LMFDB - Embedded newform 8003.2.a.c.1.17

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:	$0$
Dimension:	$172$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-2.35311 q^{2} -1.80440 q^{3} +3.53712 q^{4} -3.84522 q^{5} +4.24595 q^{6} +1.90458 q^{7} -3.61701 q^{8} +0.255862 q^{9} +O(q^{10})$	\(q-2.35311 q^{2} -1.80440 q^{3} +3.53712 q^{4} -3.84522 q^{5} +4.24595 q^{6} +1.90458 q^{7} -3.61701 q^{8} +0.255862 q^{9} +9.04823 q^{10} -2.80030 q^{11} -6.38238 q^{12} +3.55060 q^{13} -4.48168 q^{14} +6.93832 q^{15} +1.43698 q^{16} -4.12706 q^{17} -0.602070 q^{18} -1.33253 q^{19} -13.6010 q^{20} -3.43662 q^{21} +6.58941 q^{22} -0.584909 q^{23} +6.52654 q^{24} +9.78575 q^{25} -8.35495 q^{26} +4.95152 q^{27} +6.73672 q^{28} +1.42701 q^{29} -16.3266 q^{30} +6.82428 q^{31} +3.85265 q^{32} +5.05286 q^{33} +9.71143 q^{34} -7.32352 q^{35} +0.905013 q^{36} +6.39256 q^{37} +3.13558 q^{38} -6.40671 q^{39} +13.9082 q^{40} +4.82712 q^{41} +8.08674 q^{42} -5.73628 q^{43} -9.90500 q^{44} -0.983845 q^{45} +1.37636 q^{46} -12.3330 q^{47} -2.59289 q^{48} -3.37259 q^{49} -23.0269 q^{50} +7.44687 q^{51} +12.5589 q^{52} -1.00000 q^{53} -11.6515 q^{54} +10.7678 q^{55} -6.88888 q^{56} +2.40441 q^{57} -3.35790 q^{58} -0.538284 q^{59} +24.5417 q^{60} +0.689413 q^{61} -16.0583 q^{62} +0.487308 q^{63} -11.9397 q^{64} -13.6529 q^{65} -11.8899 q^{66} -11.9097 q^{67} -14.5979 q^{68} +1.05541 q^{69} +17.2330 q^{70} +9.00501 q^{71} -0.925454 q^{72} +12.8350 q^{73} -15.0424 q^{74} -17.6574 q^{75} -4.71331 q^{76} -5.33339 q^{77} +15.0757 q^{78} +4.71078 q^{79} -5.52551 q^{80} -9.70212 q^{81} -11.3587 q^{82} +1.64652 q^{83} -12.1557 q^{84} +15.8695 q^{85} +13.4981 q^{86} -2.57489 q^{87} +10.1287 q^{88} -4.30222 q^{89} +2.31510 q^{90} +6.76239 q^{91} -2.06889 q^{92} -12.3137 q^{93} +29.0209 q^{94} +5.12387 q^{95} -6.95173 q^{96} -8.95518 q^{97} +7.93607 q^{98} -0.716489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) $ 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * 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 $

$2$	−2.35311	−1.66390	−0.831950	−	0.554851i	$-0.812775\pi$
$2$	−2.35311	−1.66390	−0.831950	+	0.554851i	$0.812775\pi$
$3$	−1.80440	−1.04177	−0.520886	−	0.853626i	$-0.674398\pi$
$3$	−1.80440	−1.04177	−0.520886	+	0.853626i	$0.674398\pi$
$4$	3.53712	1.76856
$5$	−3.84522	−1.71964	−0.859818	−	0.510600i	$-0.829423\pi$
$5$	−3.84522	−1.71964	−0.859818	+	0.510600i	$0.829423\pi$
$6$	4.24595	1.73340
$7$	1.90458	0.719862	0.359931	−	0.932979i	$-0.382800\pi$
$7$	1.90458	0.719862	0.359931	+	0.932979i	$0.382800\pi$
$8$	−3.61701	−1.27881
$9$	0.255862	0.0852872
$10$	9.04823	2.86130
$11$	−2.80030	−0.844322	−0.422161	−	0.906521i	$-0.638728\pi$
$11$	−2.80030	−0.844322	−0.422161	+	0.906521i	$0.638728\pi$
$12$	−6.38238	−1.84244
$13$	3.55060	0.984759	0.492380	−	0.870381i	$-0.336127\pi$
$13$	3.55060	0.984759	0.492380	+	0.870381i	$0.336127\pi$
$14$	−4.48168	−1.19778
$15$	6.93832	1.79147
$16$	1.43698	0.359245
$17$	−4.12706	−1.00096	−0.500480	−	0.865748i	$-0.666843\pi$
$17$	−4.12706	−1.00096	−0.500480	+	0.865748i	$0.666843\pi$
$18$	−0.602070	−0.141909
$19$	−1.33253	−0.305703	−0.152851	−	0.988249i	$-0.548846\pi$
$19$	−1.33253	−0.305703	−0.152851	+	0.988249i	$0.548846\pi$
$20$	−13.6010	−3.04128
$21$	−3.43662	−0.749932
$22$	6.58941	1.40487
$23$	−0.584909	−0.121962	−0.0609810	−	0.998139i	$-0.519423\pi$
$23$	−0.584909	−0.121962	−0.0609810	+	0.998139i	$0.519423\pi$
$24$	6.52654	1.33222
$25$	9.78575	1.95715
$26$	−8.35495	−1.63854
$27$	4.95152	0.952921
$28$	6.73672	1.27312
$29$	1.42701	0.264988	0.132494	−	0.991184i	$-0.457701\pi$
$29$	1.42701	0.264988	0.132494	+	0.991184i	$0.457701\pi$
$30$	−16.3266	−2.98082
$31$	6.82428	1.22568	0.612838	−	0.790208i	$-0.290028\pi$
$31$	6.82428	1.22568	0.612838	+	0.790208i	$0.290028\pi$
$32$	3.85265	0.681059
$33$	5.05286	0.879591
$34$	9.71143	1.66550
$35$	−7.32352	−1.23790
$36$	0.905013	0.150836
$37$	6.39256	1.05093	0.525465	−	0.850815i	$-0.323891\pi$
$37$	6.39256	1.05093	0.525465	+	0.850815i	$0.323891\pi$
$38$	3.13558	0.508659
$39$	−6.40671	−1.02589
$40$	13.9082	2.19908
$41$	4.82712	0.753870	0.376935	−	0.926240i	$-0.376978\pi$
$41$	4.82712	0.753870	0.376935	+	0.926240i	$0.376978\pi$
$42$	8.08674	1.24781
$43$	−5.73628	−0.874774	−0.437387	−	0.899273i	$-0.644096\pi$
$43$	−5.73628	−0.874774	−0.437387	+	0.899273i	$0.644096\pi$
$44$	−9.90500	−1.49323
$45$	−0.983845	−0.146663
$46$	1.37636	0.202933
$47$	−12.3330	−1.79896	−0.899478	−	0.436966i	$-0.856053\pi$
$47$	−12.3330	−1.79896	−0.899478	+	0.436966i	$0.856053\pi$
$48$	−2.59289	−0.374251
$49$	−3.37259	−0.481798
$50$	−23.0269	−3.25650
$51$	7.44687	1.04277
$52$	12.5589	1.74161
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−11.6515	−1.58557
$55$	10.7678	1.45193
$56$	−6.88888	−0.920565
$57$	2.40441	0.318472
$58$	−3.35790	−0.440914
$59$	−0.538284	−0.0700786	−0.0350393	−	0.999386i	$-0.511156\pi$
$59$	−0.538284	−0.0700786	−0.0350393	+	0.999386i	$0.511156\pi$
$60$	24.5417	3.16832
$61$	0.689413	0.0882702	0.0441351	−	0.999026i	$-0.485947\pi$
$61$	0.689413	0.0882702	0.0441351	+	0.999026i	$0.485947\pi$
$62$	−16.0583	−2.03940
$63$	0.487308	0.0613951
$64$	−11.9397	−1.49246
$65$	−13.6529	−1.69343
$66$	−11.8899	−1.46355
$67$	−11.9097	−1.45500	−0.727499	−	0.686109i	$-0.759317\pi$
$67$	−11.9097	−1.45500	−0.727499	+	0.686109i	$0.759317\pi$
$68$	−14.5979	−1.77026
$69$	1.05541	0.127057
$70$	17.2330	2.05974
$71$	9.00501	1.06870	0.534349	−	0.845264i	$-0.320557\pi$
$71$	9.00501	1.06870	0.534349	+	0.845264i	$0.320557\pi$
$72$	−0.925454	−0.109066
$73$	12.8350	1.50222	0.751109	−	0.660178i	$-0.229519\pi$
$73$	12.8350	1.50222	0.751109	+	0.660178i	$0.229519\pi$
$74$	−15.0424	−1.74864
$75$	−17.6574	−2.03890
$76$	−4.71331	−0.540654
$77$	−5.33339	−0.607796
$78$	15.0757	1.70698
