LMFDB - Embedded newform 8003.2.a.b.1.5

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:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
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)

$f(q)$	$=$	$q-2.64082 q^{2} +1.90424 q^{3} +4.97394 q^{4} +2.87158 q^{5} -5.02877 q^{6} +0.865912 q^{7} -7.85365 q^{8} +0.626146 q^{9} +O(q^{10})$	\(q-2.64082 q^{2} +1.90424 q^{3} +4.97394 q^{4} +2.87158 q^{5} -5.02877 q^{6} +0.865912 q^{7} -7.85365 q^{8} +0.626146 q^{9} -7.58334 q^{10} -5.07692 q^{11} +9.47160 q^{12} -1.58864 q^{13} -2.28672 q^{14} +5.46820 q^{15} +10.7922 q^{16} +4.06347 q^{17} -1.65354 q^{18} -2.49635 q^{19} +14.2831 q^{20} +1.64891 q^{21} +13.4073 q^{22} +3.25725 q^{23} -14.9553 q^{24} +3.24599 q^{25} +4.19532 q^{26} -4.52040 q^{27} +4.30700 q^{28} +4.81083 q^{29} -14.4405 q^{30} -7.75030 q^{31} -12.7930 q^{32} -9.66770 q^{33} -10.7309 q^{34} +2.48654 q^{35} +3.11442 q^{36} +2.59888 q^{37} +6.59241 q^{38} -3.02516 q^{39} -22.5524 q^{40} -8.69377 q^{41} -4.35447 q^{42} +8.52505 q^{43} -25.2523 q^{44} +1.79803 q^{45} -8.60181 q^{46} -4.47985 q^{47} +20.5510 q^{48} -6.25020 q^{49} -8.57208 q^{50} +7.73783 q^{51} -7.90182 q^{52} -1.00000 q^{53} +11.9376 q^{54} -14.5788 q^{55} -6.80057 q^{56} -4.75366 q^{57} -12.7046 q^{58} -7.84810 q^{59} +27.1985 q^{60} -5.71184 q^{61} +20.4672 q^{62} +0.542187 q^{63} +12.1997 q^{64} -4.56192 q^{65} +25.5307 q^{66} -2.28294 q^{67} +20.2114 q^{68} +6.20260 q^{69} -6.56650 q^{70} -10.9402 q^{71} -4.91754 q^{72} -5.06707 q^{73} -6.86317 q^{74} +6.18116 q^{75} -12.4167 q^{76} -4.39617 q^{77} +7.98892 q^{78} -7.96414 q^{79} +30.9908 q^{80} -10.4864 q^{81} +22.9587 q^{82} +3.51804 q^{83} +8.20157 q^{84} +11.6686 q^{85} -22.5131 q^{86} +9.16100 q^{87} +39.8724 q^{88} +3.47330 q^{89} -4.74828 q^{90} -1.37562 q^{91} +16.2014 q^{92} -14.7585 q^{93} +11.8305 q^{94} -7.16847 q^{95} -24.3610 q^{96} +10.2628 q^{97} +16.5057 q^{98} -3.17890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) $ 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * 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 $

$2$	−2.64082	−1.86734	−0.933672	−	0.358130i	$-0.883414\pi$
$2$	−2.64082	−1.86734	−0.933672	+	0.358130i	$0.883414\pi$
$3$	1.90424	1.09942	0.549708	−	0.835357i	$-0.314739\pi$
$3$	1.90424	1.09942	0.549708	+	0.835357i	$0.314739\pi$
$4$	4.97394	2.48697
$5$	2.87158	1.28421	0.642105	−	0.766616i	$-0.278061\pi$
$5$	2.87158	1.28421	0.642105	+	0.766616i	$0.278061\pi$
$6$	−5.02877	−2.05299
$7$	0.865912	0.327284	0.163642	−	0.986520i	$-0.447676\pi$
$7$	0.865912	0.327284	0.163642	+	0.986520i	$0.447676\pi$
$8$	−7.85365	−2.77669
$9$	0.626146	0.208715
$10$	−7.58334	−2.39806
$11$	−5.07692	−1.53075	−0.765375	−	0.643584i	$-0.777447\pi$
$11$	−5.07692	−1.53075	−0.765375	+	0.643584i	$0.777447\pi$
$12$	9.47160	2.73422
$13$	−1.58864	−0.440610	−0.220305	−	0.975431i	$-0.570705\pi$
$13$	−1.58864	−0.440610	−0.220305	+	0.975431i	$0.570705\pi$
$14$	−2.28672	−0.611151
$15$	5.46820	1.41188
$16$	10.7922	2.69805
$17$	4.06347	0.985535	0.492768	−	0.870161i	$-0.335985\pi$
$17$	4.06347	0.985535	0.492768	+	0.870161i	$0.335985\pi$
$18$	−1.65354	−0.389743
$19$	−2.49635	−0.572702	−0.286351	−	0.958125i	$-0.592442\pi$
$19$	−2.49635	−0.572702	−0.286351	+	0.958125i	$0.592442\pi$
$20$	14.2831	3.19380
$21$	1.64891	0.359821
$22$	13.4073	2.85844
$23$	3.25725	0.679183	0.339592	−	0.940573i	$-0.389711\pi$
$23$	3.25725	0.679183	0.339592	+	0.940573i	$0.389711\pi$
$24$	−14.9553	−3.05273
$25$	3.24599	0.649198
$26$	4.19532	0.822770
$27$	−4.52040	−0.869951
$28$	4.30700	0.813946
$29$	4.81083	0.893349	0.446675	−	0.894696i	$-0.352608\pi$
$29$	4.81083	0.893349	0.446675	+	0.894696i	$0.352608\pi$
$30$	−14.4405	−2.63647
$31$	−7.75030	−1.39199	−0.695997	−	0.718044i	$-0.745038\pi$
$31$	−7.75030	−1.39199	−0.695997	+	0.718044i	$0.745038\pi$
$32$	−12.7930	−2.26151
$33$	−9.66770	−1.68293
$34$	−10.7309	−1.84033
$35$	2.48654	0.420302
$36$	3.11442	0.519069
$37$	2.59888	0.427253	0.213626	−	0.976915i	$-0.431472\pi$
$37$	2.59888	0.427253	0.213626	+	0.976915i	$0.431472\pi$
$38$	6.59241	1.06943
$39$	−3.02516	−0.484414
$40$	−22.5524	−3.56585
$41$	−8.69377	−1.35774	−0.678869	−	0.734259i	$-0.737530\pi$
$41$	−8.69377	−1.35774	−0.678869	+	0.734259i	$0.737530\pi$
$42$	−4.35447	−0.671910
$43$	8.52505	1.30006	0.650029	−	0.759909i	$-0.274757\pi$
$43$	8.52505	1.30006	0.650029	+	0.759909i	$0.274757\pi$
$44$	−25.2523	−3.80693
$45$	1.79803	0.268035
$46$	−8.60181	−1.26827
$47$	−4.47985	−0.653453	−0.326726	−	0.945119i	$-0.605946\pi$
$47$	−4.47985	−0.653453	−0.326726	+	0.945119i	$0.605946\pi$
$48$	20.5510	2.96628
$49$	−6.25020	−0.892885
$50$	−8.57208	−1.21228
$51$	7.73783	1.08351
$52$	−7.90182	−1.09578
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	11.9376	1.62450
$55$	−14.5788	−1.96581
$56$	−6.80057	−0.908765
$57$	−4.75366	−0.629637
$58$	−12.7046	−1.66819
$59$	−7.84810	−1.02174	−0.510868	−	0.859659i	$-0.670676\pi$
$59$	−7.84810	−1.02174	−0.510868	+	0.859659i	$0.670676\pi$
$60$	27.1985	3.51131
$61$	−5.71184	−0.731326	−0.365663	−	0.930747i	$-0.619158\pi$
$61$	−5.71184	−0.731326	−0.365663	+	0.930747i	$0.619158\pi$
$62$	20.4672	2.59933
$63$	0.542187	0.0683092
$64$	12.1997	1.52496
$65$	−4.56192	−0.565836
$66$	25.5307	3.14261
$67$	−2.28294	−0.278906	−0.139453	−	0.990229i	$-0.544534\pi$
$67$	−2.28294	−0.278906	−0.139453	+	0.990229i	$0.544534\pi$
$68$	20.2114	2.45100
$69$	6.20260	0.746705
$70$	−6.56650	−0.784847
$71$	−10.9402	−1.29836	−0.649179	−	0.760636i	$-0.724887\pi$
$71$	−10.9402	−1.29836	−0.649179	+	0.760636i	$0.724887\pi$
$72$	−4.91754	−0.579537
$73$	−5.06707	−0.593056	−0.296528	−	0.955024i	$-0.595829\pi$
$73$	−5.06707	−0.593056	−0.296528	+	0.955024i	$0.595829\pi$
$74$	−6.86317	−0.797828
$75$	6.18116	0.713738
$76$	−12.4167	−1.42429
$77$	−4.39617	−0.500990
$78$	7.98892	0.904567
