LMFDB - Embedded newform 4021.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4021,2,Mod(1,4021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4021, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4021.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:	$32.1078466528$
Analytic rank:	$0$
Dimension:	$182$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69235 q^{2} -2.05539 q^{3} +5.24877 q^{4} -1.71000 q^{5} +5.53383 q^{6} -4.72268 q^{7} -8.74684 q^{8} +1.22462 q^{9} +O(q^{10})$	\(q-2.69235 q^{2} -2.05539 q^{3} +5.24877 q^{4} -1.71000 q^{5} +5.53383 q^{6} -4.72268 q^{7} -8.74684 q^{8} +1.22462 q^{9} +4.60392 q^{10} +0.578308 q^{11} -10.7883 q^{12} +1.78134 q^{13} +12.7151 q^{14} +3.51471 q^{15} +13.0521 q^{16} -1.97512 q^{17} -3.29711 q^{18} -5.79138 q^{19} -8.97539 q^{20} +9.70695 q^{21} -1.55701 q^{22} +6.41023 q^{23} +17.9782 q^{24} -2.07591 q^{25} -4.79601 q^{26} +3.64909 q^{27} -24.7883 q^{28} +5.35779 q^{29} -9.46285 q^{30} +1.82832 q^{31} -17.6471 q^{32} -1.18865 q^{33} +5.31771 q^{34} +8.07578 q^{35} +6.42775 q^{36} -0.547119 q^{37} +15.5924 q^{38} -3.66135 q^{39} +14.9571 q^{40} -11.0343 q^{41} -26.1345 q^{42} -9.03513 q^{43} +3.03541 q^{44} -2.09410 q^{45} -17.2586 q^{46} -5.67069 q^{47} -26.8270 q^{48} +15.3037 q^{49} +5.58907 q^{50} +4.05963 q^{51} +9.34987 q^{52} -12.5488 q^{53} -9.82465 q^{54} -0.988906 q^{55} +41.3086 q^{56} +11.9035 q^{57} -14.4251 q^{58} -0.677477 q^{59} +18.4479 q^{60} -11.3013 q^{61} -4.92249 q^{62} -5.78350 q^{63} +21.4080 q^{64} -3.04610 q^{65} +3.20026 q^{66} -9.83984 q^{67} -10.3669 q^{68} -13.1755 q^{69} -21.7429 q^{70} +4.12141 q^{71} -10.7116 q^{72} -14.8356 q^{73} +1.47304 q^{74} +4.26679 q^{75} -30.3976 q^{76} -2.73117 q^{77} +9.85766 q^{78} +17.3418 q^{79} -22.3190 q^{80} -11.1742 q^{81} +29.7082 q^{82} -7.51330 q^{83} +50.9495 q^{84} +3.37745 q^{85} +24.3258 q^{86} -11.0123 q^{87} -5.05837 q^{88} +2.96007 q^{89} +5.63806 q^{90} -8.41273 q^{91} +33.6458 q^{92} -3.75791 q^{93} +15.2675 q^{94} +9.90324 q^{95} +36.2716 q^{96} -9.85693 q^{97} -41.2031 q^{98} +0.708208 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) $ 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * 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 $

$2$	−2.69235	−1.90378	−0.951891	−	0.306437i	$-0.900863\pi$
$2$	−2.69235	−1.90378	−0.951891	+	0.306437i	$0.900863\pi$
$3$	−2.05539	−1.18668	−0.593339	−	0.804952i	$-0.702191\pi$
$3$	−2.05539	−1.18668	−0.593339	+	0.804952i	$0.702191\pi$
$4$	5.24877	2.62439
$5$	−1.71000	−0.764735	−0.382367	−	0.924010i	$-0.624891\pi$
$5$	−1.71000	−0.764735	−0.382367	+	0.924010i	$0.624891\pi$
$6$	5.53383	2.25918
$7$	−4.72268	−1.78501	−0.892503	−	0.451041i	$-0.851053\pi$
$7$	−4.72268	−1.78501	−0.892503	+	0.451041i	$0.851053\pi$
$8$	−8.74684	−3.09248
$9$	1.22462	0.408207
$10$	4.60392	1.45589
$11$	0.578308	0.174366	0.0871832	−	0.996192i	$-0.472213\pi$
$11$	0.578308	0.174366	0.0871832	+	0.996192i	$0.472213\pi$
$12$	−10.7883	−3.11430
$13$	1.78134	0.494056	0.247028	−	0.969008i	$-0.420546\pi$
$13$	1.78134	0.494056	0.247028	+	0.969008i	$0.420546\pi$
$14$	12.7151	3.39826
$15$	3.51471	0.907494
$16$	13.0521	3.26301
$17$	−1.97512	−0.479036	−0.239518	−	0.970892i	$-0.576989\pi$
$17$	−1.97512	−0.479036	−0.239518	+	0.970892i	$0.576989\pi$
$18$	−3.29711	−0.777137
$19$	−5.79138	−1.32863	−0.664316	−	0.747451i	$-0.731277\pi$
$19$	−5.79138	−1.32863	−0.664316	+	0.747451i	$0.731277\pi$
$20$	−8.97539	−2.00696
$21$	9.70695	2.11823
$22$	−1.55701	−0.331956
$23$	6.41023	1.33662	0.668312	−	0.743881i	$-0.267017\pi$
$23$	6.41023	1.33662	0.668312	+	0.743881i	$0.267017\pi$
$24$	17.9782	3.66978
$25$	−2.07591	−0.415181
$26$	−4.79601	−0.940575
$27$	3.64909	0.702268
$28$	−24.7883	−4.68454
$29$	5.35779	0.994916	0.497458	−	0.867488i	$-0.334267\pi$
$29$	5.35779	0.994916	0.497458	+	0.867488i	$0.334267\pi$
$30$	−9.46285	−1.72767
$31$	1.82832	0.328376	0.164188	−	0.986429i	$-0.447500\pi$
$31$	1.82832	0.328376	0.164188	+	0.986429i	$0.447500\pi$
$32$	−17.6471	−3.11959
$33$	−1.18865	−0.206917
$34$	5.31771	0.911980
$35$	8.07578	1.36506
$36$	6.42775	1.07129
$37$	−0.547119	−0.0899459	−0.0449729	−	0.998988i	$-0.514320\pi$
$37$	−0.547119	−0.0899459	−0.0449729	+	0.998988i	$0.514320\pi$
$38$	15.5924	2.52943
$39$	−3.66135	−0.586286
$40$	14.9571	2.36492
$41$	−11.0343	−1.72327	−0.861633	−	0.507531i	$-0.830558\pi$
$41$	−11.0343	−1.72327	−0.861633	+	0.507531i	$0.830558\pi$
$42$	−26.1345	−4.03265
$43$	−9.03513	−1.37784	−0.688922	−	0.724835i	$-0.741916\pi$
$43$	−9.03513	−1.37784	−0.688922	+	0.724835i	$0.741916\pi$
$44$	3.03541	0.457605
$45$	−2.09410	−0.312170
$46$	−17.2586	−2.54464
$47$	−5.67069	−0.827156	−0.413578	−	0.910469i	$-0.635721\pi$
$47$	−5.67069	−0.827156	−0.413578	+	0.910469i	$0.635721\pi$
$48$	−26.8270	−3.87215
$49$	15.3037	2.18625
$50$	5.58907	0.790414
$51$	4.05963	0.568462
$52$	9.34987	1.29659
$53$	−12.5488	−1.72371	−0.861856	−	0.507152i	$-0.830698\pi$
$53$	−12.5488	−1.72371	−0.861856	+	0.507152i	$0.830698\pi$
$54$	−9.82465	−1.33697
$55$	−0.988906	−0.133344
$56$	41.3086	5.52009
$57$	11.9035	1.57666
$58$	−14.4251	−1.89410
$59$	−0.677477	−0.0881999	−0.0441000	−	0.999027i	$-0.514042\pi$
$59$	−0.677477	−0.0881999	−0.0441000	+	0.999027i	$0.514042\pi$
$60$	18.4479	2.38162
$61$	−11.3013	−1.44699	−0.723493	−	0.690331i	$-0.757465\pi$
$61$	−11.3013	−1.44699	−0.723493	+	0.690331i	$0.757465\pi$
$62$	−4.92249	−0.625156
$63$	−5.78350	−0.728652
$64$	21.4080	2.67601
$65$	−3.04610	−0.377822
$66$	3.20026	0.393925
$67$	−9.83984	−1.20213	−0.601064	−	0.799201i	$-0.705256\pi$
$67$	−9.83984	−1.20213	−0.601064	+	0.799201i	$0.705256\pi$
$68$	−10.3669	−1.25718
$69$	−13.1755	−1.58614
$70$	−21.7429	−2.59877
$71$	4.12141	0.489122	0.244561	−	0.969634i	$-0.421356\pi$
$71$	4.12141	0.489122	0.244561	+	0.969634i	$0.421356\pi$
$72$	−10.7116	−1.26237
$73$	−14.8356	−1.73637	−0.868187	−	0.496236i	$-0.834715\pi$
