	$-0.655086\pi$
$503$	−20.9998	−0.936335	−0.468167	+	0.883640i	$0.655086\pi$
$504$	23.5654	1.04969
$505$	5.89789	0.262453
$506$	9.43808	0.419574
$507$	23.2759	1.03372
$508$	20.4804	0.908671
$509$	8.84543	0.392067	0.196033	−	0.980597i	$-0.437194\pi$
$509$	8.84543	0.392067	0.196033	+	0.980597i	$0.437194\pi$
$510$	−27.4145	−1.21394
$511$	11.9820	0.530050
$512$	−95.1588	−4.20547
$513$	−1.29729	−0.0572767
$514$	51.1249	2.25502
$515$	3.31958	0.146278
$516$	100.428	4.42111
$517$	17.0978	0.751960
$518$	−19.5942	−0.860920
$519$	32.4018	1.42228
$520$	−13.1964	−0.578699
$521$	−22.6578	−0.992658	−0.496329	−	0.868134i	$-0.665319\pi$
$521$	−22.6578	−0.992658	−0.496329	+	0.868134i	$0.665319\pi$
$522$	−38.4177	−1.68150
$523$	2.80213	0.122529	0.0612643	−	0.998122i	$-0.480487\pi$
$523$	2.80213	0.122529	0.0612643	+	0.998122i	$0.480487\pi$
$524$	12.6689	0.553443
$525$	−11.9135	−0.519949
$526$	4.93223	0.215055
$527$	−8.13509	−0.354370
$528$	−74.2378	−3.23078
$529$	−20.1476	−0.875980
$530$	−2.31342	−0.100488
$531$	−23.0717	−1.00123
$532$	3.64891	0.158200
$533$	7.51162	0.325365
$534$	92.8144	4.01647
$535$	9.62529	0.416137
$536$	−89.6122	−3.87066
$537$	−1.42327	−0.0614185
$538$	67.5038	2.91030
$539$	−10.9428	−0.471342
$540$	11.9621	0.514766
$541$	0.785493	0.0337710	0.0168855	−	0.999857i	$-0.494625\pi$
$541$	0.785493	0.0337710	0.0168855	+	0.999857i	$0.494625\pi$
$542$	−40.4921	−1.73928
$543$	−40.4675	−1.73663
$544$	139.565	5.98381
$545$	−6.68315	−0.286275
$546$	−11.9552	−0.511634
$547$	−17.2218	−0.736352	−0.368176	−	0.929756i	$-0.620018\pi$
$547$	−17.2218	−0.736352	−0.368176	+	0.929756i	$0.620018\pi$
$548$	−66.1497	−2.82578
$549$	23.5150	1.00359
$550$	24.0353	1.02487
$551$	−3.84561	−0.163829
$552$	−37.6475	−1.60239
$553$	17.9143	0.761794
$554$	−80.8975	−3.43700
$555$	10.3692	0.440149
$556$	−85.0967	−3.60890
$557$	28.7204	1.21692	0.608462	−	0.793583i	$-0.291787\pi$
$557$	28.7204	1.21692	0.608462	+	0.793583i	$0.291787\pi$
$558$	−7.74815	−0.328006
$559$	−12.5709	−0.531690
$560$	−17.5457	−0.741442
$561$	23.9314	1.01038
$562$	29.6883	1.25232
$563$	−13.1113	−0.552575	−0.276287	−	0.961075i	$-0.589104\pi$
$563$	−13.1113	−0.552575	−0.276287	+	0.961075i	$0.589104\pi$
$564$	−105.499	−4.44230
$565$	−2.93260	−0.123375
$566$	−67.2683	−2.82750
$567$	13.9916	0.587590
$568$	−88.3682	−3.70785
$569$	35.0423	1.46905	0.734526	−	0.678581i	$-0.237405\pi$
$569$	35.0423	1.46905	0.734526	+	0.678581i	$0.237405\pi$
$570$	−2.61367	−0.109475
$571$	7.20752	0.301625	0.150813	−	0.988562i	$-0.451811\pi$
$571$	7.20752	0.301625	0.150813	+	0.988562i	$0.451811\pi$
$572$	17.8195	0.745071
$573$	26.4133	1.10343
