LMFDB - Embedded newform 8003.2.a.c.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.68137 q^{2} +1.21893 q^{3} +5.18975 q^{4} +2.92126 q^{5} -3.26842 q^{6} +4.69101 q^{7} -8.55290 q^{8} -1.51420 q^{9} +O(q^{10})$	\(q-2.68137 q^{2} +1.21893 q^{3} +5.18975 q^{4} +2.92126 q^{5} -3.26842 q^{6} +4.69101 q^{7} -8.55290 q^{8} -1.51420 q^{9} -7.83297 q^{10} -1.10078 q^{11} +6.32596 q^{12} +3.44785 q^{13} -12.5783 q^{14} +3.56082 q^{15} +12.5540 q^{16} -4.01060 q^{17} +4.06013 q^{18} -2.14032 q^{19} +15.1606 q^{20} +5.71803 q^{21} +2.95159 q^{22} +2.58440 q^{23} -10.4254 q^{24} +3.53374 q^{25} -9.24496 q^{26} -5.50251 q^{27} +24.3452 q^{28} -6.97941 q^{29} -9.54788 q^{30} +6.93849 q^{31} -16.5561 q^{32} -1.34178 q^{33} +10.7539 q^{34} +13.7036 q^{35} -7.85831 q^{36} +10.6920 q^{37} +5.73900 q^{38} +4.20270 q^{39} -24.9852 q^{40} -4.96455 q^{41} -15.3322 q^{42} -4.73081 q^{43} -5.71276 q^{44} -4.42336 q^{45} -6.92974 q^{46} +10.5871 q^{47} +15.3025 q^{48} +15.0056 q^{49} -9.47527 q^{50} -4.88866 q^{51} +17.8935 q^{52} -1.00000 q^{53} +14.7543 q^{54} -3.21565 q^{55} -40.1217 q^{56} -2.60891 q^{57} +18.7144 q^{58} +10.0989 q^{59} +18.4798 q^{60} +9.99290 q^{61} -18.6047 q^{62} -7.10312 q^{63} +19.2851 q^{64} +10.0720 q^{65} +3.59780 q^{66} +0.502039 q^{67} -20.8140 q^{68} +3.15022 q^{69} -36.7445 q^{70} +2.73221 q^{71} +12.9508 q^{72} -8.16872 q^{73} -28.6693 q^{74} +4.30740 q^{75} -11.1077 q^{76} -5.16375 q^{77} -11.2690 q^{78} -10.5454 q^{79} +36.6734 q^{80} -2.16460 q^{81} +13.3118 q^{82} -14.2677 q^{83} +29.6751 q^{84} -11.7160 q^{85} +12.6851 q^{86} -8.50744 q^{87} +9.41484 q^{88} +11.6919 q^{89} +11.8607 q^{90} +16.1739 q^{91} +13.4124 q^{92} +8.45756 q^{93} -28.3878 q^{94} -6.25243 q^{95} -20.1808 q^{96} -3.98600 q^{97} -40.2355 q^{98} +1.66680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.68137	−1.89602	−0.948008	−	0.318247i	$-0.896906\pi$
$2$	−2.68137	−1.89602	−0.948008	+	0.318247i	$0.896906\pi$
$3$	1.21893	0.703752	0.351876	−	0.936047i	$-0.385544\pi$
$3$	1.21893	0.703752	0.351876	+	0.936047i	$0.385544\pi$
$4$	5.18975	2.59487
$5$	2.92126	1.30643	0.653213	−	0.757174i	$-0.273421\pi$
$5$	2.92126	1.30643	0.653213	+	0.757174i	$0.273421\pi$
$6$	−3.26842	−1.33432
$7$	4.69101	1.77303	0.886517	−	0.462696i	$-0.153118\pi$
$7$	4.69101	1.77303	0.886517	+	0.462696i	$0.153118\pi$
$8$	−8.55290	−3.02391
$9$	−1.51420	−0.504733
$10$	−7.83297	−2.47700
$11$	−1.10078	−0.331897	−0.165948	−	0.986134i	$-0.553069\pi$
$11$	−1.10078	−0.331897	−0.165948	+	0.986134i	$0.553069\pi$
$12$	6.32596	1.82615
$13$	3.44785	0.956261	0.478130	−	0.878289i	$-0.341315\pi$
$13$	3.44785	0.956261	0.478130	+	0.878289i	$0.341315\pi$
$14$	−12.5783	−3.36170
$15$	3.56082	0.919400
$16$	12.5540	3.13850
$17$	−4.01060	−0.972715	−0.486357	−	0.873760i	$-0.661675\pi$
$17$	−4.01060	−0.972715	−0.486357	+	0.873760i	$0.661675\pi$
$18$	4.06013	0.956981
$19$	−2.14032	−0.491024	−0.245512	−	0.969394i	$-0.578956\pi$
$19$	−2.14032	−0.491024	−0.245512	+	0.969394i	$0.578956\pi$
$20$	15.1606	3.39001
$21$	5.71803	1.24778
$22$	2.95159	0.629281
$23$	2.58440	0.538885	0.269443	−	0.963016i	$-0.413161\pi$
$23$	2.58440	0.538885	0.269443	+	0.963016i	$0.413161\pi$
$24$	−10.4254	−2.12808
$25$	3.53374	0.706748
$26$	−9.24496	−1.81309
$27$	−5.50251	−1.05896
$28$	24.3452	4.60080
$29$	−6.97941	−1.29604	−0.648022	−	0.761622i	$-0.724404\pi$
$29$	−6.97941	−1.29604	−0.648022	+	0.761622i	$0.724404\pi$
$30$	−9.54788	−1.74320
$31$	6.93849	1.24619	0.623095	−	0.782147i	$-0.285875\pi$
$31$	6.93849	1.24619	0.623095	+	0.782147i	$0.285875\pi$
$32$	−16.5561	−2.92674
$33$	−1.34178	−0.233573
$34$	10.7539	1.84428
$35$	13.7036	2.31634
$36$	−7.85831	−1.30972
$37$	10.6920	1.75776	0.878878	−	0.477046i	$-0.158292\pi$
$37$	10.6920	1.75776	0.878878	+	0.477046i	$0.158292\pi$
$38$	5.73900	0.930988
$39$	4.20270	0.672971
$40$	−24.9852	−3.95051
$41$	−4.96455	−0.775333	−0.387666	−	0.921800i	$-0.626719\pi$
$41$	−4.96455	−0.775333	−0.387666	+	0.921800i	$0.626719\pi$
$42$	−15.3322	−2.36580
$43$	−4.73081	−0.721442	−0.360721	−	0.932674i	$-0.617469\pi$
$43$	−4.73081	−0.721442	−0.360721	+	0.932674i	$0.617469\pi$
$44$	−5.71276	−0.861231
$45$	−4.42336	−0.659396
$46$	−6.92974	−1.02173
$47$	10.5871	1.54428	0.772140	−	0.635452i	$-0.219186\pi$
$47$	10.5871	1.54428	0.772140	+	0.635452i	$0.219186\pi$
$48$	15.3025	2.20873
$49$	15.0056	2.14365
$50$	−9.47527	−1.34001
$51$	−4.88866	−0.684550
$52$	17.8935	2.48138
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	14.7543	2.00780
$55$	−3.21565	−0.433599
$56$	−40.1217	−5.36149
$57$	−2.60891	−0.345559
$58$	18.7144	2.45732
$59$	10.0989	1.31476	0.657381	−	0.753558i	$-0.271664\pi$
$59$	10.0989	1.31476	0.657381	+	0.753558i	$0.271664\pi$
$60$	18.4798	2.38573
$61$	9.99290	1.27946	0.639730	−	0.768600i	$-0.279046\pi$
$61$	9.99290	1.27946	0.639730	+	0.768600i	$0.279046\pi$
$62$	−18.6047	−2.36279
$63$	−7.10312	−0.894909
$64$	19.2851	2.41064
$65$	10.0720	1.24928
$66$	3.59780	0.442858
$67$	0.502039	0.0613338	0.0306669	−	0.999530i	$-0.490237\pi$
$67$	0.502039	0.0613338	0.0306669	+	0.999530i	$0.490237\pi$
$68$	−20.8140	−2.52407
$69$	3.15022	0.379242
$70$	−36.7445	−4.39181
$71$	2.73221	0.324254	0.162127	−	0.986770i	$-0.448165\pi$
$71$	2.73221	0.324254	0.162127	+	0.986770i	$0.448165\pi$
$72$	12.9508	1.52627
$73$	−8.16872	−0.956076	−0.478038	−	0.878339i	$-0.658652\pi$
$73$	−8.16872	−0.956076	−0.478038	+	0.878339i	$0.658652\pi$
$74$	−28.6693	−3.33273
$75$	4.30740	0.497376
$76$	−11.1077	−1.27414