$79$	−7.96414	−0.896035	−0.448018	−	0.894025i	$-0.647870\pi$
$79$	−7.96414	−0.896035	−0.448018	+	0.894025i	$0.647870\pi$
$80$	30.9908	3.46487
$81$	−10.4864	−1.16515
$82$	22.9587	2.53536
$83$	3.51804	0.386155	0.193077	−	0.981184i	$-0.438153\pi$
$83$	3.51804	0.386155	0.193077	+	0.981184i	$0.438153\pi$
$84$	8.20157	0.894865
$85$	11.6686	1.26564
$86$	−22.5131	−2.42765
$87$	9.16100	0.982162
$88$	39.8724	4.25041
$89$	3.47330	0.368169	0.184084	−	0.982910i	$-0.441068\pi$
$89$	3.47330	0.368169	0.184084	+	0.982910i	$0.441068\pi$
$90$	−4.74828	−0.500513
$91$	−1.37562	−0.144205
$92$	16.2014	1.68911
$93$	−14.7585	−1.53038
$94$	11.8305	1.22022
$95$	−7.16847	−0.735470
$96$	−24.3610	−2.48634
$97$	10.2628	1.04203	0.521015	−	0.853548i	$-0.325554\pi$
$97$	10.2628	1.04203	0.521015	+	0.853548i	$0.325554\pi$
$98$	16.5057	1.66732
$99$	−3.17890	−0.319491
$100$	16.1454	1.61454
$101$	−6.44317	−0.641119	−0.320560	−	0.947228i	$-0.603871\pi$
$101$	−6.44317	−0.641119	−0.320560	+	0.947228i	$0.603871\pi$
$102$	−20.4342	−2.02329
$103$	18.9566	1.86785	0.933923	−	0.357474i	$-0.116362\pi$
$103$	18.9566	1.86785	0.933923	+	0.357474i	$0.116362\pi$
$104$	12.4766	1.22344
$105$	4.73497	0.462086
$106$	2.64082	0.256499
$107$	7.46514	0.721682	0.360841	−	0.932627i	$-0.382490\pi$
$107$	7.46514	0.721682	0.360841	+	0.932627i	$0.382490\pi$
$108$	−22.4842	−2.16354
$109$	−15.2660	−1.46222	−0.731111	−	0.682259i	$-0.760998\pi$
$109$	−15.2660	−1.46222	−0.731111	+	0.682259i	$0.760998\pi$
$110$	38.5000	3.67084
$111$	4.94890	0.469729
$112$	9.34511	0.883030
$113$	−7.09890	−0.667809	−0.333904	−	0.942607i	$-0.608366\pi$
$113$	−7.09890	−0.667809	−0.333904	+	0.942607i	$0.608366\pi$
$114$	12.5536	1.17575
$115$	9.35346	0.872215
$116$	23.9288	2.22173
$117$	−0.994723	−0.0919622
$118$	20.7254	1.90793
$119$	3.51860	0.322550
$120$	−42.9453	−3.92035
$121$	14.7752	1.34320
$122$	15.0840	1.36564
$123$	−16.5551	−1.49272
$124$	−38.5495	−3.46185
$125$	−5.03679	−0.450504
$126$	−1.43182	−0.127557
$127$	4.37883	0.388559	0.194279	−	0.980946i	$-0.437763\pi$
$127$	4.37883	0.388559	0.194279	+	0.980946i	$0.437763\pi$
$128$	−6.63111	−0.586113
$129$	16.2338	1.42930
$130$	12.0472	1.05661
$131$	10.4704	0.914806	0.457403	−	0.889260i	$-0.348780\pi$
$131$	10.4704	0.914806	0.457403	+	0.889260i	$0.348780\pi$
$132$	−48.0866	−4.18540
$133$	−2.16162	−0.187436
$134$	6.02884	0.520812
$135$	−12.9807	−1.11720
$136$	−31.9131	−2.73652
$137$	2.51642	0.214992	0.107496	−	0.994206i	$-0.465717\pi$
$137$	2.51642	0.214992	0.107496	+	0.994206i	$0.465717\pi$
$138$	−16.3800	−1.39435
$139$	−13.4906	−1.14426	−0.572129	−	0.820164i	$-0.693882\pi$
$139$	−13.4906	−1.14426	−0.572129	+	0.820164i	$0.693882\pi$
$140$	12.3679	1.04528
$141$	−8.53072	−0.718416
$142$	28.8910	2.42448
$143$	8.06542	0.674464
$144$	6.75751	0.563126
$145$	13.8147	1.14725
$146$	13.3812	1.10744
$147$	−11.9019	−0.981652
$148$	12.9267	1.06257
$149$	2.61309	0.214073	0.107036	−	0.994255i	$-0.465864\pi$
$149$	2.61309	0.214073	0.107036	+	0.994255i	$0.465864\pi$
$150$	−16.3233	−1.33279
$151$	−1.00000	−0.0813788
$151$	−1.00000	−0.0813788
$152$	19.6055	1.59021
$153$	2.54432	0.205696
$154$	11.6095	0.935520
$155$	−22.2556	−1.78762
$156$	−15.0470	−1.20472
$157$	−18.2827	−1.45912	−0.729559	−	0.683918i	$-0.760275\pi$
$157$	−18.2827	−1.45912	−0.729559	+	0.683918i	$0.760275\pi$
$158$	21.0319	1.67321
$159$	−1.90424	−0.151016
$160$	−36.7362	−2.90425
$161$	2.82049	0.222286
$162$	27.6927	2.17574
$163$	−4.77495	−0.374003	−0.187002	−	0.982360i	$-0.559877\pi$
$163$	−4.77495	−0.374003	−0.187002	+	0.982360i	$0.559877\pi$
$164$	−43.2423	−3.37666
$165$	−27.7616	−2.16124
$166$	−9.29051	−0.721083
$167$	−7.01823	−0.543087	−0.271543	−	0.962426i	$-0.587534\pi$
$167$	−7.01823	−0.543087	−0.271543	+	0.962426i	$0.587534\pi$
$168$	−12.9499	−0.999110
$169$	−10.4762	−0.805863
$170$	−30.8146	−2.36338
$171$	−1.56308	−0.119532
$172$	42.4031	3.23321
$173$	19.9581	1.51739	0.758695	−	0.651446i	$-0.225837\pi$
$173$	19.9581	1.51739	0.758695	+	0.651446i	$0.225837\pi$
$174$	−24.1926	−1.83403
$175$	2.81074	0.212472
$176$	−54.7913	−4.13005
$177$	−14.9447	−1.12331
$178$	−9.17236	−0.687498
$179$	0.783302	0.0585467	0.0292734	−	0.999571i	$-0.490681\pi$
$179$	0.783302	0.0585467	0.0292734	+	0.999571i	$0.490681\pi$
$180$	8.94330	0.666595
$181$	−11.8315	−0.879425	−0.439713	−	0.898139i	$-0.644920\pi$
$181$	−11.8315	−0.879425	−0.439713	+	0.898139i	$0.644920\pi$
$182$	3.63278	0.269280
$183$	−10.8767	−0.804031
$184$	−25.5813	−1.88588
$185$	7.46289	0.548683
$186$	38.9745	2.85775
$187$	−20.6299	−1.50861
$188$	−22.2825	−1.62512
$189$	−3.91426	−0.284721
$190$	18.9307	1.37337
$191$	4.27886	0.309607	0.154804	−	0.987945i	$-0.450526\pi$
$191$	4.27886	0.309607	0.154804	+	0.987945i	$0.450526\pi$
$192$	23.2312	1.67656
$193$	−19.3397	−1.39210	−0.696052	−	0.717991i	$-0.745062\pi$
$193$	−19.3397	−1.39210	−0.696052	+	0.717991i	$0.745062\pi$
$194$	−27.1022	−1.94583
$195$	−8.68701	−0.622090
$196$	−31.0881	−2.22058
$197$	8.32141	0.592876	0.296438	−	0.955052i	$-0.404201\pi$
$197$	8.32141	0.592876	0.296438	+	0.955052i	$0.404201\pi$
$198$	8.39490	0.596600
$199$	−4.18541	−0.296696	−0.148348	−	0.988935i	$-0.547396\pi$
$199$	−4.18541	−0.296696	−0.148348	+	0.988935i	$0.547396\pi$
$200$	−25.4929	−1.80262
$201$	−4.34728	−0.306633
$202$	17.0153	1.19719
$203$	4.16576	0.292379
$204$	38.4875	2.69467
$205$	−24.9649	−1.74362
$206$	−50.0609	−3.48791
$207$	2.03951	0.141756
$208$	−17.1450	−1.18879
$209$	12.6738	0.876663
$210$	−12.5042	−0.862874
$211$	26.5581	1.82834	0.914168	−	0.405335i	$-0.132845\pi$
$211$	26.5581	1.82834	0.914168	+	0.405335i	$0.132845\pi$
$212$	−4.97394	−0.341612
$213$	−20.8327	−1.42744
$214$	−19.7141	−1.34763
$215$	24.4804	1.66955
$216$	35.5016	2.41558
$217$	−6.71108	−0.455577
$218$	40.3149	2.73047
$219$	−9.64894	−0.652015
$220$	−72.5142	−4.88890
$221$	−6.45539	−0.434237