$574$	16.7582	0.699474
$575$	7.26415	0.302936
$576$	71.1189	2.96329
$577$	−11.4634	−0.477226	−0.238613	−	0.971115i	$-0.576693\pi$
$577$	−11.4634	−0.477226	−0.238613	+	0.971115i	$0.576693\pi$
$578$	−33.0505	−1.37472
$579$	−24.8503	−1.03274
$580$	35.4597	1.47239
$581$	−11.3393	−0.470435
$582$	49.3804	2.04688
$583$	2.01948	0.0836385
$584$	96.4251	3.99010
$585$	2.41466	0.0998340
$586$	−15.3283	−0.633208
$587$	−4.47398	−0.184661	−0.0923305	−	0.995728i	$-0.529432\pi$
$587$	−4.47398	−0.184661	−0.0923305	+	0.995728i	$0.529432\pi$
$588$	67.5208	2.78451
$589$	−0.775590	−0.0319576
$590$	28.8239	1.18666
$591$	−35.5647	−1.46294
$592$	−93.9751	−3.86235
$593$	−17.8343	−0.732365	−0.366183	−	0.930543i	$-0.619335\pi$
$593$	−17.8343	−0.732365	−0.366183	+	0.930543i	$0.619335\pi$
$594$	−14.1339	−0.579923
$595$	5.65606	0.231876
$596$	1.14469	0.0468882
$597$	37.6578	1.54123
$598$	7.28953	0.298091
$599$	−14.9541	−0.611007	−0.305504	−	0.952191i	$-0.598825\pi$
$599$	−14.9541	−0.611007	−0.305504	+	0.952191i	$0.598825\pi$
$600$	−95.8745	−3.91406
$601$	−25.6630	−1.04682	−0.523409	−	0.852082i	$-0.675340\pi$
$601$	−25.6630	−1.04682	−0.523409	+	0.852082i	$0.675340\pi$
$602$	−28.0452	−1.14304
$603$	16.3972	0.667744
$604$	5.65717	0.230187
$605$	−5.78670	−0.235263
$606$	42.9992	1.74672
$607$	37.9183	1.53905	0.769527	−	0.638614i	$-0.220492\pi$
$607$	37.9183	1.53905	0.769527	+	0.638614i	$0.220492\pi$
$608$	13.3060	0.539630
$609$	20.7674	0.841537
$610$	−29.3777	−1.18947
$611$	13.2055	0.534239
$612$	−56.3582	−2.27815
$613$	31.6955	1.28017	0.640084	−	0.768305i	$-0.278900\pi$
$613$	31.6955	1.28017	0.640084	+	0.768305i	$0.278900\pi$
$614$	−70.7682	−2.85597
$615$	−8.86841	−0.357609
$616$	25.7001	1.03549
$617$	−4.40570	−0.177367	−0.0886834	−	0.996060i	$-0.528266\pi$
$617$	−4.40570	−0.177367	−0.0886834	+	0.996060i	$0.528266\pi$
$618$	24.2017	0.973536
$619$	27.1296	1.09043	0.545215	−	0.838296i	$-0.316448\pi$
$619$	27.1296	1.09043	0.545215	+	0.838296i	$0.316448\pi$
$620$	7.15159	0.287215
$621$	−4.27167	−0.171416
$622$	49.4116	1.98122
$623$	−19.1491	−0.767193
$624$	−57.3378	−2.29535
$625$	15.0044	0.600177
$626$	−70.7897	−2.82933
$627$	2.28159	0.0911180
$628$	−23.5676	−0.940448
$629$	30.2939	1.20790
$630$	5.38704	0.214625
$631$	26.2526	1.04510	0.522549	−	0.852609i	$-0.324981\pi$
$631$	26.2526	1.04510	0.522549	+	0.852609i	$0.324981\pi$
$632$	144.166	5.73462
$633$	−33.8491	−1.34538
$634$	−24.3825	−0.968352
$635$	3.02663	0.120108
$636$	−12.4609	−0.494105
$637$	−8.45174	−0.334870
$638$	−41.8978	−1.65875
$639$	16.1695	0.639657
$640$	−45.4743	−1.79753
$641$	−28.6797	−1.13278	−0.566390	−	0.824138i	$-0.691660\pi$