$79$	4.71078	0.530004	0.265002	−	0.964248i	$-0.414627\pi$
$79$	4.71078	0.530004	0.265002	+	0.964248i	$0.414627\pi$
$80$	−5.52551	−0.617771
$81$	−9.70212	−1.07801
$82$	−11.3587	−1.25436
$83$	1.64652	0.180729	0.0903644	−	0.995909i	$-0.471197\pi$
$83$	1.64652	0.180729	0.0903644	+	0.995909i	$0.471197\pi$
$84$	−12.1557	−1.32630
$85$	15.8695	1.72129
$86$	13.4981	1.45554
$87$	−2.57489	−0.276057
$88$	10.1287	1.07972
$89$	−4.30222	−0.456035	−0.228017	−	0.973657i	$-0.573224\pi$
$89$	−4.30222	−0.456035	−0.228017	+	0.973657i	$0.573224\pi$
$90$	2.31510	0.244032
$91$	6.76239	0.708891
$92$	−2.06889	−0.215697
$93$	−12.3137	−1.27687
$94$	29.0209	2.99328
$95$	5.12387	0.525698
$96$	−6.95173	−0.709508
$97$	−8.95518	−0.909261	−0.454630	−	0.890680i	$-0.650229\pi$
$97$	−8.95518	−0.909261	−0.454630	+	0.890680i	$0.650229\pi$
$98$	7.93607	0.801664
$99$	−0.716489	−0.0720099
$100$	34.6134	3.46134
$101$	16.4544	1.63727	0.818636	−	0.574312i	$-0.194731\pi$
$101$	16.4544	1.63727	0.818636	+	0.574312i	$0.194731\pi$
$102$	−17.5233	−1.73507
$103$	3.10359	0.305806	0.152903	−	0.988241i	$-0.451138\pi$
$103$	3.10359	0.305806	0.152903	+	0.988241i	$0.451138\pi$
$104$	−12.8426	−1.25932
$105$	13.2146	1.28961
$106$	2.35311	0.228554
$107$	15.2027	1.46970	0.734848	−	0.678232i	$-0.237253\pi$
$107$	15.2027	1.46970	0.734848	+	0.678232i	$0.237253\pi$
$108$	17.5141	1.68530
$109$	10.1527	0.972455	0.486227	−	0.873832i	$-0.338373\pi$
$109$	10.1527	0.972455	0.486227	+	0.873832i	$0.338373\pi$
$110$	−25.3378	−2.41586
$111$	−11.5347	−1.09483
$112$	2.73684	0.258607
$113$	18.3745	1.72853	0.864265	−	0.503038i	$-0.167784\pi$
$113$	18.3745	1.72853	0.864265	+	0.503038i	$0.167784\pi$
$114$	−5.65785	−0.529906
$115$	2.24911	0.209730
$116$	5.04749	0.468648
$117$	0.908462	0.0839874
$118$	1.26664	0.116604
$119$	−7.86031	−0.720553
$120$	−25.0960	−2.29094
$121$	−3.15832	−0.287120
$122$	−1.62226	−0.146873
$123$	−8.71006	−0.785360
$124$	24.1383	2.16768
$125$	−18.4023	−1.64595
$126$	−1.14669	−0.102155
$127$	−15.8265	−1.40438	−0.702188	−	0.711991i	$-0.747793\pi$
$127$	−15.8265	−1.40438	−0.702188	+	0.711991i	$0.747793\pi$
$128$	20.3900	1.80224
$129$	10.3505	0.911315
$130$	32.1266	2.81769
$131$	−15.6303	−1.36562	−0.682811	−	0.730595i	$-0.739243\pi$
$131$	−15.6303	−1.36562	−0.682811	+	0.730595i	$0.739243\pi$
$132$	17.8726	1.55561
$133$	−2.53790	−0.220064
$134$	28.0247	2.42097
$135$	−19.0397	−1.63868
$136$	14.9276	1.28003
$137$	−15.1757	−1.29655	−0.648273	−	0.761408i	$-0.724508\pi$
$137$	−15.1757	−1.29655	−0.648273	+	0.761408i	$0.724508\pi$
$138$	−2.48350	−0.211409
$139$	10.4954	0.890209	0.445105	−	0.895479i	$-0.353166\pi$
$139$	10.4954	0.890209	0.445105	+	0.895479i	$0.353166\pi$
$140$	−25.9042	−2.18930
$141$	22.2537	1.87410
$142$	−21.1898	−1.77821
$143$	−9.94275	−0.831454
$144$	0.367668	0.0306390
$145$	−5.48716	−0.455684
$146$	−30.2020	−2.49954
$147$	6.08550	0.501924
$148$	22.6113	1.85863
$149$	7.04647	0.577269	0.288635	−	0.957439i	$-0.406799\pi$
$149$	7.04647	0.577269	0.288635	+	0.957439i	$0.406799\pi$
$150$	41.5498	3.39253
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	4.81977	0.390935
$153$	−1.05596	−0.0853691
$154$	12.5500	1.01131
$155$	−26.2409	−2.10772
$156$	−22.6613	−1.81436
$157$	4.70891	0.375812	0.187906	−	0.982187i	$-0.439830\pi$
$157$	4.70891	0.375812	0.187906	+	0.982187i	$0.439830\pi$
$158$	−11.0850	−0.881873
$159$	1.80440	0.143098
$160$	−14.8143	−1.17117
$161$	−1.11400	−0.0877959
$162$	22.8301	1.79371
$163$	5.02629	0.393690	0.196845	−	0.980435i	$-0.436930\pi$
$163$	5.02629	0.393690	0.196845	+	0.980435i	$0.436930\pi$
$164$	17.0741	1.33326
$165$	−19.4294	−1.51258
$166$	−3.87444	−0.300715
$167$	−7.00578	−0.542124	−0.271062	−	0.962562i	$-0.587375\pi$
$167$	−7.00578	−0.542124	−0.271062	+	0.962562i	$0.587375\pi$
$168$	12.4303	0.959018
$169$	−0.393238	−0.0302491
$170$	−37.3426	−2.86405
$171$	−0.340943	−0.0260725
$172$	−20.2899	−1.54709
$173$	−17.8212	−1.35492	−0.677462	−	0.735558i	$-0.736920\pi$
$173$	−17.8212	−1.35492	−0.677462	+	0.735558i	$0.736920\pi$
$174$	6.05900	0.459331
$175$	18.6377	1.40888
$176$	−4.02398	−0.303319
$177$	0.971280	0.0730058
$178$	10.1236	0.758796
$179$	−9.72363	−0.726778	−0.363389	−	0.931637i	$-0.618380\pi$
$179$	−9.72363	−0.726778	−0.363389	+	0.931637i	$0.618380\pi$
$180$	−3.47998	−0.259382
$181$	−5.81566	−0.432274	−0.216137	−	0.976363i	$-0.569346\pi$
$181$	−5.81566	−0.432274	−0.216137	+	0.976363i	$0.569346\pi$
$182$	−15.9126	−1.17952
$183$	−1.24398	−0.0919574
$184$	2.11562	0.155966
$185$	−24.5808	−1.80722
$186$	28.9756	2.12459
$187$	11.5570	0.845132
$188$	−43.6234	−3.18156
$189$	9.43056	0.685972
$190$	−12.0570	−0.874708
$191$	−25.8370	−1.86950	−0.934752	−	0.355302i	$-0.884378\pi$
$191$	−25.8370	−1.86950	−0.934752	+	0.355302i	$0.884378\pi$
$192$	21.5439	1.55480
$193$	−8.83345	−0.635845	−0.317923	−	0.948117i	$-0.602985\pi$
$193$	−8.83345	−0.635845	−0.317923	+	0.948117i	$0.602985\pi$
$194$	21.0725	1.51292
$195$	24.6352	1.76416
$196$	−11.9292	−0.852089
$197$	15.4238	1.09890	0.549452	−	0.835526i	$-0.314837\pi$
$197$	15.4238	1.09890	0.549452	+	0.835526i	$0.314837\pi$
$198$	1.68598	0.119817
$199$	−14.7189	−1.04340	−0.521698	−	0.853130i	$-0.674701\pi$
$199$	−14.7189	−1.04340	−0.521698	+	0.853130i	$0.674701\pi$
$200$	−35.3952	−2.50282
$201$	21.4898	1.51577
$202$	−38.7190	−2.72426
$203$	2.71784	0.190755
$204$	26.3405	1.84420
$205$	−18.5614	−1.29638
$206$	−7.30309	−0.508830
$207$	−0.149656	−0.0104018
$208$	5.10214	0.353770
$209$	3.73148	0.258112
$210$	−31.0953	−2.14578
$211$	−15.9379	−1.09721	−0.548604	−	0.836083i	$-0.684840\pi$
$211$	−15.9379	−1.09721	−0.548604	+	0.836083i	$0.684840\pi$
$212$	−3.53712	−0.242930
$213$	−16.2486	−1.11334
$214$	−35.7735	−2.44543
$215$	22.0573	1.50429
$216$	−17.9097	−1.21860
$217$	12.9974	0.882318
$218$	−23.8905	−1.61807
$219$	−23.1594	−1.56497