$222$	−13.0692	−0.877145
$223$	−20.0528	−1.34283	−0.671417	−	0.741080i	$-0.734314\pi$
$223$	−20.0528	−1.34283	−0.671417	+	0.741080i	$0.734314\pi$
$224$	−11.0776	−0.740155
$225$	2.03246	0.135498
$226$	18.7469	1.24703
$227$	8.96692	0.595155	0.297578	−	0.954698i	$-0.403821\pi$
$227$	8.96692	0.595155	0.297578	+	0.954698i	$0.403821\pi$
$228$	−23.6444	−1.56589
$229$	1.31289	0.0867579	0.0433790	−	0.999059i	$-0.486188\pi$
$229$	1.31289	0.0867579	0.0433790	+	0.999059i	$0.486188\pi$
$230$	−24.7008	−1.62872
$231$	−8.37138	−0.550796
$232$	−37.7826	−2.48055
$233$	−28.7788	−1.88536	−0.942681	−	0.333694i	$-0.891705\pi$
$233$	−28.7788	−1.88536	−0.942681	+	0.333694i	$0.891705\pi$
$234$	2.62689	0.171725
$235$	−12.8642	−0.839171
$236$	−39.0360	−2.54103
$237$	−15.1657	−0.985115
$238$	−9.29200	−0.602311
$239$	−6.14669	−0.397596	−0.198798	−	0.980040i	$-0.563704\pi$
$239$	−6.14669	−0.397596	−0.198798	+	0.980040i	$0.563704\pi$
$240$	59.0140	3.80934
$241$	2.46131	0.158547	0.0792734	−	0.996853i	$-0.474740\pi$
$241$	2.46131	0.158547	0.0792734	+	0.996853i	$0.474740\pi$
$242$	−39.0186	−2.50821
$243$	−6.40744	−0.411037
$244$	−28.4104	−1.81879
$245$	−17.9480	−1.14665
$246$	43.7190	2.78742
$247$	3.96581	0.252338
$248$	60.8682	3.86513
$249$	6.69920	0.424545
$250$	13.3013	0.841246
$251$	19.3759	1.22299	0.611497	−	0.791247i	$-0.290568\pi$
$251$	19.3759	1.22299	0.611497	+	0.791247i	$0.290568\pi$
$252$	2.69681	0.169883
$253$	−16.5368	−1.03966
$254$	−11.5637	−0.725572
$255$	22.2198	1.39146
$256$	−6.88775	−0.430485
$257$	−26.2452	−1.63713	−0.818566	−	0.574412i	$-0.805231\pi$
$257$	−26.2452	−1.63713	−0.818566	+	0.574412i	$0.805231\pi$
$258$	−42.8705	−2.66900
$259$	2.25040	0.139833
$260$	−22.6907	−1.40722
$261$	3.01229	0.186456
$262$	−27.6505	−1.70826
$263$	24.3298	1.50024	0.750120	−	0.661301i	$-0.229996\pi$
$263$	24.3298	1.50024	0.750120	+	0.661301i	$0.229996\pi$
$264$	75.9268	4.67297
$265$	−2.87158	−0.176400
$266$	5.70845	0.350007
$267$	6.61401	0.404771
$268$	−11.3552	−0.693630
$269$	19.3453	1.17950	0.589751	−	0.807585i	$-0.299226\pi$
$269$	19.3453	1.17950	0.589751	+	0.807585i	$0.299226\pi$
$270$	34.2797	2.08620
$271$	2.17924	0.132379	0.0661897	−	0.997807i	$-0.478916\pi$
$271$	2.17924	0.132379	0.0661897	+	0.997807i	$0.478916\pi$
$272$	43.8538	2.65903
$273$	−2.61952	−0.158541
$274$	−6.64541	−0.401464
$275$	−16.4796	−0.993760
$276$	30.8514	1.85703
$277$	−18.5180	−1.11264	−0.556319	−	0.830969i	$-0.687787\pi$
$277$	−18.5180	−1.11264	−0.556319	+	0.830969i	$0.687787\pi$
$278$	35.6263	2.13672
$279$	−4.85282	−0.290531
$280$	−19.5284	−1.16705
$281$	26.5933	1.58642	0.793212	−	0.608945i	$-0.208407\pi$
$281$	26.5933	1.58642	0.793212	+	0.608945i	$0.208407\pi$
$282$	22.5281	1.34153
$283$	8.82135	0.524375	0.262188	−	0.965017i	$-0.415556\pi$
$283$	8.82135	0.524375	0.262188	+	0.965017i	$0.415556\pi$
$284$	−54.4157	−3.22898
$285$	−13.6505	−0.808587
$286$	−21.2993	−1.25946
$287$	−7.52803	−0.444366
$288$	−8.01031	−0.472012
$289$	−0.488247	−0.0287204
$290$	−36.4822	−2.14231
$291$	19.5429	1.14562
$292$	−25.2033	−1.47491
$293$	19.4358	1.13545	0.567726	−	0.823218i	$-0.307823\pi$
$293$	19.4358	1.13545	0.567726	+	0.823218i	$0.307823\pi$
$294$	31.4308	1.83308
$295$	−22.5365	−1.31212
$296$	−20.4107	−1.18635
$297$	22.9497	1.33168
$298$	−6.90071	−0.399747
$299$	−5.17460	−0.299255
$300$	30.7447	1.77505
$301$	7.38194	0.425488
$302$	2.64082	0.151962
$303$	−12.2694	−0.704857
$304$	−26.9411	−1.54518
$305$	−16.4020	−0.939177
$306$	−6.71911	−0.384106
$307$	−6.14086	−0.350478	−0.175239	−	0.984526i	$-0.556070\pi$
$307$	−6.14086	−0.350478	−0.175239	+	0.984526i	$0.556070\pi$
$308$	−21.8663	−1.24595
$309$	36.0979	2.05354
$310$	58.7732	3.33809
$311$	2.20631	0.125108	0.0625541	−	0.998042i	$-0.480075\pi$
$311$	2.20631	0.125108	0.0625541	+	0.998042i	$0.480075\pi$
$312$	23.7586	1.34507
$313$	−15.8019	−0.893177	−0.446588	−	0.894739i	$-0.647361\pi$
$313$	−15.8019	−0.893177	−0.446588	+	0.894739i	$0.647361\pi$
$314$	48.2814	2.72468
$315$	1.55694	0.0877234
$316$	−39.6132	−2.22841
$317$	−10.0983	−0.567176	−0.283588	−	0.958946i	$-0.591525\pi$
$317$	−10.0983	−0.567176	−0.283588	+	0.958946i	$0.591525\pi$
$318$	5.02877	0.281999
$319$	−24.4242	−1.36749
$320$	35.0324	1.95837
$321$	14.2154	0.793429
$322$	−7.44841	−0.415084
$323$	−10.1438	−0.564418
$324$	−52.1587	−2.89770
$325$	−5.15672	−0.286043
$326$	12.6098	0.698393
$327$	−29.0703	−1.60759
$328$	68.2778	3.77001
$329$	−3.87915	−0.213865
$330$	73.3135	4.03577
$331$	−1.86507	−0.102514	−0.0512568	−	0.998686i	$-0.516323\pi$
$331$	−1.86507	−0.102514	−0.0512568	+	0.998686i	$0.516323\pi$
$332$	17.4985	0.960356
$333$	1.62728	0.0891743
$334$	18.5339	1.01413
$335$	−6.55565	−0.358174
$336$	17.7954	0.970817
$337$	−3.39581	−0.184981	−0.0924907	−	0.995714i	$-0.529483\pi$
$337$	−3.39581	−0.184981	−0.0924907	+	0.995714i	$0.529483\pi$
$338$	27.6658	1.50482
$339$	−13.5180	−0.734200
$340$	58.0388	3.14760
$341$	39.3477	2.13080
$342$	4.12782	0.223207
$343$	−11.4735	−0.619511
$344$	−66.9528	−3.60985
$345$	17.8113	0.958927
$346$	−52.7059	−2.83349
$347$	6.18277	0.331908	0.165954	−	0.986133i	$-0.446930\pi$
$347$	6.18277	0.331908	0.165954	+	0.986133i	$0.446930\pi$
$348$	45.5663	2.44261
$349$	−17.1937	−0.920357	−0.460179	−	0.887826i	$-0.652215\pi$
$349$	−17.1937	−0.920357	−0.460179	+	0.887826i	$0.652215\pi$
$350$	−7.42266	−0.396758
$351$	7.18130	0.383309
$352$	64.9492	3.46181
$353$	−20.6151	−1.09723	−0.548615	−	0.836075i	$-0.684845\pi$
$353$	−20.6151	−1.09723	−0.548615	+	0.836075i	$0.684845\pi$
$354$	39.4663	2.09761
$355$	−31.4156	−1.66737
$356$	17.2760	0.915625
$357$	6.70028	0.354616
$358$	−2.06856	−0.109327
$359$	36.4022	1.92123	0.960617	−	0.277877i	$-0.0896309\pi$
$359$	36.4022	1.92123	0.960617	+	0.277877i	$0.0896309\pi$
$360$	−14.1211	−0.744248
$361$	−12.7682	−0.672013
$362$	31.2448	1.64219