$641$	−28.6797	−1.13278	−0.566390	+	0.824138i	$0.691660\pi$
$642$	70.1741	2.76955
$643$	−50.4025	−1.98768	−0.993840	−	0.110822i	$-0.964652\pi$
$643$	−50.4025	−1.98768	−0.993840	+	0.110822i	$0.964652\pi$
$644$	12.0150	0.473458
$645$	14.8415	0.584382
$646$	−7.63591	−0.300431
$647$	−9.12848	−0.358878	−0.179439	−	0.983769i	$-0.557428\pi$
$647$	−9.12848	−0.358878	−0.179439	+	0.983769i	$0.557428\pi$
$648$	112.597	4.42325
$649$	−25.1617	−0.987682
$650$	18.5638	0.728131
$651$	4.18841	0.164157
$652$	−79.3140	−3.10618
$653$	−45.3052	−1.77293	−0.886464	−	0.462798i	$-0.846846\pi$
$653$	−45.3052	−1.77293	−0.886464	+	0.462798i	$0.846846\pi$
$654$	−48.7242	−1.90527
$655$	1.87223	0.0731540
$656$	80.3735	3.13806
$657$	−17.6438	−0.688350
$658$	29.4612	1.14852
$659$	−11.1669	−0.435000	−0.217500	−	0.976060i	$-0.569790\pi$
$659$	−11.1669	−0.435000	−0.217500	+	0.976060i	$0.569790\pi$
$660$	−21.0382	−0.818909
$661$	−4.22616	−0.164379	−0.0821893	−	0.996617i	$-0.526191\pi$
$661$	−4.22616	−0.164379	−0.0821893	+	0.996617i	$0.526191\pi$
$662$	−71.4081	−2.77535
$663$	18.4835	0.717838
$664$	−91.2538	−3.54133
$665$	0.539243	0.0209109
$666$	28.8531	1.11803
$667$	−12.6627	−0.490301
$668$	−56.6867	−2.19327
$669$	35.6294	1.37751
$670$	−20.4853	−0.791415
$671$	25.6451	0.990019
$672$	−71.8562	−2.77191
$673$	−48.3610	−1.86418	−0.932089	−	0.362230i	$-0.882016\pi$
$673$	−48.3610	−1.86418	−0.932089	+	0.362230i	$0.882016\pi$
$674$	62.2349	2.39720
$675$	−10.8784	−0.418709
$676$	−59.7802	−2.29924
$677$	9.66081	0.371295	0.185647	−	0.982616i	$-0.440562\pi$
$677$	9.66081	0.371295	0.185647	+	0.982616i	$0.440562\pi$
$678$	−21.3804	−0.821110
$679$	−10.1880	−0.390979
$680$	45.5173	1.74551
$681$	19.2204	0.736529
$682$	−8.45004	−0.323569
$683$	−30.8968	−1.18223	−0.591117	−	0.806586i	$-0.701313\pi$
$683$	−30.8968	−1.18223	−0.591117	+	0.806586i	$0.701313\pi$
$684$	−5.37313	−0.205447
$685$	−9.77571	−0.373511
$686$	−43.2140	−1.64992
$687$	−5.74676	−0.219253
$688$	−134.507	−5.12802
$689$	1.55975	0.0594219
$690$	−8.60620	−0.327632
$691$	−25.2849	−0.961884	−0.480942	−	0.876752i	$-0.659705\pi$
$691$	−25.2849	−0.961884	−0.480942	+	0.876752i	$0.659705\pi$
$692$	−83.2185	−3.16349
$693$	−4.70259	−0.178637
$694$	−52.5174	−1.99353
$695$	−12.5757	−0.477025
$696$	167.126	6.33490
$697$	−25.9093	−0.981385
$698$	−3.13564	−0.118686
$699$	−35.4153	−1.33953
$700$	30.5978	1.15649
$701$	−42.3945	−1.60122	−0.800609	−	0.599187i	$-0.795491\pi$
$701$	−42.3945	−1.60122	−0.800609	+	0.599187i	$0.795491\pi$
$702$	−10.9164	−0.412013
$703$	2.88819	0.108930
$704$	77.5614	2.92320
$705$	−15.5908	−0.587183
$706$	30.7175	1.15607
