LMFDB - Embedded newform 8017.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.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:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58337 q^{2} +1.72136 q^{3} +4.67379 q^{4} +0.176863 q^{5} -4.44690 q^{6} +3.62607 q^{7} -6.90738 q^{8} -0.0369272 q^{9} +O(q^{10})$	\(q-2.58337 q^{2} +1.72136 q^{3} +4.67379 q^{4} +0.176863 q^{5} -4.44690 q^{6} +3.62607 q^{7} -6.90738 q^{8} -0.0369272 q^{9} -0.456901 q^{10} -3.55533 q^{11} +8.04526 q^{12} +1.19466 q^{13} -9.36747 q^{14} +0.304444 q^{15} +8.49672 q^{16} +4.66127 q^{17} +0.0953965 q^{18} +2.28736 q^{19} +0.826618 q^{20} +6.24176 q^{21} +9.18474 q^{22} -6.19278 q^{23} -11.8901 q^{24} -4.96872 q^{25} -3.08624 q^{26} -5.22764 q^{27} +16.9475 q^{28} +2.60668 q^{29} -0.786490 q^{30} +4.82333 q^{31} -8.13539 q^{32} -6.12000 q^{33} -12.0418 q^{34} +0.641316 q^{35} -0.172590 q^{36} -2.00519 q^{37} -5.90909 q^{38} +2.05644 q^{39} -1.22166 q^{40} -9.19241 q^{41} -16.1248 q^{42} +3.43409 q^{43} -16.6169 q^{44} -0.00653104 q^{45} +15.9982 q^{46} -9.44386 q^{47} +14.6259 q^{48} +6.14837 q^{49} +12.8360 q^{50} +8.02371 q^{51} +5.58359 q^{52} -9.96364 q^{53} +13.5049 q^{54} -0.628806 q^{55} -25.0466 q^{56} +3.93736 q^{57} -6.73402 q^{58} -9.87362 q^{59} +1.42291 q^{60} -3.92327 q^{61} -12.4604 q^{62} -0.133901 q^{63} +4.02327 q^{64} +0.211291 q^{65} +15.8102 q^{66} -0.162951 q^{67} +21.7858 q^{68} -10.6600 q^{69} -1.65675 q^{70} -0.200214 q^{71} +0.255070 q^{72} -4.15846 q^{73} +5.18014 q^{74} -8.55294 q^{75} +10.6906 q^{76} -12.8919 q^{77} -5.31253 q^{78} -8.50861 q^{79} +1.50275 q^{80} -8.88785 q^{81} +23.7474 q^{82} +9.72734 q^{83} +29.1727 q^{84} +0.824404 q^{85} -8.87152 q^{86} +4.48704 q^{87} +24.5580 q^{88} +4.11413 q^{89} +0.0168721 q^{90} +4.33192 q^{91} -28.9437 q^{92} +8.30267 q^{93} +24.3970 q^{94} +0.404548 q^{95} -14.0039 q^{96} -14.0891 q^{97} -15.8835 q^{98} +0.131289 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.58337	−1.82672	−0.913358	−	0.407157i	$-0.866520\pi$
$2$	−2.58337	−1.82672	−0.913358	+	0.407157i	$0.866520\pi$
$3$	1.72136	0.993826	0.496913	−	0.867800i	$-0.334467\pi$
$3$	1.72136	0.993826	0.496913	+	0.867800i	$0.334467\pi$
$4$	4.67379	2.33689
$5$	0.176863	0.0790954	0.0395477	−	0.999218i	$-0.487408\pi$
$5$	0.176863	0.0790954	0.0395477	+	0.999218i	$0.487408\pi$
$6$	−4.44690	−1.81544
$7$	3.62607	1.37052	0.685262	−	0.728296i	$-0.259688\pi$
$7$	3.62607	1.37052	0.685262	+	0.728296i	$0.259688\pi$
$8$	−6.90738	−2.44213
$9$	−0.0369272	−0.0123091
$10$	−0.456901	−0.144485
$11$	−3.55533	−1.07197	−0.535987	−	0.844226i	$-0.680060\pi$
$11$	−3.55533	−1.07197	−0.535987	+	0.844226i	$0.680060\pi$
$12$	8.04526	2.32247
$13$	1.19466	0.331339	0.165669	−	0.986181i	$-0.447022\pi$
$13$	1.19466	0.331339	0.165669	+	0.986181i	$0.447022\pi$
$14$	−9.36747	−2.50356
$15$	0.304444	0.0786071
$16$	8.49672	2.12418
$17$	4.66127	1.13052	0.565262	−	0.824912i	$-0.308775\pi$
$17$	4.66127	1.13052	0.565262	+	0.824912i	$0.308775\pi$
$18$	0.0953965	0.0224852
$19$	2.28736	0.524756	0.262378	−	0.964965i	$-0.415493\pi$
$19$	2.28736	0.524756	0.262378	+	0.964965i	$0.415493\pi$
$20$	0.826618	0.184837
$21$	6.24176	1.36206
$22$	9.18474	1.95819
