LMFDB - Embedded newform 8027.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54629 q^{2} -1.60651 q^{3} +4.48361 q^{4} -2.62778 q^{5} +4.09064 q^{6} +1.52719 q^{7} -6.32399 q^{8} -0.419134 q^{9} +O(q^{10})$	\(q-2.54629 q^{2} -1.60651 q^{3} +4.48361 q^{4} -2.62778 q^{5} +4.09064 q^{6} +1.52719 q^{7} -6.32399 q^{8} -0.419134 q^{9} +6.69110 q^{10} +5.10899 q^{11} -7.20295 q^{12} -1.33779 q^{13} -3.88867 q^{14} +4.22155 q^{15} +7.13553 q^{16} +8.04275 q^{17} +1.06724 q^{18} +1.96955 q^{19} -11.7819 q^{20} -2.45344 q^{21} -13.0090 q^{22} -1.00000 q^{23} +10.1595 q^{24} +1.90523 q^{25} +3.40640 q^{26} +5.49286 q^{27} +6.84731 q^{28} -1.53961 q^{29} -10.7493 q^{30} -0.387715 q^{31} -5.52115 q^{32} -8.20763 q^{33} -20.4792 q^{34} -4.01311 q^{35} -1.87923 q^{36} -2.04595 q^{37} -5.01506 q^{38} +2.14917 q^{39} +16.6181 q^{40} +4.23437 q^{41} +6.24717 q^{42} +3.28050 q^{43} +22.9067 q^{44} +1.10139 q^{45} +2.54629 q^{46} -11.3962 q^{47} -11.4633 q^{48} -4.66770 q^{49} -4.85127 q^{50} -12.9207 q^{51} -5.99812 q^{52} -6.27772 q^{53} -13.9864 q^{54} -13.4253 q^{55} -9.65793 q^{56} -3.16410 q^{57} +3.92029 q^{58} +10.4129 q^{59} +18.9278 q^{60} -1.99373 q^{61} +0.987236 q^{62} -0.640096 q^{63} -0.212579 q^{64} +3.51542 q^{65} +20.8990 q^{66} -5.26560 q^{67} +36.0605 q^{68} +1.60651 q^{69} +10.2186 q^{70} -1.29235 q^{71} +2.65060 q^{72} -7.26158 q^{73} +5.20959 q^{74} -3.06076 q^{75} +8.83071 q^{76} +7.80239 q^{77} -5.47241 q^{78} -0.403796 q^{79} -18.7506 q^{80} -7.56692 q^{81} -10.7820 q^{82} -0.356139 q^{83} -11.0003 q^{84} -21.1346 q^{85} -8.35311 q^{86} +2.47339 q^{87} -32.3092 q^{88} -9.46136 q^{89} -2.80447 q^{90} -2.04306 q^{91} -4.48361 q^{92} +0.622867 q^{93} +29.0181 q^{94} -5.17555 q^{95} +8.86977 q^{96} -4.67822 q^{97} +11.8853 q^{98} -2.14135 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) $ 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * 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 $

$2$	−2.54629	−1.80050	−0.900251	−	0.435372i	$-0.856617\pi$
$2$	−2.54629	−1.80050	−0.900251	+	0.435372i	$0.856617\pi$
$3$	−1.60651	−0.927517	−0.463759	−	0.885962i	$-0.653500\pi$
$3$	−1.60651	−0.927517	−0.463759	+	0.885962i	$0.653500\pi$
$4$	4.48361	2.24180
$5$	−2.62778	−1.17518	−0.587590	−	0.809159i	$-0.699923\pi$
$5$	−2.62778	−1.17518	−0.587590	+	0.809159i	$0.699923\pi$
$6$	4.09064	1.67000
$7$	1.52719	0.577223	0.288611	−	0.957446i	$-0.406806\pi$
$7$	1.52719	0.577223	0.288611	+	0.957446i	$0.406806\pi$
$8$	−6.32399	−2.23587
$9$	−0.419134	−0.139711
$10$	6.69110	2.11591
$11$	5.10899	1.54042	0.770209	−	0.637791i	$-0.220152\pi$
$11$	5.10899	1.54042	0.770209	+	0.637791i	$0.220152\pi$
$12$	−7.20295	−2.07931
$13$	−1.33779	−0.371036	−0.185518	−	0.982641i	$-0.559396\pi$
$13$	−1.33779	−0.371036	−0.185518	+	0.982641i	$0.559396\pi$
$14$	−3.88867	−1.03929
$15$	4.22155	1.09000
$16$	7.13553	1.78388
$17$	8.04275	1.95065	0.975326	−	0.220768i	$-0.0708563\pi$
$17$	8.04275	1.95065	0.975326	+	0.220768i	$0.0708563\pi$
$18$	1.06724	0.251550
$19$	1.96955	0.451847	0.225923	−	0.974145i	$-0.427460\pi$
$19$	1.96955	0.451847	0.225923	+	0.974145i	$0.427460\pi$
$20$	−11.7819	−2.63452
$21$	−2.45344	−0.535384
$22$	−13.0090	−2.77353
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	10.1595	2.07381
$25$	1.90523	0.381046
$26$	3.40640	0.668051
$27$	5.49286	1.05710
$28$	6.84731	1.29402
$29$	−1.53961	−0.285898	−0.142949	−	0.989730i	$-0.545658\pi$
$29$	−1.53961	−0.285898	−0.142949	+	0.989730i	$0.545658\pi$
$30$	−10.7493	−1.96254
$31$	−0.387715	−0.0696357	−0.0348178	−	0.999394i	$-0.511085\pi$
$31$	−0.387715	−0.0696357	−0.0348178	+	0.999394i	$0.511085\pi$
$32$	−5.52115	−0.976011
$33$	−8.20763	−1.42877
$34$	−20.4792	−3.51215
$35$	−4.01311	−0.678340
$36$	−1.87923	−0.313205
$37$	−2.04595	−0.336353	−0.168176	−	0.985757i	$-0.553788\pi$
$37$	−2.04595	−0.336353	−0.168176	+	0.985757i	$0.553788\pi$
$38$	−5.01506	−0.813550
$39$	2.14917	0.344142
$40$	16.6181	2.62755
$41$	4.23437	0.661298	0.330649	−	0.943754i	$-0.392732\pi$
$41$	4.23437	0.661298	0.330649	+	0.943754i	$0.392732\pi$
$42$	6.24717	0.963960
$43$	3.28050	0.500272	0.250136	−	0.968211i	$-0.419525\pi$
$43$	3.28050	0.500272	0.250136	+	0.968211i	$0.419525\pi$
$44$	22.9067	3.45332
$45$	1.10139	0.164186
$46$	2.54629	0.375430
$47$	−11.3962	−1.66231	−0.831155	−	0.556040i	$-0.812320\pi$
$47$	−11.3962	−1.66231	−0.831155	+	0.556040i	$0.812320\pi$
$48$	−11.4633	−1.65458
$49$	−4.66770	−0.666814
$50$	−4.85127	−0.686073
$51$	−12.9207	−1.80926
$52$	−5.99812	−0.831790
$53$	−6.27772	−0.862311	−0.431156	−	0.902278i	$-0.641894\pi$
$53$	−6.27772	−0.862311	−0.431156	+	0.902278i	$0.641894\pi$
$54$	−13.9864	−1.90331
$55$	−13.4253	−1.81027
$56$	−9.65793	−1.29059
$57$	−3.16410	−0.419096
$58$	3.92029	0.514759
$59$	10.4129	1.35564	0.677822	−	0.735226i	$-0.262924\pi$
$59$	10.4129	1.35564	0.677822	+	0.735226i	$0.262924\pi$
$60$	18.9278	2.44356
$61$	−1.99373	−0.255272	−0.127636	−	0.991821i	$-0.540739\pi$
$61$	−1.99373	−0.255272	−0.127636	+	0.991821i	$0.540739\pi$
$62$	0.987236	0.125379
$63$	−0.640096	−0.0806446
$64$	−0.212579	−0.0265724
$65$	3.51542	0.436034
$66$	20.8990	2.57249
$67$	−5.26560	−0.643295	−0.321647	−	0.946860i	$-0.604237\pi$
$67$	−5.26560	−0.643295	−0.321647	+	0.946860i	$0.604237\pi$
$68$	36.0605	4.37298
$69$	1.60651	0.193401
$70$	10.2186	1.22135
$71$	−1.29235	−0.153374	−0.0766871	−	0.997055i	$-0.524434\pi$
$71$	−1.29235	−0.153374	−0.0766871	+	0.997055i	$0.524434\pi$
$72$	2.65060	0.312376
$73$	−7.26158	−0.849903	−0.424952	−	0.905216i	$-0.639709\pi$
$73$	−7.26158	−0.849903	−0.424952	+	0.905216i	$0.639709\pi$
$74$	5.20959	0.605603
$75$	−3.06076	−0.353427
$76$	8.83071	1.01295
$77$	7.80239	0.889165
$78$	−5.47241	−0.619629
$79$	−0.403796	−0.0454306	−0.0227153	−	0.999742i	$-0.507231\pi$
$79$	−0.403796	−0.0454306	−0.0227153	+	0.999742i	$0.507231\pi$