$73$	−14.8356	−1.73637	−0.868187	+	0.496236i	$0.834715\pi$
$74$	1.47304	0.171237
$75$	4.26679	0.492687
$76$	−30.3976	−3.48684
$77$	−2.73117	−0.311245
$78$	9.85766	1.11616
$79$	17.3418	1.95110	0.975552	−	0.219767i	$-0.0705296\pi$
$79$	17.3418	1.95110	0.975552	+	0.219767i	$0.0705296\pi$
$80$	−22.3190	−2.49534
$81$	−11.1742	−1.24157
$82$	29.7082	3.28072
$83$	−7.51330	−0.824692	−0.412346	−	0.911027i	$-0.635291\pi$
$83$	−7.51330	−0.824692	−0.412346	+	0.911027i	$0.635291\pi$
$84$	50.9495	5.55905
$85$	3.37745	0.366336
$86$	24.3258	2.62312
$87$	−11.0123	−1.18065
$88$	−5.05837	−0.539224
$89$	2.96007	0.313767	0.156883	−	0.987617i	$-0.449855\pi$
$89$	2.96007	0.313767	0.156883	+	0.987617i	$0.449855\pi$
$90$	5.63806	0.594304
$91$	−8.41273	−0.881893
$92$	33.6458	3.50782
$93$	−3.75791	−0.389677
$94$	15.2675	1.57472
$95$	9.90324	1.01605
$96$	36.2716	3.70195
$97$	−9.85693	−1.00082	−0.500410	−	0.865789i	$-0.666817\pi$
$97$	−9.85693	−1.00082	−0.500410	+	0.865789i	$0.666817\pi$
$98$	−41.2031	−4.16214
$99$	0.708208	0.0711776
$100$	−10.8960	−1.08960
$101$	15.9093	1.58303	0.791516	−	0.611148i	$-0.209292\pi$
$101$	15.9093	1.58303	0.791516	+	0.611148i	$0.209292\pi$
$102$	−10.9300	−1.08223
$103$	−10.6577	−1.05013	−0.525067	−	0.851061i	$-0.675960\pi$
$103$	−10.6577	−1.05013	−0.525067	+	0.851061i	$0.675960\pi$
$104$	−15.5811	−1.52786
$105$	−16.5989	−1.61988
$106$	33.7859	3.28157
$107$	14.7087	1.42194	0.710971	−	0.703221i	$-0.248256\pi$
$107$	14.7087	1.42194	0.710971	+	0.703221i	$0.248256\pi$
$108$	19.1533	1.84302
$109$	5.84009	0.559379	0.279689	−	0.960091i	$-0.409768\pi$
$109$	5.84009	0.559379	0.279689	+	0.960091i	$0.409768\pi$
$110$	2.66248	0.253858
$111$	1.12454	0.106737
$112$	−61.6407	−5.82450
$113$	−19.5675	−1.84076	−0.920378	−	0.391029i	$-0.872119\pi$
$113$	−19.5675	−1.84076	−0.920378	+	0.391029i	$0.872119\pi$
$114$	−32.0485	−3.00162
$115$	−10.9615	−1.02216
$116$	28.1218	2.61104
$117$	2.18147	0.201677
$118$	1.82401	0.167913
$119$	9.32785	0.855083
$120$	−30.7426	−2.80640
$121$	−10.6656	−0.969596
$122$	30.4272	2.75475
$123$	22.6798	2.04496
$124$	9.59643	0.861785
$125$	12.0998	1.08224
$126$	15.5712	1.38719
$127$	−1.33979	−0.118887	−0.0594435	−	0.998232i	$-0.518933\pi$
$127$	−1.33979	−0.118887	−0.0594435	+	0.998232i	$0.518933\pi$
$128$	−22.3439	−1.97494
$129$	18.5707	1.63506
$130$	8.20117	0.719290
$131$	−13.4644	−1.17639	−0.588196	−	0.808718i	$-0.700162\pi$
$131$	−13.4644	−1.17639	−0.588196	+	0.808718i	$0.700162\pi$
$132$	−6.23894	−0.543030
$133$	27.3508	2.37162
$134$	26.4923	2.28859
$135$	−6.23994	−0.537049
$136$	17.2760	1.48141
$137$	0.121473	0.0103781	0.00518905	−	0.999987i	$-0.498348\pi$
$137$	0.121473	0.0103781	0.00518905	+	0.999987i	$0.498348\pi$
$138$	35.4731	3.01967
$139$	−21.7884	−1.84807	−0.924033	−	0.382312i	$-0.875128\pi$
$139$	−21.7884	−1.84807	−0.924033	+	0.382312i	$0.875128\pi$
$140$	42.3879	3.58243
$141$	11.6555	0.981568
$142$	−11.0963	−0.931181
$143$	1.03017	0.0861468
$144$	15.9838	1.33198
$145$	−9.16181	−0.760847
$146$	39.9427	3.30568
$147$	−31.4551	−2.59437
$148$	−2.87170	−0.236053
$149$	−20.6910	−1.69507	−0.847536	−	0.530737i	$-0.821915\pi$
$149$	−20.6910	−1.69507	−0.847536	+	0.530737i	$0.821915\pi$
$150$	−11.4877	−0.937968
$151$	−24.5293	−1.99617	−0.998083	−	0.0618925i	$-0.980286\pi$
$151$	−24.5293	−1.99617	−0.998083	+	0.0618925i	$0.980286\pi$
$152$	50.6563	4.10876
$153$	−2.41877	−0.195546
$154$	7.35326	0.592543
$155$	−3.12642	−0.251120
$156$	−19.2176	−1.53864
$157$	−12.4807	−0.996066	−0.498033	−	0.867158i	$-0.665944\pi$
$157$	−12.4807	−0.996066	−0.498033	+	0.867158i	$0.665944\pi$
$158$	−46.6903	−3.71448
$159$	25.7927	2.04549
$160$	30.1765	2.38566
$161$	−30.2735	−2.38588
$162$	30.0848	2.36369
$163$	0.127333	0.00997345	0.00498673	−	0.999988i	$-0.498413\pi$
$163$	0.127333	0.00997345	0.00498673	+	0.999988i	$0.498413\pi$
$164$	−57.9165	−4.52252
$165$	2.03259	0.158237
$166$	20.2285	1.57003
$167$	5.38076	0.416375	0.208188	−	0.978089i	$-0.433243\pi$
$167$	5.38076	0.416375	0.208188	+	0.978089i	$0.433243\pi$
$168$	−84.9051	−6.55057
$169$	−9.82681	−0.755909
$170$	−9.09328	−0.697423
$171$	−7.09224	−0.542357
$172$	−47.4233	−3.61600
$173$	2.21598	0.168478	0.0842391	−	0.996446i	$-0.473154\pi$
$173$	2.21598	0.168478	0.0842391	+	0.996446i	$0.473154\pi$
$174$	29.6491	2.24769
$175$	9.80384	0.741101
$176$	7.54811	0.568960
$177$	1.39248	0.104665
$178$	−7.96955	−0.597343
$179$	−1.52041	−0.113641	−0.0568205	−	0.998384i	$-0.518096\pi$
$179$	−1.52041	−0.113641	−0.0568205	+	0.998384i	$0.518096\pi$
$180$	−10.9914	−0.819254
$181$	3.15341	0.234391	0.117196	−	0.993109i	$-0.462610\pi$
$181$	3.15341	0.234391	0.117196	+	0.993109i	$0.462610\pi$
$182$	22.6500	1.67893
$183$	23.2286	1.71711
$184$	−56.0692	−4.13348
$185$	0.935573	0.0687847
$186$	10.1176	0.741860
$187$	−1.14223	−0.0835278
$188$	−29.7642	−2.17078
$189$	−17.2335	−1.25355
$190$	−26.6630	−1.93434
$191$	6.57900	0.476040	0.238020	−	0.971260i	$-0.423502\pi$
$191$	6.57900	0.476040	0.238020	+	0.971260i	$0.423502\pi$
$192$	−44.0018	−3.17556
$193$	−5.38354	−0.387516	−0.193758	−	0.981049i	$-0.562068\pi$
$193$	−5.38354	−0.387516	−0.193758	+	0.981049i	$0.562068\pi$
$194$	26.5384	1.90534
$195$	6.26091	0.448353
$196$	80.3258	5.73756
$197$	15.6275	1.11342	0.556708	−	0.830708i	$-0.312064\pi$
$197$	15.6275	1.11342	0.556708	+	0.830708i	$0.312064\pi$
$198$	−1.90675	−0.135507
$199$	−11.6450	−0.825495	−0.412747	−	0.910846i	$-0.635431\pi$
$199$	−11.6450	−0.825495	−0.412747	+	0.910846i	$0.635431\pi$
$200$	18.1576	1.28394
$201$	20.2247	1.42654
$202$	−42.8334	−3.01375
$203$	−25.3031	−1.77593
$204$	21.3081	1.49186
$205$	18.8686	1.31784
$206$	28.6943	1.99923
$207$	7.85010	0.545620
$208$	23.2502	1.61211
$209$	−3.34920	−0.231669
$210$	44.6900	3.08390
$211$	17.6998	1.21850	0.609251	−	0.792978i	$-0.291470\pi$
$211$	17.6998	1.21850	0.609251	+	0.792978i	$0.291470\pi$
$212$	−65.8659	−4.52369