$220$	38.0869	2.56782
$221$	−14.6535	−0.985704
$222$	27.1425	1.82168
$223$	−8.83776	−0.591820	−0.295910	−	0.955216i	$-0.595623\pi$
$223$	−8.83776	−0.591820	−0.295910	+	0.955216i	$0.595623\pi$
$224$	7.33767	0.490269
$225$	2.50380	0.166920
$226$	−43.2372	−2.87610
$227$	6.91640	0.459058	0.229529	−	0.973302i	$-0.426281\pi$
$227$	6.91640	0.459058	0.229529	+	0.973302i	$0.426281\pi$
$228$	8.50470	0.563238
$229$	−28.3674	−1.87457	−0.937287	−	0.348559i	$-0.886671\pi$
$229$	−28.3674	−1.87457	−0.937287	+	0.348559i	$0.886671\pi$
$230$	−5.29239	−0.348970
$231$	9.62356	0.633184
$232$	−5.16150	−0.338869
$233$	18.5452	1.21494	0.607468	−	0.794344i	$-0.292185\pi$
$233$	18.5452	1.21494	0.607468	+	0.794344i	$0.292185\pi$
$234$	−2.13771	−0.139747
$235$	47.4232	3.09355
$236$	−1.90397	−0.123938
$237$	−8.50013	−0.552143
$238$	18.4962	1.19893
$239$	16.4167	1.06191	0.530955	−	0.847400i	$-0.321833\pi$
$239$	16.4167	1.06191	0.530955	+	0.847400i	$0.321833\pi$
$240$	9.97024	0.643576
$241$	−25.0950	−1.61651	−0.808256	−	0.588832i	$-0.799588\pi$
$241$	−25.0950	−1.61651	−0.808256	+	0.588832i	$0.799588\pi$
$242$	7.43187	0.477739
$243$	2.65194	0.170122
$244$	2.43854	0.156111
$245$	12.9684	0.828518
$246$	20.4957	1.30676
$247$	−4.73127	−0.301044
$248$	−24.6835	−1.56740
$249$	−2.97098	−0.188278
$250$	43.3026	2.73869
$251$	15.1638	0.957131	0.478565	−	0.878052i	$-0.341157\pi$
$251$	15.1638	0.957131	0.478565	+	0.878052i	$0.341157\pi$
$252$	1.72367	0.108581
$253$	1.63792	0.102975
$254$	37.2415	2.33674
$255$	−28.6349	−1.79319
$256$	−24.1006	−1.50629
$257$	−29.0134	−1.80980	−0.904902	−	0.425620i	$-0.860056\pi$
$257$	−29.0134	−1.80980	−0.904902	+	0.425620i	$0.860056\pi$
$258$	−24.3560	−1.51634
$259$	12.1751	0.756525
$260$	−48.2918	−2.99493
$261$	0.365116	0.0226001
$262$	36.7797	2.27226
$263$	2.55500	0.157548	0.0787740	−	0.996892i	$-0.474899\pi$
$263$	2.55500	0.157548	0.0787740	+	0.996892i	$0.474899\pi$
$264$	−18.2763	−1.12483
$265$	3.84522	0.236210
$266$	5.97196	0.366164
$267$	7.76294	0.475084
$268$	−42.1259	−2.57325
$269$	19.0170	1.15949	0.579743	−	0.814800i	$-0.303153\pi$
$269$	19.0170	1.15949	0.579743	+	0.814800i	$0.303153\pi$
$270$	44.8025	2.72660
$271$	−12.6717	−0.769750	−0.384875	−	0.922969i	$-0.625755\pi$
$271$	−12.6717	−0.769750	−0.384875	+	0.922969i	$0.625755\pi$
$272$	−5.93051	−0.359590
$273$	−12.2021	−0.738502
$274$	35.7100	2.15732
$275$	−27.4030	−1.65246
$276$	3.73311	0.224707
$277$	6.45196	0.387661	0.193830	−	0.981035i	$-0.437909\pi$
$277$	6.45196	0.387661	0.193830	+	0.981035i	$0.437909\pi$
$278$	−24.6968	−1.48122
$279$	1.74607	0.104535
$280$	26.4893	1.58304
$281$	−31.0699	−1.85347	−0.926736	−	0.375713i	$-0.877398\pi$
$281$	−31.0699	−1.85347	−0.926736	+	0.375713i	$0.877398\pi$
$282$	−52.3654	−3.11831
$283$	9.12172	0.542230	0.271115	−	0.962547i	$-0.412608\pi$
$283$	9.12172	0.542230	0.271115	+	0.962547i	$0.412608\pi$
$284$	31.8518	1.89006
$285$	−9.24551	−0.547657
$286$	23.3964	1.38346
$287$	9.19362	0.542682
$288$	0.985746	0.0580856
$289$	0.0326444	0.00192026
$290$	12.9119	0.758212
$291$	16.1587	0.947242
$292$	45.3988	2.65676
$293$	−19.8562	−1.16001	−0.580006	−	0.814612i	$-0.696950\pi$
$293$	−19.8562	−1.16001	−0.580006	+	0.814612i	$0.696950\pi$
$294$	−14.3198	−0.835150
$295$	2.06982	0.120510
$296$	−23.1220	−1.34394
$297$	−13.8658	−0.804573
$298$	−16.5811	−0.960518
$299$	−2.07678	−0.120103
$300$	−62.4564	−3.60592
$301$	−10.9252	−0.629717
$302$	−2.35311	−0.135406
$303$	−29.6903	−1.70566
$304$	−1.91482	−0.109822
$305$	−2.65095	−0.151793
$306$	2.48478	0.142046
$307$	−9.39714	−0.536323	−0.268162	−	0.963374i	$-0.586416\pi$
$307$	−9.39714	−0.536323	−0.268162	+	0.963374i	$0.586416\pi$
$308$	−18.8648	−1.07492
$309$	−5.60012	−0.318580
$310$	61.7476	3.50703
$311$	5.40836	0.306680	0.153340	−	0.988174i	$-0.450997\pi$
$311$	5.40836	0.306680	0.153340	+	0.988174i	$0.450997\pi$
$312$	23.1731	1.31192
$313$	14.1408	0.799286	0.399643	−	0.916671i	$-0.369134\pi$
$313$	14.1408	0.799286	0.399643	+	0.916671i	$0.369134\pi$
$314$	−11.0806	−0.625313
$315$	−1.87381	−0.105577
$316$	16.6626	0.937343
$317$	−12.1072	−0.680008	−0.340004	−	0.940424i	$-0.610428\pi$
$317$	−12.1072	−0.680008	−0.340004	+	0.940424i	$0.610428\pi$
$318$	−4.24595	−0.238101
$319$	−3.99604	−0.223736
$320$	45.9107	2.56649
$321$	−27.4317	−1.53109
$322$	2.62137	0.146083
$323$	5.49942	0.305996
$324$	−34.3176	−1.90653
$325$	34.7453	1.92732
$326$	−11.8274	−0.655060
$327$	−18.3196	−1.01308
$328$	−17.4598	−0.964054
$329$	−23.4892	−1.29500
$330$	45.7195	2.51677
$331$	10.6090	0.583126	0.291563	−	0.956552i	$-0.405825\pi$
$331$	10.6090	0.583126	0.291563	+	0.956552i	$0.405825\pi$
$332$	5.82393	0.319630
$333$	1.63561	0.0896309
$334$	16.4854	0.902039
$335$	45.7953	2.50207
$336$	−4.93835	−0.269409
$337$	6.83443	0.372295	0.186148	−	0.982522i	$-0.440400\pi$
$337$	6.83443	0.372295	0.186148	+	0.982522i	$0.440400\pi$
$338$	0.925332	0.0503314
$339$	−33.1550	−1.80073
$340$	56.1323	3.04420
$341$	−19.1100	−1.03487
$342$	0.802275	0.0433821
$343$	−19.7554	−1.06669
$344$	20.7482	1.11867
$345$	−4.05829	−0.218491
$346$	41.9353	2.25446
$347$	23.2338	1.24725	0.623627	−	0.781722i	$-0.285659\pi$
$347$	23.2338	1.24725	0.623627	+	0.781722i	$0.285659\pi$
$348$	−9.10770	−0.488224
$349$	8.32539	0.445648	0.222824	−	0.974859i	$-0.428473\pi$
$349$	8.32539	0.445648	0.222824	+	0.974859i	$0.428473\pi$
$350$	−43.8566	−2.34423
$351$	17.5809	0.938398
$352$	−10.7886	−0.575033
$353$	17.1503	0.912819	0.456409	−	0.889770i	$-0.349135\pi$
$353$	17.1503	0.912819	0.456409	+	0.889770i	$0.349135\pi$
$354$	−2.28553	−0.121474
$355$	−34.6263	−1.83777
$356$	−15.2175	−0.806525
$357$	14.1831	0.750651
$358$	22.8808	1.20929
$359$	−30.5554	−1.61265	−0.806326	−	0.591471i	$-0.798547\pi$
$359$	−30.5554	−1.61265	−0.806326	+	0.591471i	$0.798547\pi$
$360$	3.55858	0.187554
$361$	−17.2244	−0.906546