$80$	−18.7506	−2.09638
$81$	−7.56692	−0.840769
$82$	−10.7820	−1.19067
$83$	−0.356139	−0.0390913	−0.0195457	−	0.999809i	$-0.506222\pi$
$83$	−0.356139	−0.0390913	−0.0195457	+	0.999809i	$0.506222\pi$
$84$	−11.0003	−1.20023
$85$	−21.1346	−2.29237
$86$	−8.35311	−0.900739
$87$	2.47339	0.265175
$88$	−32.3092	−3.44418
$89$	−9.46136	−1.00290	−0.501451	−	0.865186i	$-0.667200\pi$
$89$	−9.46136	−1.00290	−0.501451	+	0.865186i	$0.667200\pi$
$90$	−2.80447	−0.295617
$91$	−2.04306	−0.214170
$92$	−4.48361	−0.467448
$93$	0.622867	0.0645883
$94$	29.0181	2.99299
$95$	−5.17555	−0.531001
$96$	8.86977	0.905267
$97$	−4.67822	−0.475002	−0.237501	−	0.971387i	$-0.576328\pi$
$97$	−4.67822	−0.475002	−0.237501	+	0.971387i	$0.576328\pi$
$98$	11.8853	1.20060
$99$	−2.14135	−0.215214
$100$	8.54230	0.854230
$101$	6.08076	0.605058	0.302529	−	0.953140i	$-0.402169\pi$
$101$	6.08076	0.605058	0.302529	+	0.953140i	$0.402169\pi$
$102$	32.9000	3.25758
$103$	−14.6581	−1.44430	−0.722151	−	0.691736i	$-0.756846\pi$
$103$	−14.6581	−1.44430	−0.722151	+	0.691736i	$0.756846\pi$
$104$	8.46017	0.829588
$105$	6.44710	0.629172
$106$	15.9849	1.55259
$107$	−7.37667	−0.713130	−0.356565	−	0.934271i	$-0.616052\pi$
$107$	−7.37667	−0.713130	−0.356565	+	0.934271i	$0.616052\pi$
$108$	24.6279	2.36982
$109$	11.8779	1.13770	0.568849	−	0.822442i	$-0.307389\pi$
$109$	11.8779	1.13770	0.568849	+	0.822442i	$0.307389\pi$
$110$	34.1848	3.25939
$111$	3.28684	0.311973
$112$	10.8973	1.02970
$113$	9.75422	0.917600	0.458800	−	0.888540i	$-0.348279\pi$
$113$	9.75422	0.917600	0.458800	+	0.888540i	$0.348279\pi$
$114$	8.05673	0.754582
$115$	2.62778	0.245042
$116$	−6.90299	−0.640926
$117$	0.560713	0.0518379
$118$	−26.5143	−2.44084
$119$	12.2828	1.12596
$120$	−26.6970	−2.43710
$121$	15.1018	1.37289
$122$	5.07663	0.459617
$123$	−6.80255	−0.613366
$124$	−1.73836	−0.156110
$125$	8.13238	0.727382
$126$	1.62987	0.145201
$127$	−5.79595	−0.514308	−0.257154	−	0.966370i	$-0.582785\pi$
$127$	−5.79595	−0.514308	−0.257154	+	0.966370i	$0.582785\pi$
$128$	11.5836	1.02385
$129$	−5.27015	−0.464011
$130$	−8.95128	−0.785079
$131$	0.869136	0.0759368	0.0379684	−	0.999279i	$-0.487911\pi$
$131$	0.869136	0.0759368	0.0379684	+	0.999279i	$0.487911\pi$
$132$	−36.7998	−3.20301
$133$	3.00788	0.260816
$134$	13.4077	1.15825
$135$	−14.4340	−1.24228
$136$	−50.8623	−4.36141
$137$	6.32598	0.540465	0.270232	−	0.962795i	$-0.412899\pi$
$137$	6.32598	0.540465	0.270232	+	0.962795i	$0.412899\pi$
$138$	−4.09064	−0.348218
$139$	−0.946949	−0.0803192	−0.0401596	−	0.999193i	$-0.512787\pi$
$139$	−0.946949	−0.0803192	−0.0401596	+	0.999193i	$0.512787\pi$
$140$	−17.9932	−1.52071
$141$	18.3081	1.54182
$142$	3.29071	0.276150
$143$	−6.83475	−0.571551
$144$	−2.99074	−0.249228
$145$	4.04574	0.335981
$146$	18.4901	1.53025
$147$	7.49869	0.618481
$148$	−9.17325	−0.754036
$149$	−4.65166	−0.381079	−0.190539	−	0.981680i	$-0.561024\pi$
$149$	−4.65166	−0.381079	−0.190539	+	0.981680i	$0.561024\pi$
$150$	7.79360	0.636345
$151$	−12.8405	−1.04494	−0.522472	−	0.852657i	$-0.674990\pi$
$151$	−12.8405	−1.04494	−0.522472	+	0.852657i	$0.674990\pi$
$152$	−12.4554	−1.01027
$153$	−3.37099	−0.272528
$154$	−19.8672	−1.60094
$155$	1.01883	0.0818344
$156$	9.63603	0.771500
$157$	−12.7064	−1.01408	−0.507041	−	0.861922i	$-0.669261\pi$
$157$	−12.7064	−1.01408	−0.507041	+	0.861922i	$0.669261\pi$
$158$	1.02818	0.0817979
$159$	10.0852	0.799809
$160$	14.5084	1.14699
$161$	−1.52719	−0.120359
$162$	19.2676	1.51381
$163$	14.8356	1.16201	0.581005	−	0.813900i	$-0.302660\pi$
$163$	14.8356	1.16201	0.581005	+	0.813900i	$0.302660\pi$
$164$	18.9853	1.48250
$165$	21.5679	1.67906
$166$	0.906834	0.0703840
$167$	−4.43384	−0.343101	−0.171551	−	0.985175i	$-0.554878\pi$
$167$	−4.43384	−0.343101	−0.171551	+	0.985175i	$0.554878\pi$
$168$	15.5155	1.19705
$169$	−11.2103	−0.862332
$170$	53.8148	4.12741
$171$	−0.825507	−0.0631281
$172$	14.7085	1.12151
$173$	−0.920078	−0.0699522	−0.0349761	−	0.999388i	$-0.511136\pi$
$173$	−0.920078	−0.0699522	−0.0349761	+	0.999388i	$0.511136\pi$
$174$	−6.29797	−0.477448
$175$	2.90964	0.219948
$176$	36.4553	2.74792
$177$	−16.7284	−1.25738
$178$	24.0914	1.80573
$179$	6.90774	0.516309	0.258154	−	0.966104i	$-0.416886\pi$
$179$	6.90774	0.516309	0.258154	+	0.966104i	$0.416886\pi$
$180$	4.93821	0.368072
$181$	−21.2944	−1.58280	−0.791400	−	0.611299i	$-0.790647\pi$
$181$	−21.2944	−1.58280	−0.791400	+	0.611299i	$0.790647\pi$
$182$	5.20222	0.385614
$183$	3.20295	0.236769
$184$	6.32399	0.466211
$185$	5.37631	0.395274
$186$	−1.58600	−0.116291
$187$	41.0903	3.00482
$188$	−51.0962	−3.72657
$189$	8.38864	0.610183
$190$	13.1785	0.956067
$191$	15.5126	1.12245	0.561227	−	0.827662i	$-0.310330\pi$
$191$	15.5126	1.12245	0.561227	+	0.827662i	$0.310330\pi$
$192$	0.341510	0.0246464
$193$	−4.76602	−0.343066	−0.171533	−	0.985178i	$-0.554872\pi$
$193$	−4.76602	−0.343066	−0.171533	+	0.985178i	$0.554872\pi$
$194$	11.9121	0.855241
$195$	−5.64754	−0.404429
$196$	−20.9281	−1.49487
$197$	−22.0340	−1.56986	−0.784929	−	0.619586i	$-0.787301\pi$
$197$	−22.0340	−1.56986	−0.784929	+	0.619586i	$0.787301\pi$
$198$	5.45251	0.387493
$199$	−7.90731	−0.560534	−0.280267	−	0.959922i	$-0.590423\pi$
$199$	−7.90731	−0.560534	−0.280267	+	0.959922i	$0.590423\pi$
$200$	−12.0487	−0.851969
$201$	8.45922	0.596667
$202$	−15.4834	−1.08941
$203$	−2.35127	−0.165027
$204$	−57.9315	−4.05602
$205$	−11.1270	−0.777144
$206$	37.3237	2.60047
$207$	0.419134	0.0291318
$208$	−9.54583	−0.661884
$209$	10.0624	0.696033
$210$	−16.4162	−1.13283
$211$	−13.4808	−0.928060	−0.464030	−	0.885819i	$-0.653597\pi$
$211$	−13.4808	−0.928060	−0.464030	+	0.885819i	$0.653597\pi$
$212$	−28.1468	−1.93313
$213$	2.07618	0.142257
$214$	18.7832	1.28399
$215$	−8.62043	−0.587909
$216$	−34.7368	−2.36354
$217$	−0.592114	−0.0401953
$218$	−30.2446	−2.04842
$219$	11.6658	0.788300
$220$	−60.1938	−4.05827