$213$	−8.47111	−0.580431
$214$	−39.6010	−2.70707
$215$	15.4501	1.05369
$216$	−31.9180	−2.17175
$217$	−8.63458	−0.586153
$218$	−15.7236	−1.06494
$219$	30.4929	2.06052
$220$	−5.19054	−0.349946
$221$	−3.51836	−0.236671
$222$	−3.02767	−0.203204
$223$	10.1843	0.681992	0.340996	−	0.940065i	$-0.389236\pi$
$223$	10.1843	0.681992	0.340996	+	0.940065i	$0.389236\pi$
$224$	83.3415	5.56849
$225$	−2.54220	−0.169480
$226$	52.6827	3.50440
$227$	−10.3941	−0.689879	−0.344939	−	0.938625i	$-0.612101\pi$
$227$	−10.3941	−0.689879	−0.344939	+	0.938625i	$0.612101\pi$
$228$	62.4789	4.13777
$229$	−20.1836	−1.33377	−0.666884	−	0.745162i	$-0.732372\pi$
$229$	−20.1836	−1.33377	−0.666884	+	0.745162i	$0.732372\pi$
$230$	29.5122	1.94598
$231$	5.61361	0.369348
$232$	−46.8637	−3.07675
$233$	−4.73547	−0.310231	−0.155115	−	0.987896i	$-0.549575\pi$
$233$	−4.73547	−0.310231	−0.155115	+	0.987896i	$0.549575\pi$
$234$	−5.87329	−0.383949
$235$	9.69688	0.632554
$236$	−3.55592	−0.231471
$237$	−35.6441	−2.31534
$238$	−25.1139	−1.62789
$239$	−0.596268	−0.0385693	−0.0192847	−	0.999814i	$-0.506139\pi$
$239$	−0.596268	−0.0385693	−0.0192847	+	0.999814i	$0.506139\pi$
$240$	45.8742	2.96117
$241$	−18.6249	−1.19974	−0.599869	−	0.800098i	$-0.704781\pi$
$241$	−18.6249	−1.19974	−0.599869	+	0.800098i	$0.704781\pi$
$242$	28.7155	1.84590
$243$	12.0200	0.771081
$244$	−59.3181	−3.79745
$245$	−26.1694	−1.67190
$246$	−61.0619	−3.89317
$247$	−10.3164	−0.656419
$248$	−15.9920	−1.01549
$249$	15.4428	0.978645
$250$	−32.5769	−2.06034
$251$	18.6374	1.17638	0.588191	−	0.808722i	$-0.299841\pi$
$251$	18.6374	1.17638	0.588191	+	0.808722i	$0.299841\pi$
$252$	−30.3562	−1.91226
$253$	3.70709	0.233063
$254$	3.60718	0.226335
$255$	−6.94196	−0.434723
$256$	17.3416	1.08385
$257$	−9.44884	−0.589402	−0.294701	−	0.955589i	$-0.595220\pi$
$257$	−9.44884	−0.589402	−0.294701	+	0.955589i	$0.595220\pi$
$258$	−49.9989	−3.11280
$259$	2.58387	0.160554
$260$	−15.9883	−0.991550
$261$	6.56126	0.406132
$262$	36.2510	2.23960
$263$	16.4902	1.01683	0.508415	−	0.861112i	$-0.330232\pi$
$263$	16.4902	1.01683	0.508415	+	0.861112i	$0.330232\pi$
$264$	10.3969	0.639886
$265$	21.4585	1.31818
$266$	−73.6381	−4.51504
$267$	−6.08409	−0.372340
$268$	−51.6471	−3.15485
$269$	−17.0613	−1.04024	−0.520122	−	0.854092i	$-0.674114\pi$
$269$	−17.0613	−1.04024	−0.520122	+	0.854092i	$0.674114\pi$
$270$	16.8001	1.02242
$271$	3.12500	0.189830	0.0949152	−	0.995485i	$-0.469742\pi$
$271$	3.12500	0.189830	0.0949152	+	0.995485i	$0.469742\pi$
$272$	−25.7793	−1.56310
$273$	17.2914	1.04652
$274$	−0.327047	−0.0197576
$275$	−1.20051	−0.0723936
$276$	−69.1552	−4.16265
$277$	−29.3477	−1.76333	−0.881667	−	0.471872i	$-0.843578\pi$
$277$	−29.3477	−1.76333	−0.881667	+	0.471872i	$0.843578\pi$
$278$	58.6621	3.51832
$279$	2.23900	0.134045
$280$	−70.6376	−4.22140
$281$	−11.2855	−0.673239	−0.336619	−	0.941641i	$-0.609284\pi$
$281$	−11.2855	−0.673239	−0.336619	+	0.941641i	$0.609284\pi$
$282$	−31.3807	−1.86869
$283$	1.34939	0.0802126	0.0401063	−	0.999195i	$-0.487230\pi$
$283$	1.34939	0.0802126	0.0401063	+	0.999195i	$0.487230\pi$
$284$	21.6324	1.28364
$285$	−20.3550	−1.20573
$286$	−2.77357	−0.164005
$287$	52.1115	3.07604
$288$	−21.6110	−1.27344
$289$	−13.0989	−0.770524
$290$	24.6668	1.44849
$291$	20.2598	1.18765
$292$	−77.8686	−4.55692
$293$	−26.3162	−1.53741	−0.768706	−	0.639603i	$-0.779099\pi$
$293$	−26.3162	−1.53741	−0.768706	+	0.639603i	$0.779099\pi$
$294$	84.6883	4.93912
$295$	1.15848	0.0674495
$296$	4.78557	0.278155
$297$	2.11030	0.122452
$298$	55.7075	3.22705
$299$	11.4188	0.660368
$300$	22.3954	1.29300
$301$	42.6701	2.45946
$302$	66.0415	3.80026
$303$	−32.6997	−1.87855
$304$	−75.5894	−4.33535
$305$	19.3253	1.10656
$306$	6.51218	0.372277
$307$	−20.1562	−1.15037	−0.575186	−	0.818023i	$-0.695070\pi$
$307$	−20.1562	−1.15037	−0.575186	+	0.818023i	$0.695070\pi$
$308$	−14.3353	−0.816827
$309$	21.9057	1.24617
$310$	8.41744	0.478079
$311$	17.6237	0.999350	0.499675	−	0.866213i	$-0.333453\pi$
$311$	17.6237	0.999350	0.499675	+	0.866213i	$0.333453\pi$
$312$	32.0253	1.81307
$313$	3.92260	0.221719	0.110859	−	0.993836i	$-0.464640\pi$
$313$	3.92260	0.221719	0.110859	+	0.993836i	$0.464640\pi$
$314$	33.6024	1.89629
$315$	9.88977	0.557225
$316$	91.0231	5.12045
$317$	23.5381	1.32203	0.661015	−	0.750373i	$-0.270126\pi$
$317$	23.5381	1.32203	0.661015	+	0.750373i	$0.270126\pi$
$318$	−69.4431	−3.89417
$319$	3.09845	0.173480
$320$	−36.6077	−2.04643
$321$	−30.2321	−1.68739
$322$	81.5069	4.54220
$323$	11.4386	0.636463
$324$	−58.6506	−3.25837
$325$	−3.69790	−0.205123
$326$	−0.342824	−0.0189873
$327$	−12.0036	−0.663803
$328$	96.5152	5.32916
$329$	26.7809	1.47648
$330$	−5.47244	−0.301248
$331$	4.63268	0.254635	0.127318	−	0.991862i	$-0.459363\pi$
$331$	4.63268	0.254635	0.127318	+	0.991862i	$0.459363\pi$
$332$	−39.4356	−2.16431
$333$	−0.670014	−0.0367165
$334$	−14.4869	−0.792688
$335$	16.8261	0.919309
$336$	126.696	6.91181
$337$	25.4905	1.38856	0.694279	−	0.719706i	$-0.255723\pi$
$337$	25.4905	1.38856	0.694279	+	0.719706i	$0.255723\pi$
$338$	26.4573	1.43909
$339$	40.2188	2.18439
$340$	17.7274	0.961406
$341$	1.05733	0.0572578
$342$	19.0948	1.03253
$343$	−39.2159	−2.11746
$344$	79.0289	4.26095
$345$	22.5301	1.21298
$346$	−5.96621	−0.320746
$347$	−15.9120	−0.854200	−0.427100	−	0.904204i	$-0.640465\pi$
$347$	−15.9120	−0.854200	−0.427100	+	0.904204i	$0.640465\pi$
$348$	−57.8012	−3.09847
$349$	−10.1736	−0.544578	−0.272289	−	0.962216i	$-0.587781\pi$
$349$	−10.1736	−0.544578	−0.272289	+	0.962216i	$0.587781\pi$
$350$	−26.3954	−1.41089
$351$	6.50029	0.346960
$352$	−10.2054	−0.543952
$353$	6.50202	0.346068	0.173034	−	0.984916i	$-0.444643\pi$
$353$	6.50202	0.346068	0.173034	+	0.984916i	$0.444643\pi$
$354$	−3.74904	−0.199259
$355$	−7.04761	−0.374048
$356$	15.5367	0.823445
$357$	−19.1724	−1.01471
$358$	4.09349	0.216348
$359$	6.44917	0.340374	0.170187	−	0.985412i	$-0.445563\pi$