$23$	−6.19278	−1.29128	−0.645642	−	0.763640i	$-0.723410\pi$
$23$	−6.19278	−1.29128	−0.645642	+	0.763640i	$0.723410\pi$
$24$	−11.8901	−2.42705
$25$	−4.96872	−0.993744
$26$	−3.08624	−0.605262
$27$	−5.22764	−1.00606
$28$	16.9475	3.20277
$29$	2.60668	0.484049	0.242025	−	0.970270i	$-0.422189\pi$
$29$	2.60668	0.484049	0.242025	+	0.970270i	$0.422189\pi$
$30$	−0.786490	−0.143593
$31$	4.82333	0.866295	0.433148	−	0.901323i	$-0.357403\pi$
$31$	4.82333	0.866295	0.433148	+	0.901323i	$0.357403\pi$
$32$	−8.13539	−1.43815
$33$	−6.12000	−1.06536
$34$	−12.0418	−2.06515
$35$	0.641316	0.108402
$36$	−0.172590	−0.0287650
$37$	−2.00519	−0.329651	−0.164825	−	0.986323i	$-0.552706\pi$
$37$	−2.00519	−0.329651	−0.164825	+	0.986323i	$0.552706\pi$
$38$	−5.90909	−0.958581
$39$	2.05644	0.329293
$40$	−1.22166	−0.193161
$41$	−9.19241	−1.43561	−0.717807	−	0.696243i	$-0.754854\pi$
$41$	−9.19241	−1.43561	−0.717807	+	0.696243i	$0.754854\pi$
$42$	−16.1248	−2.48810
$43$	3.43409	0.523694	0.261847	−	0.965109i	$-0.415668\pi$
$43$	3.43409	0.523694	0.261847	+	0.965109i	$0.415668\pi$
$44$	−16.6169	−2.50509
$45$	−0.00653104	−0.000973590 0
$46$	15.9982	2.35881
$47$	−9.44386	−1.37753	−0.688764	−	0.724986i	$-0.741846\pi$
$47$	−9.44386	−1.37753	−0.688764	+	0.724986i	$0.741846\pi$
$48$	14.6259	2.11107
$49$	6.14837	0.878338
$50$	12.8360	1.81529
$51$	8.02371	1.12354
$52$	5.58359	0.774304
$53$	−9.96364	−1.36861	−0.684306	−	0.729195i	$-0.739895\pi$
$53$	−9.96364	−1.36861	−0.684306	+	0.729195i	$0.739895\pi$
$54$	13.5049	1.83779
$55$	−0.628806	−0.0847882
$56$	−25.0466	−3.34700
$57$	3.93736	0.521516
$58$	−6.73402	−0.884221
$59$	−9.87362	−1.28544	−0.642718	−	0.766103i	$-0.722193\pi$
$59$	−9.87362	−1.28544	−0.642718	+	0.766103i	$0.722193\pi$
$60$	1.42291	0.183696
$61$	−3.92327	−0.502323	−0.251162	−	0.967945i	$-0.580813\pi$
$61$	−3.92327	−0.502323	−0.251162	+	0.967945i	$0.580813\pi$
$62$	−12.4604	−1.58248
$63$	−0.133901	−0.0168699
$64$	4.02327	0.502909
$65$	0.211291	0.0262074
$66$	15.8102	1.94610
$67$	−0.162951	−0.0199077	−0.00995385	−	0.999950i	$-0.503168\pi$
$67$	−0.162951	−0.0199077	−0.00995385	+	0.999950i	$0.503168\pi$
$68$	21.7858	2.64191
$69$	−10.6600	−1.28331
$70$	−1.65675	−0.198020
$71$	−0.200214	−0.0237610	−0.0118805	−	0.999929i	$-0.503782\pi$
$71$	−0.200214	−0.0237610	−0.0118805	+	0.999929i	$0.503782\pi$
$72$	0.255070	0.0300603
$73$	−4.15846	−0.486711	−0.243356	−	0.969937i	$-0.578248\pi$
$73$	−4.15846	−0.486711	−0.243356	+	0.969937i	$0.578248\pi$
$74$	5.18014	0.602179
$75$	−8.55294	−0.987609
$76$	10.6906	1.22630
$77$	−12.8919	−1.46917
$78$	−5.31253	−0.601526
$79$	−8.50861	−0.957294	−0.478647	−	0.878007i	$-0.658873\pi$
$79$	−8.50861	−0.957294	−0.478647	+	0.878007i	$0.658873\pi$
$80$	1.50275	0.168013
$81$	−8.88785	−0.987539
$82$	23.7474	2.62246
$83$	9.72734	1.06771	0.533857	−	0.845575i	$-0.320742\pi$
$83$	9.72734	1.06771	0.533857	+	0.845575i	$0.320742\pi$
$84$	29.1727	3.18300
$85$	0.824404	0.0894192
$86$	−8.87152	−0.956641
$87$	4.48704	0.481061
$88$	24.5580	2.61790
$89$	4.11413	0.436096	0.218048	−	0.975938i	$-0.430031\pi$
$89$	4.11413	0.436096	0.218048	+	0.975938i	$0.430031\pi$
$90$	0.0168721	0.00177847
$91$	4.33192	0.454108
$92$	−28.9437	−3.01759
$93$	8.30267	0.860947
$94$	24.3970	2.51635