$221$	−10.7595	−0.723763
$222$	−8.36925	−0.561707
$223$	−10.0199	−0.670981	−0.335490	−	0.942044i	$-0.608902\pi$
$223$	−10.0199	−0.670981	−0.335490	+	0.942044i	$0.608902\pi$
$224$	−8.43184	−0.563376
$225$	−0.798546	−0.0532364
$226$	−24.8371	−1.65214
$227$	−9.99004	−0.663063	−0.331531	−	0.943444i	$-0.607565\pi$
$227$	−9.99004	−0.663063	−0.331531	+	0.943444i	$0.607565\pi$
$228$	−14.1866	−0.939530
$229$	24.3177	1.60696	0.803478	−	0.595334i	$-0.202980\pi$
$229$	24.3177	1.60696	0.803478	+	0.595334i	$0.202980\pi$
$230$	−6.69110	−0.441198
$231$	−12.5346	−0.824716
$232$	9.73646	0.639230
$233$	23.5754	1.54447	0.772237	−	0.635335i	$-0.219138\pi$
$233$	23.5754	1.54447	0.772237	+	0.635335i	$0.219138\pi$
$234$	−1.42774	−0.0933343
$235$	29.9468	1.95351
$236$	46.6874	3.03909
$237$	0.648701	0.0421377
$238$	−31.2756	−2.02729
$239$	12.0981	0.782562	0.391281	−	0.920271i	$-0.372032\pi$
$239$	12.0981	0.782562	0.391281	+	0.920271i	$0.372032\pi$
$240$	30.1230	1.94443
$241$	−7.70332	−0.496214	−0.248107	−	0.968733i	$-0.579809\pi$
$241$	−7.70332	−0.496214	−0.248107	+	0.968733i	$0.579809\pi$
$242$	−38.4536	−2.47189
$243$	−4.32227	−0.277274
$244$	−8.93913	−0.572269
$245$	12.2657	0.783626
$246$	17.3213	1.10437
$247$	−2.63485	−0.167651
$248$	2.45191	0.155696
$249$	0.572140	0.0362579
$250$	−20.7074	−1.30965
$251$	5.42594	0.342483	0.171241	−	0.985229i	$-0.445222\pi$
$251$	5.42594	0.342483	0.171241	+	0.985229i	$0.445222\pi$
$252$	−2.86994	−0.180789
$253$	−5.10899	−0.321200
$254$	14.7582	0.926011
$255$	33.9528	2.12621
$256$	−29.0701	−1.81688
$257$	2.63411	0.164311	0.0821557	−	0.996620i	$-0.473820\pi$
$257$	2.63411	0.164311	0.0821557	+	0.996620i	$0.473820\pi$
$258$	13.4193	0.835452
$259$	−3.12455	−0.194150
$260$	15.7618	0.977502
$261$	0.645301	0.0399431
$262$	−2.21308	−0.136724
$263$	−6.13122	−0.378067	−0.189034	−	0.981971i	$-0.560535\pi$
$263$	−6.13122	−0.378067	−0.189034	+	0.981971i	$0.560535\pi$
$264$	51.9050	3.19453
$265$	16.4965	1.01337
$266$	−7.65894	−0.469600
$267$	15.1997	0.930209
$268$	−23.6089	−1.44214
$269$	9.32753	0.568709	0.284355	−	0.958719i	$-0.408221\pi$
$269$	9.32753	0.568709	0.284355	+	0.958719i	$0.408221\pi$
$270$	36.7533	2.23673
$271$	−11.9052	−0.723189	−0.361594	−	0.932335i	$-0.617767\pi$
$271$	−11.9052	−0.723189	−0.361594	+	0.932335i	$0.617767\pi$
$272$	57.3892	3.47973
$273$	3.28218	0.198647
$274$	−16.1078	−0.973107
$275$	9.73380	0.586970
$276$	7.20295	0.433567
$277$	13.4598	0.808721	0.404360	−	0.914600i	$-0.367494\pi$
$277$	13.4598	0.808721	0.404360	+	0.914600i	$0.367494\pi$
$278$	2.41121	0.144615
$279$	0.162505	0.00972890
$280$	25.3789	1.51668
$281$	31.0836	1.85429	0.927146	−	0.374699i	$-0.122254\pi$
$281$	31.0836	1.85429	0.927146	+	0.374699i	$0.122254\pi$
$282$	−46.6178	−2.77605
$283$	4.65902	0.276950	0.138475	−	0.990366i	$-0.455780\pi$
$283$	4.65902	0.276950	0.138475	+	0.990366i	$0.455780\pi$
$284$	−5.79441	−0.343835
$285$	8.31457	0.492512
$286$	17.4033	1.02908
$287$	6.46668	0.381716
$288$	2.31410	0.136360
$289$	47.6858	2.80505
$290$	−10.3017	−0.604934
$291$	7.51560	0.440572
$292$	−32.5581	−1.90532
$293$	−2.85562	−0.166827	−0.0834135	−	0.996515i	$-0.526582\pi$
$293$	−2.85562	−0.166827	−0.0834135	+	0.996515i	$0.526582\pi$
$294$	−19.0939	−1.11358
$295$	−27.3628	−1.59312
$296$	12.9386	0.752040
$297$	28.0630	1.62838
$298$	11.8445	0.686133
$299$	1.33779	0.0773664
$300$	−13.7233	−0.792313
$301$	5.00994	0.288768
$302$	32.6956	1.88142
$303$	−9.76878	−0.561202
$304$	14.0538	0.806041
$305$	5.23910	0.299990
$306$	8.58353	0.490688
$307$	−5.20447	−0.297035	−0.148517	−	0.988910i	$-0.547450\pi$
$307$	−5.20447	−0.297035	−0.148517	+	0.988910i	$0.547450\pi$
$308$	34.9829	1.99333
$309$	23.5483	1.33961
$310$	−2.59424	−0.147343
$311$	2.56691	0.145556	0.0727780	−	0.997348i	$-0.476814\pi$
$311$	2.56691	0.145556	0.0727780	+	0.997348i	$0.476814\pi$
$312$	−13.5913	−0.769458
$313$	31.9725	1.80719	0.903595	−	0.428387i	$-0.140918\pi$
$313$	31.9725	1.80719	0.903595	+	0.428387i	$0.140918\pi$
$314$	32.3542	1.82585
$315$	1.68203	0.0947718
$316$	−1.81046	−0.101847
$317$	−26.7395	−1.50184	−0.750921	−	0.660392i	$-0.770390\pi$
$317$	−26.7395	−1.50184	−0.750921	+	0.660392i	$0.770390\pi$
$318$	−25.6799	−1.44006
$319$	−7.86583	−0.440402
$320$	0.558612	0.0312273
$321$	11.8507	0.661440
$322$	3.88867	0.216707
$323$	15.8406	0.881396
$324$	−33.9271	−1.88484
$325$	−2.54879	−0.141382
$326$	−37.7757	−2.09220
$327$	−19.0819	−1.05523
$328$	−26.7782	−1.47858
$329$	−17.4042	−0.959524
$330$	−54.9181	−3.02314
$331$	−31.7835	−1.74698	−0.873489	−	0.486844i	$-0.838148\pi$
$331$	−31.7835	−1.74698	−0.873489	+	0.486844i	$0.838148\pi$
$332$	−1.59679	−0.0876351
$333$	0.857528	0.0469923
$334$	11.2899	0.617754
$335$	13.8368	0.755987
$336$	−17.5066	−0.955062
$337$	−19.7424	−1.07544	−0.537720	−	0.843124i	$-0.680714\pi$
$337$	−19.7424	−1.07544	−0.537720	+	0.843124i	$0.680714\pi$
$338$	28.5448	1.55263
$339$	−15.6702	−0.851090
$340$	−94.7591	−5.13904
$341$	−1.98083	−0.107268
$342$	2.10198	0.113662
$343$	−17.8188	−0.962123
$344$	−20.7459	−1.11854
$345$	−4.22155	−0.227281
$346$	2.34279	0.125949
$347$	−33.2441	−1.78464	−0.892319	−	0.451405i	$-0.850923\pi$
$347$	−33.2441	−1.78464	−0.892319	+	0.451405i	$0.850923\pi$
$348$	11.0897	0.594470
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−7.40880	−0.396017
$351$	−7.34830	−0.392223
$352$	−28.2075	−1.50347
$353$	−26.7161	−1.42195	−0.710976	−	0.703216i	$-0.751747\pi$
$353$	−26.7161	−1.42195	−0.710976	+	0.703216i	$0.751747\pi$
$354$	42.5954	2.26392
$355$	3.39602	0.180242
$356$	−42.4210	−2.24831
$357$	−19.7324	−1.04435
$358$	−17.5891	−0.929614
$359$	23.3415	1.23192	0.615959	−	0.787778i	$-0.288769\pi$
$359$	23.3415	1.23192	0.615959	+	0.787778i	$0.288769\pi$
$360$	−6.96520	−0.367098
$361$	−15.1209	−0.795835
$362$	54.2218	2.84983
$363$	−24.2611	−1.27338
$364$	−9.16026	−0.480128
$365$	19.0818	0.998788