$359$	6.44917	0.340374	0.170187	+	0.985412i	$0.445563\pi$
$360$	18.3168	0.965378
$361$	14.5400	0.765265
$362$	−8.49010	−0.446230
$363$	21.9219	1.15060
$364$	−44.1565	−2.31443
$365$	25.3688	1.32787
$366$	−62.5397	−3.26900
$367$	14.6746	0.766007	0.383003	−	0.923747i	$-0.374890\pi$
$367$	14.6746	0.766007	0.383003	+	0.923747i	$0.374890\pi$
$368$	83.6666	4.36142
$369$	−13.5128	−0.703450
$370$	−2.51889	−0.130951
$371$	59.2641	3.07684
$372$	−19.7244	−1.02266
$373$	6.54485	0.338879	0.169440	−	0.985541i	$-0.445804\pi$
$373$	6.54485	0.338879	0.169440	+	0.985541i	$0.445804\pi$
$374$	3.07528	0.159019
$375$	−24.8698	−1.28427
$376$	49.6007	2.55796
$377$	9.54407	0.491545
$378$	46.3987	2.38649
$379$	3.98427	0.204658	0.102329	−	0.994751i	$-0.467371\pi$
$379$	3.98427	0.204658	0.102329	+	0.994751i	$0.467371\pi$
$380$	51.9799	2.66651
$381$	2.75378	0.141081
$382$	−17.7130	−0.906276
$383$	3.33292	0.170304	0.0851522	−	0.996368i	$-0.472862\pi$
$383$	3.33292	0.170304	0.0851522	+	0.996368i	$0.472862\pi$
$384$	45.9254	2.34362
$385$	4.67029	0.238020
$386$	14.4944	0.737745
$387$	−11.0646	−0.562446
$388$	−51.7368	−2.62654
$389$	−13.7551	−0.697413	−0.348706	−	0.937232i	$-0.613379\pi$
$389$	−13.7551	−0.697413	−0.348706	+	0.937232i	$0.613379\pi$
$390$	−16.8566	−0.853567
$391$	−12.6609	−0.640292
$392$	−133.859	−6.76092
$393$	27.6746	1.39600
$394$	−42.0749	−2.11970
$395$	−29.6544	−1.49208
$396$	3.71722	0.186797
$397$	16.7191	0.839107	0.419553	−	0.907731i	$-0.362187\pi$
$397$	16.7191	0.839107	0.419553	+	0.907731i	$0.362187\pi$
$398$	31.3526	1.57156
$399$	−56.2166	−2.81435
$400$	−27.0948	−1.35474
$401$	20.7723	1.03732	0.518659	−	0.854981i	$-0.326432\pi$
$401$	20.7723	1.03732	0.518659	+	0.854981i	$0.326432\pi$
$402$	−54.4520	−2.71582
$403$	3.25687	0.162236
$404$	83.5041	4.15449
$405$	19.1078	0.949475
$406$	68.1250	3.38099
$407$	−0.316404	−0.0156835
$408$	−35.5090	−1.75796
$409$	7.08269	0.350216	0.175108	−	0.984549i	$-0.443972\pi$
$409$	7.08269	0.350216	0.175108	+	0.984549i	$0.443972\pi$
$410$	−50.8010	−2.50888
$411$	−0.249673	−0.0123155
$412$	−55.9398	−2.75596
$413$	3.19951	0.157437
$414$	−21.1352	−1.03874
$415$	12.8477	0.630671
$416$	−31.4355	−1.54125
$417$	44.7836	2.19306
$418$	9.01723	0.441047
$419$	−15.9910	−0.781210	−0.390605	−	0.920558i	$-0.627734\pi$
$419$	−15.9910	−0.781210	−0.390605	+	0.920558i	$0.627734\pi$
$420$	−87.1236	−4.25120
$421$	8.99297	0.438290	0.219145	−	0.975692i	$-0.429673\pi$
$421$	8.99297	0.438290	0.219145	+	0.975692i	$0.429673\pi$
$422$	−47.6540	−2.31976
$423$	−6.94445	−0.337651
$424$	109.763	5.33054
$425$	4.10016	0.198887
$426$	22.8072	1.10501
$427$	53.3726	2.58288
$428$	77.2025	3.73172
$429$	−2.11739	−0.102229
$430$	−41.5970	−2.00599
$431$	−8.25543	−0.397650	−0.198825	−	0.980035i	$-0.563713\pi$
$431$	−8.25543	−0.397650	−0.198825	+	0.980035i	$0.563713\pi$
$432$	47.6282	2.29151
$433$	39.2094	1.88429	0.942143	−	0.335213i	$-0.108808\pi$
$433$	39.2094	1.88429	0.942143	+	0.335213i	$0.108808\pi$
$434$	23.2473	1.11591
$435$	18.8311	0.902881
$436$	30.6533	1.46803
$437$	−37.1240	−1.77588
$438$	−82.0977	−3.92278
$439$	−28.9509	−1.38175	−0.690874	−	0.722975i	$-0.742774\pi$
$439$	−28.9509	−1.38175	−0.690874	+	0.722975i	$0.742774\pi$
$440$	8.64980	0.412363
$441$	18.7413	0.892441
$442$	9.47268	0.450569
$443$	19.7577	0.938718	0.469359	−	0.883007i	$-0.344485\pi$
$443$	19.7577	0.938718	0.469359	+	0.883007i	$0.344485\pi$
$444$	5.90247	0.280119
$445$	−5.06171	−0.239948
$446$	−27.4198	−1.29836
$447$	42.5280	2.01151
$448$	−101.103	−4.77669
$449$	0.743265	0.0350768	0.0175384	−	0.999846i	$-0.494417\pi$
$449$	0.743265	0.0350768	0.0175384	+	0.999846i	$0.494417\pi$
$450$	6.84449	0.322653
$451$	−6.38122	−0.300480
$452$	−102.705	−4.83086
$453$	50.4172	2.36881
$454$	27.9845	1.31338
$455$	14.3857	0.674414
$456$	−104.118	−4.87578
$457$	−20.4612	−0.957136	−0.478568	−	0.878050i	$-0.658844\pi$
$457$	−20.4612	−0.957136	−0.478568	+	0.878050i	$0.658844\pi$
$458$	54.3413	2.53920
$459$	−7.20739	−0.336412
$460$	−57.5343	−2.68255
$461$	13.3843	0.623369	0.311684	−	0.950186i	$-0.399107\pi$
$461$	13.3843	0.623369	0.311684	+	0.950186i	$0.399107\pi$
$462$	−15.1138	−0.703158
$463$	1.59821	0.0742751	0.0371375	−	0.999310i	$-0.488176\pi$
$463$	1.59821	0.0742751	0.0371375	+	0.999310i	$0.488176\pi$
$464$	69.9301	3.24643
$465$	6.42602	0.297999
$466$	12.7496	0.590612
$467$	21.6879	1.00360	0.501798	−	0.864985i	$-0.332672\pi$
$467$	21.6879	1.00360	0.501798	+	0.864985i	$0.332672\pi$
$468$	11.4500	0.529279
$469$	46.4704	2.14581
$470$	−26.1074	−1.20425
$471$	25.6526	1.18201
$472$	5.92578	0.272756
$473$	−5.22509	−0.240250
$474$	95.9666	4.40789
$475$	12.0223	0.551623
$476$	48.9597	2.24407
$477$	−15.3675	−0.703632
$478$	1.60536	0.0734276
$479$	13.7579	0.628612	0.314306	−	0.949322i	$-0.398228\pi$
$479$	13.7579	0.628612	0.314306	+	0.949322i	$0.398228\pi$
$480$	−62.0243	−2.83101
$481$	−0.974608	−0.0444383
$482$	50.1449	2.28404
$483$	62.2237	2.83128
$484$	−55.9811	−2.54459
$485$	16.8553	0.765361
$486$	−32.3620	−1.46797
$487$	26.6537	1.20779	0.603897	−	0.797062i	$-0.293614\pi$
$487$	26.6537	1.20779	0.603897	+	0.797062i	$0.293614\pi$
$488$	98.8509	4.47477
$489$	−0.261718	−0.0118353
$490$	70.4572	3.18293
$491$	−13.9804	−0.630927	−0.315463	−	0.948938i	$-0.602160\pi$
$491$	−13.9804	−0.630927	−0.315463	+	0.948938i	$0.602160\pi$
$492$	119.041	5.36678
$493$	−10.5823	−0.476601
$494$	27.7755	1.24968
$495$	−1.21103	−0.0544320
$496$	23.8633	1.07150
$497$	−19.4641	−0.873086
$498$	−41.5774	−1.86313
$499$	18.5912	0.832256	0.416128	−	0.909306i	$-0.363387\pi$
$499$	18.5912	0.832256	0.416128	+	0.909306i	$0.363387\pi$
$500$	63.5090	2.84021
$501$	−11.0595	−0.494104
$502$	−50.1784	−2.23957
$503$	−31.4427	−1.40196	−0.700980	−	0.713181i	$-0.747254\pi$
$503$	−31.4427	−1.40196	−0.700980	+	0.713181i	$0.747254\pi$
$504$	50.5873	2.25334
$505$	−27.2048	−1.21060
$506$	−9.98079	−0.443700