$363$	28.1355	1.47673
$364$	−6.84228	−0.358633
$365$	−14.5505	−0.761609
$366$	28.7235	1.50140
$367$	−4.84571	−0.252944	−0.126472	−	0.991970i	$-0.540365\pi$
$367$	−4.84571	−0.252944	−0.126472	+	0.991970i	$0.540365\pi$
$368$	35.1529	1.83247
$369$	−5.44357	−0.283381
$370$	−19.7082	−1.02458
$371$	−0.865912	−0.0449559
$372$	−73.4078	−3.80601
$373$	24.2899	1.25768	0.628842	−	0.777533i	$-0.283529\pi$
$373$	24.2899	1.25768	0.628842	+	0.777533i	$0.283529\pi$
$374$	54.4799	2.81709
$375$	−9.59128	−0.495291
$376$	35.1832	1.81443
$377$	−7.64269	−0.393619
$378$	10.3369	0.531672
$379$	−12.1224	−0.622685	−0.311343	−	0.950298i	$-0.600779\pi$
$379$	−12.1224	−0.622685	−0.311343	+	0.950298i	$0.600779\pi$
$380$	−35.6556	−1.82909
$381$	8.33837	0.427188
$382$	−11.2997	−0.578143
$383$	−0.255363	−0.0130484	−0.00652422	−	0.999979i	$-0.502077\pi$
$383$	−0.255363	−0.0130484	−0.00652422	+	0.999979i	$0.502077\pi$
$384$	−12.6273	−0.644382
$385$	−12.6240	−0.643377
$386$	51.0728	2.59954
$387$	5.33793	0.271342
$388$	51.0466	2.59150
$389$	−17.5238	−0.888494	−0.444247	−	0.895904i	$-0.646529\pi$
$389$	−17.5238	−0.888494	−0.444247	+	0.895904i	$0.646529\pi$
$390$	22.9408	1.16165
$391$	13.2357	0.669359
$392$	49.0869	2.47926
$393$	19.9383	1.00575
$394$	−21.9754	−1.10710
$395$	−22.8697	−1.15070
$396$	−15.8117	−0.794566
$397$	15.1018	0.757936	0.378968	−	0.925410i	$-0.376279\pi$
$397$	15.1018	0.757936	0.378968	+	0.925410i	$0.376279\pi$
$398$	11.0529	0.554034
$399$	−4.11625	−0.206070
$400$	35.0314	1.75157
$401$	−37.5996	−1.87764	−0.938818	−	0.344413i	$-0.888078\pi$
$401$	−37.5996	−1.87764	−0.938818	+	0.344413i	$0.888078\pi$
$402$	11.4804	0.572589
$403$	12.3125	0.613327
$404$	−32.0480	−1.59445
$405$	−30.1125	−1.49630
$406$	−11.0010	−0.545972
$407$	−13.1943	−0.654017
$408$	−60.7703	−3.00858
$409$	−12.6670	−0.626345	−0.313172	−	0.949696i	$-0.601392\pi$
$409$	−12.6670	−0.626345	−0.313172	+	0.949696i	$0.601392\pi$
$410$	65.9278	3.25594
$411$	4.79187	0.236366
$412$	94.2889	4.64528
$413$	−6.79576	−0.334397
$414$	−5.38599	−0.264707
$415$	10.1023	0.495904
$416$	20.3235	0.996444
$417$	−25.6894	−1.25802
$418$	−33.4692	−1.63703
$419$	26.9680	1.31747	0.658735	−	0.752375i	$-0.271092\pi$
$419$	26.9680	1.31747	0.658735	+	0.752375i	$0.271092\pi$
$420$	23.5515	1.14920
$421$	−34.3404	−1.67365	−0.836824	−	0.547472i	$-0.815590\pi$
$421$	−34.3404	−1.67365	−0.836824	+	0.547472i	$0.815590\pi$
$422$	−70.1353	−3.41413
$423$	−2.80504	−0.136386
$424$	7.85365	0.381407
$425$	13.1900	0.639807
$426$	55.0155	2.66551
$427$	−4.94595	−0.239351
$428$	37.1312	1.79480
$429$	15.3585	0.741517
$430$	−64.6484	−3.11762
$431$	−40.8154	−1.96601	−0.983005	−	0.183580i	$-0.941231\pi$
$431$	−40.8154	−1.96601	−0.983005	+	0.183580i	$0.941231\pi$
$432$	−48.7851	−2.34718
$433$	15.6625	0.752694	0.376347	−	0.926479i	$-0.377180\pi$
$433$	15.6625	0.752694	0.376347	+	0.926479i	$0.377180\pi$
$434$	17.7228	0.850720
$435$	26.3066	1.26130
$436$	−75.9324	−3.63650
$437$	−8.13123	−0.388969
$438$	25.4811	1.21754
$439$	−29.5994	−1.41270	−0.706351	−	0.707862i	$-0.749660\pi$
$439$	−29.5994	−1.41270	−0.706351	+	0.707862i	$0.749660\pi$
$440$	114.497	5.45843
$441$	−3.91354	−0.186359
$442$	17.0475	0.810869
$443$	−4.78264	−0.227230	−0.113615	−	0.993525i	$-0.536243\pi$
$443$	−4.78264	−0.227230	−0.113615	+	0.993525i	$0.536243\pi$
$444$	24.6155	1.16820
$445$	9.97386	0.472806
$446$	52.9558	2.50753
$447$	4.97596	0.235355
$448$	10.5638	0.499094
$449$	0.156761	0.00739800	0.00369900	−	0.999993i	$-0.498823\pi$
$449$	0.156761	0.00739800	0.00369900	+	0.999993i	$0.498823\pi$
$450$	−5.36738	−0.253021
$451$	44.1376	2.07836
$452$	−35.3095	−1.66082
$453$	−1.90424	−0.0894692
$454$	−23.6800	−1.11136
$455$	−3.95022	−0.185189
$456$	37.3336	1.74831
$457$	−10.5875	−0.495263	−0.247632	−	0.968854i	$-0.579652\pi$
$457$	−10.5875	−0.495263	−0.247632	+	0.968854i	$0.579652\pi$
$458$	−3.46710	−0.162007
$459$	−18.3685	−0.857367
$460$	46.5236	2.16917
$461$	24.7311	1.15184	0.575921	−	0.817505i	$-0.304643\pi$
$461$	24.7311	1.15184	0.575921	+	0.817505i	$0.304643\pi$
$462$	22.1073	1.02853
$463$	34.1252	1.58593	0.792967	−	0.609264i	$-0.208535\pi$
$463$	34.1252	1.58593	0.792967	+	0.609264i	$0.208535\pi$
$464$	51.9196	2.41031
$465$	−42.3802	−1.96533
$466$	75.9997	3.52062
$467$	2.51842	0.116539	0.0582693	−	0.998301i	$-0.481442\pi$
$467$	2.51842	0.116539	0.0582693	+	0.998301i	$0.481442\pi$
$468$	−4.94769	−0.228707
$469$	−1.97682	−0.0912813
$470$	33.9722	1.56702
$471$	−34.8147	−1.60418
$472$	61.6362	2.83704
$473$	−43.2810	−1.99006
$474$	40.0498	1.83955
$475$	−8.10312	−0.371797
$476$	17.5013	0.802172
$477$	−0.626146	−0.0286693
$478$	16.2323	0.742449
$479$	24.7135	1.12919	0.564595	−	0.825368i	$-0.309032\pi$
$479$	24.7135	1.12919	0.564595	+	0.825368i	$0.309032\pi$
$480$	−69.9548	−3.19298
$481$	−4.12869	−0.188252
$482$	−6.49988	−0.296061
$483$	5.37090	0.244384
$484$	73.4908	3.34049
$485$	29.4705	1.33819
$486$	16.9209	0.767548
$487$	26.2202	1.18815	0.594076	−	0.804409i	$-0.297518\pi$
$487$	26.2202	1.18815	0.594076	+	0.804409i	$0.297518\pi$
$488$	44.8588	2.03066
$489$	−9.09268	−0.411185
$490$	47.3974	2.14119
$491$	16.1862	0.730475	0.365237	−	0.930914i	$-0.380988\pi$
$491$	16.1862	0.730475	0.365237	+	0.930914i	$0.380988\pi$
$492$	−82.3439	−3.71235
$493$	19.5487	0.880427
$494$	−10.4730	−0.471202
$495$	−9.12847	−0.410294
$496$	−83.6429	−3.75568
$497$	−9.47321	−0.424932
$498$	−17.6914	−0.792771
$499$	−23.0880	−1.03356	−0.516781	−	0.856118i	$-0.672870\pi$
$499$	−23.0880	−1.03356	−0.516781	+	0.856118i	$0.672870\pi$
$500$	−25.0527	−1.12039
$501$	−13.3644	−0.597078
$502$	−51.1682	−2.28375
$503$	31.4981	1.40443	0.702216	−	0.711964i	$-0.252194\pi$
$503$	31.4981	1.40443	0.702216	+	0.711964i	$0.252194\pi$
$504$	−4.25815	−0.189673
$505$	−18.5021	−0.823333
$506$	43.6708	1.94140
$507$	−19.9493	−0.885978