$366$	−8.15565	−0.426303
$367$	30.9911	1.61772	0.808861	−	0.587999i	$-0.200084\pi$
$367$	30.9911	1.61772	0.808861	+	0.587999i	$0.200084\pi$
$368$	−7.13553	−0.371965
$369$	−1.77477	−0.0923908
$370$	−13.6897	−0.711692
$371$	−9.58726	−0.497746
$372$	2.79269	0.144794
$373$	38.0076	1.96796	0.983980	−	0.178281i	$-0.0570537\pi$
$373$	38.0076	1.96796	0.983980	+	0.178281i	$0.0570537\pi$
$374$	−104.628	−5.41019
$375$	−13.0647	−0.674660
$376$	72.0697	3.71671
$377$	2.05967	0.106078
$378$	−21.3599	−1.09864
$379$	−8.24751	−0.423646	−0.211823	−	0.977308i	$-0.567940\pi$
$379$	−8.24751	−0.423646	−0.211823	+	0.977308i	$0.567940\pi$
$380$	−23.2052	−1.19040
$381$	9.31124	0.477029
$382$	−39.4997	−2.02098
$383$	6.29241	0.321527	0.160764	−	0.986993i	$-0.448604\pi$
$383$	6.29241	0.321527	0.160764	+	0.986993i	$0.448604\pi$
$384$	−18.6091	−0.949643
$385$	−20.5030	−1.04493
$386$	12.1357	0.617690
$387$	−1.37497	−0.0698936
$388$	−20.9753	−1.06486
$389$	−18.9030	−0.958420	−0.479210	−	0.877700i	$-0.659077\pi$
$389$	−18.9030	−0.958420	−0.479210	+	0.877700i	$0.659077\pi$
$390$	14.3803	0.728175
$391$	−8.04275	−0.406739
$392$	29.5185	1.49091
$393$	−1.39627	−0.0704327
$394$	56.1050	2.82653
$395$	1.06109	0.0533891
$396$	−9.60098	−0.482468
$397$	27.6357	1.38700	0.693499	−	0.720458i	$-0.256068\pi$
$397$	27.6357	1.38700	0.693499	+	0.720458i	$0.256068\pi$
$398$	20.1343	1.00924
$399$	−4.83218	−0.241912
$400$	13.5948	0.679741
$401$	9.74106	0.486445	0.243223	−	0.969970i	$-0.421795\pi$
$401$	9.74106	0.486445	0.243223	+	0.969970i	$0.421795\pi$
$402$	−21.5396	−1.07430
$403$	0.518681	0.0258374
$404$	27.2637	1.35642
$405$	19.8842	0.988055
$406$	5.98701	0.297131
$407$	−10.4528	−0.518124
$408$	81.7107	4.04528
$409$	29.3823	1.45286	0.726431	−	0.687239i	$-0.241178\pi$
$409$	29.3823	1.45286	0.726431	+	0.687239i	$0.241178\pi$
$410$	28.3326	1.39925
$411$	−10.1627	−0.501290
$412$	−65.7210	−3.23784
$413$	15.9025	0.782509
$414$	−1.06724	−0.0524519
$415$	0.935855	0.0459393
$416$	7.38614	0.362135
$417$	1.52128	0.0744975
$418$	−25.6219	−1.25321
$419$	12.5802	0.614584	0.307292	−	0.951615i	$-0.400577\pi$
$419$	12.5802	0.614584	0.307292	+	0.951615i	$0.400577\pi$
$420$	28.9063	1.41048
$421$	−23.2363	−1.13247	−0.566234	−	0.824244i	$-0.691600\pi$
$421$	−23.2363	−1.13247	−0.566234	+	0.824244i	$0.691600\pi$
$422$	34.3262	1.67097
$423$	4.77655	0.232244
$424$	39.7003	1.92802
$425$	15.3233	0.743288
$426$	−5.28655	−0.256134
$427$	−3.04481	−0.147349
$428$	−33.0741	−1.59870
$429$	10.9801	0.530123
$430$	21.9501	1.05853
$431$	17.0229	0.819963	0.409981	−	0.912094i	$-0.365535\pi$
$431$	17.0229	0.819963	0.409981	+	0.912094i	$0.365535\pi$
$432$	39.1945	1.88575
$433$	10.2488	0.492527	0.246263	−	0.969203i	$-0.420797\pi$
$433$	10.2488	0.492527	0.246263	+	0.969203i	$0.420797\pi$
$434$	1.50770	0.0723717
$435$	−6.49952	−0.311628
$436$	53.2559	2.55049
$437$	−1.96955	−0.0942165
$438$	−29.7045	−1.41934
$439$	−30.1627	−1.43959	−0.719793	−	0.694188i	$-0.755763\pi$
$439$	−30.1627	−1.43959	−0.719793	+	0.694188i	$0.755763\pi$
$440$	84.9016	4.04752
$441$	1.95639	0.0931614
$442$	27.3968	1.30314
$443$	−8.82172	−0.419133	−0.209566	−	0.977794i	$-0.567205\pi$
$443$	−8.82172	−0.419133	−0.209566	+	0.977794i	$0.567205\pi$
$444$	14.7369	0.699382
$445$	24.8624	1.17859
$446$	25.5135	1.20810
$447$	7.47292	0.353457
$448$	−0.324649	−0.0153382
$449$	18.3084	0.864026	0.432013	−	0.901867i	$-0.357803\pi$
$449$	18.3084	0.864026	0.432013	+	0.901867i	$0.357803\pi$
$450$	2.03333	0.0958522
$451$	21.6334	1.01868
$452$	43.7341	2.05708
$453$	20.6283	0.969204
$454$	25.4376	1.19384
$455$	5.36870	0.251689
$456$	20.0098	0.937043
$457$	−7.15503	−0.334698	−0.167349	−	0.985898i	$-0.553521\pi$
$457$	−7.15503	−0.334698	−0.167349	+	0.985898i	$0.553521\pi$
$458$	−61.9199	−2.89333
$459$	44.1777	2.06204
$460$	11.7819	0.549336
$461$	−7.25422	−0.337863	−0.168931	−	0.985628i	$-0.554032\pi$
$461$	−7.25422	−0.337863	−0.168931	+	0.985628i	$0.554032\pi$
$462$	31.9168	1.48490
$463$	−4.16125	−0.193390	−0.0966949	−	0.995314i	$-0.530827\pi$
$463$	−4.16125	−0.193390	−0.0966949	+	0.995314i	$0.530827\pi$
$464$	−10.9859	−0.510007
$465$	−1.63676	−0.0759028
$466$	−60.0298	−2.78083
$467$	−19.9135	−0.921489	−0.460745	−	0.887533i	$-0.652418\pi$
$467$	−19.9135	−0.921489	−0.460745	+	0.887533i	$0.652418\pi$
$468$	2.51402	0.116211
$469$	−8.04155	−0.371324
$470$	−76.2533	−3.51730
$471$	20.4129	0.940578
$472$	−65.8511	−3.03104
$473$	16.7600	0.770628
$474$	−1.65178	−0.0758689
$475$	3.75245	0.172174
$476$	55.0712	2.52418
$477$	2.63121	0.120475
$478$	−30.8053	−1.40900
$479$	1.78452	0.0815366	0.0407683	−	0.999169i	$-0.487019\pi$
$479$	1.78452	0.0815366	0.0407683	+	0.999169i	$0.487019\pi$
$480$	−23.3078	−1.06385
$481$	2.73705	0.124799
$482$	19.6149	0.893434
$483$	2.45344	0.111635
$484$	67.7105	3.07775
$485$	12.2933	0.558212
$486$	11.0058	0.499232
$487$	17.0334	0.771855	0.385927	−	0.922529i	$-0.373882\pi$
$487$	17.0334	0.771855	0.385927	+	0.922529i	$0.373882\pi$
$488$	12.6084	0.570754
$489$	−23.8334	−1.07779
$490$	−31.2320	−1.41092
$491$	13.9714	0.630520	0.315260	−	0.949005i	$-0.397908\pi$
$491$	13.9714	0.630520	0.315260	+	0.949005i	$0.397908\pi$
$492$	−30.5000	−1.37505
$493$	−12.3827	−0.557687
$494$	6.70910	0.301856
$495$	5.62700	0.252915
$496$	−2.76655	−0.124222
$497$	−1.97367	−0.0885311
$498$	−1.45684	−0.0652824
$499$	30.4182	1.36171	0.680853	−	0.732420i	$-0.261609\pi$
$499$	30.4182	1.36171	0.680853	+	0.732420i	$0.261609\pi$
$500$	36.4624	1.63065
$501$	7.12300	0.318232
$502$	−13.8160	−0.616640
$503$	−6.42637	−0.286537	−0.143269	−	0.989684i	$-0.545761\pi$
$503$	−6.42637	−0.286537	−0.143269	+	0.989684i	$0.545761\pi$
$504$	4.04797	0.180311
$505$	−15.9789	−0.711051
$506$	13.0090	0.578320
$507$	18.0095	0.799828
$508$	−25.9868	−1.15298
$509$	29.1581	1.29241	0.646206	−	0.763163i	$-0.276355\pi$