$507$	20.1979	0.897021
$508$	−7.03224	−0.312005
$509$	−30.1433	−1.33608	−0.668040	−	0.744125i	$-0.732867\pi$
$509$	−30.1433	−1.33608	−0.668040	+	0.744125i	$0.732867\pi$
$510$	18.6902	0.827617
$511$	70.0638	3.09944
$512$	−2.00198	−0.0884756
$513$	−21.1333	−0.933057
$514$	25.4396	1.12209
$515$	18.2246	0.803074
$516$	97.4734	4.29103
$517$	−3.27941	−0.144228
$518$	−6.95670	−0.305660
$519$	−4.55471	−0.199929
$520$	26.6437	1.16840
$521$	−2.51894	−0.110357	−0.0551783	−	0.998477i	$-0.517573\pi$
$521$	−2.51894	−0.110357	−0.0551783	+	0.998477i	$0.517573\pi$
$522$	−17.6652	−0.773186
$523$	25.5887	1.11892	0.559458	−	0.828859i	$-0.311009\pi$
$523$	25.5887	1.11892	0.559458	+	0.828859i	$0.311009\pi$
$524$	−70.6717	−3.08731
$525$	−20.1507	−0.879449
$526$	−44.3975	−1.93582
$527$	−3.61115	−0.157304
$528$	−15.5143	−0.675173
$529$	18.0910	0.786566
$530$	−57.7738	−2.50953
$531$	−0.829652	−0.0360038
$532$	143.558	6.22404
$533$	−19.6559	−0.851390
$534$	16.3805	0.708855
$535$	−25.1518	−1.08741
$536$	86.0675	3.71755
$537$	3.12504	0.134855
$538$	45.9350	1.98040
$539$	8.85027	0.381208
$540$	−32.7520	−1.40942
$541$	40.8835	1.75772	0.878861	−	0.477079i	$-0.158304\pi$
$541$	40.8835	1.75772	0.878861	+	0.477079i	$0.158304\pi$
$542$	−8.41361	−0.361396
$543$	−6.48148	−0.278147
$544$	34.8550	1.49440
$545$	−9.98654	−0.427776
$546$	−46.5546	−1.99235
$547$	−18.1868	−0.777610	−0.388805	−	0.921320i	$-0.627112\pi$
$547$	−18.1868	−0.777610	−0.388805	+	0.921320i	$0.627112\pi$
$548$	0.637582	0.0272361
$549$	−13.8398	−0.590670
$550$	3.23221	0.137822
$551$	−31.0290	−1.32188
$552$	115.244	4.90511
$553$	−81.8998	−3.48273
$554$	79.0145	3.35700
$555$	−1.92297	−0.0816254
$556$	−114.362	−4.85004
$557$	−10.6639	−0.451846	−0.225923	−	0.974145i	$-0.572540\pi$
$557$	−10.6639	−0.451846	−0.225923	+	0.974145i	$0.572540\pi$
$558$	−6.02818	−0.255193
$559$	−16.0947	−0.680733
$560$	105.406	4.45420
$561$	2.34772	0.0991207
$562$	30.3847	1.28170
$563$	−17.5783	−0.740836	−0.370418	−	0.928865i	$-0.620786\pi$
$563$	−17.5783	−0.740836	−0.370418	+	0.928865i	$0.620786\pi$
$564$	61.1769	2.57601
$565$	33.4604	1.40769
$566$	−3.63302	−0.152707
$567$	52.7720	2.21622
$568$	−36.0494	−1.51260
$569$	−31.1651	−1.30651	−0.653254	−	0.757138i	$-0.726597\pi$
$569$	−31.1651	−1.30651	−0.653254	+	0.757138i	$0.726597\pi$
$570$	54.8029	2.29544
$571$	−47.7483	−1.99820	−0.999102	−	0.0423779i	$-0.986507\pi$
$571$	−47.7483	−1.99820	−0.999102	+	0.0423779i	$0.986507\pi$
$572$	5.40710	0.226082
$573$	−13.5224	−0.564907
$574$	−140.303	−5.85611
$575$	−13.3070	−0.554941
$576$	26.2167	1.09236
$577$	−38.5645	−1.60546	−0.802731	−	0.596342i	$-0.796620\pi$
$577$	−38.5645	−1.60546	−0.802731	+	0.596342i	$0.796620\pi$
$578$	35.2669	1.46691
$579$	11.0653	0.459857
$580$	−48.0882	−1.99676
$581$	35.4829	1.47208
$582$	−54.5466	−2.26103
$583$	−7.25708	−0.300558
$584$	129.765	5.36970
$585$	−3.73031	−0.154229
$586$	70.8527	2.92690
$587$	10.9247	0.450909	0.225454	−	0.974254i	$-0.427613\pi$
$587$	10.9247	0.450909	0.225454	+	0.974254i	$0.427613\pi$
$588$	−165.101	−6.80864
$589$	−10.5885	−0.436291
$590$	−3.11905	−0.128409
$591$	−32.1207	−1.32127
$592$	−7.14103	−0.293495
$593$	11.8661	0.487281	0.243641	−	0.969866i	$-0.421658\pi$
$593$	11.8661	0.487281	0.243641	+	0.969866i	$0.421658\pi$
$594$	−5.68168	−0.233122
$595$	−15.9506	−0.653911
$596$	−108.602	−4.44852
$597$	23.9351	0.979597
$598$	−30.7435	−1.25720
$599$	3.01027	0.122996	0.0614982	−	0.998107i	$-0.480412\pi$
$599$	3.01027	0.122996	0.0614982	+	0.998107i	$0.480412\pi$
$600$	−37.3209	−1.52362
$601$	7.44423	0.303656	0.151828	−	0.988407i	$-0.451484\pi$
$601$	7.44423	0.303656	0.151828	+	0.988407i	$0.451484\pi$
$602$	−114.883	−4.68228
$603$	−12.0501	−0.490717
$604$	−128.749	−5.23871
$605$	18.2381	0.741484
$606$	88.0393	3.57635
$607$	41.4322	1.68168	0.840840	−	0.541283i	$-0.182061\pi$
$607$	41.4322	1.68168	0.840840	+	0.541283i	$0.182061\pi$
$608$	102.201	4.14479
$609$	52.0078	2.10746
$610$	−52.0304	−2.10665
$611$	−10.1015	−0.408661
$612$	−12.6956	−0.513188
$613$	−19.5532	−0.789748	−0.394874	−	0.918735i	$-0.629212\pi$
$613$	−19.5532	−0.789748	−0.394874	+	0.918735i	$0.629212\pi$
$614$	54.2675	2.19006
$615$	−38.7823	−1.56386
$616$	23.8891	0.962518
$617$	−29.3628	−1.18210	−0.591051	−	0.806634i	$-0.701287\pi$
$617$	−29.3628	−1.18210	−0.591051	+	0.806634i	$0.701287\pi$
$618$	−58.9779	−2.37244
$619$	−9.54814	−0.383772	−0.191886	−	0.981417i	$-0.561460\pi$
$619$	−9.54814	−0.383772	−0.191886	+	0.981417i	$0.561460\pi$
$620$	−16.4099	−0.659037
$621$	23.3915	0.938669
$622$	−47.4493	−1.90254
$623$	−13.9795	−0.560075
$624$	−47.7882	−1.91306
$625$	−10.3111	−0.412444
$626$	−10.5610	−0.422104
$627$	6.88391	0.274917
$628$	−65.5082	−2.61406
$629$	1.08062	0.0430873
$630$	−26.6268	−1.06084
$631$	1.52325	0.0606397	0.0303199	−	0.999540i	$-0.490347\pi$
$631$	1.52325	0.0606397	0.0303199	+	0.999540i	$0.490347\pi$
$632$	−151.686	−6.03374
$633$	−36.3799	−1.44597
$634$	−63.3728	−2.51686
$635$	2.29103	0.0909169
$636$	135.380	5.36816
$637$	27.2612	1.08013
$638$	−8.34213	−0.330268
$639$	5.04717	0.199663
$640$	38.2081	1.51031
$641$	14.5315	0.573959	0.286980	−	0.957937i	$-0.407349\pi$
$641$	14.5315	0.573959	0.286980	+	0.957937i	$0.407349\pi$
$642$	81.3954	3.21242
$643$	2.97054	0.117147	0.0585734	−	0.998283i	$-0.481345\pi$
$643$	2.97054	0.117147	0.0585734	+	0.998283i	$0.481345\pi$
$644$	−158.899	−6.26148
$645$	−31.7559	−1.25039
$646$	−30.7969	−1.21169
$647$	26.3486	1.03587	0.517935	−	0.855420i	$-0.326701\pi$
$647$	26.3486	1.03587	0.517935	+	0.855420i	$0.326701\pi$
$648$	97.7387	3.83954
$649$	−0.391790	−0.0153791
$650$	9.95606	0.390509
$651$	17.7474	0.695576
$652$	0.668339	0.0261742
$653$	5.39109	0.210970	0.105485	−	0.994421i	$-0.466361\pi$
$653$	5.39109	0.210970	0.105485	+	0.994421i	$0.466361\pi$
$654$	32.3181	1.26374
$655$	23.0242	0.899628
$656$	−144.020	−5.62304
$657$	−18.1680	−0.708800