$508$	21.7801	0.966334
$509$	37.2875	1.65274	0.826371	−	0.563127i	$-0.190402\pi$
$509$	37.2875	1.65274	0.826371	+	0.563127i	$0.190402\pi$
$510$	−58.6786	−2.59833
$511$	−4.38764	−0.194098
$512$	31.4516	1.38998
$513$	11.2845	0.498222
$514$	69.3090	3.05709
$515$	54.4354	2.39871
$516$	80.7459	3.55464
$517$	22.7438	1.00027
$518$	−5.94290	−0.261116
$519$	38.0052	1.66824
$520$	35.8277	1.57115
$521$	6.58312	0.288412	0.144206	−	0.989548i	$-0.453937\pi$
$521$	6.58312	0.288412	0.144206	+	0.989548i	$0.453937\pi$
$522$	−7.95491	−0.348177
$523$	−7.06556	−0.308956	−0.154478	−	0.987996i	$-0.549370\pi$
$523$	−7.06556	−0.308956	−0.154478	+	0.987996i	$0.549370\pi$
$524$	52.0793	2.27510
$525$	5.35233	0.233595
$526$	−64.2507	−2.80146
$527$	−31.4931	−1.37186
$528$	−104.336	−4.54064
$529$	−12.3903	−0.538710
$530$	7.58334	0.329399
$531$	−4.91406	−0.213252
$532$	−10.7518	−0.466148
$533$	13.8113	0.598233
$534$	−17.4664	−0.755846
$535$	21.4368	0.926792
$536$	17.9294	0.774433
$537$	1.49160	0.0643672
$538$	−51.0874	−2.20253
$539$	31.7318	1.36678
$540$	−64.5652	−2.77845
$541$	−12.9548	−0.556969	−0.278485	−	0.960441i	$-0.589832\pi$
$541$	−12.9548	−0.556969	−0.278485	+	0.960441i	$0.589832\pi$
$542$	−5.75499	−0.247198
$543$	−22.5300	−0.966854
$544$	−51.9840	−2.22880
$545$	−43.8377	−1.87780
$546$	6.91770	0.296050
$547$	−21.6112	−0.924028	−0.462014	−	0.886873i	$-0.652873\pi$
$547$	−21.6112	−0.924028	−0.462014	+	0.886873i	$0.652873\pi$
$548$	12.5165	0.534679
$549$	−3.57645	−0.152639
$550$	43.5198	1.85569
$551$	−12.0095	−0.511623
$552$	−48.7130	−2.07337
$553$	−6.89624	−0.293258
$554$	48.9027	2.07768
$555$	14.2112	0.603231
$556$	−67.1015	−2.84574
$557$	−39.4774	−1.67271	−0.836356	−	0.548187i	$-0.815318\pi$
$557$	−39.4774	−1.67271	−0.836356	+	0.548187i	$0.815318\pi$
$558$	12.8154	0.542521
$559$	−13.5433	−0.572819
$560$	26.8353	1.13400
$561$	−39.2844	−1.65859
$562$	−70.2282	−2.96240
$563$	1.94790	0.0820944	0.0410472	−	0.999157i	$-0.486931\pi$
$563$	1.94790	0.0820944	0.0410472	+	0.999157i	$0.486931\pi$
$564$	−42.4313	−1.78668
$565$	−20.3851	−0.857607
$566$	−23.2956	−0.979188
$567$	−9.08028	−0.381336
$568$	85.9202	3.60513
$569$	−27.5057	−1.15310	−0.576549	−	0.817062i	$-0.695601\pi$
$569$	−27.5057	−1.15310	−0.576549	+	0.817062i	$0.695601\pi$
$570$	36.0486	1.50991
$571$	15.5208	0.649525	0.324762	−	0.945796i	$-0.394716\pi$
$571$	15.5208	0.649525	0.324762	+	0.945796i	$0.394716\pi$
$572$	40.1169	1.67737
$573$	8.14799	0.340387
$574$	19.8802	0.829783
$575$	10.5730	0.440924
$576$	7.63878	0.318283
$577$	−23.1851	−0.965210	−0.482605	−	0.875838i	$-0.660309\pi$
$577$	−23.1851	−0.965210	−0.482605	+	0.875838i	$0.660309\pi$
$578$	1.28937	0.0536309
$579$	−36.8276	−1.53050
$580$	68.7136	2.85317
$581$	3.04631	0.126382
$582$	−51.6093	−2.13927
$583$	5.07692	0.210265
$584$	39.7950	1.64673
$585$	−2.85643	−0.118099
$586$	−51.3265	−2.12028
$587$	−11.1928	−0.461976	−0.230988	−	0.972957i	$-0.574196\pi$
$587$	−11.1928	−0.461976	−0.230988	+	0.972957i	$0.574196\pi$
$588$	−59.1994	−2.44134
$589$	19.3474	0.797198
$590$	59.5148	2.45019
$591$	15.8460	0.651817
$592$	28.0477	1.15275
$593$	6.05389	0.248603	0.124302	−	0.992244i	$-0.460331\pi$
$593$	6.05389	0.248603	0.124302	+	0.992244i	$0.460331\pi$
$594$	−60.6061	−2.48670
$595$	10.1040	0.414222
$596$	12.9974	0.532393
$597$	−7.97005	−0.326193
$598$	13.6652	0.558812
$599$	34.0434	1.39097	0.695487	−	0.718539i	$-0.255189\pi$
$599$	34.0434	1.39097	0.695487	+	0.718539i	$0.255189\pi$
$600$	−48.5447	−1.98183
$601$	7.09683	0.289486	0.144743	−	0.989469i	$-0.453764\pi$
$601$	7.09683	0.289486	0.144743	+	0.989469i	$0.453764\pi$
$602$	−19.4944	−0.794532
$603$	−1.42945	−0.0582119
$604$	−4.97394	−0.202387
$605$	42.4281	1.72495
$606$	32.4012	1.31621
$607$	35.9856	1.46061	0.730305	−	0.683121i	$-0.239378\pi$
$607$	35.9856	1.46061	0.730305	+	0.683121i	$0.239378\pi$
$608$	31.9359	1.29517
$609$	7.93262	0.321446
$610$	43.3148	1.75377
$611$	7.11687	0.287918
$612$	12.6553	0.511561
$613$	−12.8668	−0.519687	−0.259843	−	0.965651i	$-0.583671\pi$
$613$	−12.8668	−0.519687	−0.259843	+	0.965651i	$0.583671\pi$
$614$	16.2169	0.654462
$615$	−47.5392	−1.91697
$616$	34.5260	1.39109
$617$	−13.5505	−0.545524	−0.272762	−	0.962081i	$-0.587937\pi$
$617$	−13.5505	−0.545524	−0.272762	+	0.962081i	$0.587937\pi$
$618$	−95.3282	−3.83466
$619$	−10.5374	−0.423534	−0.211767	−	0.977320i	$-0.567922\pi$
$619$	−10.5374	−0.423534	−0.211767	+	0.977320i	$0.567922\pi$
$620$	−110.698	−4.44575
$621$	−14.7241	−0.590856
$622$	−5.82647	−0.233620
$623$	3.00757	0.120496
$624$	−32.6482	−1.30698
$625$	−30.6935	−1.22774
$626$	41.7300	1.66787
$627$	24.1340	0.963817
$628$	−90.9371	−3.62879
$629$	10.5604	0.421073
$630$	−4.11159	−0.163810
$631$	12.4768	0.496694	0.248347	−	0.968671i	$-0.420113\pi$
$631$	12.4768	0.496694	0.248347	+	0.968671i	$0.420113\pi$
$632$	62.5476	2.48801
$633$	50.5731	2.01010
$634$	26.6678	1.05911
$635$	12.5742	0.498991
$636$	−9.47160	−0.375573
$637$	9.92933	0.393414
$638$	64.5001	2.55358
$639$	−6.85014	−0.270987
$640$	−19.0418	−0.752693
$641$	−34.4431	−1.36042	−0.680210	−	0.733017i	$-0.738112\pi$
$641$	−34.4431	−1.36042	−0.680210	+	0.733017i	$0.738112\pi$
$642$	−37.5405	−1.48160
$643$	41.7518	1.64653	0.823265	−	0.567657i	$-0.192150\pi$
$643$	41.7518	1.64653	0.823265	+	0.567657i	$0.192150\pi$
$644$	14.0290	0.552818
$645$	46.6166	1.83553
$646$	26.7880	1.05396
$647$	0.0702995	0.00276376	0.00138188	−	0.999999i	$-0.499560\pi$
$647$	0.0702995	0.00276376	0.00138188	+	0.999999i	$0.499560\pi$
$648$	82.3564	3.23526
$649$	39.8442	1.56402
$650$	13.6180	0.534141
$651$	−12.7795	−0.500869
$652$	−23.7504	−0.930135
$653$	−0.441920	−0.0172936	−0.00864682	−	0.999963i	$-0.502752\pi$
$653$	−0.441920	−0.0172936	−0.00864682	+	0.999963i	$0.502752\pi$
$654$	76.7694	3.00192
$655$	30.0667	1.17480
$656$	−93.8250	−3.66325
$657$	−3.17273	−0.123780