$95$	0.404548	0.0415058
$96$	−14.0039	−1.42927
$97$	−14.0891	−1.43053	−0.715265	−	0.698853i	$-0.753694\pi$
$97$	−14.0891	−1.43053	−0.715265	+	0.698853i	$0.753694\pi$
$98$	−15.8835	−1.60447
$99$	0.131289	0.0131950
$100$	−23.2227	−2.32227
$101$	3.66132	0.364315	0.182157	−	0.983269i	$-0.441692\pi$
$101$	3.66132	0.364315	0.182157	+	0.983269i	$0.441692\pi$
$102$	−20.7282	−2.05240
$103$	13.4288	1.32318	0.661592	−	0.749864i	$-0.269881\pi$
$103$	13.4288	1.32318	0.661592	+	0.749864i	$0.269881\pi$
$104$	−8.25196	−0.809172
$105$	1.10393	0.107733
$106$	25.7398	2.50007
$107$	−0.744078	−0.0719327	−0.0359663	−	0.999353i	$-0.511451\pi$
$107$	−0.744078	−0.0719327	−0.0359663	+	0.999353i	$0.511451\pi$
$108$	−24.4329	−2.35105
$109$	−8.69927	−0.833239	−0.416620	−	0.909081i	$-0.636785\pi$
$109$	−8.69927	−0.833239	−0.416620	+	0.909081i	$0.636785\pi$
$110$	1.62444	0.154884
$111$	−3.45165	−0.327616
$112$	30.8097	2.91124
$113$	−9.21187	−0.866580	−0.433290	−	0.901255i	$-0.642647\pi$
$113$	−9.21187	−0.866580	−0.433290	+	0.901255i	$0.642647\pi$
$114$	−10.1717	−0.952663
$115$	−1.09527	−0.102135
$116$	12.1831	1.13117
$117$	−0.0441154	−0.00407847
$118$	25.5072	2.34813
$119$	16.9021	1.54941
$120$	−2.10291	−0.191968
$121$	1.64040	0.149128
$122$	10.1352	0.917602
$123$	−15.8234	−1.42675
$124$	22.5432	2.02444
$125$	−1.76309	−0.157696
$126$	0.345914	0.0308165
$127$	12.9797	1.15177	0.575883	−	0.817532i	$-0.304659\pi$
$127$	12.9797	1.15177	0.575883	+	0.817532i	$0.304659\pi$
$128$	5.87719	0.519475
$129$	5.91130	0.520461
$130$	−0.545841	−0.0478735
$131$	−14.3341	−1.25237	−0.626187	−	0.779673i	$-0.715385\pi$
$131$	−14.3341	−1.25237	−0.626187	+	0.779673i	$0.715385\pi$
$132$	−28.6036	−2.48962
$133$	8.29412	0.719191
$134$	0.420964	0.0363657
$135$	−0.924574	−0.0795746
$136$	−32.1971	−2.76088
$137$	6.51906	0.556961	0.278480	−	0.960442i	$-0.410169\pi$
$137$	6.51906	0.556961	0.278480	+	0.960442i	$0.410169\pi$
$138$	27.5387	2.34425
$139$	6.45688	0.547665	0.273833	−	0.961777i	$-0.411709\pi$
$139$	6.45688	0.547665	0.273833	+	0.961777i	$0.411709\pi$
$140$	2.99737	0.253324
$141$	−16.2563	−1.36902
$142$	0.517226	0.0434046
$143$	−4.24741	−0.355187
$144$	−0.313760	−0.0261467
$145$	0.461025	0.0382860
$146$	10.7428	0.889084
$147$	10.5835	0.872915
$148$	−9.37182	−0.770359
$149$	23.0763	1.89048	0.945241	−	0.326372i	$-0.105826\pi$
$149$	23.0763	1.89048	0.945241	+	0.326372i	$0.105826\pi$
$150$	22.0954	1.80408
$151$	8.48058	0.690140	0.345070	−	0.938577i	$-0.387855\pi$
$151$	8.48058	0.690140	0.345070	+	0.938577i	$0.387855\pi$
$152$	−15.7997	−1.28152
$153$	−0.172128	−0.0139157
$154$	33.3045	2.68375
$155$	0.853066	0.0685199
$156$	9.61135	0.769524
$157$	−7.28218	−0.581181	−0.290591	−	0.956847i	$-0.593852\pi$
$157$	−7.28218	−0.581181	−0.290591	+	0.956847i	$0.593852\pi$
$158$	21.9809	1.74870
$159$	−17.1510	−1.36016
$160$	−1.43885	−0.113751
$161$	−22.4554	−1.76974
$162$	22.9606	1.80395
$163$	−19.6380	−1.53817	−0.769083	−	0.639149i	$-0.779287\pi$
$163$	−19.6380	−1.53817	−0.769083	+	0.639149i	$0.779287\pi$
$164$	−42.9634	−3.35488
$165$	−1.08240	−0.0842647
$166$	−25.1293	−1.95041
$167$	−11.1330	−0.861497	−0.430749	−	0.902472i	$-0.641750\pi$
$167$	−11.1330	−0.861497	−0.430749	+	0.902472i	$0.641750\pi$