$658$	−72.1036	−2.81089
$659$	19.7824	0.770614	0.385307	−	0.922789i	$-0.374096\pi$
$659$	19.7824	0.770614	0.385307	+	0.922789i	$0.374096\pi$
$660$	10.6686	0.415274
$661$	16.2507	0.632080	0.316040	−	0.948746i	$-0.397647\pi$
$661$	16.2507	0.632080	0.316040	+	0.948746i	$0.397647\pi$
$662$	−12.4728	−0.484770
$663$	7.23160	0.280852
$664$	65.7177	2.55034
$665$	−46.7699	−1.81366
$666$	1.80391	0.0699003
$667$	34.3446	1.32983
$668$	28.2424	1.09273
$669$	−20.9327	−0.809306
$670$	−45.3018	−1.75016
$671$	−6.53565	−0.252306
$672$	−171.299	−6.60801
$673$	0.908069	0.0350035	0.0175017	−	0.999847i	$-0.494429\pi$
$673$	0.908069	0.0350035	0.0175017	+	0.999847i	$0.494429\pi$
$674$	−68.6295	−2.64351
$675$	−7.57517	−0.291569
$676$	−51.5787	−1.98380
$677$	−50.2097	−1.92972	−0.964858	−	0.262773i	$-0.915363\pi$
$677$	−50.2097	−1.92972	−0.964858	+	0.262773i	$0.915363\pi$
$678$	−108.283	−4.15860
$679$	46.5512	1.78647
$680$	−29.5420	−1.13288
$681$	21.3639	0.818665
$682$	−2.84671	−0.109006
$683$	−35.5647	−1.36085	−0.680423	−	0.732819i	$-0.738204\pi$
$683$	−35.5647	−1.36085	−0.680423	+	0.732819i	$0.738204\pi$
$684$	−37.2255	−1.42335
$685$	−0.207718	−0.00793649
$686$	105.583	4.03118
$687$	41.4851	1.58275
$688$	−117.927	−4.49593
$689$	−22.3538	−0.851611
$690$	−60.6590	−2.30925
$691$	−1.04904	−0.0399073	−0.0199537	−	0.999801i	$-0.506352\pi$
$691$	−1.04904	−0.0399073	−0.0199537	+	0.999801i	$0.506352\pi$
$692$	11.6312	0.442152
$693$	−3.34464	−0.127052
$694$	42.8407	1.62621
$695$	37.2581	1.41328
$696$	96.3232	3.65112
$697$	21.7940	0.825507
$698$	27.3908	1.03676
$699$	9.73323	0.368144
$700$	51.4581	1.94493
$701$	45.4042	1.71489	0.857446	−	0.514575i	$-0.172050\pi$
$701$	45.4042	1.71489	0.857446	+	0.514575i	$0.172050\pi$
$702$	−17.5011	−0.660536
$703$	3.16857	0.119505
$704$	12.3804	0.466606
$705$	−19.9308	−0.750639
$706$	−17.5057	−0.658837
$707$	−75.1345	−2.82572
$708$	7.30879	0.274681
$709$	12.9762	0.487330	0.243665	−	0.969860i	$-0.421650\pi$
$709$	12.9762	0.487330	0.243665	+	0.969860i	$0.421650\pi$
$710$	18.9747	0.712107
$711$	21.2371	0.796455
$712$	−25.8913	−0.970316
$713$	11.7199	0.438916
$714$	51.6188	1.93178
$715$	−1.76158	−0.0658794
$716$	−7.98030	−0.298238
$717$	1.22556	0.0457694
$718$	−17.3634	−0.647998
$719$	−43.7474	−1.63150	−0.815751	−	0.578403i	$-0.803676\pi$
$719$	−43.7474	−1.63150	−0.815751	+	0.578403i	$0.803676\pi$
$720$	−27.3323	−1.01861
$721$	50.3329	1.87450
$722$	−39.1469	−1.45690
$723$	38.2815	1.42370
$724$	16.5515	0.615133
$725$	−11.1223	−0.413070
$726$	−59.0214	−2.19049
$727$	−0.0657597	−0.00243889	−0.00121945	−	0.999999i	$-0.500388\pi$
$727$	−0.0657597	−0.00243889	−0.00121945	+	0.999999i	$0.500388\pi$
$728$	73.5848	2.72723
$729$	8.81679	0.326548
$730$	−68.3019	−2.52797
$731$	17.8454	0.660038
$732$	121.922	4.50636
$733$	−15.5308	−0.573642	−0.286821	−	0.957984i	$-0.592599\pi$
$733$	−15.5308	−0.573642	−0.286821	+	0.957984i	$0.592599\pi$
$734$	−39.5092	−1.45831
$735$	53.7882	1.98401
$736$	−113.122	−4.16972
$737$	−5.69046	−0.209611
$738$	36.3813	1.33921
$739$	−46.1650	−1.69821	−0.849104	−	0.528226i	$-0.822857\pi$
$739$	−46.1650	−1.69821	−0.849104	+	0.528226i	$0.822857\pi$
$740$	4.91061	0.180518
$741$	21.2043	0.778959
$742$	−159.560	−5.85763
$743$	−24.0093	−0.880816	−0.440408	−	0.897798i	$-0.645166\pi$
$743$	−24.0093	−0.880816	−0.440408	+	0.897798i	$0.645166\pi$
$744$	32.8698	1.20507
$745$	35.3816	1.29628
$746$	−17.6210	−0.645152
$747$	−9.20095	−0.336645
$748$	−5.99528	−0.219209
$749$	−69.4644	−2.53818
$750$	66.9582	2.44497
$751$	12.5415	0.457647	0.228824	−	0.973468i	$-0.426512\pi$
$751$	12.5415	0.457647	0.228824	+	0.973468i	$0.426512\pi$
$752$	−74.0142	−2.69902
$753$	−38.3071	−1.39599
$754$	−25.6960	−0.935794
$755$	41.9451	1.52654
$756$	−90.4547	−3.28981
$757$	0.0201753	0.000733283 0	0.000366641	−	1.00000i	$-0.499883\pi$
$757$	0.0201753	0.000733283 0	0.000366641		1.00000i	$0.499883\pi$
$758$	−10.7271	−0.389624
$759$	−7.61950	−0.276570
$760$	−86.6221	−3.14211
$761$	−22.4268	−0.812973	−0.406486	−	0.913657i	$-0.633246\pi$
$761$	−22.4268	−0.812973	−0.406486	+	0.913657i	$0.633246\pi$
$762$	−7.41416	−0.268587
$763$	−27.5809	−0.998495
$764$	34.5317	1.24931
$765$	4.13609	0.149541
$766$	−8.97341	−0.324222
$767$	−1.20682	−0.0435757
$768$	−35.6438	−1.28618
$769$	28.2006	1.01694	0.508471	−	0.861079i	$-0.330211\pi$
$769$	28.2006	1.01694	0.508471	+	0.861079i	$0.330211\pi$
$770$	−12.5741	−0.453138
$771$	19.4210	0.699431
$772$	−28.2570	−1.01699
$773$	−23.6421	−0.850347	−0.425174	−	0.905112i	$-0.639787\pi$
$773$	−23.6421	−0.850347	−0.425174	+	0.905112i	$0.639787\pi$
$774$	29.7899	1.07077
$775$	−3.79542	−0.136335
$776$	86.2170	3.09501
$777$	−5.31086	−0.190526
$778$	37.0337	1.32772
$779$	63.9037	2.28959
$780$	32.8621	1.17665
$781$	2.38345	0.0852864
$782$	34.0878	1.21898
$783$	19.5511	0.698698
$784$	199.745	7.13375
$785$	21.3419	0.761726
$786$	−74.5099	−2.65768
$787$	−23.1845	−0.826439	−0.413220	−	0.910631i	$-0.635596\pi$
$787$	−23.1845	−0.826439	−0.413220	+	0.910631i	$0.635596\pi$
$788$	82.0254	2.92203
$789$	−33.8938	−1.20665
$790$	79.8403	2.84059
$791$	92.4112	3.28576
$792$	−6.19458	−0.220115
$793$	−20.1316	−0.714893
$794$	−45.0137	−1.59748
$795$	−44.1055	−1.56426
$796$	−61.1221	−2.16642
$797$	36.2418	1.28375	0.641875	−	0.766809i	$-0.278157\pi$
$797$	36.2418	1.28375	0.641875	+	0.766809i	$0.278157\pi$
$798$	151.355	5.35791
$799$	11.2003	0.396237
$800$	36.6336	1.29519
$801$	3.62496	0.128082
$802$	−55.9263	−1.97483
$803$	−8.57954	−0.302766
$804$	106.155	3.74379
$805$	51.7676	1.82457
$806$	−8.76864	−0.308862
$807$	35.0676	1.23444
$808$	−139.156	−4.89549
$809$	−27.9988	−0.984387	−0.492193	−	0.870486i	$-0.663805\pi$
$809$	−27.9988	−0.984387	−0.492193	+	0.870486i	$0.663805\pi$
$810$	−51.4450	−1.80759
$811$	32.8693	1.15420	0.577099	−	0.816674i	$-0.304185\pi$
$811$	32.8693	1.15420	0.577099	+	0.816674i	$0.304185\pi$
$812$	−132.810	−4.66073