$509$	29.1581	1.29241	0.646206	+	0.763163i	$0.276355\pi$
$510$	−86.4539	−3.82824
$511$	−11.0898	−0.490584
$512$	50.8537	2.24744
$513$	10.8185	0.477648
$514$	−6.70722	−0.295843
$515$	38.5182	1.69731
$516$	−23.6293	−1.04022
$517$	−58.2232	−2.56065
$518$	7.95603	0.349568
$519$	1.47811	0.0648819
$520$	−22.2315	−0.974915
$521$	2.01853	0.0884332	0.0442166	−	0.999022i	$-0.485921\pi$
$521$	2.01853	0.0884332	0.0442166	+	0.999022i	$0.485921\pi$
$522$	−1.64313	−0.0719176
$523$	−12.0847	−0.528428	−0.264214	−	0.964464i	$-0.585113\pi$
$523$	−12.0847	−0.528428	−0.264214	+	0.964464i	$0.585113\pi$
$524$	3.89687	0.170235
$525$	−4.67436	−0.204006
$526$	15.6119	0.680710
$527$	−3.11829	−0.135835
$528$	−58.5658	−2.54875
$529$	1.00000	0.0434783
$530$	−42.0048	−1.82457
$531$	−4.36440	−0.189399
$532$	13.4862	0.584699
$533$	−5.66470	−0.245365
$534$	−38.7030	−1.67484
$535$	19.3843	0.838055
$536$	33.2996	1.43832
$537$	−11.0973	−0.478885
$538$	−23.7506	−1.02396
$539$	−23.8472	−1.02717
$540$	−64.7166	−2.78496
$541$	−2.16631	−0.0931368	−0.0465684	−	0.998915i	$-0.514829\pi$
$541$	−2.16631	−0.0931368	−0.0465684	+	0.998915i	$0.514829\pi$
$542$	30.3141	1.30210
$543$	34.2096	1.46807
$544$	−44.4052	−1.90386
$545$	−31.2125	−1.33700
$546$	−8.35740	−0.357664
$547$	−46.3017	−1.97972	−0.989858	−	0.142059i	$-0.954628\pi$
$547$	−46.3017	−1.97972	−0.989858	+	0.142059i	$0.954628\pi$
$548$	28.3632	1.21162
$549$	0.835642	0.0356643
$550$	−24.7851	−1.05684
$551$	−3.03234	−0.129182
$552$	−10.1595	−0.432419
$553$	−0.616673	−0.0262236
$554$	−34.2726	−1.45610
$555$	−8.63709	−0.366624
$556$	−4.24575	−0.180060
$557$	−1.63646	−0.0693392	−0.0346696	−	0.999399i	$-0.511038\pi$
$557$	−1.63646	−0.0693392	−0.0346696	+	0.999399i	$0.511038\pi$
$558$	−0.413784	−0.0175169
$559$	−4.38862	−0.185619
$560$	−28.6357	−1.21008
$561$	−66.0119	−2.78703
$562$	−79.1480	−3.33866
$563$	−3.07380	−0.129545	−0.0647726	−	0.997900i	$-0.520632\pi$
$563$	−3.07380	−0.129545	−0.0647726	+	0.997900i	$0.520632\pi$
$564$	82.0865	3.45646
$565$	−25.6319	−1.07834
$566$	−11.8632	−0.498649
$567$	−11.5561	−0.485311
$568$	8.17284	0.342925
$569$	26.4595	1.10924	0.554619	−	0.832104i	$-0.312864\pi$
$569$	26.4595	1.10924	0.554619	+	0.832104i	$0.312864\pi$
$570$	−21.1713	−0.886769
$571$	−9.93247	−0.415661	−0.207830	−	0.978165i	$-0.566640\pi$
$571$	−9.93247	−0.415661	−0.207830	+	0.978165i	$0.566640\pi$
$572$	−30.6444	−1.28131
$573$	−24.9211	−1.04110
$574$	−16.4661	−0.687281
$575$	−1.90523	−0.0794535
$576$	0.0890992	0.00371247
$577$	20.5127	0.853955	0.426977	−	0.904262i	$-0.359578\pi$
$577$	20.5127	0.853955	0.426977	+	0.904262i	$0.359578\pi$
$578$	−121.422	−5.05049
$579$	7.65665	0.318200
$580$	18.1395	0.753203
$581$	−0.543891	−0.0225644
$582$	−19.1369	−0.793251
$583$	−32.0728	−1.32832
$584$	45.9222	1.90027
$585$	−1.47343	−0.0609189
$586$	7.27124	0.300372
$587$	−44.0187	−1.81685	−0.908424	−	0.418051i	$-0.862713\pi$
$587$	−44.0187	−1.81685	−0.908424	+	0.418051i	$0.862713\pi$
$588$	33.6212	1.38651
$589$	−0.763626	−0.0314647
$590$	69.6738	2.86842
$591$	35.3978	1.45607
$592$	−14.5989	−0.600013
$593$	−44.8438	−1.84152	−0.920758	−	0.390135i	$-0.872428\pi$
$593$	−44.8438	−1.84152	−0.920758	+	0.390135i	$0.872428\pi$
$594$	−71.4566	−2.93190
$595$	−32.2765	−1.32321
$596$	−20.8562	−0.854304
$597$	12.7032	0.519905
$598$	−3.40640	−0.139298
$599$	15.0766	0.616014	0.308007	−	0.951384i	$-0.400338\pi$
$599$	15.0766	0.616014	0.308007	+	0.951384i	$0.400338\pi$
$600$	19.3563	0.790216
$601$	−3.60476	−0.147041	−0.0735207	−	0.997294i	$-0.523423\pi$
$601$	−3.60476	−0.147041	−0.0735207	+	0.997294i	$0.523423\pi$
$602$	−12.7568	−0.519927
$603$	2.20699	0.0898756
$604$	−57.5717	−2.34256
$605$	−39.6842	−1.61339
$606$	24.8742	1.01044
$607$	−2.83743	−0.115168	−0.0575839	−	0.998341i	$-0.518340\pi$
$607$	−2.83743	−0.115168	−0.0575839	+	0.998341i	$0.518340\pi$
$608$	−10.8742	−0.441007
$609$	3.77733	0.153065
$610$	−13.3403	−0.540132
$611$	15.2458	0.616777
$612$	−15.1142	−0.610955
$613$	0.464346	0.0187548	0.00937738	−	0.999956i	$-0.497015\pi$
$613$	0.464346	0.0187548	0.00937738	+	0.999956i	$0.497015\pi$
$614$	13.2521	0.534811
$615$	17.8756	0.720814
$616$	−49.3423	−1.98806
$617$	1.02117	0.0411108	0.0205554	−	0.999789i	$-0.493457\pi$
$617$	1.02117	0.0411108	0.0205554	+	0.999789i	$0.493457\pi$
$618$	−59.9608	−2.41198
$619$	−37.9016	−1.52340	−0.761698	−	0.647933i	$-0.775634\pi$
$619$	−37.9016	−1.52340	−0.761698	+	0.647933i	$0.775634\pi$
$620$	4.56804	0.183457
$621$	−5.49286	−0.220421
$622$	−6.53610	−0.262074
$623$	−14.4493	−0.578898
$624$	15.3355	0.613909
$625$	−30.8962	−1.23585
$626$	−81.4113	−3.25385
$627$	−16.1654	−0.645583
$628$	−56.9705	−2.27337
$629$	−16.4551	−0.656107
$630$	−4.28295	−0.170637
$631$	−14.3486	−0.571210	−0.285605	−	0.958347i	$-0.592194\pi$
$631$	−14.3486	−0.571210	−0.285605	+	0.958347i	$0.592194\pi$
$632$	2.55360	0.101577
$633$	21.6571	0.860792
$634$	68.0867	2.70407
$635$	15.2305	0.604404
$636$	45.2181	1.79301
$637$	6.24440	0.247412
$638$	20.0287	0.792944
$639$	0.541670	0.0214281
$640$	−30.4391	−1.20321
$641$	2.17110	0.0857532	0.0428766	−	0.999080i	$-0.486348\pi$
$641$	2.17110	0.0857532	0.0428766	+	0.999080i	$0.486348\pi$
$642$	−30.1753	−1.19092
$643$	−6.73012	−0.265410	−0.132705	−	0.991156i	$-0.542366\pi$
$643$	−6.73012	−0.265410	−0.132705	+	0.991156i	$0.542366\pi$
$644$	−6.84731	−0.269822
$645$	13.8488	0.545296
$646$	−40.3349	−1.58695
$647$	19.6801	0.773705	0.386853	−	0.922142i	$-0.373562\pi$
$647$	19.6801	0.773705	0.386853	+	0.922142i	$0.373562\pi$
$648$	47.8532	1.87985
$649$	53.1994	2.08826
$650$	6.48998	0.254558
$651$	0.951235	0.0372819
$652$	66.5168	2.60500
$653$	−29.6818	−1.16154	−0.580770	−	0.814068i	$-0.697248\pi$
$653$	−29.6818	−1.16154	−0.580770	+	0.814068i	$0.697248\pi$
$654$	48.5882	1.89995
$655$	−2.28390	−0.0892393
$656$	30.2145	1.17968
$657$	3.04357	0.118741