$77$	−5.16375	−0.588464
$78$	−11.2690	−1.27596
$79$	−10.5454	−1.18645	−0.593223	−	0.805038i	$-0.702145\pi$
$79$	−10.5454	−1.18645	−0.593223	+	0.805038i	$0.702145\pi$
$80$	36.6734	4.10022
$81$	−2.16460	−0.240512
$82$	13.3118	1.47004
$83$	−14.2677	−1.56609	−0.783044	−	0.621966i	$-0.786334\pi$
$83$	−14.2677	−1.56609	−0.783044	+	0.621966i	$0.786334\pi$
$84$	29.6751	3.23782
$85$	−11.7160	−1.27078
$86$	12.6851	1.36786
$87$	−8.50744	−0.912094
$88$	9.41484	1.00362
$89$	11.6919	1.23934	0.619671	−	0.784862i	$-0.287266\pi$
$89$	11.6919	1.23934	0.619671	+	0.784862i	$0.287266\pi$
$90$	11.8607	1.25023
$91$	16.1739	1.69548
$92$	13.4124	1.39834
$93$	8.45756	0.877008
$94$	−28.3878	−2.92798
$95$	−6.25243	−0.641486
$96$	−20.1808	−2.05970
$97$	−3.98600	−0.404717	−0.202358	−	0.979312i	$-0.564861\pi$
$97$	−3.98600	−0.404717	−0.202358	+	0.979312i	$0.564861\pi$
$98$	−40.2355	−4.06440
$99$	1.66680	0.167519
$100$	18.3392	1.83392
$101$	14.4279	1.43563	0.717813	−	0.696236i	$-0.245143\pi$
$101$	14.4279	1.43563	0.717813	+	0.696236i	$0.245143\pi$
$102$	13.1083	1.29792
$103$	20.1616	1.98658	0.993292	−	0.115634i	$-0.0368899\pi$
$103$	20.1616	1.98658	0.993292	+	0.115634i	$0.0368899\pi$
$104$	−29.4891	−2.89164
$105$	16.7038	1.63013
$106$	2.68137	0.260438
$107$	−8.95035	−0.865263	−0.432632	−	0.901571i	$-0.642415\pi$
$107$	−8.95035	−0.865263	−0.432632	+	0.901571i	$0.642415\pi$
$108$	−28.5567	−2.74787
$109$	−1.93614	−0.185449	−0.0927244	−	0.995692i	$-0.529558\pi$
$109$	−1.93614	−0.185449	−0.0927244	+	0.995692i	$0.529558\pi$
$110$	8.62236	0.822109
$111$	13.0329	1.23703
$112$	58.8909	5.56467
$113$	−13.8443	−1.30237	−0.651183	−	0.758920i	$-0.725727\pi$
$113$	−13.8443	−1.30237	−0.651183	+	0.758920i	$0.725727\pi$
$114$	6.99546	0.655185
$115$	7.54970	0.704013
$116$	−36.2214	−3.36307
$117$	−5.22073	−0.482656
$118$	−27.0789	−2.49281
$119$	−18.8138	−1.72466
$120$	−30.4553	−2.78018
$121$	−9.78829	−0.889845
$122$	−26.7947	−2.42587
$123$	−6.05146	−0.545642
$124$	36.0090	3.23370
$125$	−4.28332	−0.383112
$126$	19.0461	1.69676
$127$	18.3916	1.63199	0.815994	−	0.578060i	$-0.196190\pi$
$127$	18.3916	1.63199	0.815994	+	0.578060i	$0.196190\pi$
$128$	−18.5983	−1.64387
$129$	−5.76655	−0.507716
$130$	−27.0069	−2.36866
$131$	3.95117	0.345215	0.172607	−	0.984991i	$-0.444781\pi$
$131$	3.95117	0.345215	0.172607	+	0.984991i	$0.444781\pi$
$132$	−6.96348	−0.606093
$133$	−10.0403	−0.870602
$134$	−1.34615	−0.116290
$135$	−16.0743	−1.38345
$136$	34.3023	2.94140
$137$	−6.80345	−0.581258	−0.290629	−	0.956836i	$-0.593865\pi$
$137$	−6.80345	−0.581258	−0.290629	+	0.956836i	$0.593865\pi$
$138$	−8.44690	−0.719048
$139$	12.4855	1.05900	0.529502	−	0.848309i	$-0.322379\pi$
$139$	12.4855	1.05900	0.529502	+	0.848309i	$0.322379\pi$
$140$	71.1184	6.01061
$141$	12.9049	1.08679
$142$	−7.32608	−0.614791
$143$	−3.79531	−0.317380
$144$	−19.0092	−1.58410
$145$	−20.3886	−1.69319
$146$	21.9034	1.81273
$147$	18.2908	1.50860
$148$	55.4889	4.56116
$149$	22.6396	1.85471	0.927353	−	0.374187i	$-0.122078\pi$
$149$	22.6396	1.85471	0.927353	+	0.374187i	$0.122078\pi$
$150$	−11.5497	−0.943032
$151$	1.00000	0.0813788
$151$	1.00000	0.0813788
$152$	18.3060	1.48481
$153$	6.07285	0.490961
$154$	13.8459	1.11574
$155$	20.2691	1.62805
$156$	21.8110	1.74627
$157$	6.35976	0.507564	0.253782	−	0.967261i	$-0.418325\pi$
$157$	6.35976	0.507564	0.253782	+	0.967261i	$0.418325\pi$
$158$	28.2760	2.24952
$159$	−1.21893	−0.0966678
$160$	−48.3647	−3.82356
$161$	12.1235	0.955462
$162$	5.80411	0.456014
$163$	−11.9469	−0.935757	−0.467879	−	0.883793i	$-0.654982\pi$
$163$	−11.9469	−0.935757	−0.467879	+	0.883793i	$0.654982\pi$
$164$	−25.7648	−2.01189
$165$	−3.91967	−0.305146
$166$	38.2571	2.96933
$167$	−3.56868	−0.276153	−0.138076	−	0.990422i	$-0.544092\pi$
$167$	−3.56868	−0.276153	−0.138076	+	0.990422i	$0.544092\pi$
$168$	−48.9057	−3.77316
$169$	−1.11235	−0.0855651
$170$	31.4150	2.40942
$171$	3.24087	0.247836
$172$	−24.5517	−1.87205
$173$	22.3688	1.70067	0.850336	−	0.526240i	$-0.176399\pi$
$173$	22.3688	1.70067	0.850336	+	0.526240i	$0.176399\pi$
$174$	22.8116	1.72934
$175$	16.5768	1.25309
$176$	−13.8192	−1.04166
$177$	12.3099	0.925267
$178$	−31.3504	−2.34981
$179$	16.6744	1.24630	0.623151	−	0.782102i	$-0.285852\pi$
$179$	16.6744	1.24630	0.623151	+	0.782102i	$0.285852\pi$
$180$	−22.9561	−1.71105
$181$	1.81418	0.134847	0.0674235	−	0.997724i	$-0.478522\pi$
$181$	1.81418	0.134847	0.0674235	+	0.997724i	$0.478522\pi$
$182$	−43.3682	−3.21466
$183$	12.1807	0.900422
$184$	−22.1041	−1.62954
$185$	31.2341	2.29638
$186$	−22.6779	−1.66282
$187$	4.41478	0.322841
$188$	54.9442	4.00721
$189$	−25.8123	−1.87757
$190$	16.7651	1.21627
$191$	1.51412	0.109558	0.0547788	−	0.998499i	$-0.482555\pi$
$191$	1.51412	0.109558	0.0547788	+	0.998499i	$0.482555\pi$
$192$	23.5073	1.69649
$193$	19.2116	1.38288	0.691441	−	0.722433i	$-0.256976\pi$
$193$	19.2116	1.38288	0.691441	+	0.722433i	$0.256976\pi$
$194$	10.6879	0.767349
$195$	12.2772	0.879186
$196$	77.8751	5.56251
$197$	−9.90637	−0.705800	−0.352900	−	0.935661i	$-0.614804\pi$
$197$	−9.90637	−0.705800	−0.352900	+	0.935661i	$0.614804\pi$
$198$	−4.46930	−0.317619
$199$	21.5854	1.53015	0.765074	−	0.643942i	$-0.222702\pi$
$199$	21.5854	1.53015	0.765074	+	0.643942i	$0.222702\pi$
$200$	−30.2237	−2.13714
$201$	0.611952	0.0431638
$202$	−38.6864	−2.72197
$203$	−32.7405	−2.29793
$204$	−25.3709	−1.77632
$205$	−14.5027	−1.01291
$206$	−54.0608	−3.76659
$207$	−3.91330	−0.271993
$208$	43.2843	3.00122
$209$	2.35602	0.162969