$813$	−6.42309	−0.225268
$814$	0.851870	0.0298580
$815$	−0.217738	−0.00762705
$816$	52.9865	1.85490
$817$	52.3258	1.83065
$818$	−19.0691	−0.666736
$819$	−10.3024	−0.359995
$820$	99.0371	3.45852
$821$	−3.48419	−0.121599	−0.0607995	−	0.998150i	$-0.519365\pi$
$821$	−3.48419	−0.121599	−0.0607995	+	0.998150i	$0.519365\pi$
$822$	0.672209	0.0234460
$823$	4.89726	0.170708	0.0853538	−	0.996351i	$-0.472798\pi$
$823$	4.89726	0.170708	0.0853538	+	0.996351i	$0.472798\pi$
$824$	93.2212	3.24751
$825$	2.46752	0.0859080
$826$	−8.61421	−0.299727
$827$	−19.9188	−0.692646	−0.346323	−	0.938115i	$-0.612570\pi$
$827$	−19.9188	−0.692646	−0.346323	+	0.938115i	$0.612570\pi$
$828$	41.2034	1.43192
$829$	3.49550	0.121404	0.0607018	−	0.998156i	$-0.480666\pi$
$829$	3.49550	0.121404	0.0607018	+	0.998156i	$0.480666\pi$
$830$	−34.5907	−1.20066
$831$	60.3210	2.09251
$832$	38.1351	1.32210
$833$	−30.2267	−1.04729
$834$	−120.573	−4.17511
$835$	−9.20109	−0.318417
$836$	−17.5792	−0.607989
$837$	6.67171	0.230608
$838$	43.0533	1.48725
$839$	24.9867	0.862637	0.431318	−	0.902200i	$-0.358049\pi$
$839$	24.9867	0.862637	0.431318	+	0.902200i	$0.358049\pi$
$840$	145.188	5.00945
$841$	−0.294097	−0.0101413
$842$	−24.2123	−0.834409
$843$	23.1962	0.798919
$844$	92.9019	3.19782
$845$	16.8038	0.578069
$846$	18.6969	0.642813
$847$	50.3701	1.73074
$848$	−163.788	−5.62450
$849$	−2.77351	−0.0951867
$850$	−11.0391	−0.378637
$851$	−3.50716	−0.120224
$852$	−44.4629	−1.52327
$853$	45.2249	1.54847	0.774235	−	0.632898i	$-0.218135\pi$
$853$	45.2249	1.54847	0.774235	+	0.632898i	$0.218135\pi$
$854$	−143.698	−4.91724
$855$	12.1277	0.414759
$856$	−128.655	−4.39732
$857$	−11.6029	−0.396348	−0.198174	−	0.980167i	$-0.563501\pi$
$857$	−11.6029	−0.396348	−0.198174	+	0.980167i	$0.563501\pi$
$858$	5.70077	0.194621
$859$	−16.7338	−0.570949	−0.285475	−	0.958386i	$-0.592151\pi$
$859$	−16.7338	−0.570949	−0.285475	+	0.958386i	$0.592151\pi$
$860$	81.0938	2.76528
$861$	−107.109	−3.65027
$862$	22.2265	0.757039
$863$	−29.7197	−1.01167	−0.505835	−	0.862630i	$-0.668816\pi$
$863$	−29.7197	−1.01167	−0.505835	+	0.862630i	$0.668816\pi$
$864$	−64.3958	−2.19079
$865$	−3.78933	−0.128841
$866$	−105.566	−3.58727
$867$	26.9234	0.914365
$868$	−45.3209	−1.53829
$869$	10.0289	0.340207
$870$	−50.6999	−1.71889
$871$	−17.5281	−0.593919
$872$	−51.0823	−1.72987
$873$	−12.0710	−0.408542
$874$	99.9511	3.38090
$875$	−57.1435	−1.93180
$876$	160.050	5.40760
$877$	4.79304	0.161849	0.0809247	−	0.996720i	$-0.474213\pi$
$877$	4.79304	0.161849	0.0809247	+	0.996720i	$0.474213\pi$
$878$	77.9460	2.63055
$879$	54.0901	1.82441
$880$	−12.9073	−0.435103
$881$	−2.35815	−0.0794480	−0.0397240	−	0.999211i	$-0.512648\pi$
$881$	−2.35815	−0.0794480	−0.0397240	+	0.999211i	$0.512648\pi$
$882$	−50.4581	−1.69901
$883$	51.3123	1.72680	0.863398	−	0.504524i	$-0.168332\pi$
$883$	51.3123	1.72680	0.863398	+	0.504524i	$0.168332\pi$
$884$	−18.4671	−0.621115
$885$	−2.38113	−0.0800409
$886$	−53.1948	−1.78711
$887$	22.9074	0.769154	0.384577	−	0.923093i	$-0.374347\pi$
$887$	22.9074	0.769154	0.384577	+	0.923093i	$0.374347\pi$
$888$	−9.83620	−0.330081
$889$	6.32739	0.212214
$890$	13.6279	0.456809
$891$	−6.46211	−0.216489
$892$	53.4551	1.78981
$893$	32.8411	1.09899
$894$	−114.501	−3.82947
$895$	2.59990	0.0869052
$896$	105.523	3.52528
$897$	−23.4701	−0.783644
$898$	−2.00113	−0.0667786
$899$	9.79575	0.326707
$900$	−13.3434	−0.444780
$901$	24.7854	0.825721
$902$	17.1805	0.572048
$903$	−87.7035	−2.91859
$904$	171.154	5.69250
$905$	−5.39233	−0.179247
$906$	−135.741	−4.50969
$907$	20.9862	0.696836	0.348418	−	0.937339i	$-0.386719\pi$
$907$	20.9862	0.696836	0.348418	+	0.937339i	$0.386719\pi$
$908$	−54.5561	−1.81051
$909$	19.4828	0.646205
$910$	−38.7315	−1.28394
$911$	−10.0426	−0.332725	−0.166363	−	0.986065i	$-0.553202\pi$
$911$	−10.0426	−0.332725	−0.166363	+	0.986065i	$0.553202\pi$
$912$	155.365	5.14466
$913$	−4.34500	−0.143799
$914$	55.0889	1.82218
$915$	−39.7209	−1.31313
$916$	−105.939	−3.50032
$917$	63.5882	2.09987
$918$	19.4048	0.640455
$919$	38.5260	1.27085	0.635427	−	0.772161i	$-0.280824\pi$
$919$	38.5260	1.27085	0.635427	+	0.772161i	$0.280824\pi$
$920$	95.8783	3.16101
$921$	41.4287	1.36512
$922$	−36.0353	−1.18676
$923$	7.34166	0.241654
$924$	29.4645	0.969312
$925$	1.13577	0.0373438
$926$	−4.30294	−0.141404
$927$	−13.0516	−0.428672
$928$	−94.5493	−3.10373
$929$	6.36258	0.208750	0.104375	−	0.994538i	$-0.466716\pi$
$929$	6.36258	0.208750	0.104375	+	0.994538i	$0.466716\pi$
$930$	−17.3011	−0.567326
$931$	−88.6297	−2.90472
$932$	−24.8554	−0.814165
$933$	−36.2236	−1.18591
$934$	−58.3915	−1.91063
$935$	1.95320	0.0638766
$936$	−19.0810	−0.623682
$937$	−29.1861	−0.953469	−0.476735	−	0.879047i	$-0.658180\pi$
$937$	−29.1861	−0.953469	−0.476735	+	0.879047i	$0.658180\pi$
$938$	−125.115	−4.08515
$939$	−8.06247	−0.263109
$940$	50.8967	1.66007
$941$	−54.3532	−1.77187	−0.885933	−	0.463814i	$-0.846481\pi$
$941$	−54.3532	−1.77187	−0.885933	+	0.463814i	$0.846481\pi$
$942$	−69.0659	−2.25029
$943$	−70.7323	−2.30336
$944$	−8.84246	−0.287798
$945$	29.4693	0.958636
$946$	14.0678	0.457383
$947$	22.9919	0.747136	0.373568	−	0.927603i	$-0.378134\pi$
$947$	22.9919	0.747136	0.373568	+	0.927603i	$0.378134\pi$
$948$	−187.088	−6.07633
$949$	−26.4273	−0.857867
$950$	−32.3684	−1.05017
$951$	−48.3799	−1.56883
$952$	−81.5892	−2.64432
$953$	15.6555	0.507131	0.253565	−	0.967318i	$-0.418397\pi$
$953$	15.6555	0.507131	0.253565	+	0.967318i	$0.418397\pi$
$954$	41.3749	1.33956
$955$	−11.2501	−0.364044
$956$	−3.12967	−0.101221
$957$	−6.36852	−0.205865
$958$	−37.0410	−1.19674
$959$	−0.573676	−0.0185250
$960$	75.2431	2.42846
$961$	−27.6572	−0.892169
$962$	2.62399	0.0846008
$963$	18.0126	0.580447
$964$	−97.7580	−3.14857
$965$	9.20584	0.296347
$966$	−167.528	−5.39014
$967$	−8.70840	−0.280043	−0.140022	−	0.990148i	$-0.544717\pi$
$967$	−8.70840	−0.280043	−0.140022	+	0.990148i	$0.544717\pi$