$362$	13.6849	0.719261
$363$	5.69888	0.299113
$364$	23.9194	1.25372
$365$	−49.3533	−2.58327
$366$	2.92721	0.153008
$367$	−1.31055	−0.0684099	−0.0342050	−	0.999415i	$-0.510890\pi$
$367$	−1.31055	−0.0684099	−0.0342050	+	0.999415i	$0.510890\pi$
$368$	−0.840503	−0.0438143
$369$	1.23508	0.0642954
$370$	57.8413	3.00703
$371$	−1.90458	−0.0988807
$372$	−43.5552	−2.25823
$373$	9.53902	0.493912	0.246956	−	0.969027i	$-0.420570\pi$
$373$	9.53902	0.493912	0.246956	+	0.969027i	$0.420570\pi$
$374$	−27.1949	−1.40622
$375$	33.2051	1.71470
$376$	44.6087	2.30052
$377$	5.06673	0.260950
$378$	−22.1911	−1.14139
$379$	−19.5084	−1.00208	−0.501039	−	0.865425i	$-0.667049\pi$
$379$	−19.5084	−1.00208	−0.501039	+	0.865425i	$0.667049\pi$
$380$	18.1237	0.929728
$381$	28.5574	1.46304
$382$	60.7974	3.11066
$383$	9.17255	0.468696	0.234348	−	0.972153i	$-0.424705\pi$
$383$	9.17255	0.468696	0.234348	+	0.972153i	$0.424705\pi$
$384$	−36.7918	−1.87752
$385$	20.5081	1.04519
$386$	20.7861	1.05798
$387$	−1.46769	−0.0746071
$388$	−31.6755	−1.60808
$389$	−21.2039	−1.07508	−0.537539	−	0.843239i	$-0.680646\pi$
$389$	−21.2039	−1.07508	−0.537539	+	0.843239i	$0.680646\pi$
$390$	−57.9693	−2.93539
$391$	2.41396	0.122079
$392$	12.1987	0.616127
$393$	28.2033	1.42267
$394$	−36.2940	−1.82846
$395$	−18.1140	−0.911414
$396$	−2.53431	−0.127354
$397$	−22.4239	−1.12542	−0.562711	−	0.826654i	$-0.690242\pi$
$397$	−22.4239	−1.12542	−0.562711	+	0.826654i	$0.690242\pi$
$398$	34.6352	1.73611
$399$	4.57939	0.229256
$400$	14.0619	0.703096
$401$	1.91817	0.0957888	0.0478944	−	0.998852i	$-0.484749\pi$
$401$	1.91817	0.0957888	0.0478944	+	0.998852i	$0.484749\pi$
$402$	−50.5679	−2.52210
$403$	24.2303	1.20700
$404$	58.2011	2.89561
$405$	37.3068	1.85379
$406$	−6.39538	−0.317397
$407$	−17.9011	−0.887324
$408$	−26.9354	−1.33350
$409$	−9.61261	−0.475313	−0.237657	−	0.971349i	$-0.576379\pi$
$409$	−9.61261	−0.475313	−0.237657	+	0.971349i	$0.576379\pi$
$410$	43.6769	2.15705
$411$	27.3830	1.35070
$412$	10.9778	0.540836
$413$	−1.02520	−0.0504469
$414$	0.352156	0.0173075
$415$	−6.33123	−0.310788
$416$	13.6792	0.670679
$417$	−18.9379	−0.927394
$418$	−8.78057	−0.429472
$419$	36.2877	1.77277	0.886386	−	0.462946i	$-0.153208\pi$
$419$	36.2877	1.77277	0.886386	+	0.462946i	$0.153208\pi$
$420$	46.7415	2.28075
$421$	10.2013	0.497183	0.248592	−	0.968608i	$-0.420032\pi$
$421$	10.2013	0.497183	0.248592	+	0.968608i	$0.420032\pi$
$422$	37.5035	1.82564
$423$	−3.15555	−0.153428
$424$	3.61701	0.175658
$425$	−40.3864	−1.95903
$426$	38.2348	1.85248
$427$	1.31304	0.0635424
$428$	53.7736	2.59925
$429$	17.9407	0.866185
$430$	−51.9032	−2.50299
$431$	−40.8801	−1.96912	−0.984562	−	0.175038i	$-0.943995\pi$
$431$	−40.8801	−1.96912	−0.984562	+	0.175038i	$0.943995\pi$
$432$	7.11524	0.342332
$433$	35.3484	1.69874	0.849368	−	0.527801i	$-0.176983\pi$
$433$	35.3484	1.69874	0.849368	+	0.527801i	$0.176983\pi$
$434$	−30.5842	−1.46809
$435$	9.90103	0.474718
$436$	35.9114	1.71984
$437$	0.779408	0.0372841
$438$	54.4966	2.60395
$439$	−22.0036	−1.05017	−0.525087	−	0.851049i	$-0.675967\pi$
$439$	−22.0036	−1.05017	−0.525087	+	0.851049i	$0.675967\pi$
$440$	−38.9472	−1.85673
$441$	−0.862916	−0.0410912
$442$	34.4814	1.64011
$443$	25.8762	1.22942	0.614708	−	0.788755i	$-0.289274\pi$
$443$	25.8762	1.22942	0.614708	+	0.788755i	$0.289274\pi$
$444$	−40.7998	−1.93627
$445$	16.5430	0.784214
$446$	20.7962	0.984729
$447$	−12.7147	−0.601382
$448$	−22.7400	−1.07436
$449$	0.645734	0.0304741	0.0152370	−	0.999884i	$-0.495150\pi$
$449$	0.645734	0.0304741	0.0152370	+	0.999884i	$0.495150\pi$
$450$	−5.89171	−0.277738
$451$	−13.5174	−0.636509
$452$	64.9929	3.05701
$453$	−1.80440	−0.0847781
$454$	−16.2750	−0.763826
$455$	−26.0029	−1.21904
$456$	−8.69679	−0.407265
$457$	24.9280	1.16608	0.583042	−	0.812442i	$-0.301862\pi$
$457$	24.9280	1.16608	0.583042	+	0.812442i	$0.301862\pi$
$458$	66.7517	3.11910
$459$	−20.4353	−0.953836
$460$	7.95536	0.370921
$461$	28.2474	1.31561	0.657806	−	0.753187i	$-0.271485\pi$
$461$	28.2474	1.31561	0.657806	+	0.753187i	$0.271485\pi$
$462$	−22.6453	−1.05355
$463$	−34.5296	−1.60473	−0.802363	−	0.596836i	$-0.796424\pi$
$463$	−34.5296	−1.60473	−0.802363	+	0.596836i	$0.796424\pi$
$464$	2.05058	0.0951958
$465$	47.3491	2.19576
$466$	−43.6389	−2.02153
$467$	8.17572	0.378327	0.189164	−	0.981946i	$-0.439422\pi$
$467$	8.17572	0.378327	0.189164	+	0.981946i	$0.439422\pi$
$468$	3.21334	0.148537
$469$	−22.6829	−1.04740
$470$	−111.592	−5.14736
$471$	−8.49675	−0.391510
$472$	1.94698	0.0896169
$473$	16.0633	0.738591
$474$	20.0017	0.918709
$475$	−13.0398	−0.598306
$476$	−27.8029	−1.27434
$477$	−0.255862	−0.0117151
$478$	−38.6304	−1.76691
$479$	34.4184	1.57262	0.786309	−	0.617833i	$-0.211989\pi$
$479$	34.4184	1.57262	0.786309	+	0.617833i	$0.211989\pi$
$480$	26.7310	1.22010
$481$	22.6974	1.03491
$482$	59.0513	2.68971
$483$	2.01011	0.0914632
$484$	−11.1714	−0.507789
$485$	34.4347	1.56360
$486$	−6.24029	−0.283065
$487$	26.7313	1.21131	0.605657	−	0.795726i	$-0.292911\pi$
$487$	26.7313	1.21131	0.605657	+	0.795726i	$0.292911\pi$
$488$	−2.49361	−0.112881
$489$	−9.06944	−0.410134
$490$	−30.5160	−1.37857
$491$	−33.9627	−1.53271	−0.766357	−	0.642415i	$-0.777932\pi$
$491$	−33.9627	−1.53271	−0.766357	+	0.642415i	$0.777932\pi$
$492$	−30.8085	−1.38896
$493$	−5.88934	−0.265243
$494$	11.1332	0.500906
$495$	2.75506	0.123831
$496$	9.80635	0.440318
$497$	17.1507	0.769315
$498$	6.99103	0.313276
$499$	−25.0656	−1.12209	−0.561045	−	0.827786i	$-0.689600\pi$
$499$	−25.0656	−1.12209	−0.561045	+	0.827786i	$0.689600\pi$
$500$	−65.0911	−2.91096
$501$	12.6412	0.564769
$502$	−35.6821	−1.59257
$503$	−10.6357	−0.474224	−0.237112	−	0.971482i	$-0.576201\pi$
$503$	−10.6357	−0.474224	−0.237112	+	0.971482i	$0.576201\pi$
$504$	−1.76260	−0.0785124
$505$	−63.2708	−2.81551