$210$	−44.7892	−3.09075
$211$	−17.6455	−1.21476	−0.607382	−	0.794410i	$-0.707780\pi$
$211$	−17.6455	−1.21476	−0.607382	+	0.794410i	$0.707780\pi$
$212$	−5.18975	−0.356433
$213$	3.33039	0.228194
$214$	23.9992	1.64055
$215$	−13.8199	−0.942510
$216$	47.0624	3.20219
$217$	32.5485	2.20954
$218$	5.19151	0.351614
$219$	−9.95713	−0.672840
$220$	−16.6884	−1.12513
$221$	−13.8280	−0.930169
$222$	−34.9459	−2.34542
$223$	19.6702	1.31721	0.658606	−	0.752488i	$-0.271146\pi$
$223$	19.6702	1.31721	0.658606	+	0.752488i	$0.271146\pi$
$224$	−77.6649	−5.18920
$225$	−5.35079	−0.356719
$226$	37.1218	2.46931
$227$	−12.2203	−0.811092	−0.405546	−	0.914075i	$-0.632919\pi$
$227$	−12.2203	−0.811092	−0.405546	+	0.914075i	$0.632919\pi$
$228$	−13.5396	−0.896682
$229$	10.4380	0.689763	0.344882	−	0.938646i	$-0.387919\pi$
$229$	10.4380	0.689763	0.344882	+	0.938646i	$0.387919\pi$
$230$	−20.2435	−1.33482
$231$	−6.29428	−0.414133
$232$	59.6942	3.91912
$233$	27.0294	1.77076	0.885378	−	0.464872i	$-0.153900\pi$
$233$	27.0294	1.77076	0.885378	+	0.464872i	$0.153900\pi$
$234$	13.9987	0.915124
$235$	30.9275	2.01749
$236$	52.4107	3.41164
$237$	−12.8541	−0.834963
$238$	50.4467	3.26998
$239$	26.8055	1.73390	0.866951	−	0.498393i	$-0.166076\pi$
$239$	26.8055	1.73390	0.866951	+	0.498393i	$0.166076\pi$
$240$	44.7025	2.88554
$241$	−7.27693	−0.468748	−0.234374	−	0.972146i	$-0.575304\pi$
$241$	−7.27693	−0.468748	−0.234374	+	0.972146i	$0.575304\pi$
$242$	26.2460	1.68716
$243$	13.8690	0.889698
$244$	51.8606	3.32004
$245$	43.8351	2.80052
$246$	16.2262	1.03455
$247$	−7.37950	−0.469547
$248$	−59.3442	−3.76836
$249$	−17.3914	−1.10214
$250$	11.4852	0.726386
$251$	4.84985	0.306120	0.153060	−	0.988217i	$-0.451087\pi$
$251$	4.84985	0.306120	0.153060	+	0.988217i	$0.451087\pi$
$252$	−36.8634	−2.32218
$253$	−2.84485	−0.178854
$254$	−49.3146	−3.09427
$255$	−14.2810	−0.894314
$256$	11.2986	0.706164
$257$	−10.6034	−0.661423	−0.330711	−	0.943732i	$-0.607289\pi$
$257$	−10.6034	−0.661423	−0.330711	+	0.943732i	$0.607289\pi$
$258$	15.4623	0.962638
$259$	50.1563	3.11656
$260$	52.2714	3.24173
$261$	10.5682	0.654156
$262$	−10.5945	−0.654533
$263$	17.7058	1.09179	0.545893	−	0.837855i	$-0.316190\pi$
$263$	17.7058	1.09179	0.545893	+	0.837855i	$0.316190\pi$
$264$	11.4761	0.706303
$265$	−2.92126	−0.179451
$266$	26.9217	1.65067
$267$	14.2517	0.872190
$268$	2.60545	0.159153
$269$	−9.75188	−0.594583	−0.297291	−	0.954787i	$-0.596083\pi$
$269$	−9.75188	−0.594583	−0.297291	+	0.954787i	$0.596083\pi$
$270$	43.1010	2.62304
$271$	−30.1988	−1.83445	−0.917223	−	0.398375i	$-0.869574\pi$
$271$	−30.1988	−1.83445	−0.917223	+	0.398375i	$0.869574\pi$
$272$	−50.3491	−3.05286
$273$	19.7149	1.19320
$274$	18.2426	1.10207
$275$	−3.88986	−0.234567
$276$	16.3488	0.984084
$277$	3.77798	0.226997	0.113499	−	0.993538i	$-0.463794\pi$
$277$	3.77798	0.226997	0.113499	+	0.993538i	$0.463794\pi$
$278$	−33.4782	−2.00789
$279$	−10.5062	−0.628993
$280$	−117.206	−7.00439
$281$	−11.4653	−0.683960	−0.341980	−	0.939707i	$-0.611098\pi$
$281$	−11.4653	−0.683960	−0.341980	+	0.939707i	$0.611098\pi$
$282$	−34.6029	−2.06057
$283$	9.27547	0.551370	0.275685	−	0.961248i	$-0.411095\pi$
$283$	9.27547	0.551370	0.275685	+	0.961248i	$0.411095\pi$
$284$	14.1795	0.841398
$285$	−7.62130	−0.451447
$286$	10.1766	0.601757
$287$	−23.2888	−1.37469
$288$	25.0693	1.47722
$289$	−0.915049	−0.0538264
$290$	54.6695	3.21031
$291$	−4.85867	−0.284820
$292$	−42.3936	−2.48090
$293$	−1.38509	−0.0809179	−0.0404589	−	0.999181i	$-0.512882\pi$
$293$	−1.38509	−0.0809179	−0.0404589	+	0.999181i	$0.512882\pi$
$294$	−49.0444	−2.86033
$295$	29.5014	1.71764
$296$	−91.4477	−5.31529
$297$	6.05704	0.351465
$298$	−60.7051	−3.51655
$299$	8.91062	0.515315
$300$	22.3543	1.29063
$301$	−22.1923	−1.27914
$302$	−2.68137	−0.154296
$303$	17.5866	1.01032
$304$	−26.8696	−1.54108
$305$	29.1918	1.67152
$306$	−16.2836	−0.930870
$307$	−23.3056	−1.33012	−0.665059	−	0.746791i	$-0.731594\pi$
$307$	−23.3056	−1.33012	−0.665059	+	0.746791i	$0.731594\pi$
$308$	−26.7986	−1.52699
$309$	24.5757	1.39806
$310$	−54.3490	−3.08681
$311$	32.3049	1.83184	0.915922	−	0.401356i	$-0.131461\pi$
$311$	32.3049	1.83184	0.915922	+	0.401356i	$0.131461\pi$
$312$	−35.9453	−2.03500
$313$	−19.2743	−1.08945	−0.544724	−	0.838616i	$-0.683365\pi$
$313$	−19.2743	−1.08945	−0.544724	+	0.838616i	$0.683365\pi$
$314$	−17.0529	−0.962349
$315$	−20.7500	−1.16913
$316$	−54.7278	−3.07868
$317$	4.17938	0.234737	0.117369	−	0.993088i	$-0.462554\pi$
$317$	4.17938	0.234737	0.117369	+	0.993088i	$0.462554\pi$
$318$	3.26842	0.183284
$319$	7.68278	0.430153
$320$	56.3367	3.14932
$321$	−10.9099	−0.608931
$322$	−32.5075	−1.81157
$323$	8.58399	0.477626
$324$	−11.2338	−0.624098
$325$	12.1838	0.675836
$326$	32.0342	1.77421
$327$	−2.36003	−0.130510
$328$	42.4613	2.34453
$329$	49.6640	2.73806
$330$	10.5101	0.578561
$331$	8.60300	0.472864	0.236432	−	0.971648i	$-0.424022\pi$
$331$	8.60300	0.472864	0.236432	+	0.971648i	$0.424022\pi$
$332$	−74.0460	−4.06380
$333$	−16.1898	−0.887198
$334$	9.56896	0.523590
$335$	1.46658	0.0801280
$336$	71.7841	3.91615
$337$	−18.7729	−1.02262	−0.511312	−	0.859395i	$-0.670840\pi$
$337$	−18.7729	−1.02262	−0.511312	+	0.859395i	$0.670840\pi$
$338$	2.98261	0.162233
$339$	−16.8754	−0.916543
$340$	−60.8031	−3.29751
$341$	−7.63773	−0.413606
$342$	−8.68998	−0.469900
$343$	37.5541	2.02773
$344$	40.4621	2.18157
$345$	9.20259	0.495451
$346$	−59.9792	−3.22450
$347$	6.54416	0.351309	0.175654	−	0.984452i	$-0.443796\pi$
$347$	6.54416	0.351309	0.175654	+	0.984452i	$0.443796\pi$