$968$	93.2900	2.99845
$969$	−23.5109	−0.755278
$970$	−45.3805	−1.45708
$971$	−0.335714	−0.0107736	−0.00538679	−	0.999985i	$-0.501715\pi$
$971$	−0.335714	−0.0107736	−0.00538679	+	0.999985i	$0.501715\pi$
$972$	63.0901	2.02361
$973$	102.900	3.29881
$974$	−71.7612	−2.29938
$975$	7.60063	0.243415
$976$	−147.506	−4.72154
$977$	−8.29608	−0.265415	−0.132708	−	0.991155i	$-0.542367\pi$
$977$	−8.29608	−0.265415	−0.132708	+	0.991155i	$0.542367\pi$
$978$	0.704637	0.0225318
$979$	1.71183	0.0547104
$980$	−137.357	−4.38771
$981$	7.15189	0.228342
$982$	37.6402	1.20115
$983$	21.6362	0.690089	0.345044	−	0.938586i	$-0.387864\pi$
$983$	21.6362	0.690089	0.345044	+	0.938586i	$0.387864\pi$
$984$	−198.376	−6.32400
$985$	−26.7231	−0.851468
$986$	28.4912	0.907344
$987$	−55.0451	−1.75211
$988$	−54.1486	−1.72270
$989$	−57.9173	−1.84166
$990$	3.26053	0.103627
$991$	−31.7353	−1.00810	−0.504052	−	0.863673i	$-0.668158\pi$
$991$	−31.7353	−1.00810	−0.504052	+	0.863673i	$0.668158\pi$
$992$	−32.2645	−1.02440
$993$	−9.52196	−0.302170
$994$	52.4043	1.66216
$995$	19.9130	0.631284
$996$	81.0555	2.56834
$997$	−7.24691	−0.229512	−0.114756	−	0.993394i	$-0.536609\pi$
$997$	−7.24691	−0.229512	−0.114756	+	0.993394i	$0.536609\pi$
$998$	−50.0541	−1.58443
$999$	−1.99649	−0.0631661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4021.2.a.c.1.4	✓	182

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4021.2.a.c.1.4	✓	182	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:	\( N \)	\(=\)	\( 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69235 q^{2} -2.05539 q^{3} +5.24877 q^{4} -1.71000 q^{5} +5.53383 q^{6} -4.72268 q^{7} -8.74684 q^{8} +1.22462 q^{9} +O(q^{10})\)	\(q-2.69235 q^{2} -2.05539 q^{3} +5.24877 q^{4} -1.71000 q^{5} +5.53383 q^{6} -4.72268 q^{7} -8.74684 q^{8} +1.22462 q^{9} +4.60392 q^{10} +0.578308 q^{11} -10.7883 q^{12} +1.78134 q^{13} +12.7151 q^{14} +3.51471 q^{15} +13.0521 q^{16} -1.97512 q^{17} -3.29711 q^{18} -5.79138 q^{19} -8.97539 q^{20} +9.70695 q^{21} -1.55701 q^{22} +6.41023 q^{23} +17.9782 q^{24} -2.07591 q^{25} -4.79601 q^{26} +3.64909 q^{27} -24.7883 q^{28} +5.35779 q^{29} -9.46285 q^{30} +1.82832 q^{31} -17.6471 q^{32} -1.18865 q^{33} +5.31771 q^{34} +8.07578 q^{35} +6.42775 q^{36} -0.547119 q^{37} +15.5924 q^{38} -3.66135 q^{39} +14.9571 q^{40} -11.0343 q^{41} -26.1345 q^{42} -9.03513 q^{43} +3.03541 q^{44} -2.09410 q^{45} -17.2586 q^{46} -5.67069 q^{47} -26.8270 q^{48} +15.3037 q^{49} +5.58907 q^{50} +4.05963 q^{51} +9.34987 q^{52} -12.5488 q^{53} -9.82465 q^{54} -0.988906 q^{55} +41.3086 q^{56} +11.9035 q^{57} -14.4251 q^{58} -0.677477 q^{59} +18.4479 q^{60} -11.3013 q^{61} -4.92249 q^{62} -5.78350 q^{63} +21.4080 q^{64} -3.04610 q^{65} +3.20026 q^{66} -9.83984 q^{67} -10.3669 q^{68} -13.1755 q^{69} -21.7429 q^{70} +4.12141 q^{71} -10.7116 q^{72} -14.8356 q^{73} +1.47304 q^{74} +4.26679 q^{75} -30.3976 q^{76} -2.73117 q^{77} +9.85766 q^{78} +17.3418 q^{79} -22.3190 q^{80} -11.1742 q^{81} +29.7082 q^{82} -7.51330 q^{83} +50.9495 q^{84} +3.37745 q^{85} +24.3258 q^{86} -11.0123 q^{87} -5.05837 q^{88} +2.96007 q^{89} +5.63806 q^{90} -8.41273 q^{91} +33.6458 q^{92} -3.75791 q^{93} +15.2675 q^{94} +9.90324 q^{95} +36.2716 q^{96} -9.85693 q^{97} -41.2031 q^{98} +0.708208 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9}+O(q^{10}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9	\( 182 q + 18 q^{2} + 28 q^{3} + 208 q^{4} + 22 q^{5} + 18 q^{6} + 14 q^{7} + 54 q^{8} + 238 q^{9} + 7 q^{10} + 138 q^{11} + 47 q^{12} + 5 q^{13} + 72 q^{14} + 41 q^{15} + 256 q^{16} + 29 q^{17} + 35 q^{18} + 48 q^{19} + 56 q^{20} + 22 q^{21} + 19 q^{22} + 91 q^{23} + 46 q^{24} + 230 q^{25} + 88 q^{26} + 103 q^{27} + 15 q^{28} + 75 q^{29} + 18 q^{30} + 43 q^{31} + 116 q^{32} + 15 q^{33} + 13 q^{34} + 185 q^{35} + 364 q^{36} + 15 q^{37} + 53 q^{38} + 80 q^{39} - 13 q^{40} + 68 q^{41} + 32 q^{42} + 82 q^{43} + 259 q^{44} + 37 q^{45} + 13 q^{46} + 121 q^{47} + 53 q^{48} + 244 q^{49} + 93 q^{50} + 144 q^{51} - 16 q^{52} + 101 q^{53} + 47 q^{54} + 49 q^{55} + 199 q^{56} + 3 q^{57} + 4 q^{58} + 254 q^{59} + 24 q^{60} + 8 q^{61} + 37 q^{62} + 19 q^{63} + 326 q^{64} + 65 q^{65} + 41 q^{66} + 91 q^{67} + 50 q^{68} + 50 q^{69} + 5 q^{70} + 212 q^{71} + 77 q^{72} + 5 q^{73} + 101 q^{74} + 127 q^{75} + 22 q^{76} + 87 q^{77} - 20 q^{78} + 86 q^{79} + 71 q^{80} + 358 q^{81} - 20 q^{82} + 139 q^{83} - 30 q^{84} + 25 q^{85} + 82 q^{86} + 36 q^{87} - 8 q^{88} + 100 q^{89} - 87 q^{90} + 74 q^{91} + 171 q^{92} + 50 q^{93} - 13 q^{94} + 217 q^{95} + 42 q^{96} + 20 q^{97} + 47 q^{98} + 389 q^{99}+O(q^{100}) \) 182 * q + 18 * q^2 + 28 * q^3 + 208 * q^4 + 22 * q^5 + 18 * q^6 + 14 * q^7 + 54 * q^8 + 238 * q^9 + 7 * q^10 + 138 * q^11 + 47 * q^12 + 5 * q^13 + 72 * q^14 + 41 * q^15 + 256 * q^16 + 29 * q^17 + 35 * q^18 + 48 * q^19 + 56 * q^20 + 22 * q^21 + 19 * q^22 + 91 * q^23 + 46 * q^24 + 230 * q^25 + 88 * q^26 + 103 * q^27 + 15 * q^28 + 75 * q^29 + 18 * q^30 + 43 * q^31 + 116 * q^32 + 15 * q^33 + 13 * q^34 + 185 * q^35 + 364 * q^36 + 15 * q^37 + 53 * q^38 + 80 * q^39 - 13 * q^40 + 68 * q^41 + 32 * q^42 + 82 * q^43 + 259 * q^44 + 37 * q^45 + 13 * q^46 + 121 * q^47 + 53 * q^48 + 244 * q^49 + 93 * q^50 + 144 * q^51 - 16 * q^52 + 101 * q^53 + 47 * q^54 + 49 * q^55 + 199 * q^56 + 3 * q^57 + 4 * q^58 + 254 * q^59 + 24 * q^60 + 8 * q^61 + 37 * q^62 + 19 * q^63 + 326 * q^64 + 65 * q^65 + 41 * q^66 + 91 * q^67 + 50 * q^68 + 50 * q^69 + 5 * q^70 + 212 * q^71 + 77 * q^72 + 5 * q^73 + 101 * q^74 + 127 * q^75 + 22 * q^76 + 87 * q^77 - 20 * q^78 + 86 * q^79 + 71 * q^80 + 358 * q^81 - 20 * q^82 + 139 * q^83 - 30 * q^84 + 25 * q^85 + 82 * q^86 + 36 * q^87 - 8 * q^88 + 100 * q^89 - 87 * q^90 + 74 * q^91 + 171 * q^92 + 50 * q^93 - 13 * q^94 + 217 * q^95 + 42 * q^96 + 20 * q^97 + 47 * q^98 + 389 * q^99

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