$707$	−8.87143	−0.333644
$708$	155.255	5.83485
$709$	23.2801	0.874302	0.437151	−	0.899388i	$-0.355988\pi$
$709$	23.2801	0.874302	0.437151	+	0.899388i	$0.355988\pi$
$710$	−20.2009	−0.758126
$711$	−26.3794	−0.989304
$712$	−154.103	−5.77526
$713$	−2.55384	−0.0956419
$714$	41.2361	1.54322
$715$	2.63340	0.0984835
$716$	3.65541	0.136609
$717$	−51.7315	−1.93195
$718$	4.85122	0.181046
$719$	40.4581	1.50883	0.754416	−	0.656396i	$-0.227920\pi$
$719$	40.4581	1.50883	0.754416	+	0.656396i	$0.227920\pi$
$720$	25.8366	0.962873
$721$	−4.99321	−0.185957
$722$	51.8480	1.92958
$723$	50.5252	1.87905
$724$	103.934	3.86266
$725$	−32.2473	−1.19763
$726$	−42.1885	−1.56576
$727$	−31.2604	−1.15938	−0.579692	−	0.814836i	$-0.696827\pi$
$727$	−31.2604	−1.15938	−0.579692	+	0.814836i	$0.696827\pi$
$728$	19.8496	0.735674
$729$	−3.88982	−0.144068
$730$	22.0427	0.815838
$731$	43.3597	1.60372
$732$	−158.238	−5.84866
$733$	−24.5736	−0.907646	−0.453823	−	0.891092i	$-0.649940\pi$
$733$	−24.5736	−0.907646	−0.453823	+	0.891092i	$0.649940\pi$
$734$	−72.2479	−2.66672
$735$	9.97834	0.368057
$736$	43.8135	1.61499
$737$	17.8825	0.658711
$738$	−24.6770	−0.908372
$739$	−20.4394	−0.751876	−0.375938	−	0.926645i	$-0.622679\pi$
$739$	−20.4394	−0.751876	−0.375938	+	0.926645i	$0.622679\pi$
$740$	−26.6315	−0.978994
$741$	1.76219	0.0647358
$742$	3.47977	0.127746
$743$	−28.1251	−1.03181	−0.515905	−	0.856646i	$-0.672544\pi$
$743$	−28.1251	−1.03181	−0.515905	+	0.856646i	$0.672544\pi$
$744$	33.7063	1.23573
$745$	0.169164	0.00619768
$746$	36.2249	1.32629
$747$	16.6975	0.610931
$748$	−61.4636	−2.24733
$749$	−14.4781	−0.529017
$750$	−47.3953	−1.73063
$751$	11.8780	0.433433	0.216716	−	0.976235i	$-0.430465\pi$
$751$	11.8780	0.433433	0.216716	+	0.976235i	$0.430465\pi$
$752$	141.298	5.15260
$753$	−67.6654	−2.46586
$754$	−32.3599	−1.17848
$755$	0.836026	0.0304261
$756$	−17.9930	−0.654399
$757$	−29.4333	−1.06977	−0.534886	−	0.844924i	$-0.679645\pi$
$757$	−29.4333	−1.06977	−0.534886	+	0.844924i	$0.679645\pi$
$758$	95.1676	3.45664
$759$	7.51274	0.272695
$760$	4.33957	0.157413
$761$	−48.1077	−1.74390	−0.871951	−	0.489593i	$-0.837145\pi$
$761$	−48.1077	−1.74390	−0.871951	+	0.489593i	$0.837145\pi$
$762$	22.0659	0.799365
$763$	10.0526	0.363928
$764$	−67.8381	−2.45429
$765$	−8.32872	−0.301125
$766$	−79.1874	−2.86116
$767$	−19.4337	−0.701710
$768$	−162.341	−5.85799
$769$	−16.8853	−0.608901	−0.304451	−	0.952528i	$-0.598473\pi$
$769$	−16.8853	−0.608901	−0.304451	+	0.952528i	$0.598473\pi$
$770$	5.87503	0.211721
$771$	40.6956	1.46562
$772$	63.8238	2.29707
$773$	13.8931	0.499700	0.249850	−	0.968285i	$-0.419619\pi$