$348$	−44.1515	−2.36677
$349$	−8.26401	−0.442362	−0.221181	−	0.975233i	$-0.570991\pi$
$349$	−8.26401	−0.442362	−0.221181	+	0.975233i	$0.570991\pi$
$350$	−44.4486	−2.37588
$351$	−18.9718	−1.01264
$352$	18.2246	0.971374
$353$	−14.8491	−0.790338	−0.395169	−	0.918608i	$-0.629314\pi$
$353$	−14.8491	−0.790338	−0.395169	+	0.918608i	$0.629314\pi$
$354$	−33.0073	−1.75432
$355$	7.98150	0.423614
$356$	60.6782	3.21594
$357$	−22.9328	−1.21373
$358$	−44.7102	−2.36301
$359$	−28.2270	−1.48976	−0.744882	−	0.667196i	$-0.767494\pi$
$359$	−28.2270	−1.48976	−0.744882	+	0.667196i	$0.767494\pi$
$360$	37.8326	1.99395
$361$	−14.4190	−0.758896
$362$	−4.86449	−0.255672
$363$	−11.9313	−0.626230
$364$	83.9384	4.39957
$365$	−23.8629	−1.24904
$366$	−32.6609	−1.70721
$367$	2.86588	0.149598	0.0747989	−	0.997199i	$-0.476169\pi$
$367$	2.86588	0.149598	0.0747989	+	0.997199i	$0.476169\pi$
$368$	32.4446	1.69129
$369$	7.51732	0.391336
$370$	−83.7503	−4.35397
$371$	−4.69101	−0.243545
$372$	43.8926	2.27573
$373$	−13.8612	−0.717706	−0.358853	−	0.933394i	$-0.616832\pi$
$373$	−13.8612	−0.717706	−0.358853	+	0.933394i	$0.616832\pi$
$374$	−11.8377	−0.612111
$375$	−5.22108	−0.269616
$376$	−90.5500	−4.66976
$377$	−24.0639	−1.23936
$378$	69.2124	3.55990
$379$	13.2846	0.682383	0.341192	−	0.939994i	$-0.389169\pi$
$379$	13.2846	0.682383	0.341192	+	0.939994i	$0.389169\pi$
$380$	−32.4485	−1.66458
$381$	22.4181	1.14852
$382$	−4.05991	−0.207723
$383$	20.4233	1.04358	0.521792	−	0.853073i	$-0.325264\pi$
$383$	20.4233	1.04358	0.521792	+	0.853073i	$0.325264\pi$
$384$	−22.6701	−1.15688
$385$	−15.0847	−0.768785
$386$	−51.5134	−2.62196
$387$	7.16339	0.364135
$388$	−20.6863	−1.05019
$389$	2.83500	0.143740	0.0718701	−	0.997414i	$-0.477103\pi$
$389$	2.83500	0.143740	0.0718701	+	0.997414i	$0.477103\pi$
$390$	−32.9196	−1.66695
$391$	−10.3650	−0.524181
$392$	−128.341	−6.48220
$393$	4.81621	0.242946
$394$	26.5627	1.33821
$395$	−30.8057	−1.55000
$396$	8.65025	0.434691
$397$	−32.0599	−1.60904	−0.804519	−	0.593926i	$-0.797577\pi$
$397$	−32.0599	−1.60904	−0.804519	+	0.593926i	$0.797577\pi$
$398$	−57.8785	−2.90118
$399$	−12.2384	−0.612688
$400$	44.3626	2.21813
$401$	18.2701	0.912367	0.456183	−	0.889886i	$-0.349216\pi$
$401$	18.2701	0.912367	0.456183	+	0.889886i	$0.349216\pi$
$402$	−1.64087	−0.0818392
$403$	23.9228	1.19168
$404$	74.8770	3.72527
$405$	−6.32337	−0.314211
$406$	87.7893	4.35691
$407$	−11.7695	−0.583394
$408$	41.8123	2.07001
$409$	−7.24990	−0.358484	−0.179242	−	0.983805i	$-0.557365\pi$
$409$	−7.24990	−0.358484	−0.179242	+	0.983805i	$0.557365\pi$
$410$	38.8872	1.92050
$411$	−8.29296	−0.409061
$412$	104.634	5.15494
$413$	47.3740	2.33112
$414$	10.4930	0.515703
$415$	−41.6797	−2.04598
$416$	−57.0830	−2.79872
$417$	15.2190	0.745276
$418$	−6.31736	−0.308992
$419$	−28.7534	−1.40470	−0.702349	−	0.711833i	$-0.747865\pi$
$419$	−28.7534	−1.40470	−0.702349	+	0.711833i	$0.747865\pi$
$420$	86.6887	4.22998
$421$	−18.2925	−0.891523	−0.445762	−	0.895152i	$-0.647067\pi$
$421$	−18.2925	−0.891523	−0.445762	+	0.895152i	$0.647067\pi$
$422$	47.3141	2.30321
$423$	−16.0309	−0.779449
$424$	8.55290	0.415365
$425$	−14.1724	−0.687464
$426$	−8.93001	−0.432660
$427$	46.8768	2.26853
$428$	−46.4501	−2.24525
$429$	−4.62624	−0.223357
$430$	37.0563	1.78701
$431$	−19.6897	−0.948420	−0.474210	−	0.880412i	$-0.657266\pi$
$431$	−19.6897	−0.948420	−0.474210	+	0.880412i	$0.657266\pi$
$432$	−69.0785	−3.32354
$433$	6.68017	0.321028	0.160514	−	0.987034i	$-0.448685\pi$
$433$	6.68017	0.321028	0.160514	+	0.987034i	$0.448685\pi$
$434$	−87.2746	−4.18931
$435$	−24.8524	−1.19158
$436$	−10.0481	−0.481216
$437$	−5.53145	−0.264605
$438$	26.6988	1.27572
$439$	40.9152	1.95277	0.976387	−	0.216029i	$-0.0693105\pi$
$439$	40.9152	1.95277	0.976387	+	0.216029i	$0.0693105\pi$
$440$	27.5032	1.31116
$441$	−22.7214	−1.08197
$442$	37.0779	1.76361
$443$	15.2464	0.724376	0.362188	−	0.932105i	$-0.382030\pi$
$443$	15.2464	0.724376	0.362188	+	0.932105i	$0.382030\pi$
$444$	67.6373	3.20992
$445$	34.1551	1.61911
$446$	−52.7430	−2.49745
$447$	27.5962	1.30525
$448$	90.4665	4.27414
$449$	22.5313	1.06332	0.531658	−	0.846959i	$-0.321569\pi$
$449$	22.5313	1.06332	0.531658	+	0.846959i	$0.321569\pi$
$450$	14.3474	0.676345
$451$	5.46487	0.257330
$452$	−71.8487	−3.37948
$453$	1.21893	0.0572705
$454$	32.7672	1.53784
$455$	47.2481	2.21502
$456$	22.3138	1.04494
$457$	−4.16085	−0.194636	−0.0973181	−	0.995253i	$-0.531026\pi$
$457$	−4.16085	−0.194636	−0.0973181	+	0.995253i	$0.531026\pi$
$458$	−27.9882	−1.30780
$459$	22.0684	1.03006
$460$	39.1811	1.82683
$461$	−9.73043	−0.453191	−0.226596	−	0.973989i	$-0.572760\pi$
$461$	−9.73043	−0.453191	−0.226596	+	0.973989i	$0.572760\pi$
$462$	16.8773	0.785203
$463$	−29.0575	−1.35042	−0.675209	−	0.737627i	$-0.735946\pi$
$463$	−29.0575	−1.35042	−0.675209	+	0.737627i	$0.735946\pi$
$464$	−87.6195	−4.06763
$465$	24.7067	1.14575
$466$	−72.4759	−3.35738
$467$	6.80629	0.314958	0.157479	−	0.987522i	$-0.449663\pi$
$467$	6.80629	0.314958	0.157479	+	0.987522i	$0.449663\pi$
$468$	−27.0943	−1.25243
$469$	2.35507	0.108747
$470$	−82.9281	−3.82519
$471$	7.75213	0.357199
$472$	−86.3747	−3.97572
$473$	5.20757	0.239444
$474$	34.4666	1.58310
$475$	−7.56334	−0.347030
$476$	−97.6388	−4.47527
$477$	1.51420	0.0693304
$478$	−71.8754	−3.28751
$479$	−29.4706	−1.34654	−0.673272	−	0.739395i	$-0.735112\pi$
$479$	−29.4706	−1.34654	−0.673272	+	0.739395i	$0.735112\pi$
$480$	−58.9534	−2.69084
$481$	36.8644	1.68087
$482$	19.5122	0.888754