$658$	10.2441	0.399358
$659$	−50.9099	−1.98317	−0.991585	−	0.129459i	$-0.958676\pi$
$659$	−50.9099	−1.98317	−0.991585	+	0.129459i	$0.958676\pi$
$660$	−138.085	−5.37494
$661$	−33.8203	−1.31546	−0.657728	−	0.753256i	$-0.728482\pi$
$661$	−33.8203	−1.31546	−0.657728	+	0.753256i	$0.728482\pi$
$662$	4.92533	0.191428
$663$	−12.2926	−0.477407
$664$	−27.6294	−1.07223
$665$	−6.20726	−0.240707
$666$	−4.29735	−0.166519
$667$	15.6701	0.606748
$668$	−34.9083	−1.35064
$669$	−38.1854	−1.47633
$670$	17.3123	0.668833
$671$	28.9986	1.11948
$672$	−21.0945	−0.813739
$673$	42.6052	1.64231	0.821155	−	0.570705i	$-0.193330\pi$
$673$	42.6052	1.64231	0.821155	+	0.570705i	$0.193330\pi$
$674$	8.96772	0.345424
$675$	−14.6732	−0.564770
$676$	−52.1081	−2.00416
$677$	−35.8751	−1.37879	−0.689395	−	0.724385i	$-0.742124\pi$
$677$	−35.8751	−1.37879	−0.689395	+	0.724385i	$0.742124\pi$
$678$	35.6988	1.37100
$679$	8.88668	0.341039
$680$	−91.6410	−3.51427
$681$	17.0752	0.654323
$682$	−103.910	−3.97893
$683$	−36.2126	−1.38563	−0.692817	−	0.721113i	$-0.743631\pi$
$683$	−36.2126	−1.38563	−0.692817	+	0.721113i	$0.743631\pi$
$684$	−7.77467	−0.297272
$685$	7.22610	0.276095
$686$	30.2995	1.15684
$687$	2.50006	0.0953831
$688$	92.0042	3.50763
$689$	1.58864	0.0605225
$690$	−47.0364	−1.79065
$691$	37.1473	1.41315	0.706575	−	0.707638i	$-0.250239\pi$
$691$	37.1473	1.41315	0.706575	+	0.707638i	$0.250239\pi$
$692$	99.2707	3.77370
$693$	−2.75264	−0.104564
$694$	−16.3276	−0.619787
$695$	−38.7394	−1.46947
$696$	−71.9473	−2.72716
$697$	−35.3268	−1.33810
$698$	45.4055	1.71862
$699$	−54.8019	−2.07280
$700$	13.9805	0.528412
$701$	14.7737	0.557996	0.278998	−	0.960292i	$-0.409998\pi$
$701$	14.7737	0.557996	0.278998	+	0.960292i	$0.409998\pi$
$702$	−18.9645	−0.715770
$703$	−6.48770	−0.244688
$704$	−61.9368	−2.33433
$705$	−24.4967	−0.922598
$706$	54.4408	2.04891
$707$	−5.57922	−0.209828
$708$	−74.3341	−2.79364
$709$	14.7950	0.555637	0.277818	−	0.960634i	$-0.410389\pi$
$709$	14.7950	0.555637	0.277818	+	0.960634i	$0.410389\pi$
$710$	82.9629	3.11354
$711$	−4.98671	−0.187016
$712$	−27.2781	−1.02229
$713$	−25.2447	−0.945420
$714$	−17.6942	−0.662191
$715$	23.1605	0.866154
$716$	3.89610	0.145604
$717$	−11.7048	−0.437124
$718$	−96.1317	−3.58760
$719$	−11.5355	−0.430200	−0.215100	−	0.976592i	$-0.569008\pi$
$719$	−11.5355	−0.430200	−0.215100	+	0.976592i	$0.569008\pi$
$720$	19.4047	0.723172
$721$	16.4147	0.611316
$722$	33.7187	1.25488
$723$	4.68693	0.174309
$724$	−58.8490	−2.18710
$725$	15.6159	0.579960
$726$	−74.3009	−2.75756
$727$	−9.23117	−0.342365	−0.171183	−	0.985239i	$-0.554759\pi$
$727$	−9.23117	−0.342365	−0.171183	+	0.985239i	$0.554759\pi$
$728$	10.8037	0.400411
$729$	19.2578	0.713252
$730$	38.4253	1.42219
$731$	34.6413	1.28125
$732$	−54.1003	−1.99960
$733$	19.9165	0.735635	0.367817	−	0.929898i	$-0.380105\pi$
$733$	19.9165	0.735635	0.367817	+	0.929898i	$0.380105\pi$
$734$	12.7967	0.472333
$735$	−34.1773	−1.26065
$736$	−41.6701	−1.53598
$737$	11.5903	0.426935
$738$	14.3755	0.529170
$739$	48.2890	1.77634	0.888170	−	0.459515i	$-0.151977\pi$
$739$	48.2890	1.77634	0.888170	+	0.459515i	$0.151977\pi$
$740$	37.1200	1.36456
$741$	7.55186	0.277425
$742$	2.28672	0.0839481
$743$	6.43494	0.236075	0.118038	−	0.993009i	$-0.462340\pi$
$743$	6.43494	0.236075	0.118038	+	0.993009i	$0.462340\pi$
$744$	115.908	4.24939
$745$	7.50370	0.274914
$746$	−64.1453	−2.34853
$747$	2.20281	0.0805965
$748$	−102.612	−3.75187
$749$	6.46415	0.236195
$750$	25.3289	0.924879
$751$	−12.7479	−0.465176	−0.232588	−	0.972575i	$-0.574719\pi$
$751$	−12.7479	−0.465176	−0.232588	+	0.972575i	$0.574719\pi$
$752$	−48.3475	−1.76305
$753$	36.8964	1.34458
$754$	20.1830	0.735021
$755$	−2.87158	−0.104508
$756$	−19.4693	−0.708093
$757$	19.0511	0.692422	0.346211	−	0.938157i	$-0.387468\pi$
$757$	19.0511	0.692422	0.346211	+	0.938157i	$0.387468\pi$
$758$	32.0131	1.16277
$759$	−31.4901	−1.14302
$760$	56.2987	2.04217
$761$	−18.3824	−0.666361	−0.333181	−	0.942863i	$-0.608122\pi$
$761$	−18.3824	−0.666361	−0.333181	+	0.942863i	$0.608122\pi$
$762$	−22.0201	−0.797706
$763$	−13.2190	−0.478561
$764$	21.2828	0.769984
$765$	7.30624	0.264158
$766$	0.674368	0.0243659
$767$	12.4678	0.450187
$768$	−13.1160	−0.473282
$769$	−6.83555	−0.246496	−0.123248	−	0.992376i	$-0.539331\pi$
$769$	−6.83555	−0.246496	−0.123248	+	0.992376i	$0.539331\pi$
$770$	33.3376	1.20141
$771$	−49.9773	−1.79989
$772$	−96.1947	−3.46212
$773$	30.1651	1.08496	0.542482	−	0.840067i	$-0.317485\pi$
$773$	30.1651	1.08496	0.542482	+	0.840067i	$0.317485\pi$
$774$	−14.0965	−0.506689
$775$	−25.1574	−0.903680
$776$	−80.6005	−2.89339
$777$	4.28531	0.153735
$778$	46.2773	1.65912
$779$	21.7027	0.777579
$780$	−43.2087	−1.54712
$781$	55.5423	1.98746
$782$	−34.9532	−1.24992
$783$	−21.7469	−0.777170
$784$	−67.4535	−2.40905
$785$	−52.5003	−1.87382
$786$	−52.6534	−1.87808
$787$	21.4998	0.766385	0.383193	−	0.923668i	$-0.374825\pi$
$787$	21.4998	0.766385	0.383193	+	0.923668i	$0.374825\pi$
$788$	41.3902	1.47447
$789$	46.3299	1.64939
$790$	60.3948	2.14875
$791$	−6.14702	−0.218563
$792$	24.9660	0.887127
$793$	9.07407	0.322230
$794$	−39.8811	−1.41533
$795$	−5.46820	−0.193937
$796$	−20.8180	−0.737875
$797$	33.4073	1.18335	0.591673	−	0.806178i	$-0.298468\pi$
$797$	33.4073	1.18335	0.591673	+	0.806178i	$0.298468\pi$
$798$	10.8703	0.384804
$799$	−18.2037	−0.644001
$800$	−41.5260	−1.46817
$801$	2.17479	0.0768425
$802$	99.2940	3.50619
$803$	25.7251	0.907820
$804$	−21.6231	−0.762588
$805$	8.09927	0.285462
$806$	−32.5150	−1.14529
$807$	36.8381	1.29676
$808$	50.6024	1.78019
$809$	−33.2202	−1.16796	−0.583980	−	0.811768i	$-0.698506\pi$
$809$	−33.2202	−1.16796	−0.583980	+	0.811768i	$0.698506\pi$
$810$	79.5218	2.79411
$811$	−29.0169	−1.01892	−0.509460	−	0.860494i	$-0.670155\pi$
$811$	−29.0169	−1.01892	−0.509460	+	0.860494i	$0.670155\pi$