$773$	13.8931	0.499700	0.249850	+	0.968285i	$0.419619\pi$
$774$	41.2974	1.48440
$775$	−6.50369	−0.233619
$776$	−81.9881	−2.94320
$777$	−15.5970	−0.559541
$778$	−58.9363	−2.11297
$779$	−2.47016	−0.0885028
$780$	−16.2489	−0.581804
$781$	17.6343	0.631004
$782$	−25.1432	−0.899120
$783$	18.9629	0.677680
$784$	−90.4327	−3.22974
$785$	−3.48286	−0.124308
$786$	13.6497	0.486868
$787$	17.3554	0.618653	0.309326	−	0.950956i	$-0.399896\pi$
$787$	17.3554	0.618653	0.309326	+	0.950956i	$0.399896\pi$
$788$	91.3418	3.25392
$789$	3.92607	0.139772
$790$	32.9562	1.17253
$791$	4.41113	0.156842
$792$	−37.8442	−1.34474
$793$	19.8071	0.703370
$794$	−2.90329	−0.103034
$795$	−1.84149	−0.0653108
$796$	−96.7174	−3.42806
$797$	30.5805	1.08322	0.541609	−	0.840630i	$-0.317815\pi$
$797$	30.5805	1.08322	0.541609	+	0.840630i	$0.317815\pi$
$798$	3.93140	0.139170
$799$	−45.5489	−1.61140
$800$	111.577	3.94484
$801$	28.1977	0.996315
$802$	5.94745	0.210012
$803$	−19.2421	−0.679038
$804$	−110.341	−3.89142
$805$	1.77560	0.0625816
$806$	−6.52641	−0.229883
$807$	53.7332	1.89150
$808$	−71.3931	−2.51160
$809$	−12.4071	−0.436211	−0.218105	−	0.975925i	$-0.569988\pi$
$809$	−12.4071	−0.436211	−0.218105	+	0.975925i	$0.569988\pi$
$810$	25.7397	0.904401
$811$	32.7807	1.15108	0.575542	−	0.817772i	$-0.304791\pi$
$811$	32.7807	1.15108	0.575542	+	0.817772i	$0.304791\pi$
$812$	−53.3374	−1.87178
$813$	−32.2318	−1.13042
$814$	31.4668	1.10291
$815$	−11.7212	−0.410574
$816$	197.771	6.92337
$817$	4.13387	0.144626
$818$	42.8370	1.49776
$819$	−3.63206	−0.126914
$820$	22.7770	0.795406
$821$	−9.60362	−0.335168	−0.167584	−	0.985858i	$-0.553597\pi$
$821$	−9.60362	−0.335168	−0.167584	+	0.985858i	$0.553597\pi$
$822$	−71.2708	−2.48586
$823$	−21.5027	−0.749538	−0.374769	−	0.927118i	$-0.622278\pi$
$823$	−21.5027	−0.749538	−0.374769	+	0.927118i	$0.622278\pi$
$824$	−40.1830	−1.39984
$825$	19.1322	0.666098
$826$	−43.3560	−1.50855
$827$	14.3316	0.498359	0.249179	−	0.968457i	$-0.419839\pi$
$827$	14.3316	0.498359	0.249179	+	0.968457i	$0.419839\pi$
$828$	−17.6925	−0.614855
$829$	−35.5313	−1.23405	−0.617027	−	0.786942i	$-0.711663\pi$
$829$	−35.5313	−1.23405	−0.617027	+	0.786942i	$0.711663\pi$
$830$	−20.8605	−0.724080
$831$	−64.3946	−2.23383
$832$	59.9047	2.07682
$833$	29.1520	1.01006
$834$	−91.6847	−3.17478
$835$	−8.37725	−0.289907
$836$	−5.85987	−0.202668
$837$	3.82448	0.132193
$838$	−65.8043	−2.27317
$839$	−18.7234	−0.646404	−0.323202	−	0.946330i	$-0.604759\pi$
$839$	−18.7234	−0.646404	−0.323202	+	0.946330i	$0.604759\pi$
$840$	−23.4349	−0.808581
$841$	27.2127	0.938368
$842$	70.0458	2.41394
$843$	23.6319	0.813927
$844$	86.9356	2.99245
$845$	−8.83442	−0.303913