$168$	−43.1142	−3.32633
$169$	−11.5728	−0.890215
$170$	−2.12974	−0.163344
$171$	−0.0844658	−0.00645926
$172$	16.0502	1.22382
$173$	3.13734	0.238527	0.119264	−	0.992863i	$-0.461947\pi$
$173$	3.13734	0.238527	0.119264	+	0.992863i	$0.461947\pi$
$174$	−11.5917	−0.878762
$175$	−18.0169	−1.36195
$176$	−30.2087	−2.27706
$177$	−16.9960	−1.27750
$178$	−10.6283	−0.796625
$179$	6.65966	0.497766	0.248883	−	0.968534i	$-0.419937\pi$
$179$	6.65966	0.497766	0.248883	+	0.968534i	$0.419937\pi$
$180$	−0.0305247	−0.00227518
$181$	−17.2907	−1.28520	−0.642602	−	0.766200i	$-0.722145\pi$
$181$	−17.2907	−1.28520	−0.642602	+	0.766200i	$0.722145\pi$
$182$	−11.1909	−0.829527
$183$	−6.75335	−0.499222
$184$	42.7759	3.15348
$185$	−0.354643	−0.0260739
$186$	−21.4489	−1.57271
$187$	−16.5724	−1.21189
$188$	−44.1386	−3.21914
$189$	−18.9558	−1.37883
$190$	−1.04510	−0.0758193
$191$	−14.3553	−1.03871	−0.519356	−	0.854558i	$-0.673828\pi$
$191$	−14.3553	−1.03871	−0.519356	+	0.854558i	$0.673828\pi$
$192$	6.92550	0.499805
$193$	16.5866	1.19393	0.596965	−	0.802267i	$-0.296373\pi$
$193$	16.5866	1.19393	0.596965	+	0.802267i	$0.296373\pi$
$194$	36.3973	2.61317
$195$	0.363707	0.0260456
$196$	28.7362	2.05258
$197$	−2.97495	−0.211956	−0.105978	−	0.994368i	$-0.533797\pi$
$197$	−2.97495	−0.211956	−0.105978	+	0.994368i	$0.533797\pi$
$198$	−0.339167	−0.0241035
$199$	−19.2793	−1.36667	−0.683336	−	0.730104i	$-0.739472\pi$
$199$	−19.2793	−1.36667	−0.683336	+	0.730104i	$0.739472\pi$
$200$	34.3208	2.42685
$201$	−0.280498	−0.0197848
$202$	−9.45854	−0.665500
$203$	9.45201	0.663401
$204$	37.5011	2.62560
$205$	−1.62579	−0.113550
$206$	−34.6917	−2.41708
$207$	0.228682	0.0158945
$208$	10.1507	0.703824
$209$	−8.13233	−0.562525
$210$	−2.85187	−0.196798
$211$	14.4367	0.993863	0.496932	−	0.867790i	$-0.334460\pi$
$211$	14.4367	0.993863	0.496932	+	0.867790i	$0.334460\pi$
$212$	−46.5680	−3.19830
$213$	−0.344640	−0.0236143
$214$	1.92223	0.131401
$215$	0.607363	0.0414218
$216$	36.1093	2.45692
$217$	17.4897	1.18728
$218$	22.4734	1.52209
$219$	−7.15820	−0.483707
$220$	−2.93890	−0.198141
$221$	5.56863	0.374587
$222$	8.91687	0.598461
$223$	0.638465	0.0427548	0.0213774	−	0.999771i	$-0.493195\pi$
$223$	0.638465	0.0427548	0.0213774	+	0.999771i	$0.493195\pi$
$224$	−29.4995	−1.97102
$225$	0.183481	0.0122321
$226$	23.7976	1.58300
$227$	0.0533141	0.00353858	0.00176929	−	0.999998i	$-0.499437\pi$
$227$	0.0533141	0.00353858	0.00176929	+	0.999998i	$0.499437\pi$
$228$	18.4024	1.21873
$229$	−16.8202	−1.11151	−0.555756	−	0.831346i	$-0.687571\pi$
$229$	−16.8202	−1.11151	−0.555756	+	0.831346i	$0.687571\pi$
$230$	2.82949	0.186571
$231$	−22.1915	−1.46010
$232$	−18.0054	−1.18211
$233$	14.0445	0.920088	0.460044	−	0.887896i	$-0.347834\pi$
$233$	14.0445	0.920088	0.460044	+	0.887896i	$0.347834\pi$
$234$	0.113966	0.00745022
$235$	−1.67027	−0.108956
$236$	−46.1472	−3.00393
$237$	−14.6464	−0.951384
$238$	−43.6643	−2.83033
$239$	−18.3591	−1.18755	−0.593774	−	0.804632i	$-0.702363\pi$
$239$	−18.3591	−1.18755	−0.593774	+	0.804632i	$0.702363\pi$
$240$	2.58677	0.166976
$241$	3.16491	0.203870	0.101935	−	0.994791i	$-0.467497\pi$
$241$	3.16491	0.203870	0.101935	+	0.994791i	$0.467497\pi$
$242$	−4.23776	−0.272414
$243$	0.383737	0.0246167