$658$	44.3161	1.72762
$659$	−4.07108	−0.158587	−0.0792933	−	0.996851i	$-0.525266\pi$
$659$	−4.07108	−0.158587	−0.0792933	+	0.996851i	$0.525266\pi$
$660$	96.7018	3.76411
$661$	34.0856	1.32578	0.662889	−	0.748718i	$-0.269330\pi$
$661$	34.0856	1.32578	0.662889	+	0.748718i	$0.269330\pi$
$662$	80.9300	3.14544
$663$	17.2852	0.671302
$664$	2.25222	0.0874031
$665$	−7.90404	−0.306506
$666$	−2.18352	−0.0846096
$667$	1.53961	0.0596138
$668$	−19.8796	−0.769165
$669$	16.0970	0.622346
$670$	−35.2326	−1.36115
$671$	−10.1860	−0.393225
$672$	13.5458	0.522541
$673$	−44.5570	−1.71755	−0.858773	−	0.512355i	$-0.828773\pi$
$673$	−44.5570	−1.71755	−0.858773	+	0.512355i	$0.828773\pi$
$674$	50.2700	1.93633
$675$	10.4652	0.402804
$676$	−50.2627	−1.93318
$677$	−19.5567	−0.751626	−0.375813	−	0.926695i	$-0.622637\pi$
$677$	−19.5567	−0.751626	−0.375813	+	0.926695i	$0.622637\pi$
$678$	39.9010	1.53239
$679$	−7.14453	−0.274182
$680$	133.655	5.12543
$681$	16.0491	0.615002
$682$	5.04378	0.193136
$683$	−38.3917	−1.46902	−0.734510	−	0.678598i	$-0.762588\pi$
$683$	−38.3917	−1.46902	−0.734510	+	0.678598i	$0.762588\pi$
$684$	−3.70125	−0.141521
$685$	−16.6233	−0.635143
$686$	45.3718	1.73230
$687$	−39.0665	−1.49048
$688$	23.4081	0.892425
$689$	8.39827	0.319948
$690$	10.7493	0.409219
$691$	48.9833	1.86341	0.931706	−	0.363212i	$-0.118320\pi$
$691$	48.9833	1.86341	0.931706	+	0.363212i	$0.118320\pi$
$692$	−4.12527	−0.156819
$693$	−3.27025	−0.124226
$694$	84.6493	3.21324
$695$	2.48837	0.0943894
$696$	−15.6417	−0.592897
$697$	34.0560	1.28996
$698$	2.54629	0.0963786
$699$	−37.8740	−1.43253
$700$	13.0457	0.493081
$701$	−19.9103	−0.752001	−0.376001	−	0.926619i	$-0.622701\pi$
$701$	−19.9103	−0.752001	−0.376001	+	0.926619i	$0.622701\pi$
$702$	18.7109	0.706198
$703$	−4.02961	−0.151980
$704$	−1.08607	−0.0409326
$705$	−48.1097	−1.81192
$706$	68.0269	2.56023
$707$	9.28646	0.349253
$708$	−75.0036	−2.81881
$709$	−22.0010	−0.826265	−0.413133	−	0.910671i	$-0.635565\pi$
$709$	−22.0010	−0.826265	−0.413133	+	0.910671i	$0.635565\pi$
$710$	−8.64727	−0.324526
$711$	0.169245	0.00634717
$712$	59.8336	2.24236
$713$	0.387715	0.0145200
$714$	50.2444	1.88035
$715$	17.9602	0.671675
$716$	30.9716	1.15746
$717$	−19.4357	−0.725840
$718$	−59.4343	−2.21807
$719$	16.4922	0.615054	0.307527	−	0.951539i	$-0.400499\pi$
$719$	16.4922	0.615054	0.307527	+	0.951539i	$0.400499\pi$
$720$	7.85901	0.292888
$721$	−22.3856	−0.833684
$722$	38.5021	1.43290
$723$	12.3754	0.460247
$724$	−95.4757	−3.54833
$725$	−2.93330	−0.108940
$726$	61.7760	2.29272
$727$	−35.2893	−1.30881	−0.654404	−	0.756145i	$-0.727080\pi$
$727$	−35.2893	−1.30881	−0.654404	+	0.756145i	$0.727080\pi$
$728$	12.9203	0.478857
$729$	29.6445	1.09795
$730$	−48.5879	−1.79832
$731$	26.3842	0.975856
$732$	14.3608	0.530789
$733$	−45.5732	−1.68329	−0.841643	−	0.540035i	$-0.818411\pi$
$733$	−45.5732	−1.68329	−0.841643	+	0.540035i	$0.818411\pi$
$734$	−78.9124	−2.91271
$735$	−19.7049	−0.726826
$736$	5.52115	0.203512
$737$	−26.9019	−0.990944
$738$	4.51908	0.166350
$739$	12.9550	0.476558	0.238279	−	0.971197i	$-0.423417\pi$
$739$	12.9550	0.476558	0.238279	+	0.971197i	$0.423417\pi$
$740$	24.1053	0.886128
$741$	4.23290	0.155500
$742$	24.4120	0.896192
$743$	30.4503	1.11711	0.558556	−	0.829467i	$-0.311355\pi$
$743$	30.4503	1.11711	0.558556	+	0.829467i	$0.311355\pi$
$744$	−3.93901	−0.144411
$745$	12.2235	0.447836
$746$	−96.7785	−3.54331
$747$	0.149270	0.00546150
$748$	184.233	6.73622
$749$	−11.2656	−0.411635
$750$	33.2666	1.21473
$751$	−17.8305	−0.650645	−0.325322	−	0.945603i	$-0.605473\pi$
$751$	−17.8305	−0.650645	−0.325322	+	0.945603i	$0.605473\pi$
$752$	−81.3181	−2.96537
$753$	−8.71682	−0.317659
$754$	−5.24452	−0.190994
$755$	33.7420	1.22800
$756$	37.6114	1.36791
$757$	22.9511	0.834172	0.417086	−	0.908867i	$-0.363051\pi$
$757$	22.9511	0.834172	0.417086	+	0.908867i	$0.363051\pi$
$758$	21.0006	0.762776
$759$	8.20763	0.297918
$760$	32.7302	1.18725
$761$	−33.4668	−1.21317	−0.606585	−	0.795019i	$-0.707461\pi$
$761$	−33.4668	−1.21317	−0.606585	+	0.795019i	$0.707461\pi$
$762$	−23.7091	−0.858892
$763$	18.1398	0.656705
$764$	69.5525	2.51632
$765$	8.85822	0.320270
$766$	−16.0223	−0.578910
$767$	−13.9303	−0.502993
$768$	46.7013	1.68519
$769$	23.8592	0.860386	0.430193	−	0.902737i	$-0.358445\pi$
$769$	23.8592	0.860386	0.430193	+	0.902737i	$0.358445\pi$
$770$	52.2066	1.88139
$771$	−4.23172	−0.152402
$772$	−21.3690	−0.769086
$773$	7.40155	0.266215	0.133108	−	0.991102i	$-0.457504\pi$
$773$	7.40155	0.266215	0.133108	+	0.991102i	$0.457504\pi$
$774$	3.50107	0.125844
$775$	−0.738686	−0.0265344
$776$	29.5851	1.06204
$777$	5.01962	0.180078
$778$	48.1326	1.72564
$779$	8.33983	0.298805
$780$	−25.3214	−0.906650
$781$	−6.60263	−0.236261
$782$	20.4792	0.732334
$783$	−8.45684	−0.302223
$784$	−33.3065	−1.18952
$785$	33.3896	1.19173
$786$	3.55532	0.126814
$787$	40.7223	1.45159	0.725796	−	0.687910i	$-0.241471\pi$
$787$	40.7223	1.45159	0.725796	+	0.687910i	$0.241471\pi$
$788$	−98.7918	−3.51931
$789$	9.84985	0.350664
$790$	−2.70184	−0.0961271
$791$	14.8965	0.529660
$792$	13.5419	0.481190
$793$	2.66720	0.0947150
$794$	−70.3686	−2.49729
$795$	−26.5017	−0.939918
$796$	−35.4533	−1.25661
$797$	−44.0855	−1.56159	−0.780794	−	0.624788i	$-0.785185\pi$
$797$	−44.0855	−1.56159	−0.780794	+	0.624788i	$0.785185\pi$
$798$	12.3041	0.435562
$799$	−91.6570	−3.24259
$800$	−10.5191	−0.371905
$801$	3.96558	0.140117
$802$	−24.8036	−0.875845
$803$	−37.0993	−1.30921
$804$	37.9278	1.33761
$805$	4.01311	0.141444
$806$	−1.32071	−0.0465202
$807$	−14.9847	−0.527488
$808$	−38.4547	−1.35283
$809$	38.1068	1.33976	0.669881	−	0.742468i	$-0.266345\pi$
$809$	38.1068	1.33976	0.669881	+	0.742468i	$0.266345\pi$
$810$	−50.6310	−1.77899
$811$	−40.5590	−1.42422	−0.712109	−	0.702069i	$-0.752260\pi$
$811$	−40.5590	−1.42422	−0.712109	+	0.702069i	$0.752260\pi$
$812$	−10.5422	−0.369957