$846$	−43.3824	−1.49152
$847$	8.70418	0.299079
$848$	16.6892	0.573109
$849$	−53.5458	−1.83769
$850$	−64.0306	−2.19623
$851$	9.51013	0.326003
$852$	−108.809	−3.72774
$853$	19.6299	0.672114	0.336057	−	0.941842i	$-0.390906\pi$
$853$	19.6299	0.672114	0.336057	+	0.941842i	$0.390906\pi$
$854$	44.1890	1.51212
$855$	−0.794051	−0.0271560
$856$	−116.513	−3.98232
$857$	−29.7177	−1.01514	−0.507568	−	0.861612i	$-0.669455\pi$
$857$	−29.7177	−1.01514	−0.507568	+	0.861612i	$0.669455\pi$
$858$	19.1991	0.655445
$859$	−32.6598	−1.11434	−0.557170	−	0.830399i	$-0.688113\pi$
$859$	−32.6598	−1.11434	−0.557170	+	0.830399i	$0.688113\pi$
$860$	−38.1177	−1.29980
$861$	13.3396	0.454612
$862$	106.485	3.62690
$863$	8.92297	0.303741	0.151871	−	0.988400i	$-0.451470\pi$
$863$	8.92297	0.303741	0.151871	+	0.988400i	$0.451470\pi$
$864$	−65.6127	−2.23219
$865$	−12.2982	−0.418150
$866$	67.9525	2.30912
$867$	−26.3083	−0.893478
$868$	−10.7572	−0.365123
$869$	−28.7690	−0.975921
$870$	38.2049	1.29527
$871$	13.8116	0.467989
$872$	80.8984	2.73957
$873$	15.0021	0.507744
$874$	−2.39713	−0.0810841
$875$	9.77841	0.330571
$876$	118.730	4.01150
$877$	−40.4704	−1.36659	−0.683295	−	0.730143i	$-0.739454\pi$
$877$	−40.4704	−1.36659	−0.683295	+	0.730143i	$0.739454\pi$
$878$	31.9199	1.07724
$879$	−12.2014	−0.411543
$880$	28.1771	0.949848
$881$	−9.48514	−0.319562	−0.159781	−	0.987152i	$-0.551079\pi$
$881$	−9.48514	−0.319562	−0.159781	+	0.987152i	$0.551079\pi$
$882$	27.7654	0.934910
$883$	−37.6226	−1.26610	−0.633050	−	0.774111i	$-0.718197\pi$
$883$	−37.6226	−1.26610	−0.633050	+	0.774111i	$0.718197\pi$
$884$	−47.4716	−1.59664
$885$	22.9439	0.771251
$886$	75.1613	2.52509
$887$	9.35859	0.314231	0.157115	−	0.987580i	$-0.449781\pi$
$887$	9.35859	0.314231	0.157115	+	0.987580i	$0.449781\pi$
$888$	−125.518	−4.21210
$889$	−4.55256	−0.152688
$890$	−35.2279	−1.18084
$891$	−22.4693	−0.752751
$892$	−91.5079	−3.06391
$893$	−4.34258	−0.145319
$894$	1.23331	0.0412479
$895$	0.540203	0.0180570
$896$	68.4010	2.28512
$897$	5.80249	0.193739
$898$	−0.291231	−0.00971851
$899$	11.3371	0.378113
$900$	−45.0562	−1.50187
$901$	−5.37995	−0.179232
$902$	−26.9124	−0.896084
$903$	−22.3241	−0.742899
$904$	35.4987	1.18067
$905$	15.3595	0.510567
$906$	6.09513	0.202497
$907$	−54.2340	−1.80081	−0.900405	−	0.435054i	$-0.856729\pi$
$907$	−54.2340	−1.80081	−0.900405	+	0.435054i	$0.856729\pi$
$908$	−49.3644	−1.63821
$909$	13.0634	0.433287
$910$	4.53760	0.150420
$911$	−26.4460	−0.876196	−0.438098	−	0.898927i	$-0.644348\pi$
$911$	−26.4460	−0.876196	−0.438098	+	0.898927i	$0.644348\pi$
$912$	18.8553	0.624360
$913$	18.2101	0.602667