$483$	14.7777	0.672408
$484$	−50.7988	−2.30903
$485$	−11.6441	−0.528732
$486$	−37.1880	−1.68688
$487$	27.8026	1.25986	0.629929	−	0.776653i	$-0.283084\pi$
$487$	27.8026	1.25986	0.629929	+	0.776653i	$0.283084\pi$
$488$	−85.4682	−3.86897
$489$	−14.5625	−0.658541
$490$	−117.538	−5.30983
$491$	−10.5619	−0.476652	−0.238326	−	0.971185i	$-0.576599\pi$
$491$	−10.5619	−0.476652	−0.238326	+	0.971185i	$0.576599\pi$
$492$	−31.4056	−1.41587
$493$	27.9917	1.26068
$494$	19.7872	0.890268
$495$	4.86914	0.218851
$496$	87.1057	3.91116
$497$	12.8168	0.574914
$498$	46.6329	2.08967
$499$	−18.7488	−0.839312	−0.419656	−	0.907683i	$-0.637849\pi$
$499$	−18.7488	−0.839312	−0.419656	+	0.907683i	$0.637849\pi$
$500$	−22.2293	−0.994127
$501$	−4.34999	−0.194343
$502$	−13.0042	−0.580408
$503$	16.6885	0.744102	0.372051	−	0.928212i	$-0.378655\pi$
$503$	16.6885	0.744102	0.372051	+	0.928212i	$0.378655\pi$
$504$	60.7523	2.70612
$505$	42.1475	1.87554
$506$	7.62810	0.339110
$507$	−1.35588	−0.0602166
$508$	95.4476	4.23480
$509$	15.7604	0.698566	0.349283	−	0.937017i	$-0.386425\pi$
$509$	15.7604	0.698566	0.349283	+	0.937017i	$0.386425\pi$
$510$	38.2928	1.69563
$511$	−38.3195	−1.69516
$512$	6.90070	0.304971
$513$	11.7771	0.519974
$514$	28.4317	1.25407
$515$	58.8973	2.59532
$516$	−29.9269	−1.31746
$517$	−11.6540	−0.512542
$518$	−134.488	−5.90905
$519$	27.2662	1.19685
$520$	−86.1452	−3.77772
$521$	−38.9094	−1.70465	−0.852325	−	0.523012i	$-0.824808\pi$
$521$	−38.9094	−1.70465	−0.852325	+	0.523012i	$0.824808\pi$
$522$	−28.3373	−1.24029
$523$	19.2629	0.842309	0.421155	−	0.906989i	$-0.361625\pi$
$523$	19.2629	0.842309	0.421155	+	0.906989i	$0.361625\pi$
$524$	20.5056	0.895789
$525$	20.2060	0.881864
$526$	−47.4758	−2.07004
$527$	−27.8275	−1.21219
$528$	−16.8446	−0.733069
$529$	−16.3209	−0.709603
$530$	7.83297	0.340243
$531$	−15.2917	−0.663604
$532$	−52.1065	−2.25910
$533$	−17.1170	−0.741420
$534$	−38.2141	−1.65368
$535$	−26.1463	−1.13040
$536$	−4.29389	−0.185468
$537$	20.3250	0.877087
$538$	26.1484	1.12734
$539$	−16.5178	−0.711471
$540$	−83.4213	−3.58988
$541$	30.3990	1.30696	0.653478	−	0.756946i	$-0.273309\pi$
$541$	30.3990	1.30696	0.653478	+	0.756946i	$0.273309\pi$
$542$	80.9741	3.47814
$543$	2.21137	0.0948989
$544$	66.4000	2.84688
$545$	−5.65597	−0.242275
$546$	−52.8630	−2.26233
$547$	−20.8135	−0.889919	−0.444959	−	0.895551i	$-0.646782\pi$
$547$	−20.8135	−0.889919	−0.444959	+	0.895551i	$0.646782\pi$
$548$	−35.3082	−1.50829
$549$	−15.1312	−0.645785
$550$	10.4302	0.444744
$551$	14.9382	0.636388
$552$	−26.9435	−1.14679
$553$	−49.4684	−2.10361
$554$	−10.1302	−0.430390
$555$	38.0724	1.61608
$556$	64.7964	2.74798
$557$	5.09123	0.215722	0.107861	−	0.994166i	$-0.465600\pi$
$557$	5.09123	0.215722	0.107861	+	0.994166i	$0.465600\pi$
$558$	28.1711	1.19258
$559$	−16.3111	−0.689887
$560$	172.035	7.26982
$561$	5.38133	0.227200
$562$	30.7426	1.29680
$563$	−31.5721	−1.33060	−0.665302	−	0.746574i	$-0.731697\pi$
$563$	−31.5721	−1.33060	−0.665302	+	0.746574i	$0.731697\pi$
$564$	66.9733	2.82009
$565$	−40.4429	−1.70145
$566$	−24.8710	−1.04541
$567$	−10.1542	−0.426435
$568$	−23.3683	−0.980514
$569$	−10.8687	−0.455639	−0.227819	−	0.973703i	$-0.573160\pi$
$569$	−10.8687	−0.455639	−0.227819	+	0.973703i	$0.573160\pi$
$570$	20.4355	0.855950
$571$	35.3517	1.47942	0.739711	−	0.672925i	$-0.234962\pi$
$571$	35.3517	1.47942	0.739711	+	0.672925i	$0.234962\pi$
$572$	−19.6967	−0.823561
$573$	1.84561	0.0771014
$574$	62.4458	2.60644
$575$	9.13261	0.380856
$576$	−29.2015	−1.21673
$577$	−26.1284	−1.08774	−0.543871	−	0.839169i	$-0.683042\pi$
$577$	−26.1284	−1.08774	−0.543871	+	0.839169i	$0.683042\pi$
$578$	2.45358	0.102056
$579$	23.4177	0.973206
$580$	−105.812	−4.39360
$581$	−66.9301	−2.77673
$582$	13.0279	0.540023
$583$	1.10078	0.0455895
$584$	69.8662	2.89108
$585$	−15.2511	−0.630555
$586$	3.71394	0.153422
$587$	−35.6428	−1.47114	−0.735569	−	0.677450i	$-0.763085\pi$
$587$	−35.6428	−1.47114	−0.735569	+	0.677450i	$0.763085\pi$
$588$	94.9246	3.91463
$589$	−14.8506	−0.611908
$590$	−79.1043	−3.25667
$591$	−12.0752	−0.496708
$592$	134.228	5.51672
$593$	33.8848	1.39148	0.695741	−	0.718292i	$-0.255076\pi$
$593$	33.8848	1.39148	0.695741	+	0.718292i	$0.255076\pi$
$594$	−16.2412	−0.666383
$595$	−54.9599	−2.25314
$596$	117.494	4.81273
$597$	26.3112	1.07685
$598$	−23.8927	−0.977045
$599$	−20.7880	−0.849373	−0.424687	−	0.905340i	$-0.639616\pi$
$599$	−20.7880	−0.849373	−0.424687	+	0.905340i	$0.639616\pi$
$600$	−36.8407	−1.50402
$601$	29.5459	1.20520	0.602601	−	0.798042i	$-0.294131\pi$
$601$	29.5459	1.20520	0.602601	+	0.798042i	$0.294131\pi$
$602$	59.5057	2.42527
$603$	−0.760186	−0.0309572
$604$	5.18975	0.211168
$605$	−28.5941	−1.16252
$606$	−47.1562	−1.91559
$607$	8.18796	0.332339	0.166170	−	0.986097i	$-0.446860\pi$
$607$	8.18796	0.332339	0.166170	+	0.986097i	$0.446860\pi$
$608$	35.4354	1.43710
$609$	−39.9085	−1.61717
$610$	−78.2741	−3.16922
$611$	36.5026	1.47674
$612$	31.5166	1.27398
$613$	−1.10208	−0.0445125	−0.0222563	−	0.999752i	$-0.507085\pi$
$613$	−1.10208	−0.0445125	−0.0222563	+	0.999752i	$0.507085\pi$
$614$	62.4908	2.52192
$615$	−17.6779	−0.712841
$616$	44.1651	1.77946
$617$	−12.7845	−0.514683	−0.257341	−	0.966321i	$-0.582847\pi$
$617$	−12.7845	−0.514683	−0.257341	+	0.966321i	$0.582847\pi$
$618$	−65.8966	−2.65075
$619$	8.89493	0.357517	0.178759	−	0.983893i	$-0.442792\pi$
$619$	8.89493	0.357517	0.178759	+	0.983893i	$0.442792\pi$
$620$	105.192	4.22459
$621$	−14.2207	−0.570657
$622$	−86.6215	−3.47320