$812$	20.7202	0.727138
$813$	4.14981	0.145540
$814$	34.8438	1.22128
$815$	−13.7117	−0.480299
$816$	83.5084	2.92338
$817$	−21.2815	−0.744545
$818$	33.4514	1.16960
$819$	−0.861342	−0.0300977
$820$	−124.174	−4.33634
$821$	0.0910732	0.00317848	0.00158924	−	0.999999i	$-0.499494\pi$
$821$	0.0910732	0.00317848	0.00158924	+	0.999999i	$0.499494\pi$
$822$	−12.6545	−0.441376
$823$	−39.6351	−1.38159	−0.690796	−	0.723049i	$-0.742740\pi$
$823$	−39.6351	−1.38159	−0.690796	+	0.723049i	$0.742740\pi$
$824$	−148.878	−5.18642
$825$	−31.3813	−1.09256
$826$	17.9464	0.624435
$827$	−21.9167	−0.762120	−0.381060	−	0.924550i	$-0.624441\pi$
$827$	−21.9167	−0.762120	−0.381060	+	0.924550i	$0.624441\pi$
$828$	10.1444	0.352543
$829$	−33.6380	−1.16830	−0.584149	−	0.811647i	$-0.698572\pi$
$829$	−33.6380	−1.16830	−0.584149	+	0.811647i	$0.698572\pi$
$830$	−26.6785	−0.926023
$831$	−35.2628	−1.22325
$832$	−19.3809	−0.671912
$833$	−25.3975	−0.879970
$834$	67.8412	2.34915
$835$	−20.1534	−0.697438
$836$	63.0386	2.18024
$837$	35.0344	1.21097
$838$	−71.2176	−2.46017
$839$	−52.2442	−1.80367	−0.901836	−	0.432079i	$-0.857780\pi$
$839$	−52.2442	−1.80367	−0.901836	+	0.432079i	$0.857780\pi$
$840$	−37.1869	−1.28307
$841$	−5.85589	−0.201927
$842$	90.6868	3.12527
$843$	50.6402	1.74414
$844$	132.099	4.54702
$845$	−30.0833	−1.03490
$846$	7.40761	0.254679
$847$	12.7940	0.439606
$848$	−10.7922	−0.370606
$849$	16.7980	0.576506
$850$	−34.8323	−1.19474
$851$	8.46519	0.290183
$852$	−103.621	−3.54999
$853$	29.4792	1.00935	0.504675	−	0.863310i	$-0.331612\pi$
$853$	29.4792	1.00935	0.504675	+	0.863310i	$0.331612\pi$
$854$	13.0614	0.446951
$855$	−4.48851	−0.153504
$856$	−58.6286	−2.00388
$857$	2.93122	0.100129	0.0500643	−	0.998746i	$-0.484057\pi$
$857$	2.93122	0.100129	0.0500643	+	0.998746i	$0.484057\pi$
$858$	−40.5591	−1.38467
$859$	−25.5101	−0.870395	−0.435197	−	0.900335i	$-0.643321\pi$
$859$	−25.5101	−0.870395	−0.435197	+	0.900335i	$0.643321\pi$
$860$	121.764	4.15212
$861$	−14.3352	−0.488543
$862$	107.786	3.67122
$863$	46.1314	1.57033	0.785165	−	0.619286i	$-0.212578\pi$
$863$	46.1314	1.57033	0.785165	+	0.619286i	$0.212578\pi$
$864$	57.8296	1.96740
$865$	57.3115	1.94865
$866$	−41.3620	−1.40554
$867$	−0.929742	−0.0315757
$868$	−33.3805	−1.13301
$869$	40.4333	1.37161
$870$	−69.4710	−2.35529
$871$	3.62678	0.122889
$872$	119.894	4.06013
$873$	6.42601	0.217488
$874$	21.4731	0.726339
$875$	−4.36141	−0.147443
$876$	−47.9933	−1.62154
$877$	−13.9464	−0.470935	−0.235467	−	0.971882i	$-0.575662\pi$
$877$	−13.9464	−0.470935	−0.235467	+	0.971882i	$0.575662\pi$
$878$	78.1667	2.63800
$879$	37.0105	1.24833
$880$	−157.338	−5.30385
$881$	5.63138	0.189726	0.0948630	−	0.995490i	$-0.469759\pi$
$881$	5.63138	0.189726	0.0948630	+	0.995490i	$0.469759\pi$
$882$	10.3350	0.347996
$883$	16.9208	0.569432	0.284716	−	0.958612i	$-0.408101\pi$
$883$	16.9208	0.569432	0.284716	+	0.958612i	$0.408101\pi$
$884$	−32.1088	−1.07993
$885$	−42.9149	−1.44257
$886$	12.6301	0.424317
$887$	22.3014	0.748806	0.374403	−	0.927266i	$-0.377848\pi$
$887$	22.3014	0.748806	0.374403	+	0.927266i	$0.377848\pi$
$888$	−38.8669	−1.30429
$889$	3.79168	0.127169
$890$	−26.3392	−0.882892
$891$	53.2386	1.78356
$892$	−99.7413	−3.33959
$893$	11.1833	0.374233
$894$	−13.1406	−0.439488
$895$	2.24932	0.0751864
$896$	−5.74196	−0.191825
$897$	−9.85371	−0.329006
$898$	−0.413977	−0.0138146
$899$	−37.2854	−1.24354
$900$	10.1094	0.336979
$901$	−4.06347	−0.135374
$902$	−116.560	−3.88101
$903$	14.0570	0.467788
$904$	55.7523	1.85430
$905$	−33.9750	−1.12937
$906$	5.02877	0.167070
$907$	−15.7894	−0.524280	−0.262140	−	0.965030i	$-0.584428\pi$
$907$	−15.7894	−0.524280	−0.262140	+	0.965030i	$0.584428\pi$
$908$	44.6009	1.48013
$909$	−4.03437	−0.133812
$910$	10.4318	0.345812
$911$	−33.0048	−1.09350	−0.546748	−	0.837297i	$-0.684135\pi$
$911$	−33.0048	−1.09350	−0.546748	+	0.837297i	$0.684135\pi$
$912$	−51.3025	−1.69880
$913$	−17.8608	−0.591106
$914$	27.9597	0.924826
$915$	−31.2335	−1.03255
$916$	6.53022	0.215765
$917$	9.06647	0.299401
$918$	48.5079	1.60100
$919$	1.18009	0.0389274	0.0194637	−	0.999811i	$-0.493804\pi$
$919$	1.18009	0.0389274	0.0194637	+	0.999811i	$0.493804\pi$
$920$	−73.4588	−2.42187
$921$	−11.6937	−0.385321
$922$	−65.3105	−2.15089
$923$	17.3800	0.572070
$924$	−41.6388	−1.36981
$925$	8.43593	0.277372
$926$	−90.1187	−2.96148
$927$	11.8696	0.389848
$928$	−61.5451	−2.02032
$929$	12.1282	0.397913	0.198957	−	0.980008i	$-0.436245\pi$
$929$	12.1282	0.397913	0.198957	+	0.980008i	$0.436245\pi$
$930$	111.918	3.66995
$931$	15.6027	0.511357
$932$	−143.144	−4.68884
$933$	4.20135	0.137546
$934$	−6.65070	−0.217617
$935$	−59.2405	−1.93737
$936$	7.81221	0.255350
$937$	−36.9376	−1.20670	−0.603349	−	0.797477i	$-0.706167\pi$
$937$	−36.9376	−1.20670	−0.603349	+	0.797477i	$0.706167\pi$
$938$	5.22044	0.170453
$939$	−30.0907	−0.981973
$940$	−63.9860	−2.08699
$941$	−1.04523	−0.0340737	−0.0170368	−	0.999855i	$-0.505423\pi$
$941$	−1.04523	−0.0340737	−0.0170368	+	0.999855i	$0.505423\pi$
$942$	91.9395	2.99555
$943$	−28.3178	−0.922153
$944$	−84.6984	−2.75670
$945$	−11.2401	−0.365642
$946$	114.298	3.71613
$947$	17.9855	0.584449	0.292224	−	0.956350i	$-0.405605\pi$
$947$	17.9855	0.584449	0.292224	+	0.956350i	$0.405605\pi$
$948$	−75.4331	−2.44995
$949$	8.04977	0.261306
$950$	21.3989	0.694272
$951$	−19.2296	−0.623562
$952$	−27.6339	−0.895619
$953$	36.4369	1.18031	0.590154	−	0.807291i	$-0.299067\pi$
$953$	36.4369	1.18031	0.590154	+	0.807291i	$0.299067\pi$
$954$	1.65354	0.0535354
$955$	12.2871	0.397601
$956$	−30.5733	−0.988810
$957$	−46.5097	−1.50345
$958$	−65.2641	−2.10859
$959$	2.17900	0.0703634
$960$	66.7102	2.15306
$961$	29.0671	0.937650
$962$	10.9031	0.351531
$963$	4.67427	0.150626
$964$	12.2424	0.394301
$965$	−55.5357	−1.78776
$966$	−14.1836	−0.456350
$967$	−7.14967	−0.229918	−0.114959	−	0.993370i	$-0.536674\pi$