$914$	−23.5548	−0.779123
$915$	−23.3847	−0.773076
$916$	14.7596	0.487670
$917$	−2.81615	−0.0929974
$918$	37.6531	1.24274
$919$	−29.9728	−0.988711	−0.494355	−	0.869260i	$-0.664596\pi$
$919$	−29.9728	−0.988711	−0.494355	+	0.869260i	$0.664596\pi$
$920$	14.2892	0.471100
$921$	−56.3317	−1.85619
$922$	−101.050	−3.32792
$923$	13.6199	0.448304
$924$	31.6450	1.04104
$925$	24.2188	0.796310
$926$	7.28579	0.239426
$927$	7.35265	0.241493
$928$	−194.498	−6.38472
$929$	4.57768	0.150189	0.0750945	−	0.997176i	$-0.476074\pi$
$929$	4.57768	0.150189	0.0750945	+	0.997176i	$0.476074\pi$
$930$	7.70524	0.252665
$931$	2.77932	0.0910885
$932$	90.9579	2.97943
$933$	39.3318	1.28766
$934$	−33.9178	−1.10982
$935$	−9.08319	−0.297052
$936$	−29.2291	−0.955383
$937$	−48.6219	−1.58841	−0.794205	−	0.607650i	$-0.792112\pi$
$937$	−48.6219	−1.58841	−0.794205	+	0.607650i	$0.792112\pi$
$938$	30.8133	1.00609
$939$	−56.3488	−1.83888
$940$	40.0422	1.30603
$941$	−20.3282	−0.662682	−0.331341	−	0.943511i	$-0.607501\pi$
$941$	−20.3282	−0.662682	−0.331341	+	0.943511i	$0.607501\pi$
$942$	−25.3921	−0.827319
$943$	−8.13367	−0.264869
$944$	−207.938	−6.76781
$945$	−2.65904	−0.0864985
$946$	45.0384	1.46432
$947$	−26.9393	−0.875409	−0.437704	−	0.899119i	$-0.644208\pi$
$947$	−26.9393	−0.875409	−0.437704	+	0.899119i	$0.644208\pi$
$948$	177.514	5.76538
$949$	−14.8617	−0.482431
$950$	−6.10461	−0.198060
$951$	−19.4085	−0.629365
$952$	−68.4657	−2.21899
$953$	38.8860	1.25964	0.629820	−	0.776741i	$-0.283129\pi$
$953$	38.8860	1.25964	0.629820	+	0.776741i	$0.283129\pi$
$954$	−5.12406	−0.165898
$955$	−10.0252	−0.324409
$956$	132.863	4.29711
$957$	−33.3508	−1.07808
$958$	−98.1597	−3.17140
$959$	14.7043	0.474827
$960$	−70.7250	−2.28264
$961$	−28.7135	−0.926242
$962$	24.3034	0.783575
$963$	21.3194	0.687007
$964$	−129.765	−4.17946
$965$	9.43198	0.303626
$966$	12.9452	0.416504
$967$	8.64497	0.278004	0.139002	−	0.990292i	$-0.455611\pi$
$967$	8.64497	0.278004	0.139002	+	0.990292i	$0.455611\pi$
$968$	70.0471	2.25140
$969$	−6.07821	−0.195260
$970$	−18.7424	−0.601783
$971$	−44.8576	−1.43955	−0.719775	−	0.694208i	$-0.755755\pi$
$971$	−44.8576	−1.43955	−0.719775	+	0.694208i	$0.755755\pi$
$972$	95.7181	3.07016
$973$	18.9160	0.606420
$974$	−70.9049	−2.27194
$975$	14.7768	0.473237
$976$	211.934	6.78383
$977$	−44.2373	−1.41528	−0.707638	−	0.706575i	$-0.750239\pi$
$977$	−44.2373	−1.41528	−0.707638	+	0.706575i	$0.750239\pi$
$978$	−85.4543	−2.73253
$979$	30.7520	0.982838
$980$	−25.6276	−0.818644
$981$	−14.8027	−0.472615
$982$	−91.8867	−2.93222
$983$	30.6957	0.979041	0.489520	−	0.871992i	$-0.337172\pi$
$983$	30.6957	0.979041	0.489520	+	0.871992i	$0.337172\pi$