$623$	54.8469	2.19740
$624$	52.7607	2.11212
$625$	−30.1814	−1.20726
$626$	51.6815	2.06561
$627$	2.87183	0.114690
$628$	33.0055	1.31706
$629$	−42.8815	−1.70980
$630$	55.6385	2.21669
$631$	−22.3469	−0.889618	−0.444809	−	0.895625i	$-0.646728\pi$
$631$	−22.3469	−0.889618	−0.444809	+	0.895625i	$0.646728\pi$
$632$	90.1934	3.58770
$633$	−21.5087	−0.854893
$634$	−11.2065	−0.445066
$635$	53.7265	2.13207
$636$	−6.32596	−0.250841
$637$	51.7369	2.04989
$638$	−20.6004	−0.815576
$639$	−4.13711	−0.163662
$640$	−54.3303	−2.14759
$641$	−17.7971	−0.702942	−0.351471	−	0.936199i	$-0.614318\pi$
$641$	−17.7971	−0.702942	−0.351471	+	0.936199i	$0.614318\pi$
$642$	29.2535	1.15454
$643$	−31.3236	−1.23528	−0.617642	−	0.786459i	$-0.711912\pi$
$643$	−31.3236	−1.23528	−0.617642	+	0.786459i	$0.711912\pi$
$644$	62.9177	2.47930
$645$	−16.8456	−0.663293
$646$	−23.0168	−0.905586
$647$	−27.8477	−1.09481	−0.547403	−	0.836869i	$-0.684384\pi$
$647$	−27.8477	−1.09481	−0.547403	+	0.836869i	$0.684384\pi$
$648$	18.5136	0.727285
$649$	−11.1166	−0.436366
$650$	−32.6693	−1.28139
$651$	39.6745	1.55497
$652$	−62.0017	−2.42817
$653$	6.73217	0.263450	0.131725	−	0.991286i	$-0.457948\pi$
$653$	6.73217	0.263450	0.131725	+	0.991286i	$0.457948\pi$
$654$	6.32811	0.247449
$655$	11.5424	0.450998
$656$	−62.3250	−2.43338
$657$	12.3691	0.482563
$658$	−133.167	−5.19141
$659$	−9.10358	−0.354625	−0.177313	−	0.984155i	$-0.556740\pi$
$659$	−9.10358	−0.354625	−0.177313	+	0.984155i	$0.556740\pi$
$660$	−20.3421	−0.791815
$661$	−5.01809	−0.195181	−0.0975906	−	0.995227i	$-0.531114\pi$
$661$	−5.01809	−0.195181	−0.0975906	+	0.995227i	$0.531114\pi$
$662$	−23.0678	−0.896557
$663$	−16.8554	−0.654608
$664$	122.031	4.73571
$665$	−29.3302	−1.13738
$666$	43.4110	1.68214
$667$	−18.0376	−0.698419
$668$	−18.5206	−0.716582
$669$	23.9766	0.926991
$670$	−3.93245	−0.151924
$671$	−11.0000	−0.424648
$672$	−94.6684	−3.65191
$673$	37.8902	1.46056	0.730279	−	0.683149i	$-0.239390\pi$
$673$	37.8902	1.46056	0.730279	+	0.683149i	$0.239390\pi$
$674$	50.3371	1.93891
$675$	−19.4445	−0.748417
$676$	−5.77280	−0.222031
$677$	2.85575	0.109755	0.0548777	−	0.998493i	$-0.482523\pi$
$677$	2.85575	0.109755	0.0548777	+	0.998493i	$0.482523\pi$
$678$	45.2491	1.73778
$679$	−18.6983	−0.717576
$680$	100.206	3.84272
$681$	−14.8958	−0.570808
$682$	20.4796	0.784204
$683$	15.4324	0.590502	0.295251	−	0.955420i	$-0.404597\pi$
$683$	15.4324	0.590502	0.295251	+	0.955420i	$0.404597\pi$
$684$	16.8193	0.643103
$685$	−19.8746	−0.759370
$686$	−100.697	−3.84461
$687$	12.7233	0.485422
$688$	−59.3906	−2.26424
$689$	−3.44785	−0.131353
$690$	−24.6756	−0.939382
$691$	28.5099	1.08457	0.542284	−	0.840195i	$-0.317560\pi$
$691$	28.5099	1.08457	0.542284	+	0.840195i	$0.317560\pi$
$692$	116.089	4.41303
$693$	7.81895	0.297017
$694$	−17.5473	−0.666087
$695$	36.4733	1.38351
$696$	72.7633	2.75809
$697$	19.9109	0.754177
$698$	22.1589	0.838726
$699$	32.9471	1.24617
$700$	86.0295	3.25161
$701$	−20.5586	−0.776489	−0.388245	−	0.921556i	$-0.626918\pi$
$701$	−20.5586	−0.776489	−0.388245	+	0.921556i	$0.626918\pi$
$702$	50.8705	1.91998
$703$	−22.8844	−0.863100
$704$	−21.2286	−0.800083
$705$	37.6986	1.41981
$706$	39.8160	1.49849
$707$	67.6812	2.54541
$708$	63.8852	2.40095
$709$	0.0249458	0.000936859 0	0.000468429	−	1.00000i	$-0.499851\pi$
$709$	0.0249458	0.000936859 0	0.000468429		1.00000i	$0.499851\pi$
$710$	−21.4013	−0.803178
$711$	15.9678	0.598838
$712$	−99.9999	−3.74765
$713$	17.9318	0.671553
$714$	61.4912	2.30125
$715$	−11.0871	−0.414633
$716$	86.5358	3.23400
$717$	32.6741	1.22024
$718$	75.6871	2.82462
$719$	−47.1130	−1.75702	−0.878510	−	0.477724i	$-0.841462\pi$
$719$	−47.1130	−1.75702	−0.878510	+	0.477724i	$0.841462\pi$
$720$	−55.5309	−2.06951
$721$	94.5783	3.52228
$722$	38.6627	1.43888
$723$	−8.87010	−0.329883
$724$	9.41514	0.349911
$725$	−24.6634	−0.915977
$726$	31.9922	1.18734
$727$	−34.9187	−1.29506	−0.647532	−	0.762039i	$-0.724199\pi$
$727$	−34.9187	−1.29506	−0.647532	+	0.762039i	$0.724199\pi$
$728$	−138.334	−5.12698
$729$	23.3992	0.866639
$730$	63.9853	2.36820
$731$	18.9734	0.701757
$732$	63.2147	2.33648
$733$	−1.93232	−0.0713717	−0.0356859	−	0.999363i	$-0.511362\pi$
$733$	−1.93232	−0.0713717	−0.0356859	+	0.999363i	$0.511362\pi$
$734$	−7.68449	−0.283640
$735$	53.4321	1.97087
$736$	−42.7877	−1.57717
$737$	−0.552633	−0.0203565
$738$	−20.1567	−0.741979
$739$	−23.1214	−0.850535	−0.425267	−	0.905068i	$-0.639820\pi$
$739$	−23.1214	−0.850535	−0.425267	+	0.905068i	$0.639820\pi$
$740$	162.097	5.95881
$741$	−8.99513	−0.330444
$742$	12.5783	0.461765
$743$	−42.0929	−1.54424	−0.772118	−	0.635479i	$-0.780803\pi$
$743$	−42.0929	−1.54424	−0.772118	+	0.635479i	$0.780803\pi$
$744$	−72.3367	−2.65199
$745$	66.1360	2.42304
$746$	37.1670	1.36078
$747$	21.6042	0.790457
$748$	22.9116	0.837731
$749$	−41.9862	−1.53414
$750$	13.9997	0.511195
$751$	−47.0328	−1.71625	−0.858125	−	0.513441i	$-0.828371\pi$
$751$	−47.0328	−1.71625	−0.858125	+	0.513441i	$0.828371\pi$
$752$	132.910	4.84672
$753$	5.91165	0.215432
$754$	64.5244	2.34984
$755$	2.92126	0.106315
$756$	−133.960	−4.87206
$757$	−47.2332	−1.71672	−0.858360	−	0.513048i	$-0.828516\pi$
$757$	−47.2332	−1.71672	−0.858360	+	0.513048i	$0.828516\pi$
$758$	−35.6209	−1.29381
$759$	−3.46769	−0.125869
$760$	53.4764	1.93979
$761$	18.2535	0.661690	0.330845	−	0.943685i	$-0.392666\pi$
$761$	18.2535	0.661690	0.330845	+	0.943685i	$0.392666\pi$
$762$	−60.1113	−2.17760
$763$	−9.08246	−0.328807
$764$	7.85788	0.284288
$765$	17.7404	0.641404