$813$	19.1258	0.670770
$814$	26.6158	0.932882
$815$	−38.9846	−1.36557
$816$	−92.1962	−3.22751
$817$	6.46112	0.226046
$818$	−74.8160	−2.61588
$819$	0.856314	0.0299220
$820$	−49.8891	−1.74220
$821$	−47.4762	−1.65693	−0.828466	−	0.560039i	$-0.810786\pi$
$821$	−47.4762	−1.65693	−0.828466	+	0.560039i	$0.810786\pi$
$822$	25.8773	0.902574
$823$	−20.0296	−0.698187	−0.349093	−	0.937088i	$-0.613510\pi$
$823$	−20.0296	−0.698187	−0.349093	+	0.937088i	$0.613510\pi$
$824$	92.6975	3.22927
$825$	−15.6374	−0.544425
$826$	−40.4923	−1.40891
$827$	−52.7404	−1.83396	−0.916982	−	0.398929i	$-0.869382\pi$
$827$	−52.7404	−1.83396	−0.916982	+	0.398929i	$0.869382\pi$
$828$	1.87923	0.0653078
$829$	−18.4210	−0.639788	−0.319894	−	0.947453i	$-0.603647\pi$
$829$	−18.4210	−0.639788	−0.319894	+	0.947453i	$0.603647\pi$
$830$	−2.38296	−0.0827138
$831$	−21.6233	−0.750103
$832$	0.284386	0.00985932
$833$	−37.5411	−1.30072
$834$	−3.87363	−0.134133
$835$	11.6512	0.403205
$836$	45.1160	1.56037
$837$	−2.12967	−0.0736120
$838$	−32.0329	−1.10656
$839$	41.6107	1.43656	0.718281	−	0.695753i	$-0.244929\pi$
$839$	41.6107	1.43656	0.718281	+	0.695753i	$0.244929\pi$
$840$	−40.7714	−1.40675
$841$	−26.6296	−0.918263
$842$	59.1665	2.03901
$843$	−49.9361	−1.71989
$844$	−60.4429	−2.08053
$845$	29.4583	1.01339
$846$	−12.1625	−0.418155
$847$	23.0633	0.792463
$848$	−44.7948	−1.53826
$849$	−7.48476	−0.256876
$850$	−39.0175	−1.33829
$851$	2.04595	0.0701343
$852$	9.30876	0.318913
$853$	−12.7640	−0.437031	−0.218516	−	0.975833i	$-0.570121\pi$
$853$	−12.7640	−0.437031	−0.218516	+	0.975833i	$0.570121\pi$
$854$	7.75297	0.265301
$855$	2.16925	0.0741868
$856$	46.6500	1.59446
$857$	30.4218	1.03919	0.519594	−	0.854413i	$-0.326083\pi$
$857$	30.4218	1.03919	0.519594	+	0.854413i	$0.326083\pi$
$858$	−27.9585	−0.954488
$859$	−21.9807	−0.749973	−0.374987	−	0.927030i	$-0.622353\pi$
$859$	−21.9807	−0.749973	−0.374987	+	0.927030i	$0.622353\pi$
$860$	−38.6506	−1.31798
$861$	−10.3888	−0.354049
$862$	−43.3452	−1.47634
$863$	53.9671	1.83706	0.918531	−	0.395348i	$-0.129376\pi$
$863$	53.9671	1.83706	0.918531	+	0.395348i	$0.129376\pi$
$864$	−30.3269	−1.03174
$865$	2.41776	0.0822064
$866$	−26.0965	−0.886795
$867$	−76.6076	−2.60173
$868$	−2.65481	−0.0901100
$869$	−2.06299	−0.0699822
$870$	16.5497	0.561087
$871$	7.04426	0.238686
$872$	−75.1158	−2.54374
$873$	1.96080	0.0663631
$874$	5.01506	0.169637
$875$	12.4197	0.419862
$876$	52.3048	1.76721
$877$	−36.2875	−1.22534	−0.612671	−	0.790338i	$-0.709905\pi$
$877$	−36.2875	−1.22534	−0.612671	+	0.790338i	$0.709905\pi$
$878$	76.8030	2.59198
$879$	4.58757	0.154735
$880$	−95.7966	−3.22930
$881$	11.8752	0.400086	0.200043	−	0.979787i	$-0.435892\pi$
$881$	11.8752	0.400086	0.200043	+	0.979787i	$0.435892\pi$
$882$	−4.98154	−0.167737
$883$	−14.8314	−0.499118	−0.249559	−	0.968360i	$-0.580286\pi$
$883$	−14.8314	−0.499118	−0.249559	+	0.968360i	$0.580286\pi$
$884$	−48.2414	−1.62253
$885$	43.9586	1.47765
$886$	22.4627	0.754649
$887$	9.05519	0.304044	0.152022	−	0.988377i	$-0.451422\pi$
$887$	9.05519	0.304044	0.152022	+	0.988377i	$0.451422\pi$
$888$	−20.7859	−0.697531
$889$	−8.85151	−0.296870
$890$	−63.3069	−2.12205
$891$	−38.6594	−1.29514
$892$	−44.9252	−1.50421
$893$	−22.4455	−0.751109
$894$	−19.0283	−0.636400
$895$	−18.1520	−0.606755
$896$	17.6903	0.590992
$897$	−2.14917	−0.0717587
$898$	−46.6185	−1.55568
$899$	0.596928	0.0199087
$900$	−3.58037	−0.119346
$901$	−50.4901	−1.68207
$902$	−55.0849	−1.83413
$903$	−8.04851	−0.267837
$904$	−61.6856	−2.05163
$905$	55.9570	1.86007
$906$	−52.5258	−1.74505
$907$	41.4590	1.37662	0.688311	−	0.725415i	$-0.258352\pi$
$907$	41.4590	1.37662	0.688311	+	0.725415i	$0.258352\pi$
$908$	−44.7914	−1.48646
$909$	−2.54865	−0.0845334
$910$	−13.6703	−0.453166
$911$	−38.6784	−1.28147	−0.640736	−	0.767762i	$-0.721371\pi$
$911$	−38.6784	−1.28147	−0.640736	+	0.767762i	$0.721371\pi$
$912$	−22.5775	−0.747617
$913$	−1.81951	−0.0602170
$914$	18.2188	0.602624
$915$	−8.41665	−0.278246
$916$	109.031	3.60248
$917$	1.32733	0.0438324
$918$	−112.489	−3.71270
$919$	−20.6550	−0.681344	−0.340672	−	0.940182i	$-0.610655\pi$
$919$	−20.6550	−0.681344	−0.340672	+	0.940182i	$0.610655\pi$
$920$	−16.6181	−0.547881
$921$	8.36102	0.275505
$922$	18.4714	0.608322
$923$	1.72890	0.0569074
$924$	−56.2002	−1.84885
$925$	−3.89801	−0.128166
$926$	10.5958	0.348199
$927$	6.14369	0.201785
$928$	8.50040	0.279039
$929$	41.8020	1.37148	0.685739	−	0.727847i	$-0.259479\pi$
$929$	41.8020	1.37148	0.685739	+	0.727847i	$0.259479\pi$
$930$	4.16767	0.136663
$931$	−9.19328	−0.301298
$932$	105.703	3.46241
$933$	−4.12376	−0.135006
$934$	50.7057	1.65914
$935$	−107.976	−3.53120
$936$	−3.54595	−0.115903
$937$	42.5645	1.39052	0.695261	−	0.718758i	$-0.255289\pi$
$937$	42.5645	1.39052	0.695261	+	0.718758i	$0.255289\pi$
$938$	20.4762	0.668570
$939$	−51.3640	−1.67620
$940$	134.270	4.37939
$941$	−53.9163	−1.75762	−0.878810	−	0.477171i	$-0.841662\pi$
$941$	−53.9163	−1.75762	−0.878810	+	0.477171i	$0.841662\pi$
$942$	−51.9773	−1.69351
$943$	−4.23437	−0.137890
$944$	74.3015	2.41831
$945$	−22.0435	−0.717075
$946$	−42.6760	−1.38752
$947$	−21.3516	−0.693833	−0.346917	−	0.937896i	$-0.612771\pi$
$947$	−21.3516	−0.693833	−0.346917	+	0.937896i	$0.612771\pi$
$948$	2.90852	0.0944644
$949$	9.71446	0.315345
$950$	−9.55484	−0.310000
$951$	42.9573	1.39299
$952$	−77.6763	−2.51750
$953$	0.260580	0.00844101	0.00422051	−	0.999991i	$-0.498657\pi$
$953$	0.260580	0.00844101	0.00422051	+	0.999991i	$0.498657\pi$
$954$	−6.69982	−0.216915
$955$	−40.7637	−1.31908
$956$	54.2432	1.75435
$957$	12.6365	0.408480
$958$	−4.54390	−0.146807
$959$	9.66096	0.311969
$960$	−0.897414	−0.0289639
$961$	−30.8497	−0.995151
$962$	−6.96934	−0.224701
$963$	3.09181	0.0996323
$964$	−34.5387	−1.11242
$965$	12.5241	0.403164
$966$	−6.24717	−0.201000
$967$	−14.6531	−0.471213	−0.235606	−	0.971849i	$-0.575708\pi$