$506$	−3.85421	−0.171340
$507$	0.709559	0.0315126
$508$	−55.9803	−2.48372
$509$	−10.6109	−0.470320	−0.235160	−	0.971957i	$-0.575561\pi$
$509$	−10.6109	−0.470320	−0.235160	+	0.971957i	$0.575561\pi$
$510$	67.3810	2.98368
$511$	24.4452	1.08139
$512$	15.9313	0.704072
$513$	−6.59804	−0.291311
$514$	68.2716	3.01133
$515$	−11.9340	−0.525875
$516$	36.6111	1.61171
$517$	34.5362	1.51890
$518$	−28.6494	−1.25878
$519$	32.1566	1.41152
$520$	49.3825	2.16557
$521$	33.7033	1.47657	0.738285	−	0.674489i	$-0.235636\pi$
$521$	33.7033	1.47657	0.738285	+	0.674489i	$0.235636\pi$
$522$	−0.859158	−0.0376043
$523$	36.0316	1.57555	0.787777	−	0.615961i	$-0.211232\pi$
$523$	36.0316	1.57555	0.787777	+	0.615961i	$0.211232\pi$
$524$	−55.2861	−2.41519
$525$	−33.6299	−1.46773
$526$	−6.01219	−0.262144
$527$	−28.1642	−1.22685
$528$	7.26086	0.315989
$529$	−22.6579	−0.985125
$530$	−9.04823	−0.393030
$531$	−0.137726	−0.00597681
$532$	−8.97686	−0.389196
$533$	17.1392	0.742380
$534$	−18.2670	−0.790492
$535$	−58.4576	−2.52734
$536$	43.0774	1.86066
$537$	17.5453	0.757137
$538$	−44.7490	−1.92927
$539$	9.44426	0.406793
$540$	−67.3458	−2.89810
$541$	−3.40648	−0.146456	−0.0732281	−	0.997315i	$-0.523330\pi$
$541$	−3.40648	−0.146456	−0.0732281	+	0.997315i	$0.523330\pi$
$542$	29.8179	1.28079
$543$	10.4938	0.450331
$544$	−15.9001	−0.681713
$545$	−39.0395	−1.67227
$546$	28.7128	1.22879
$547$	38.3083	1.63795	0.818973	−	0.573832i	$-0.194544\pi$
$547$	38.3083	1.63795	0.818973	+	0.573832i	$0.194544\pi$
$548$	−53.6782	−2.29302
$549$	0.176394	0.00752832
$550$	64.4823	2.74953
$551$	−1.90152	−0.0810077
$552$	−3.81743	−0.162481
$553$	8.97203	0.381530
$554$	−15.1822	−0.645029
$555$	44.3537	1.88271
$556$	37.1235	1.57439
$557$	−20.4224	−0.865326	−0.432663	−	0.901556i	$-0.642426\pi$
$557$	−20.4224	−0.865326	−0.432663	+	0.901556i	$0.642426\pi$
$558$	−4.10870	−0.173935
$559$	−20.3672	−0.861442
$560$	−10.5238	−0.444710
$561$	−20.8535	−0.880435
$562$	73.1108	3.08399
$563$	4.23181	0.178349	0.0891747	−	0.996016i	$-0.471577\pi$
$563$	4.23181	0.178349	0.0891747	+	0.996016i	$0.471577\pi$
$564$	78.7141	3.31446
$565$	−70.6541	−2.97244
$566$	−21.4644	−0.902216
$567$	−18.4784	−0.776021
$568$	−32.5712	−1.36666
$569$	−4.17826	−0.175162	−0.0875808	−	0.996157i	$-0.527914\pi$
$569$	−4.17826	−0.175162	−0.0875808	+	0.996157i	$0.527914\pi$
$570$	21.7557	0.911245
$571$	20.1383	0.842763	0.421382	−	0.906883i	$-0.361545\pi$
$571$	20.1383	0.842763	0.421382	+	0.906883i	$0.361545\pi$
$572$	−35.1687	−1.47048
$573$	46.6204	1.94759
$574$	−21.6336	−0.902969
$575$	−5.72378	−0.238698
$576$	−3.05490	−0.127288
$577$	−4.89918	−0.203956	−0.101978	−	0.994787i	$-0.532517\pi$
$577$	−4.89918	−0.203956	−0.101978	+	0.994787i	$0.532517\pi$
$578$	−0.0768159	−0.00319512
$579$	15.9391	0.662405
$580$	−19.4087	−0.805904
$581$	3.13592	0.130100
$582$	−38.0232	−1.57611
$583$	2.80030	0.115977
$584$	−46.4242	−1.92105
$585$	−3.49324	−0.144428
$586$	46.7238	1.93014
$587$	23.2312	0.958854	0.479427	−	0.877582i	$-0.340845\pi$
$587$	23.2312	0.958854	0.479427	+	0.877582i	$0.340845\pi$
$588$	21.5251	0.887682
$589$	−9.09354	−0.374693
$590$	−4.87052	−0.200516
$591$	−27.8308	−1.14481
$592$	9.18598	0.377541
$593$	43.7425	1.79629	0.898145	−	0.439700i	$-0.144915\pi$
$593$	43.7425	1.79629	0.898145	+	0.439700i	$0.144915\pi$
$594$	32.6276	1.33873
$595$	30.2246	1.23909
$596$	24.9242	1.02094
$597$	26.5588	1.08698
$598$	4.88689	0.199840
$599$	−29.6513	−1.21152	−0.605759	−	0.795648i	$-0.707131\pi$
$599$	−29.6513	−1.21152	−0.605759	+	0.795648i	$0.707131\pi$
$600$	63.8671	2.60736
$601$	−13.2691	−0.541257	−0.270629	−	0.962684i	$-0.587232\pi$
$601$	−13.2691	−0.541257	−0.270629	+	0.962684i	$0.587232\pi$
$602$	25.7081	1.04779
$603$	−3.04723	−0.124093
$604$	3.53712	0.143923
$605$	12.1444	0.493742
$606$	69.8645	2.83805
$607$	31.0067	1.25852	0.629261	−	0.777194i	$-0.283358\pi$
$607$	31.0067	1.25852	0.629261	+	0.777194i	$0.283358\pi$
$608$	−5.13377	−0.208202
$609$	−4.90408	−0.198723
$610$	6.23796	0.252568
$611$	−43.7896	−1.77154
$612$	−3.73505	−0.150980
$613$	−16.9202	−0.683402	−0.341701	−	0.939809i	$-0.611003\pi$
$613$	−16.9202	−0.683402	−0.341701	+	0.939809i	$0.611003\pi$
$614$	22.1125	0.892388
$615$	33.4921	1.35053
$616$	19.2909	0.777253
$617$	−9.24958	−0.372374	−0.186187	−	0.982514i	$-0.559613\pi$
$617$	−9.24958	−0.372374	−0.186187	+	0.982514i	$0.559613\pi$
$618$	13.1777	0.530085
$619$	28.1957	1.13328	0.566640	−	0.823965i	$-0.308243\pi$
$619$	28.1957	1.13328	0.566640	+	0.823965i	$0.308243\pi$
$620$	−92.8172	−3.72763
$621$	−2.89619	−0.116220
$622$	−12.7265	−0.510284
$623$	−8.19392	−0.328282
$624$	−9.20631	−0.368547
$625$	21.8321	0.873285
$626$	−33.2749	−1.32993
$627$	−6.73308	−0.268893
$628$	16.6560	0.664645
$629$	−26.3825	−1.05194
$630$	4.40928	0.175670
$631$	38.4034	1.52881	0.764407	−	0.644734i	$-0.223032\pi$
$631$	38.4034	1.52881	0.764407	+	0.644734i	$0.223032\pi$
$632$	−17.0389	−0.677772
$633$	28.7583	1.14304
$634$	28.4895	1.13146
$635$	60.8565	2.41502
$636$	6.38238	0.253078
$637$	−11.9747	−0.474455
$638$	9.40313	0.372273
$639$	2.30404	0.0911463
$640$	−78.4043	−3.09920
$641$	−3.75700	−0.148393	−0.0741963	−	0.997244i	$-0.523639\pi$
$641$	−3.75700	−0.148393	−0.0741963	+	0.997244i	$0.523639\pi$
$642$	64.5497	2.54757
$643$	−45.5802	−1.79751	−0.898754	−	0.438454i	$-0.855526\pi$
$643$	−45.5802	−1.79751	−0.898754	+	0.438454i	$0.855526\pi$
$644$	−3.94037	−0.155272
$645$	−39.8002	−1.56713
$646$	−12.9407	−0.509147
$647$	20.1977	0.794053	0.397026	−	0.917807i	$-0.370042\pi$
$647$	20.1977	0.794053	0.397026	+	0.917807i	$0.370042\pi$
$648$	35.0927	1.37857
$649$	1.50736	0.0591689
$650$	−81.7594	−3.20687
$651$	−23.4524	−0.919174
$652$	17.7786	0.696264
$653$	−4.27647	−0.167351	−0.0836756	−	0.996493i	$-0.526666\pi$
$653$	−4.27647	−0.167351	−0.0836756	+	0.996493i	$0.526666\pi$