$766$	−54.7625	−1.97865
$767$	34.8194	1.25726
$768$	13.7723	0.496965
$769$	−50.0820	−1.80600	−0.903001	−	0.429638i	$-0.858641\pi$
$769$	−50.0820	−1.80600	−0.903001	+	0.429638i	$0.858641\pi$
$770$	40.4475	1.45763
$771$	−12.9249	−0.465477
$772$	99.7034	3.58840
$773$	37.5683	1.35124	0.675618	−	0.737252i	$-0.263877\pi$
$773$	37.5683	1.35124	0.675618	+	0.737252i	$0.263877\pi$
$774$	−19.2077	−0.690406
$775$	24.5188	0.880742
$776$	34.0918	1.22383
$777$	61.1373	2.19329
$778$	−7.60168	−0.272533
$779$	10.6257	0.380707
$780$	63.7154	2.28138
$781$	−3.00756	−0.107619
$782$	27.7924	0.993856
$783$	38.4043	1.37246
$784$	188.380	6.72785
$785$	18.5785	0.663095
$786$	−12.9140	−0.460629
$787$	−36.2914	−1.29365	−0.646824	−	0.762640i	$-0.723903\pi$
$787$	−36.2914	−1.29365	−0.646824	+	0.762640i	$0.723903\pi$
$788$	−51.4116	−1.83146
$789$	21.5822	0.768347
$790$	82.6015	2.93883
$791$	−64.9440	−2.30914
$792$	−14.2559	−0.506563
$793$	34.4540	1.22350
$794$	85.9644	3.05076
$795$	−3.56082	−0.126289
$796$	112.023	3.97054
$797$	26.1605	0.926652	0.463326	−	0.886188i	$-0.346656\pi$
$797$	26.1605	0.926652	0.463326	+	0.886188i	$0.346656\pi$
$798$	32.8158	1.16167
$799$	−42.4605	−1.50214
$800$	−58.5050	−2.06847
$801$	−17.7039	−0.625537
$802$	−48.9890	−1.72986
$803$	8.99194	0.317319
$804$	3.17588	0.112005
$805$	35.4157	1.24824
$806$	−64.1460	−2.25945
$807$	−11.8869	−0.418439
$808$	−123.400	−4.34120
$809$	12.6907	0.446181	0.223090	−	0.974798i	$-0.428385\pi$
$809$	12.6907	0.446181	0.223090	+	0.974798i	$0.428385\pi$
$810$	16.9553	0.595748
$811$	39.4502	1.38528	0.692642	−	0.721282i	$-0.256447\pi$
$811$	39.4502	1.38528	0.692642	+	0.721282i	$0.256447\pi$
$812$	−169.915	−5.96284
$813$	−36.8103	−1.29099
$814$	31.5585	1.10612
$815$	−34.9001	−1.22250
$816$	−61.3723	−2.14846
$817$	10.1255	0.354245
$818$	19.4397	0.679692
$819$	−24.4905	−0.855766
$820$	−75.2655	−2.62839
$821$	17.1237	0.597620	0.298810	−	0.954313i	$-0.403410\pi$
$821$	17.1237	0.597620	0.298810	+	0.954313i	$0.403410\pi$
$822$	22.2365	0.775587
$823$	6.04490	0.210712	0.105356	−	0.994435i	$-0.466402\pi$
$823$	6.04490	0.210712	0.105356	+	0.994435i	$0.466402\pi$
$824$	−172.440	−6.00724
$825$	−4.74149	−0.165077
$826$	−127.027	−4.41984
$827$	−1.80795	−0.0628685	−0.0314343	−	0.999506i	$-0.510007\pi$
$827$	−1.80795	−0.0628685	−0.0314343	+	0.999506i	$0.510007\pi$
$828$	−20.3090	−0.705788
$829$	−14.8789	−0.516766	−0.258383	−	0.966043i	$-0.583190\pi$
$829$	−14.8789	−0.516766	−0.258383	+	0.966043i	$0.583190\pi$
$830$	111.759	3.87921
$831$	4.60512	0.159750
$832$	66.4921	2.30520
$833$	−60.1814	−2.08516
$834$	−40.8077	−1.41305
$835$	−10.4250	−0.360773
$836$	12.2271	0.422884
$837$	−38.1791	−1.31966
$838$	77.0986	2.66333
$839$	15.1223	0.522079	0.261039	−	0.965328i	$-0.415935\pi$
$839$	15.1223	0.522079	0.261039	+	0.965328i	$0.415935\pi$
$840$	−142.866	−4.92935
$841$	19.7122	0.679730
$842$	49.0490	1.69034
$843$	−13.9754	−0.481339
$844$	−91.5756	−3.15216
$845$	−3.24945	−0.111784
$846$	42.9848	1.47785
$847$	−45.9169	−1.57773
$848$	−12.5540	−0.431106
$849$	11.3062	0.388028
$850$	38.0016	1.30344
$851$	27.6325	0.947229
$852$	17.2839	0.592136
$853$	−11.0372	−0.377907	−0.188954	−	0.981986i	$-0.560510\pi$
$853$	−11.0372	−0.377907	−0.188954	+	0.981986i	$0.560510\pi$
$854$	−125.694	−4.30116
$855$	9.46742	0.323779
$856$	76.5515	2.61647
$857$	−38.3279	−1.30926	−0.654628	−	0.755951i	$-0.727175\pi$
$857$	−38.3279	−1.30926	−0.654628	+	0.755951i	$0.727175\pi$
$858$	12.4047	0.423488
$859$	−36.1308	−1.23277	−0.616384	−	0.787446i	$-0.711403\pi$
$859$	−36.1308	−1.23277	−0.616384	+	0.787446i	$0.711403\pi$
$860$	−71.7219	−2.44570
$861$	−28.3875	−0.967442
$862$	52.7954	1.79822
$863$	−2.15671	−0.0734153	−0.0367076	−	0.999326i	$-0.511687\pi$
$863$	−2.15671	−0.0734153	−0.0367076	+	0.999326i	$0.511687\pi$
$864$	91.1002	3.09929
$865$	65.3451	2.22180
$866$	−17.9120	−0.608674
$867$	−1.11538	−0.0378804
$868$	168.919	5.73347
$869$	11.6081	0.393777
$870$	66.6386	2.25926
$871$	1.73095	0.0586511
$872$	16.5596	0.560780
$873$	6.03559	0.204274
$874$	14.8319	0.501696
$875$	−20.0931	−0.679270
$876$	−51.6750	−1.74594
$877$	51.9149	1.75304	0.876521	−	0.481363i	$-0.159858\pi$
$877$	51.9149	1.75304	0.876521	+	0.481363i	$0.159858\pi$
$878$	−109.709	−3.70249
$879$	−1.68834	−0.0569461
$880$	−40.3693	−1.36085
$881$	−38.8556	−1.30908	−0.654539	−	0.756028i	$-0.727137\pi$
$881$	−38.8556	−1.30908	−0.654539	+	0.756028i	$0.727137\pi$
$882$	60.9245	2.05143
$883$	−11.5119	−0.387405	−0.193702	−	0.981060i	$-0.562050\pi$
$883$	−11.5119	−0.387405	−0.193702	+	0.981060i	$0.562050\pi$
$884$	−71.7636	−2.41367
$885$	35.9603	1.20879
$886$	−40.8811	−1.37343
$887$	43.7525	1.46906	0.734532	−	0.678574i	$-0.237402\pi$
$887$	43.7525	1.46906	0.734532	+	0.678574i	$0.237402\pi$
$888$	−111.469	−3.74065
$889$	86.2750	2.89357
$890$	−91.5826	−3.06985
$891$	2.38275	0.0798251
$892$	102.083	3.41800
$893$	−22.6597	−0.758278
$894$	−73.9955	−2.47478
$895$	48.7101	1.62820
$896$	−87.2446	−2.91464
$897$	10.8615	0.362654
$898$	−60.4147	−2.01606
$899$	−48.4265	−1.61512
$900$	−27.7692	−0.925641
$901$	4.01060	0.133613
$902$	−14.6533	−0.487903
$903$	−27.0509	−0.900198
$904$	118.409	3.93824
$905$	5.29969	0.176168
$906$	−3.26842	−0.108586
$907$	48.1400	1.59846	0.799231	−	0.601024i	$-0.205241\pi$
$907$	48.1400	1.59846	0.799231	+	0.601024i	$0.205241\pi$
$908$	−63.4205	−2.10468
$909$	−21.8467	−0.724608
$910$	−126.690	−4.19972
$911$	45.2253	1.49838	0.749190	−	0.662355i	$-0.230443\pi$