$244$	−18.3365	−1.17388
$245$	1.08742	0.0694725
$246$	40.8777	2.60627
$247$	2.73262	0.173872
$248$	−33.3165	−2.11560
$249$	16.7442	1.06112
$250$	4.55472	0.288066
$251$	−5.96067	−0.376234	−0.188117	−	0.982147i	$-0.560238\pi$
$251$	−5.96067	−0.376234	−0.188117	+	0.982147i	$0.560238\pi$
$252$	−0.625823	−0.0394231
$253$	22.0174	1.38422
$254$	−33.5314	−2.10395
$255$	1.41909	0.0888672
$256$	−23.2295	−1.45184
$257$	23.7926	1.48414	0.742070	−	0.670322i	$-0.233844\pi$
$257$	23.7926	1.48414	0.742070	+	0.670322i	$0.233844\pi$
$258$	−15.2711	−0.950735
$259$	−7.27095	−0.451795
$260$	0.987528	0.0612439
$261$	−0.0962576	−0.00595819
$262$	37.0302	2.28773
$263$	21.3327	1.31543	0.657716	−	0.753266i	$-0.271523\pi$
$263$	21.3327	1.31543	0.657716	+	0.753266i	$0.271523\pi$
$264$	42.2732	2.60173
$265$	−1.76220	−0.108251
$266$	−21.4268	−1.31376
$267$	7.08188	0.433404
$268$	−0.761601	−0.0465222
$269$	−4.44620	−0.271090	−0.135545	−	0.990771i	$-0.543278\pi$
$269$	−4.44620	−0.271090	−0.135545	+	0.990771i	$0.543278\pi$
$270$	2.38851	0.145360
$271$	22.5839	1.37187	0.685937	−	0.727661i	$-0.259393\pi$
$271$	22.5839	1.37187	0.685937	+	0.727661i	$0.259393\pi$
$272$	39.6055	2.40144
$273$	7.45678	0.451305
$274$	−16.8411	−1.01741
$275$	17.6655	1.06527
$276$	−49.8225	−2.99896
$277$	17.5909	1.05693	0.528467	−	0.848954i	$-0.322767\pi$
$277$	17.5909	1.05693	0.528467	+	0.848954i	$0.322767\pi$
$278$	−16.6805	−1.00043
$279$	−0.178112	−0.0106633
$280$	−4.42981	−0.264732
$281$	−18.1907	−1.08517	−0.542585	−	0.840001i	$-0.682554\pi$
$281$	−18.1907	−1.08517	−0.542585	+	0.840001i	$0.682554\pi$
$282$	41.9959	2.50082
$283$	−28.3725	−1.68657	−0.843285	−	0.537467i	$-0.819381\pi$
$283$	−28.3725	−1.68657	−0.843285	+	0.537467i	$0.819381\pi$
$284$	−0.935757	−0.0555270
$285$	0.696372	0.0412495
$286$	10.9726	0.648825
$287$	−33.3323	−1.96754
$288$	0.300417	0.0177023
$289$	4.72743	0.278084
$290$	−1.19100	−0.0699377
$291$	−24.2524	−1.42170
$292$	−19.4358	−1.13739
$293$	−4.54476	−0.265508	−0.132754	−	0.991149i	$-0.542382\pi$
$293$	−4.54476	−0.265508	−0.132754	+	0.991149i	$0.542382\pi$
$294$	−27.3412	−1.59457
$295$	−1.74627	−0.101672
$296$	13.8506	0.805049
$297$	18.5860	1.07847
$298$	−59.6145	−3.45338
$299$	−7.39826	−0.427853
$300$	−39.9747	−2.30794
$301$	12.4523	0.717736
$302$	−21.9085	−1.26069
$303$	6.30244	0.362066
$304$	19.4350	1.11468
$305$	−0.693880	−0.0397314
$306$	0.444669	0.0254200
$307$	−10.8115	−0.617045	−0.308523	−	0.951217i	$-0.599835\pi$
$307$	−10.8115	−0.617045	−0.308523	+	0.951217i	$0.599835\pi$
$308$	−60.2539	−3.43329
$309$	23.1159	1.31502
$310$	−2.20378	−0.125167
$311$	−7.37370	−0.418124	−0.209062	−	0.977902i	$-0.567041\pi$
$311$	−7.37370	−0.418124	−0.209062	+	0.977902i	$0.567041\pi$
$312$	−14.2046	−0.804176
$313$	3.10163	0.175314	0.0876571	−	0.996151i	$-0.472062\pi$
$313$	3.10163	0.175314	0.0876571	+	0.996151i	$0.472062\pi$
$314$	18.8125	1.06165
$315$	−0.0236820	−0.00133433
$316$	−39.7675	−2.23709
$317$	−8.73837	−0.490796	−0.245398	−	0.969422i	$-0.578919\pi$
$317$	−8.73837	−0.490796	−0.245398	+	0.969422i	$0.578919\pi$
$318$	44.3073	2.48463
$319$	−9.26763	−0.518888
$320$	0.711567	0.0397778
$321$	−1.28082	−0.0714886
$322$	58.0106	3.23281
$323$	10.6620	0.593249