$984$	107.351	3.42222
$985$	13.4986	0.430103
$986$	111.617	3.55460
$987$	23.4512	0.746459
$988$	−4.52589	−0.143988
$989$	13.6119	0.432832
$990$	−8.65116	−0.274952
$991$	17.0054	0.540194	0.270097	−	0.962833i	$-0.412944\pi$
$991$	17.0054	0.540194	0.270097	+	0.962833i	$0.412944\pi$
$992$	−39.2268	−1.24545
$993$	−56.8411	−1.80380
$994$	30.3856	0.963772
$995$	−14.2931	−0.453120
$996$	−112.362	−3.56033
$997$	44.5444	1.41074	0.705368	−	0.708841i	$-0.250782\pi$
$997$	44.5444	1.41074	0.705368	+	0.708841i	$0.250782\pi$
$998$	−22.3695	−0.708095
$999$	−14.2418	−0.450592

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.76716 q^{2} -2.20267 q^{3} +5.65717 q^{4} +0.836026 q^{5} +6.09513 q^{6} -1.25752 q^{7} -10.1200 q^{8} +1.85174 q^{9} +O(q^{10})\)	\(q-2.76716 q^{2} -2.20267 q^{3} +5.65717 q^{4} +0.836026 q^{5} +6.09513 q^{6} -1.25752 q^{7} -10.1200 q^{8} +1.85174 q^{9} -2.31342 q^{10} +2.01948 q^{11} -12.4609 q^{12} +1.55975 q^{13} +3.47977 q^{14} -1.84149 q^{15} +16.6892 q^{16} -5.37995 q^{17} -5.12406 q^{18} -0.512919 q^{19} +4.72954 q^{20} +2.76991 q^{21} -5.58823 q^{22} -1.68892 q^{23} +22.2909 q^{24} -4.30106 q^{25} -4.31609 q^{26} +2.52923 q^{27} -7.11402 q^{28} +7.49751 q^{29} +5.09568 q^{30} +1.51211 q^{31} -25.9417 q^{32} -4.44825 q^{33} +14.8872 q^{34} -1.05132 q^{35} +10.4756 q^{36} -5.63090 q^{37} +1.41933 q^{38} -3.43562 q^{39} -8.46054 q^{40} +4.81590 q^{41} -7.66477 q^{42} -8.05951 q^{43} +11.4246 q^{44} +1.54810 q^{45} +4.67351 q^{46} +8.46642 q^{47} -36.7607 q^{48} -5.41863 q^{49} +11.9017 q^{50} +11.8502 q^{51} +8.82379 q^{52} +1.00000 q^{53} -6.99879 q^{54} +1.68834 q^{55} +12.7261 q^{56} +1.12979 q^{57} -20.7468 q^{58} -12.4594 q^{59} -10.4176 q^{60} +12.6988 q^{61} -4.18425 q^{62} -2.32861 q^{63} +38.4065 q^{64} +1.30400 q^{65} +12.3090 q^{66} +8.85499 q^{67} -30.4353 q^{68} +3.72013 q^{69} +2.90917 q^{70} +8.73207 q^{71} -18.7395 q^{72} -9.52821 q^{73} +15.5816 q^{74} +9.47380 q^{75} -2.90167 q^{76} -2.53955 q^{77} +9.50691 q^{78} -14.2457 q^{79} +13.9526 q^{80} -11.1263 q^{81} -13.3264 q^{82} +9.01721 q^{83} +15.6698 q^{84} -4.49778 q^{85} +22.3019 q^{86} -16.5145 q^{87} -20.4371 q^{88} +15.2276 q^{89} -4.28385 q^{90} -1.96143 q^{91} -9.55450 q^{92} -3.33068 q^{93} -23.4279 q^{94} -0.428813 q^{95} +57.1410 q^{96} +8.10162 q^{97} +14.9942 q^{98} +3.73956 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 147 q - 6 q^{2} - 23 q^{3} + 130 q^{4} - 25 q^{5} - 18 q^{6} - 33 q^{7} - 15 q^{8} + 114 q^{9}+O(q^{10}) \) 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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