$911$	45.2253	1.49838	0.749190	+	0.662355i	$0.230443\pi$
$912$	−32.7523	−1.08454
$913$	15.7056	0.519780
$914$	11.1568	0.369033
$915$	35.5829	1.17633
$916$	54.1707	1.78985
$917$	18.5350	0.612078
$918$	−59.1736	−1.95302
$919$	16.6422	0.548975	0.274487	−	0.961591i	$-0.411492\pi$
$919$	16.6422	0.548975	0.274487	+	0.961591i	$0.411492\pi$
$920$	−64.5718	−2.12887
$921$	−28.4079	−0.936073
$922$	26.0909	0.859258
$923$	9.42025	0.310071
$924$	−32.6657	−1.07462
$925$	37.7828	1.24229
$926$	77.9140	2.56041
$927$	−30.5287	−1.00269
$928$	115.552	3.79318
$929$	−14.6934	−0.482075	−0.241038	−	0.970516i	$-0.577488\pi$
$929$	−14.6934	−0.482075	−0.241038	+	0.970516i	$0.577488\pi$
$930$	−66.2478	−2.17235
$931$	−32.1167	−1.05258
$932$	140.276	4.59489
$933$	39.3776	1.28916
$934$	−18.2502	−0.597165
$935$	12.8967	0.421768
$936$	44.6524	1.45951
$937$	12.8862	0.420973	0.210486	−	0.977597i	$-0.432495\pi$
$937$	12.8862	0.420973	0.210486	+	0.977597i	$0.432495\pi$
$938$	−6.31481	−0.206186
$939$	−23.4941	−0.766701
$940$	160.506	5.23513
$941$	−23.4391	−0.764092	−0.382046	−	0.924143i	$-0.624780\pi$
$941$	−23.4391	−0.764092	−0.382046	+	0.924143i	$0.624780\pi$
$942$	−20.7863	−0.677255
$943$	−12.8304	−0.417815
$944$	126.781	4.12638
$945$	−75.4044	−2.45291
$946$	−13.9634	−0.453990
$947$	−23.3185	−0.757750	−0.378875	−	0.925448i	$-0.623689\pi$
$947$	−23.3185	−0.757750	−0.378875	+	0.925448i	$0.623689\pi$
$948$	−66.7095	−2.16663
$949$	−28.1645	−0.914258
$950$	20.2801	0.657974
$951$	5.09439	0.165197
$952$	160.912	5.21520
$953$	26.3452	0.853405	0.426702	−	0.904392i	$-0.359675\pi$
$953$	26.3452	0.853405	0.426702	+	0.904392i	$0.359675\pi$
$954$	−4.06013	−0.131452
$955$	4.42312	0.143129
$956$	139.114	4.49926
$957$	9.36480	0.302721
$958$	79.0215	2.55307
$959$	−31.9150	−1.03059
$960$	68.6708	2.21634
$961$	17.1426	0.552987
$962$	−98.8472	−3.18696
$963$	13.5526	0.436727
$964$	−37.7654	−1.21634
$965$	56.1220	1.80663
$966$	−39.6245	−1.27490
$967$	49.2476	1.58369	0.791847	−	0.610719i	$-0.209120\pi$
$967$	49.2476	1.58369	0.791847	+	0.610719i	$0.209120\pi$
$968$	83.7183	2.69081
$969$	10.4633	0.336130
$970$	31.2222	1.00248
$971$	−0.471001	−0.0151151	−0.00755757	−	0.999971i	$-0.502406\pi$
$971$	−0.471001	−0.0151151	−0.00755757	+	0.999971i	$0.502406\pi$
$972$	71.9768	2.30866
$973$	58.5694	1.87765
$974$	−74.5491	−2.38871
$975$	14.8513	0.475621
$976$	125.451	4.01558
$977$	−22.2681	−0.712418	−0.356209	−	0.934406i	$-0.615931\pi$
$977$	−22.2681	−0.712418	−0.356209	+	0.934406i	$0.615931\pi$
$978$	39.0476	1.24860
$979$	−12.8702	−0.411334
$980$	227.493	7.26700
$981$	2.93170	0.0936021
$982$	28.3204	0.903739
$983$	35.3584	1.12776	0.563879	−	0.825857i	$-0.309308\pi$
$983$	35.3584	1.12776	0.563879	+	0.825857i	$0.309308\pi$
$984$	51.7576	1.64997
$985$	−28.9391	−0.922075
$986$	−75.0560	−2.39027
$987$	60.5371	1.92692
$988$	−38.2978	−1.21841
$989$	−12.2263	−0.388774
$990$	−13.0560	−0.414946
$991$	−49.8362	−1.58310	−0.791550	−	0.611105i	$-0.790725\pi$
$991$	−49.8362	−1.58310	−0.791550	+	0.611105i	$0.790725\pi$
$992$	−114.874	−3.64727
$993$	10.4865	0.332779
$994$	−34.3667	−1.09004
$995$	63.0565	1.99903
$996$	−90.2572	−2.85991
$997$	−24.2646	−0.768468	−0.384234	−	0.923236i	$-0.625534\pi$
$997$	−24.2646	−0.768468	−0.384234	+	0.923236i	$0.625534\pi$
$998$	50.2725	1.59135
$999$	−58.8330	−1.86139

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8003.2.a.c.1.6	✓	172

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8003.2.a.c.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.68137 q^{2} +1.21893 q^{3} +5.18975 q^{4} +2.92126 q^{5} -3.26842 q^{6} +4.69101 q^{7} -8.55290 q^{8} -1.51420 q^{9} +O(q^{10})\)	\(q-2.68137 q^{2} +1.21893 q^{3} +5.18975 q^{4} +2.92126 q^{5} -3.26842 q^{6} +4.69101 q^{7} -8.55290 q^{8} -1.51420 q^{9} -7.83297 q^{10} -1.10078 q^{11} +6.32596 q^{12} +3.44785 q^{13} -12.5783 q^{14} +3.56082 q^{15} +12.5540 q^{16} -4.01060 q^{17} +4.06013 q^{18} -2.14032 q^{19} +15.1606 q^{20} +5.71803 q^{21} +2.95159 q^{22} +2.58440 q^{23} -10.4254 q^{24} +3.53374 q^{25} -9.24496 q^{26} -5.50251 q^{27} +24.3452 q^{28} -6.97941 q^{29} -9.54788 q^{30} +6.93849 q^{31} -16.5561 q^{32} -1.34178 q^{33} +10.7539 q^{34} +13.7036 q^{35} -7.85831 q^{36} +10.6920 q^{37} +5.73900 q^{38} +4.20270 q^{39} -24.9852 q^{40} -4.96455 q^{41} -15.3322 q^{42} -4.73081 q^{43} -5.71276 q^{44} -4.42336 q^{45} -6.92974 q^{46} +10.5871 q^{47} +15.3025 q^{48} +15.0056 q^{49} -9.47527 q^{50} -4.88866 q^{51} +17.8935 q^{52} -1.00000 q^{53} +14.7543 q^{54} -3.21565 q^{55} -40.1217 q^{56} -2.60891 q^{57} +18.7144 q^{58} +10.0989 q^{59} +18.4798 q^{60} +9.99290 q^{61} -18.6047 q^{62} -7.10312 q^{63} +19.2851 q^{64} +10.0720 q^{65} +3.59780 q^{66} +0.502039 q^{67} -20.8140 q^{68} +3.15022 q^{69} -36.7445 q^{70} +2.73221 q^{71} +12.9508 q^{72} -8.16872 q^{73} -28.6693 q^{74} +4.30740 q^{75} -11.1077 q^{76} -5.16375 q^{77} -11.2690 q^{78} -10.5454 q^{79} +36.6734 q^{80} -2.16460 q^{81} +13.3118 q^{82} -14.2677 q^{83} +29.6751 q^{84} -11.7160 q^{85} +12.6851 q^{86} -8.50744 q^{87} +9.41484 q^{88} +11.6919 q^{89} +11.8607 q^{90} +16.1739 q^{91} +13.4124 q^{92} +8.45756 q^{93} -28.3878 q^{94} -6.25243 q^{95} -20.1808 q^{96} -3.98600 q^{97} -40.2355 q^{98} +1.66680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 172 q + 8 q^{2} + 25 q^{3} + 188 q^{4} + 27 q^{5} + 10 q^{6} + 31 q^{7} + 21 q^{8} + 179 q^{9}+O(q^{10}) \) 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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