$324$	−41.5400	−2.30778
$325$	−5.93593	−0.329266
$326$	50.7321	2.80979
$327$	−14.9746	−0.828095
$328$	63.4954	3.50595
$329$	−34.2441	−1.88794
$330$	2.79624	0.153928
$331$	1.89549	0.104186	0.0520928	−	0.998642i	$-0.483411\pi$
$331$	1.89549	0.104186	0.0520928	+	0.998642i	$0.483411\pi$
$332$	45.4635	2.49513
$333$	0.0740460	0.00405769
$334$	28.7606	1.57371
$335$	−0.0288200	−0.00157461
$336$	53.0345	2.89327
$337$	17.3280	0.943918	0.471959	−	0.881621i	$-0.343547\pi$
$337$	17.3280	0.943918	0.471959	+	0.881621i	$0.343547\pi$
$338$	29.8968	1.62617
$339$	−15.8569	−0.861230
$340$	3.85309	0.208963
$341$	−17.1485	−0.928646
$342$	0.218206	0.0117992
$343$	−3.08809	−0.166741
$344$	−23.7206	−1.27893
$345$	−1.88535	−0.101504
$346$	−8.10490	−0.435722
$347$	22.8703	1.22774	0.613872	−	0.789406i	$-0.289611\pi$
$347$	22.8703	1.22774	0.613872	+	0.789406i	$0.289611\pi$
$348$	20.9715	1.12419
$349$	14.1336	0.756554	0.378277	−	0.925692i	$-0.376517\pi$
$349$	14.1336	0.756554	0.378277	+	0.925692i	$0.376517\pi$
$350$	46.5443	2.48790
$351$	−6.24525	−0.333347
$352$	28.9240	1.54166
$353$	−9.65369	−0.513814	−0.256907	−	0.966436i	$-0.582703\pi$
$353$	−9.65369	−0.513814	−0.256907	+	0.966436i	$0.582703\pi$
$354$	43.9070	2.33363
$355$	−0.0354103	−0.00187939
$356$	19.2286	1.01911
$357$	29.0945	1.53985
$358$	−17.2043	−0.909278
$359$	−27.7572	−1.46497	−0.732486	−	0.680782i	$-0.761640\pi$
$359$	−27.7572	−1.46497	−0.732486	+	0.680782i	$0.761640\pi$
$360$	0.0451124	0.00237763
$361$	−13.7680	−0.724631
$362$	44.6681	2.34770
$363$	2.82372	0.148207
$364$	20.2465	1.06120
$365$	−0.735477	−0.0384966
$366$	17.4464	0.911937
$367$	14.0881	0.735394	0.367697	−	0.929946i	$-0.380146\pi$
$367$	14.0881	0.735394	0.367697	+	0.929946i	$0.380146\pi$
$368$	−52.6183	−2.74292
$369$	0.339450	0.0176711
$370$	0.916172	0.0476295
$371$	−36.1288	−1.87572
$372$	38.8049	2.01194
$373$	−29.7512	−1.54046	−0.770229	−	0.637767i	$-0.779858\pi$
$373$	−29.7512	−1.54046	−0.770229	+	0.637767i	$0.779858\pi$
$374$	42.8125	2.21378
$375$	−3.03492	−0.156722
$376$	65.2323	3.36410
$377$	3.11410	0.160384
$378$	48.9697	2.51873
$379$	10.5311	0.540949	0.270474	−	0.962727i	$-0.412819\pi$
$379$	10.5311	0.540949	0.270474	+	0.962727i	$0.412819\pi$
$380$	1.89077	0.0969946
$381$	22.3428	1.14465
$382$	37.0850	1.89743
$383$	0.592243	0.0302622	0.0151311	−	0.999886i	$-0.495183\pi$
$383$	0.592243	0.0302622	0.0151311	+	0.999886i	$0.495183\pi$
$384$	10.1167	0.516268
$385$	−2.28009	−0.116204
$386$	−42.8493	−2.18097
$387$	−0.126811	−0.00644619
$388$	−65.8494	−3.34300
$389$	18.2490	0.925259	0.462629	−	0.886552i	$-0.346906\pi$
$389$	18.2490	0.925259	0.462629	+	0.886552i	$0.346906\pi$
$390$	−0.939588	−0.0475779
$391$	−28.8662	−1.45983
$392$	−42.4691	−2.14501
$393$	−24.6741	−1.24464
$394$	7.68538	0.387184
$395$	−1.50486	−0.0757175
$396$	0.613615	0.0308353
$397$	5.92800	0.297518	0.148759	−	0.988873i	$-0.452472\pi$
$397$	5.92800	0.297518	0.148759	+	0.988873i	$0.452472\pi$
$398$	49.8055	2.49652
$399$	14.2771	0.714751
$400$	−42.2178	−2.11089
$401$	−33.8033	−1.68806	−0.844028	−	0.536299i	$-0.819822\pi$
$401$	−33.8033	−1.68806	−0.844028	+	0.536299i	$0.819822\pi$
$402$	0.724629	0.0361412
$403$	5.76223	0.287037
$404$	17.1122	0.851366
$405$	−1.57193	−0.0781098