$654$	43.1080	1.68565
$655$	60.1019	2.34838
$656$	6.93648	0.270824
$657$	3.28397	0.128120
$658$	55.2726	2.15475
$659$	−19.5038	−0.759759	−0.379879	−	0.925036i	$-0.624034\pi$
$659$	−19.5038	−0.759759	−0.379879	+	0.925036i	$0.624034\pi$
$660$	−68.7241	−2.67508
$661$	42.1724	1.64032	0.820159	−	0.572136i	$-0.193885\pi$
$661$	42.1724	1.64032	0.820159	+	0.572136i	$0.193885\pi$
$662$	−24.9642	−0.970262
$663$	26.4409	1.02688
$664$	−5.95547	−0.231117
$665$	9.75880	0.378430
$666$	−3.84877	−0.149137
$667$	−0.834669	−0.0323185
$668$	−24.7803	−0.958779
$669$	15.9469	0.616541
$670$	−107.761	−4.16319
$671$	−1.93056	−0.0745285
$672$	−13.2401	−0.510748
$673$	13.3046	0.512855	0.256428	−	0.966563i	$-0.417455\pi$
$673$	13.3046	0.512855	0.256428	+	0.966563i	$0.417455\pi$
$674$	−16.0822	−0.619462
$675$	48.4544	1.86501
$676$	−1.39093	−0.0534973
$677$	−12.1419	−0.466651	−0.233325	−	0.972399i	$-0.574961\pi$
$677$	−12.1419	−0.466651	−0.233325	+	0.972399i	$0.574961\pi$
$678$	78.0173	2.99624
$679$	−17.0558	−0.654542
$680$	−57.4001	−2.20119
$681$	−12.4800	−0.478233
$682$	44.9680	1.72191
$683$	37.7651	1.44504	0.722520	−	0.691350i	$-0.242984\pi$
$683$	37.7651	1.44504	0.722520	+	0.691350i	$0.242984\pi$
$684$	−1.20596	−0.0461109
$685$	58.3539	2.22959
$686$	46.4866	1.77487
$687$	51.1862	1.95288
$688$	−8.24292	−0.314258
$689$	−3.55060	−0.135267
$690$	9.54960	0.363547
$691$	−3.69727	−0.140651	−0.0703254	−	0.997524i	$-0.522404\pi$
$691$	−3.69727	−0.140651	−0.0703254	+	0.997524i	$0.522404\pi$
$692$	−63.0359	−2.39626
$693$	−1.36461	−0.0518372
$694$	−54.6715	−2.07530
$695$	−40.3572	−1.53084
$696$	9.31341	0.353024
$697$	−19.9218	−0.754593
$698$	−19.5905	−0.741513
$699$	−33.4630	−1.26569
$700$	65.9238	2.49169
$701$	16.8630	0.636905	0.318453	−	0.947939i	$-0.396837\pi$
$701$	16.8630	0.636905	0.318453	+	0.947939i	$0.396837\pi$
$702$	−41.3697	−1.56140
$703$	−8.51826	−0.321272
$704$	33.4347	1.26012
$705$	−85.5705	−3.22277
$706$	−40.3565	−1.51884
$707$	31.3386	1.17861
$708$	3.43553	0.129115
$709$	−12.9245	−0.485389	−0.242695	−	0.970103i	$-0.578031\pi$
$709$	−12.9245	−0.485389	−0.242695	+	0.970103i	$0.578031\pi$
$710$	81.4794	3.05787
$711$	1.20531	0.0452025
$712$	15.5612	0.583180
$713$	−3.99158	−0.149486
$714$	−33.3745	−1.24901
$715$	38.2321	1.42980
$716$	−34.3937	−1.28535
$717$	−29.6224	−1.10627
$718$	71.9002	2.68329
$719$	−14.9450	−0.557355	−0.278678	−	0.960385i	$-0.589896\pi$
$719$	−14.9450	−0.557355	−0.278678	+	0.960385i	$0.589896\pi$
$720$	−1.41377	−0.0526880
$721$	5.91103	0.220138
$722$	40.5308	1.50840
$723$	45.2814	1.68403
$724$	−20.5707	−0.764503
$725$	13.9643	0.518622
$726$	−13.4101	−0.497694
$727$	−49.0836	−1.82041	−0.910204	−	0.414160i	$-0.864075\pi$
$727$	−49.0836	−1.82041	−0.910204	+	0.414160i	$0.864075\pi$
$728$	−24.4596	−0.906535
$729$	24.3212	0.900785
$730$	116.134	4.29830
$731$	23.6740	0.875614
$732$	−4.40009	−0.162632
$733$	27.3340	1.00960	0.504801	−	0.863236i	$-0.331566\pi$
$733$	27.3340	1.00960	0.504801	+	0.863236i	$0.331566\pi$
$734$	3.08386	0.113827
$735$	−23.4001	−0.863126
$736$	−2.25345	−0.0830634
$737$	33.3506	1.22849
$738$	−2.90627	−0.106981
$739$	20.3891	0.750025	0.375012	−	0.927020i	$-0.377638\pi$
$739$	20.3891	0.750025	0.375012	+	0.927020i	$0.377638\pi$
$740$	−86.9453	−3.19617
$741$	8.53711	0.313619
$742$	4.48168	0.164527
$743$	−13.6273	−0.499937	−0.249968	−	0.968254i	$-0.580420\pi$
$743$	−13.6273	−0.499937	−0.249968	+	0.968254i	$0.580420\pi$
$744$	44.5389	1.63288
$745$	−27.0953	−0.992693
$746$	−22.4464	−0.821820
$747$	0.421281	0.0154139
$748$	40.8785	1.49467
$749$	28.9546	1.05798
$750$	−78.1352	−2.85309
$751$	20.3610	0.742985	0.371492	−	0.928436i	$-0.378846\pi$
$751$	20.3610	0.742985	0.371492	+	0.928436i	$0.378846\pi$
$752$	−17.7223	−0.646266
$753$	−27.3616	−0.997111
$754$	−11.9226	−0.434194
$755$	−3.84522	−0.139942
$756$	33.3570	1.21318
$757$	−10.0112	−0.363863	−0.181932	−	0.983311i	$-0.558235\pi$
$757$	−10.0112	−0.363863	−0.181932	+	0.983311i	$0.558235\pi$
$758$	45.9053	1.66736
$759$	−2.95547	−0.107277
$760$	−18.5331	−0.672266
$761$	26.7578	0.969971	0.484986	−	0.874522i	$-0.338825\pi$
$761$	26.7578	0.969971	0.484986	+	0.874522i	$0.338825\pi$
$762$	−67.1986	−2.43435
$763$	19.3366	0.700033
$764$	−91.3888	−3.30633
$765$	4.06039	0.146804
$766$	−21.5840	−0.779862
$767$	−1.91123	−0.0690105
$768$	43.4872	1.56921
$769$	49.4422	1.78293	0.891465	−	0.453090i	$-0.149678\pi$
$769$	49.4422	1.78293	0.891465	+	0.453090i	$0.149678\pi$
$770$	−48.2577	−1.73909
$771$	52.3517	1.88540
$772$	−31.2450	−1.12453
$773$	2.36338	0.0850050	0.0425025	−	0.999096i	$-0.486467\pi$
$773$	2.36338	0.0850050	0.0425025	+	0.999096i	$0.486467\pi$
$774$	3.45364	0.124139
$775$	66.7807	2.39883
$776$	32.3910	1.16277
$777$	−21.9688	−0.788126
$778$	49.8950	1.78882
$779$	−6.43227	−0.230460
$780$	87.1377	3.12003
$781$	−25.2167	−0.902325
$782$	−5.68030	−0.203127
$783$	7.06586	0.252513
$784$	−4.84634	−0.173084
$785$	−18.1068	−0.646259
$786$	−66.3654	−2.36717
$787$	−30.2935	−1.07985	−0.539923	−	0.841714i	$-0.681547\pi$
$787$	−30.2935	−1.07985	−0.539923	+	0.841714i	$0.681547\pi$
$788$	54.5560	1.94348
$789$	−4.61024	−0.164129
$790$	42.6242	1.51650
$791$	34.9957	1.24430
$792$	2.59155	0.0920867
$793$	2.44783	0.0869249
$794$	52.7658	1.87259
$795$	−6.93832	−0.246077
$796$	−52.0625	−1.84531
$797$	15.1434	0.536406	0.268203	−	0.963362i	$-0.413570\pi$
$797$	15.1434	0.536406	0.268203	+	0.963362i	$0.413570\pi$
$798$	−10.7758	−0.381459
$799$	50.8992	1.80068
$800$	37.7011	1.33293
$801$	−1.10077	−0.0388939
$802$	−4.51366	−0.159383
$803$	−35.9417	−1.26836
$804$	76.0120	2.68074
$805$	4.28360	0.150977
$806$	−57.0165	−2.00832
$807$	−34.3142	−1.20792
$808$	−59.5157	−2.09375
$809$	−14.4502	−0.508043	−0.254021	−	0.967199i	$-0.581753\pi$
$809$	−14.4502	−0.508043	−0.254021	+	0.967199i	$0.581753\pi$