$967$	−14.6531	−0.471213	−0.235606	+	0.971849i	$0.575708\pi$
$968$	−95.5036	−3.06960
$969$	−25.4481	−0.817510
$970$	−31.3025	−1.00506
$971$	−1.74029	−0.0558485	−0.0279242	−	0.999610i	$-0.508890\pi$
$971$	−1.74029	−0.0558485	−0.0279242	+	0.999610i	$0.508890\pi$
$972$	−19.3794	−0.621594
$973$	−1.44617	−0.0463621
$974$	−43.3719	−1.38973
$975$	4.09466	0.131134
$976$	−14.2263	−0.455374
$977$	−46.6213	−1.49155	−0.745773	−	0.666200i	$-0.767920\pi$
$977$	−46.6213	−1.49155	−0.745773	+	0.666200i	$0.767920\pi$
$978$	60.6869	1.94055
$979$	−48.3380	−1.54489
$980$	54.9945	1.75674
$981$	−4.97843	−0.158949
$982$	−35.5753	−1.13525
$983$	−35.0009	−1.11636	−0.558178	−	0.829721i	$-0.688499\pi$
$983$	−35.0009	−1.11636	−0.558178	+	0.829721i	$0.688499\pi$
$984$	43.0193	1.37141
$985$	57.9005	1.84486
$986$	31.5299	1.00412
$987$	27.9599	0.889975
$988$	−11.8136	−0.375842
$989$	−3.28050	−0.104314
$990$	−14.3280	−0.455374
$991$	31.1287	0.988834	0.494417	−	0.869225i	$-0.335382\pi$
$991$	31.1287	0.988834	0.494417	+	0.869225i	$0.335382\pi$
$992$	2.14063	0.0679652
$993$	51.0604	1.62035
$994$	5.02554	0.159400
$995$	20.7787	0.658728
$996$	2.56525	0.0812831
$997$	−24.5104	−0.776253	−0.388127	−	0.921606i	$-0.626878\pi$
$997$	−24.5104	−0.776253	−0.388127	+	0.921606i	$0.626878\pi$
$998$	−77.4537	−2.45175
$999$	−11.2381	−0.355559

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.d.1.11	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.d.1.11	✓	149	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54629 q^{2} -1.60651 q^{3} +4.48361 q^{4} -2.62778 q^{5} +4.09064 q^{6} +1.52719 q^{7} -6.32399 q^{8} -0.419134 q^{9} +O(q^{10})\)	\(q-2.54629 q^{2} -1.60651 q^{3} +4.48361 q^{4} -2.62778 q^{5} +4.09064 q^{6} +1.52719 q^{7} -6.32399 q^{8} -0.419134 q^{9} +6.69110 q^{10} +5.10899 q^{11} -7.20295 q^{12} -1.33779 q^{13} -3.88867 q^{14} +4.22155 q^{15} +7.13553 q^{16} +8.04275 q^{17} +1.06724 q^{18} +1.96955 q^{19} -11.7819 q^{20} -2.45344 q^{21} -13.0090 q^{22} -1.00000 q^{23} +10.1595 q^{24} +1.90523 q^{25} +3.40640 q^{26} +5.49286 q^{27} +6.84731 q^{28} -1.53961 q^{29} -10.7493 q^{30} -0.387715 q^{31} -5.52115 q^{32} -8.20763 q^{33} -20.4792 q^{34} -4.01311 q^{35} -1.87923 q^{36} -2.04595 q^{37} -5.01506 q^{38} +2.14917 q^{39} +16.6181 q^{40} +4.23437 q^{41} +6.24717 q^{42} +3.28050 q^{43} +22.9067 q^{44} +1.10139 q^{45} +2.54629 q^{46} -11.3962 q^{47} -11.4633 q^{48} -4.66770 q^{49} -4.85127 q^{50} -12.9207 q^{51} -5.99812 q^{52} -6.27772 q^{53} -13.9864 q^{54} -13.4253 q^{55} -9.65793 q^{56} -3.16410 q^{57} +3.92029 q^{58} +10.4129 q^{59} +18.9278 q^{60} -1.99373 q^{61} +0.987236 q^{62} -0.640096 q^{63} -0.212579 q^{64} +3.51542 q^{65} +20.8990 q^{66} -5.26560 q^{67} +36.0605 q^{68} +1.60651 q^{69} +10.2186 q^{70} -1.29235 q^{71} +2.65060 q^{72} -7.26158 q^{73} +5.20959 q^{74} -3.06076 q^{75} +8.83071 q^{76} +7.80239 q^{77} -5.47241 q^{78} -0.403796 q^{79} -18.7506 q^{80} -7.56692 q^{81} -10.7820 q^{82} -0.356139 q^{83} -11.0003 q^{84} -21.1346 q^{85} -8.35311 q^{86} +2.47339 q^{87} -32.3092 q^{88} -9.46136 q^{89} -2.80447 q^{90} -2.04306 q^{91} -4.48361 q^{92} +0.622867 q^{93} +29.0181 q^{94} -5.17555 q^{95} +8.86977 q^{96} -4.67822 q^{97} +11.8853 q^{98} -2.14135 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9}+O(q^{10}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9	\( 149 q - 5 q^{2} - 5 q^{3} + 135 q^{4} - 28 q^{5} - 5 q^{6} - 33 q^{7} - 15 q^{8} + 134 q^{9} - 30 q^{10} - 20 q^{11} - 32 q^{12} - 73 q^{13} - 18 q^{14} - 43 q^{15} + 99 q^{16} - 32 q^{17} - 50 q^{18} - 32 q^{19} - 67 q^{20} - 36 q^{21} - 78 q^{22} - 149 q^{23} - 27 q^{24} + 75 q^{25} + 7 q^{26} - 23 q^{27} - 90 q^{28} - 20 q^{29} - 12 q^{30} - 34 q^{31} - 35 q^{32} - 63 q^{33} - 43 q^{34} + 24 q^{35} + 98 q^{36} - 228 q^{37} - 25 q^{38} - 19 q^{39} - 79 q^{40} - 4 q^{41} - 88 q^{42} - 70 q^{43} - 80 q^{44} - 153 q^{45} + 5 q^{46} - 3 q^{47} - 95 q^{48} + 86 q^{49} - 5 q^{50} - 57 q^{51} - 146 q^{52} - 110 q^{53} - 18 q^{54} - 33 q^{55} - 75 q^{56} - 132 q^{57} - 92 q^{58} + 41 q^{59} - 107 q^{60} - 82 q^{61} - 34 q^{62} - 99 q^{63} + 35 q^{64} - 47 q^{65} - 58 q^{66} - 162 q^{67} - 80 q^{68} + 5 q^{69} - 88 q^{70} - q^{71} - 117 q^{72} - 124 q^{73} - 51 q^{74} - q^{75} - 74 q^{76} - 56 q^{77} - 95 q^{78} - 89 q^{79} - 90 q^{80} + 93 q^{81} - 91 q^{82} - 64 q^{83} - 93 q^{84} - 155 q^{85} - 21 q^{86} - 49 q^{87} - 263 q^{88} - 60 q^{89} - 122 q^{90} - 130 q^{91} - 135 q^{92} - 179 q^{93} - 21 q^{94} + 30 q^{95} - 17 q^{96} - 199 q^{97} - 72 q^{98} - 91 q^{99}+O(q^{100}) \) 149 * q - 5 * q^2 - 5 * q^3 + 135 * q^4 - 28 * q^5 - 5 * q^6 - 33 * q^7 - 15 * q^8 + 134 * q^9 - 30 * q^10 - 20 * q^11 - 32 * q^12 - 73 * q^13 - 18 * q^14 - 43 * q^15 + 99 * q^16 - 32 * q^17 - 50 * q^18 - 32 * q^19 - 67 * q^20 - 36 * q^21 - 78 * q^22 - 149 * q^23 - 27 * q^24 + 75 * q^25 + 7 * q^26 - 23 * q^27 - 90 * q^28 - 20 * q^29 - 12 * q^30 - 34 * q^31 - 35 * q^32 - 63 * q^33 - 43 * q^34 + 24 * q^35 + 98 * q^36 - 228 * q^37 - 25 * q^38 - 19 * q^39 - 79 * q^40 - 4 * q^41 - 88 * q^42 - 70 * q^43 - 80 * q^44 - 153 * q^45 + 5 * q^46 - 3 * q^47 - 95 * q^48 + 86 * q^49 - 5 * q^50 - 57 * q^51 - 146 * q^52 - 110 * q^53 - 18 * q^54 - 33 * q^55 - 75 * q^56 - 132 * q^57 - 92 * q^58 + 41 * q^59 - 107 * q^60 - 82 * q^61 - 34 * q^62 - 99 * q^63 + 35 * q^64 - 47 * q^65 - 58 * q^66 - 162 * q^67 - 80 * q^68 + 5 * q^69 - 88 * q^70 - q^71 - 117 * q^72 - 124 * q^73 - 51 * q^74 - q^75 - 74 * q^76 - 56 * q^77 - 95 * q^78 - 89 * q^79 - 90 * q^80 + 93 * q^81 - 91 * q^82 - 64 * q^83 - 93 * q^84 - 155 * q^85 - 21 * q^86 - 49 * q^87 - 263 * q^88 - 60 * q^89 - 122 * q^90 - 130 * q^91 - 135 * q^92 - 179 * q^93 - 21 * q^94 + 30 * q^95 - 17 * q^96 - 199 * q^97 - 72 * q^98 - 91 * q^99

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