$406$	−24.4180	−1.21185
$407$	7.12911	0.353377
$408$	−55.4228	−2.74384
$409$	9.01112	0.445571	0.222786	−	0.974867i	$-0.428485\pi$
$409$	9.01112	0.445571	0.222786	+	0.974867i	$0.428485\pi$
$410$	4.20002	0.207424
$411$	11.2216	0.553522
$412$	62.7636	3.09214
$413$	−35.8024	−1.76172
$414$	−0.590770	−0.0290348
$415$	1.72040	0.0844512
$416$	−9.71903	−0.476514
$417$	11.1146	0.544284
$418$	21.0088	1.02757
$419$	20.4084	0.997014	0.498507	−	0.866886i	$-0.333882\pi$
$419$	20.4084	0.997014	0.498507	+	0.866886i	$0.333882\pi$
$420$	5.15955	0.251760
$421$	17.5319	0.854452	0.427226	−	0.904145i	$-0.359491\pi$
$421$	17.5319	0.854452	0.427226	+	0.904145i	$0.359491\pi$
$422$	−37.2953	−1.81551
$423$	0.348735	0.0169561
$424$	68.8226	3.34232
$425$	−23.1605	−1.12345
$426$	0.890331	0.0431367
$427$	−14.2260	−0.688446
$428$	−3.47766	−0.168099
$429$	−7.31132	−0.352994
$430$	−1.56904	−0.0756659
$431$	−9.62952	−0.463838	−0.231919	−	0.972735i	$-0.574500\pi$
$431$	−9.62952	−0.463838	−0.231919	+	0.972735i	$0.574500\pi$
$432$	−44.4178	−2.13705
$433$	16.8421	0.809381	0.404691	−	0.914454i	$-0.367379\pi$
$433$	16.8421	0.809381	0.404691	+	0.914454i	$0.367379\pi$
$434$	−45.1824	−2.16882
$435$	0.793589	0.0380497
$436$	−40.6586	−1.94719
$437$	−14.1651	−0.677609
$438$	18.4923	0.883595
$439$	10.6323	0.507454	0.253727	−	0.967276i	$-0.418343\pi$
$439$	10.6323	0.507454	0.253727	+	0.967276i	$0.418343\pi$
$440$	4.34340	0.207063
$441$	−0.227042	−0.0108115
$442$	−14.3858	−0.684264
$443$	−14.7139	−0.699078	−0.349539	−	0.936922i	$-0.613662\pi$
$443$	−14.7139	−0.699078	−0.349539	+	0.936922i	$0.613662\pi$
$444$	−16.1323	−0.765603
$445$	0.727635	0.0344932
$446$	−1.64939	−0.0781008
$447$	39.7225	1.87881
$448$	14.5887	0.689250
$449$	14.7499	0.696092	0.348046	−	0.937477i	$-0.386845\pi$
$449$	14.7499	0.696092	0.348046	+	0.937477i	$0.386845\pi$
$450$	−0.473999	−0.0223445
$451$	32.6821	1.53894
$452$	−43.0543	−2.02511
$453$	14.5981	0.685879
$454$	−0.137730	−0.00646398
$455$	0.766154	0.0359179
$456$	−27.1969	−1.27361
$457$	−14.8306	−0.693748	−0.346874	−	0.937912i	$-0.612757\pi$
$457$	−14.8306	−0.693748	−0.346874	+	0.937912i	$0.612757\pi$
$458$	43.4528	2.03042
$459$	−24.3674	−1.13737
$460$	−5.11907	−0.238678
$461$	2.73384	0.127328	0.0636638	−	0.997971i	$-0.479721\pi$
$461$	2.73384	0.127328	0.0636638	+	0.997971i	$0.479721\pi$
$462$	57.3289	2.66718
$463$	11.5581	0.537151	0.268576	−	0.963259i	$-0.413447\pi$
$463$	11.5581	0.537151	0.268576	+	0.963259i	$0.413447\pi$
$464$	22.1483	1.02821
$465$	1.46843	0.0680969
$466$	−36.2822	−1.68074
$467$	−1.85987	−0.0860645	−0.0430323	−	0.999074i	$-0.513702\pi$
$467$	−1.85987	−0.0860645	−0.0430323	+	0.999074i	$0.513702\pi$
$468$	−0.206186	−0.00953096
$469$	−0.590873	−0.0272840
$470$	4.31491	0.199032
$471$	−12.5352	−0.577593
$472$	68.2008	3.13920
$473$	−12.2093	−0.561386
$474$	37.8370	1.73791
$475$	−11.3652	−0.521473
$476$	78.9967	3.62081
$477$	0.367929	0.0168463
$478$	47.4282	2.16932
$479$	36.4845	1.66702	0.833509	−	0.552505i	$-0.186328\pi$
$479$	36.4845	1.66702	0.833509	+	0.552505i	$0.186328\pi$
$480$	−2.47677	−0.113049
$481$	−2.39552	−0.109226
$482$	−8.17613	−0.372412
$483$	−38.6538	−1.75881
$484$	7.66690	0.348495
$485$	−2.49183	−0.113148