$810$	−87.7870	−3.08452
$811$	−38.7108	−1.35932	−0.679660	−	0.733528i	$-0.737872\pi$
$811$	−38.7108	−1.35932	−0.679660	+	0.733528i	$0.737872\pi$
$812$	9.61334	0.337362
$813$	22.8648	0.801904
$814$	42.1232	1.47642
$815$	−19.3272	−0.677003
$816$	10.7010	0.374610
$817$	7.64375	0.267421
$818$	22.6195	0.790873
$819$	1.73024	0.0604593
$820$	−65.6538	−2.29273
$821$	31.8600	1.11192	0.555961	−	0.831208i	$-0.312350\pi$
$821$	31.8600	1.11192	0.555961	+	0.831208i	$0.312350\pi$
$822$	−64.4352	−2.24744
$823$	13.7169	0.478140	0.239070	−	0.971002i	$-0.423157\pi$
$823$	13.7169	0.478140	0.239070	+	0.971002i	$0.423157\pi$
$824$	−11.2257	−0.391067
$825$	49.4460	1.72149
$826$	2.41241	0.0839386
$827$	41.9407	1.45842	0.729210	−	0.684290i	$-0.239888\pi$
$827$	41.9407	1.45842	0.729210	+	0.684290i	$0.239888\pi$
$828$	−0.529351	−0.0183962
$829$	−16.7671	−0.582346	−0.291173	−	0.956670i	$-0.594045\pi$
$829$	−16.7671	−0.582346	−0.291173	+	0.956670i	$0.594045\pi$
$830$	14.8981	0.517120
$831$	−11.6419	−0.403854
$832$	−42.3930	−1.46971
$833$	13.9189	0.482261
$834$	44.5630	1.54309
$835$	26.9388	0.932256
$836$	13.1987	0.456486
$837$	33.7906	1.16797
$838$	−85.3890	−2.94971
$839$	−7.65569	−0.264304	−0.132152	−	0.991229i	$-0.542189\pi$
$839$	−7.65569	−0.264304	−0.132152	+	0.991229i	$0.542189\pi$
$840$	−47.7973	−1.64916
$841$	−26.9637	−0.929781
$842$	−24.0049	−0.827263
$843$	56.0625	1.93089
$844$	−56.3741	−1.94048
$845$	1.51209	0.0520174
$846$	7.42535	0.255289
$847$	−6.01526	−0.206687
$848$	−1.43698	−0.0493461
$849$	−16.4592	−0.564880
$850$	95.0336	3.25962
$851$	−3.73907	−0.128174
$852$	−57.4734	−1.96901
$853$	2.64851	0.0906833	0.0453417	−	0.998972i	$-0.485562\pi$
$853$	2.64851	0.0906833	0.0453417	+	0.998972i	$0.485562\pi$
$854$	−3.08972	−0.105728
$855$	1.31100	0.0448353
$856$	−54.9882	−1.87946
$857$	53.5765	1.83014	0.915069	−	0.403297i	$-0.132136\pi$
$857$	53.5765	1.83014	0.915069	+	0.403297i	$0.132136\pi$
$858$	−42.2164	−1.44124
$859$	18.2029	0.621073	0.310537	−	0.950561i	$-0.399491\pi$
$859$	18.2029	0.621073	0.310537	+	0.950561i	$0.399491\pi$
$860$	78.0192	2.66043
$861$	−16.5890	−0.565351
$862$	96.1952	3.27642
$863$	−18.9773	−0.645994	−0.322997	−	0.946400i	$-0.604690\pi$
$863$	−18.9773	−0.645994	−0.322997	+	0.946400i	$0.604690\pi$
$864$	19.0765	0.648996
$865$	68.5266	2.32998
$866$	−83.1786	−2.82653
$867$	−0.0589036	−0.00200047
$868$	45.9732	1.56043
$869$	−13.1916	−0.447494
$870$	−23.2982	−0.789883
$871$	−42.2865	−1.43282
$872$	−36.7225	−1.24358
$873$	−2.29129	−0.0775483
$874$	−1.83403	−0.0620370
$875$	−35.0485	−1.18486
$876$	−81.9176	−2.76774
$877$	26.3519	0.889842	0.444921	−	0.895570i	$-0.353232\pi$
$877$	26.3519	0.889842	0.444921	+	0.895570i	$0.353232\pi$
$878$	51.7768	1.74738
$879$	35.8285	1.20847
$880$	15.4731	0.521598
$881$	−0.349839	−0.0117864	−0.00589318	−	0.999983i	$-0.501876\pi$
$881$	−0.349839	−0.0117864	−0.00589318	+	0.999983i	$0.501876\pi$
$882$	2.03053	0.0683717
$883$	−16.6834	−0.561443	−0.280721	−	0.959789i	$-0.590574\pi$
$883$	−16.6834	−0.561443	−0.280721	+	0.959789i	$0.590574\pi$
$884$	−51.8314	−1.74328
$885$	−3.73479	−0.125544
$886$	−60.8895	−2.04562
$887$	5.21847	0.175219	0.0876096	−	0.996155i	$-0.472077\pi$
$887$	5.21847	0.175219	0.0876096	+	0.996155i	$0.472077\pi$
$888$	41.7213	1.40007
$889$	−30.1428	−1.01096
$890$	−38.9275	−1.30485
$891$	27.1688	0.910191
$892$	−31.2602	−1.04667
$893$	16.4341	0.549946
$894$	29.9190	1.00064
$895$	37.3895	1.24979
$896$	38.8344	1.29737
$897$	3.74734	0.125120
$898$	−1.51948	−0.0507058
$899$	9.73829	0.324790
$900$	8.85623	0.295208
$901$	4.12706	0.137492
$902$	31.8079	1.05909
$903$	19.7134	0.656021
$904$	−66.4608	−2.21045
$905$	22.3625	0.743355
$906$	4.24595	0.141062
$907$	53.1472	1.76472	0.882362	−	0.470571i	$-0.155952\pi$
$907$	53.1472	1.76472	0.882362	+	0.470571i	$0.155952\pi$
$908$	24.4641	0.811871
$909$	4.21005	0.139638
$910$	61.1877	2.02835
$911$	40.8536	1.35354	0.676770	−	0.736195i	$-0.263379\pi$
$911$	40.8536	1.35354	0.676770	+	0.736195i	$0.263379\pi$
$912$	3.45509	0.114410
$913$	−4.61074	−0.152593
$914$	−58.6583	−1.94025
$915$	4.78337	0.158133
$916$	−100.339	−3.31530
$917$	−29.7690	−0.983060
$918$	48.0864	1.58709
$919$	50.7667	1.67464	0.837319	−	0.546715i	$-0.184122\pi$
$919$	50.7667	1.67464	0.837319	+	0.546715i	$0.184122\pi$
$920$	−8.13505	−0.268205
$921$	16.9562	0.558726
$922$	−66.4692	−2.18905
$923$	31.9732	1.05241
$924$	34.0397	1.11982
$925$	62.5560	2.05683
$926$	81.2519	2.67010
$927$	0.794090	0.0260813
$928$	5.49776	0.180473
$929$	−50.2826	−1.64972	−0.824860	−	0.565337i	$-0.808746\pi$
$929$	−50.2826	−1.64972	−0.824860	+	0.565337i	$0.808746\pi$
$930$	−111.417	−3.65352
$931$	4.49407	0.147287
$932$	65.5966	2.14869
$933$	−9.75884	−0.319490
$934$	−19.2384	−0.629498
$935$	−44.4393	−1.45332
$936$	−3.28592	−0.107404
$937$	34.4182	1.12439	0.562196	−	0.827004i	$-0.309957\pi$
$937$	34.4182	1.12439	0.562196	+	0.827004i	$0.309957\pi$
$938$	53.3753	1.74276
$939$	−25.5157	−0.832673
$940$	167.742	5.47113
$941$	−17.5056	−0.570667	−0.285333	−	0.958428i	$-0.592104\pi$
$941$	−17.5056	−0.570667	−0.285333	+	0.958428i	$0.592104\pi$
$942$	19.9938	0.651433
$943$	−2.82343	−0.0919435
$944$	−0.773503	−0.0251754
$945$	−36.2626	−1.17962
$946$	−37.7987	−1.22894
$947$	52.2435	1.69769	0.848843	−	0.528645i	$-0.177300\pi$
$947$	52.2435	1.69769	0.848843	+	0.528645i	$0.177300\pi$
$948$	−30.0660	−0.976497
$949$	45.5718	1.47932
$950$	30.6840	0.995521
$951$	21.8462	0.708413
$952$	28.4308	0.921448
$953$	−14.7214	−0.476871	−0.238436	−	0.971158i	$-0.576635\pi$
$953$	−14.7214	−0.476871	−0.238436	+	0.971158i	$0.576635\pi$
$954$	0.602070	0.0194927
$955$	99.3492	3.21487
$956$	58.0680	1.87805
$957$	7.21047	0.233081
$958$	−80.9903	−2.61668
$959$	−28.9033	−0.933335
$960$	−82.8413	−2.67369
$961$	15.5708	0.502283
$962$	−53.4095	−1.72199