$967$	−7.14967	−0.229918	−0.114959	+	0.993370i	$0.536674\pi$
$968$	−116.039	−3.72963
$969$	−19.3163	−0.620530
$970$	−77.8263	−2.49885
$971$	−35.5840	−1.14195	−0.570973	−	0.820969i	$-0.693434\pi$
$971$	−35.5840	−1.14195	−0.570973	+	0.820969i	$0.693434\pi$
$972$	−31.8702	−1.02224
$973$	−11.6817	−0.374497
$974$	−69.2430	−2.21869
$975$	−9.81965	−0.314480
$976$	−61.6434	−1.97316
$977$	1.93879	0.0620275	0.0310138	−	0.999519i	$-0.490126\pi$
$977$	1.93879	0.0620275	0.0310138	+	0.999519i	$0.490126\pi$
$978$	24.0122	0.767824
$979$	−17.6337	−0.563575
$980$	−89.2721	−2.85169
$981$	−9.55878	−0.305188
$982$	−42.7450	−1.36405
$983$	−25.1485	−0.802112	−0.401056	−	0.916054i	$-0.631357\pi$
$983$	−25.1485	−0.802112	−0.401056	+	0.916054i	$0.631357\pi$
$984$	130.018	4.14481
$985$	23.8956	0.761378
$986$	−51.6245	−1.64406
$987$	−7.38685	−0.235126
$988$	19.7257	0.627558
$989$	27.7682	0.882978
$990$	24.1067	0.766160
$991$	−12.8438	−0.407997	−0.203998	−	0.978971i	$-0.565394\pi$
$991$	−12.8438	−0.407997	−0.203998	+	0.978971i	$0.565394\pi$
$992$	99.1498	3.14801
$993$	−3.55155	−0.112705
$994$	25.0171	0.793493
$995$	−12.0188	−0.381021
$996$	33.3214	1.05583
$997$	−15.5568	−0.492689	−0.246344	−	0.969182i	$-0.579229\pi$
$997$	−15.5568	−0.492689	−0.246344	+	0.969182i	$0.579229\pi$
$998$	60.9714	1.93002
$999$	−11.7480	−0.371689

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.b.1.5	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.b.1.5	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.64082 q^{2} +1.90424 q^{3} +4.97394 q^{4} +2.87158 q^{5} -5.02877 q^{6} +0.865912 q^{7} -7.85365 q^{8} +0.626146 q^{9} +O(q^{10})\)	\(q-2.64082 q^{2} +1.90424 q^{3} +4.97394 q^{4} +2.87158 q^{5} -5.02877 q^{6} +0.865912 q^{7} -7.85365 q^{8} +0.626146 q^{9} -7.58334 q^{10} -5.07692 q^{11} +9.47160 q^{12} -1.58864 q^{13} -2.28672 q^{14} +5.46820 q^{15} +10.7922 q^{16} +4.06347 q^{17} -1.65354 q^{18} -2.49635 q^{19} +14.2831 q^{20} +1.64891 q^{21} +13.4073 q^{22} +3.25725 q^{23} -14.9553 q^{24} +3.24599 q^{25} +4.19532 q^{26} -4.52040 q^{27} +4.30700 q^{28} +4.81083 q^{29} -14.4405 q^{30} -7.75030 q^{31} -12.7930 q^{32} -9.66770 q^{33} -10.7309 q^{34} +2.48654 q^{35} +3.11442 q^{36} +2.59888 q^{37} +6.59241 q^{38} -3.02516 q^{39} -22.5524 q^{40} -8.69377 q^{41} -4.35447 q^{42} +8.52505 q^{43} -25.2523 q^{44} +1.79803 q^{45} -8.60181 q^{46} -4.47985 q^{47} +20.5510 q^{48} -6.25020 q^{49} -8.57208 q^{50} +7.73783 q^{51} -7.90182 q^{52} -1.00000 q^{53} +11.9376 q^{54} -14.5788 q^{55} -6.80057 q^{56} -4.75366 q^{57} -12.7046 q^{58} -7.84810 q^{59} +27.1985 q^{60} -5.71184 q^{61} +20.4672 q^{62} +0.542187 q^{63} +12.1997 q^{64} -4.56192 q^{65} +25.5307 q^{66} -2.28294 q^{67} +20.2114 q^{68} +6.20260 q^{69} -6.56650 q^{70} -10.9402 q^{71} -4.91754 q^{72} -5.06707 q^{73} -6.86317 q^{74} +6.18116 q^{75} -12.4167 q^{76} -4.39617 q^{77} +7.98892 q^{78} -7.96414 q^{79} +30.9908 q^{80} -10.4864 q^{81} +22.9587 q^{82} +3.51804 q^{83} +8.20157 q^{84} +11.6686 q^{85} -22.5131 q^{86} +9.16100 q^{87} +39.8724 q^{88} +3.47330 q^{89} -4.74828 q^{90} -1.37562 q^{91} +16.2014 q^{92} -14.7585 q^{93} +11.8305 q^{94} -7.16847 q^{95} -24.3610 q^{96} +10.2628 q^{97} +16.5057 q^{98} -3.17890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9}+O(q^{10}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9	\( 153 q - 9 q^{2} - 17 q^{3} + 137 q^{4} - 31 q^{5} - 10 q^{6} - 17 q^{7} - 30 q^{8} + 136 q^{9} - 34 q^{10} - q^{11} - 60 q^{12} - 101 q^{13} - 16 q^{14} - 14 q^{15} + 97 q^{16} - 12 q^{17} - 45 q^{18} - 45 q^{19} - 52 q^{20} - 76 q^{21} - 46 q^{22} - 28 q^{23} - 30 q^{24} + 84 q^{25} - 22 q^{26} - 68 q^{27} - 64 q^{28} - 14 q^{29} - q^{30} - 70 q^{31} - 54 q^{32} - 85 q^{33} - 59 q^{34} - 16 q^{35} + 87 q^{36} - 167 q^{37} - 48 q^{38} - 28 q^{39} - 68 q^{40} - 38 q^{41} + 2 q^{42} - 71 q^{43} - 10 q^{44} - 151 q^{45} - 37 q^{46} - 37 q^{47} - 166 q^{48} + 74 q^{49} - 3 q^{50} - 11 q^{51} - 183 q^{52} - 153 q^{53} - 40 q^{54} - 88 q^{55} - 69 q^{56} - 26 q^{57} - 43 q^{58} - 34 q^{59} - 12 q^{60} - 90 q^{61} - 37 q^{62} - 36 q^{63} + 58 q^{64} - 19 q^{65} + 52 q^{66} - 86 q^{67} - 22 q^{68} - 81 q^{69} - 144 q^{70} - 50 q^{71} - 190 q^{72} - 171 q^{73} - 14 q^{74} - 69 q^{75} - 88 q^{76} - 72 q^{77} - 61 q^{78} - 13 q^{79} - 84 q^{80} + 117 q^{81} - 124 q^{82} - 72 q^{83} - 106 q^{84} - 193 q^{85} - 44 q^{86} - 65 q^{87} - 89 q^{88} - 10 q^{89} - 152 q^{90} - 67 q^{91} - 29 q^{92} - 129 q^{93} - 43 q^{94} - 29 q^{95} - 106 q^{96} - 177 q^{97} - 69 q^{98} - 11 q^{99}+O(q^{100}) \) 153 * q - 9 * q^2 - 17 * q^3 + 137 * q^4 - 31 * q^5 - 10 * q^6 - 17 * q^7 - 30 * q^8 + 136 * q^9 - 34 * q^10 - q^11 - 60 * q^12 - 101 * q^13 - 16 * q^14 - 14 * q^15 + 97 * q^16 - 12 * q^17 - 45 * q^18 - 45 * q^19 - 52 * q^20 - 76 * q^21 - 46 * q^22 - 28 * q^23 - 30 * q^24 + 84 * q^25 - 22 * q^26 - 68 * q^27 - 64 * q^28 - 14 * q^29 - q^30 - 70 * q^31 - 54 * q^32 - 85 * q^33 - 59 * q^34 - 16 * q^35 + 87 * q^36 - 167 * q^37 - 48 * q^38 - 28 * q^39 - 68 * q^40 - 38 * q^41 + 2 * q^42 - 71 * q^43 - 10 * q^44 - 151 * q^45 - 37 * q^46 - 37 * q^47 - 166 * q^48 + 74 * q^49 - 3 * q^50 - 11 * q^51 - 183 * q^52 - 153 * q^53 - 40 * q^54 - 88 * q^55 - 69 * q^56 - 26 * q^57 - 43 * q^58 - 34 * q^59 - 12 * q^60 - 90 * q^61 - 37 * q^62 - 36 * q^63 + 58 * q^64 - 19 * q^65 + 52 * q^66 - 86 * q^67 - 22 * q^68 - 81 * q^69 - 144 * q^70 - 50 * q^71 - 190 * q^72 - 171 * q^73 - 14 * q^74 - 69 * q^75 - 88 * q^76 - 72 * q^77 - 61 * q^78 - 13 * q^79 - 84 * q^80 + 117 * q^81 - 124 * q^82 - 72 * q^83 - 106 * q^84 - 193 * q^85 - 44 * q^86 - 65 * q^87 - 89 * q^88 - 10 * q^89 - 152 * q^90 - 67 * q^91 - 29 * q^92 - 129 * q^93 - 43 * q^94 - 29 * q^95 - 106 * q^96 - 177 * q^97 - 69 * q^98 - 11 * q^99

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