$963$	3.88978	0.125346
$964$	−88.7641	−2.85890
$965$	33.9666	1.09342
$966$	−4.73001	−0.152186
$967$	27.5561	0.886144	0.443072	−	0.896486i	$-0.353889\pi$
$967$	27.5561	0.886144	0.443072	+	0.896486i	$0.353889\pi$
$968$	11.4237	0.367171
$969$	−9.92316	−0.318778
$970$	−81.0285	−2.60167
$971$	−39.5353	−1.26875	−0.634374	−	0.773026i	$-0.718742\pi$
$971$	−39.5353	−1.26875	−0.634374	+	0.773026i	$0.718742\pi$
$972$	9.38022	0.300871
$973$	19.9893	0.640828
$974$	−62.9018	−2.01550
$975$	−62.6944	−2.00783
$976$	0.990672	0.0317106
$977$	−37.9776	−1.21501	−0.607506	−	0.794315i	$-0.707830\pi$
$977$	−37.9776	−1.21501	−0.607506	+	0.794315i	$0.707830\pi$
$978$	21.3414	0.682422
$979$	12.0475	0.385040
$980$	45.8706	1.46528
$981$	2.59769	0.0829379
$982$	79.9178	2.55028
$983$	9.06913	0.289260	0.144630	−	0.989486i	$-0.453801\pi$
$983$	9.06913	0.289260	0.144630	+	0.989486i	$0.453801\pi$
$984$	31.5044	1.00432
$985$	−59.3081	−1.88971
$986$	13.8583	0.441337
$987$	42.3839	1.34909
$988$	−16.7351	−0.532414
$989$	3.35520	0.106689
$990$	−6.48296	−0.206042
$991$	−44.7024	−1.42002	−0.710009	−	0.704192i	$-0.751309\pi$
$991$	−44.7024	−1.42002	−0.710009	+	0.704192i	$0.751309\pi$
$992$	26.2916	0.834758
$993$	−19.1430	−0.607484
$994$	−40.3575	−1.28006
$995$	56.5975	1.79426
$996$	−10.5087	−0.332981
$997$	−25.7328	−0.814967	−0.407484	−	0.913212i	$-0.633594\pi$
$997$	−25.7328	−0.814967	−0.407484	+	0.913212i	$0.633594\pi$
$998$	58.9820	1.86704
$999$	31.6529	1.00145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.17	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.17	✓	172	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)

\(f(q)\)	\(=\)	\(q-2.35311 q^{2} -1.80440 q^{3} +3.53712 q^{4} -3.84522 q^{5} +4.24595 q^{6} +1.90458 q^{7} -3.61701 q^{8} +0.255862 q^{9} +O(q^{10})\)	\(q-2.35311 q^{2} -1.80440 q^{3} +3.53712 q^{4} -3.84522 q^{5} +4.24595 q^{6} +1.90458 q^{7} -3.61701 q^{8} +0.255862 q^{9} +9.04823 q^{10} -2.80030 q^{11} -6.38238 q^{12} +3.55060 q^{13} -4.48168 q^{14} +6.93832 q^{15} +1.43698 q^{16} -4.12706 q^{17} -0.602070 q^{18} -1.33253 q^{19} -13.6010 q^{20} -3.43662 q^{21} +6.58941 q^{22} -0.584909 q^{23} +6.52654 q^{24} +9.78575 q^{25} -8.35495 q^{26} +4.95152 q^{27} +6.73672 q^{28} +1.42701 q^{29} -16.3266 q^{30} +6.82428 q^{31} +3.85265 q^{32} +5.05286 q^{33} +9.71143 q^{34} -7.32352 q^{35} +0.905013 q^{36} +6.39256 q^{37} +3.13558 q^{38} -6.40671 q^{39} +13.9082 q^{40} +4.82712 q^{41} +8.08674 q^{42} -5.73628 q^{43} -9.90500 q^{44} -0.983845 q^{45} +1.37636 q^{46} -12.3330 q^{47} -2.59289 q^{48} -3.37259 q^{49} -23.0269 q^{50} +7.44687 q^{51} +12.5589 q^{52} -1.00000 q^{53} -11.6515 q^{54} +10.7678 q^{55} -6.88888 q^{56} +2.40441 q^{57} -3.35790 q^{58} -0.538284 q^{59} +24.5417 q^{60} +0.689413 q^{61} -16.0583 q^{62} +0.487308 q^{63} -11.9397 q^{64} -13.6529 q^{65} -11.8899 q^{66} -11.9097 q^{67} -14.5979 q^{68} +1.05541 q^{69} +17.2330 q^{70} +9.00501 q^{71} -0.925454 q^{72} +12.8350 q^{73} -15.0424 q^{74} -17.6574 q^{75} -4.71331 q^{76} -5.33339 q^{77} +15.0757 q^{78} +4.71078 q^{79} -5.52551 q^{80} -9.70212 q^{81} -11.3587 q^{82} +1.64652 q^{83} -12.1557 q^{84} +15.8695 q^{85} +13.4981 q^{86} -2.57489 q^{87} +10.1287 q^{88} -4.30222 q^{89} +2.31510 q^{90} +6.76239 q^{91} -2.06889 q^{92} -12.3137 q^{93} +29.0209 q^{94} +5.12387 q^{95} -6.95173 q^{96} -8.95518 q^{97} +7.93607 q^{98} -0.716489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9} + 20 q^{10} - 3 q^{11} + 66 q^{12} + 121 q^{13} + 12 q^{14} + 30 q^{15} + 212 q^{16} + 8 q^{17} + 40 q^{18} + 41 q^{19} + 64 q^{20} + 56 q^{21} + 50 q^{22} + 28 q^{23} + 30 q^{24} + 231 q^{25} + 38 q^{26} + 100 q^{27} + 80 q^{28} + 26 q^{29} + 55 q^{30} + 66 q^{31} + 65 q^{32} + 99 q^{33} + 81 q^{34} + 36 q^{35} + 212 q^{36} + 153 q^{37} + q^{38} + 20 q^{39} + 59 q^{40} + 40 q^{41} + 50 q^{42} + 39 q^{43} - 51 q^{44} + 123 q^{45} + 59 q^{46} + 29 q^{47} + 128 q^{48} + 245 q^{49} + 19 q^{50} + 36 q^{51} + 215 q^{52} - 172 q^{53} + 40 q^{54} + 40 q^{55} + 15 q^{56} + 54 q^{57} + 44 q^{58} - 54 q^{60} + 100 q^{61} - 29 q^{62} + 92 q^{63} + 253 q^{64} + 77 q^{65} + 14 q^{66} + 126 q^{67} - 27 q^{68} + 47 q^{69} + 72 q^{70} + 38 q^{71} + 65 q^{72} + 185 q^{73} + 48 q^{74} + 75 q^{75} + 38 q^{76} + 120 q^{77} + 75 q^{78} + 79 q^{79} + 43 q^{80} + 232 q^{81} + 110 q^{82} + 90 q^{83} + 158 q^{84} + 115 q^{85} + 68 q^{86} + 61 q^{87} + 15 q^{88} - 36 q^{89} - 6 q^{90} + 33 q^{91} + 139 q^{92} + 103 q^{93} - 24 q^{94} - 45 q^{95} + 34 q^{96} + 159 q^{97} - 36 q^{98} + 27 q^{99}+O(q^{100}) \) 172 * q + 8 * q^2 + 25 * q^3 + 188 * q^4 + 27 * q^5 + 10 * q^6 + 31 * q^7 + 21 * q^8 + 179 * q^9 + 20 * q^10 - 3 * q^11 + 66 * q^12 + 121 * q^13 + 12 * q^14 + 30 * q^15 + 212 * q^16 + 8 * q^17 + 40 * q^18 + 41 * q^19 + 64 * q^20 + 56 * q^21 + 50 * q^22 + 28 * q^23 + 30 * q^24 + 231 * q^25 + 38 * q^26 + 100 * q^27 + 80 * q^28 + 26 * q^29 + 55 * q^30 + 66 * q^31 + 65 * q^32 + 99 * q^33 + 81 * q^34 + 36 * q^35 + 212 * q^36 + 153 * q^37 + q^38 + 20 * q^39 + 59 * q^40 + 40 * q^41 + 50 * q^42 + 39 * q^43 - 51 * q^44 + 123 * q^45 + 59 * q^46 + 29 * q^47 + 128 * q^48 + 245 * q^49 + 19 * q^50 + 36 * q^51 + 215 * q^52 - 172 * q^53 + 40 * q^54 + 40 * q^55 + 15 * q^56 + 54 * q^57 + 44 * q^58 - 54 * q^60 + 100 * q^61 - 29 * q^62 + 92 * q^63 + 253 * q^64 + 77 * q^65 + 14 * q^66 + 126 * q^67 - 27 * q^68 + 47 * q^69 + 72 * q^70 + 38 * q^71 + 65 * q^72 + 185 * q^73 + 48 * q^74 + 75 * q^75 + 38 * q^76 + 120 * q^77 + 75 * q^78 + 79 * q^79 + 43 * q^80 + 232 * q^81 + 110 * q^82 + 90 * q^83 + 158 * q^84 + 115 * q^85 + 68 * q^86 + 61 * q^87 + 15 * q^88 - 36 * q^89 - 6 * q^90 + 33 * q^91 + 139 * q^92 + 103 * q^93 - 24 * q^94 - 45 * q^95 + 34 * q^96 + 159 * q^97 - 36 * q^98 + 27 * q^99

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