$486$	−0.991333	−0.0449678
$487$	15.8979	0.720402	0.360201	−	0.932875i	$-0.382708\pi$
$487$	15.8979	0.720402	0.360201	+	0.932875i	$0.382708\pi$
$488$	27.0995	1.22674
$489$	−33.8040	−1.52867
$490$	−2.80920	−0.126907
$491$	11.9634	0.539899	0.269950	−	0.962874i	$-0.412993\pi$
$491$	11.9634	0.539899	0.269950	+	0.962874i	$0.412993\pi$
$492$	−73.9553	−3.33416
$493$	12.1505	0.547229
$494$	−7.05935	−0.317615
$495$	0.0232200	0.00104366
$496$	40.9825	1.84017
$497$	−0.725989	−0.0325651
$498$	−43.2565	−1.93837
$499$	−15.1554	−0.678450	−0.339225	−	0.940705i	$-0.610165\pi$
$499$	−15.1554	−0.678450	−0.339225	+	0.940705i	$0.610165\pi$
$500$	−8.24033	−0.368519
$501$	−19.1639	−0.856179
$502$	15.3986	0.687273
$503$	−2.82088	−0.125777	−0.0628884	−	0.998021i	$-0.520031\pi$
$503$	−2.82088	−0.125777	−0.0628884	+	0.998021i	$0.520031\pi$
$504$	0.924902	0.0411984
$505$	0.647551	0.0288156
$506$	−56.8790	−2.52858
$507$	−19.9209	−0.884719
$508$	60.6645	2.69155
$509$	33.1969	1.47143	0.735714	−	0.677292i	$-0.236847\pi$
$509$	33.1969	1.47143	0.735714	+	0.677292i	$0.236847\pi$
$510$	−3.66604	−0.162335
$511$	−15.0789	−0.667050
$512$	48.2559	2.13263
$513$	−11.9575	−0.527936
$514$	−61.4650	−2.71110
$515$	2.37506	0.104658
$516$	27.6282	1.21626
$517$	33.5761	1.47667
$518$	18.7835	0.825301
$519$	5.40048	0.237055
$520$	−1.45946	−0.0640017
$521$	−33.1409	−1.45193	−0.725966	−	0.687731i	$-0.758607\pi$
$521$	−33.1409	−1.45193	−0.725966	+	0.687731i	$0.758607\pi$
$522$	0.248669	0.0108839
$523$	−26.2110	−1.14613	−0.573063	−	0.819511i	$-0.694245\pi$
$523$	−26.2110	−1.14613	−0.573063	+	0.819511i	$0.694245\pi$
$524$	−66.9944	−2.92666
$525$	−31.0136	−1.35354
$526$	−55.1103	−2.40292
$527$	22.4828	0.979367
$528$	−51.9999	−2.26301
$529$	15.3505	0.667414
$530$	4.55240	0.197744
$531$	0.364605	0.0158225
$532$	38.7649	1.68067
$533$	−10.9818	−0.475675
$534$	−18.2951	−0.791707
$535$	−0.131600	−0.00568954
$536$	1.12557	0.0486171
$537$	11.4637	0.494693
$538$	11.4862	0.495204
$539$	−21.8595	−0.941555
$540$	−4.32126	−0.185958
$541$	18.9984	0.816805	0.408402	−	0.912802i	$-0.366086\pi$
$541$	18.9984	0.816805	0.408402	+	0.912802i	$0.366086\pi$
$542$	−58.3425	−2.50603
$543$	−29.7634	−1.27727
$544$	−37.9213	−1.62586
$545$	−1.53858	−0.0659054
$546$	−19.2636	−0.824406
$547$	18.4581	0.789213	0.394606	−	0.918850i	$-0.370881\pi$
$547$	18.4581	0.789213	0.394606	+	0.918850i	$0.370881\pi$
$548$	30.4687	1.30156
$549$	0.144875	0.00618313
$550$	−45.6364	−1.94594
$551$	5.96242	0.254008
$552$	73.6326	3.13401
$553$	−30.8528	−1.31199
$554$	−45.4438	−1.93072
$555$	−0.610467	−0.0259129
$556$	30.1781	1.27984
$557$	−10.1870	−0.431638	−0.215819	−	0.976433i	$-0.569242\pi$
$557$	−10.1870	−0.431638	−0.215819	+	0.976433i	$0.569242\pi$
$558$	0.460129	0.0194788
$559$	4.10257	0.173520
$560$	5.44908	0.230266
$561$	−28.5270	−1.20441
$562$	46.9934	1.98230
$563$	−32.3788	−1.36460	−0.682301	−	0.731071i	$-0.739021\pi$
$563$	−32.3788	−1.36460	−0.682301	+	0.731071i	$0.739021\pi$
$564$	−75.9783	−3.19926
$565$	−1.62924	−0.0685424
$566$	73.2966	3.08089
$567$	−32.2280	−1.35345
$568$	1.38295	0.0580274
$569$	18.7693	0.786850	0.393425	−	0.919357i	$-0.371290\pi$
$569$	18.7693	0.786850	0.393425	+	0.919357i	$0.371290\pi$
$570$	−1.79899	−0.0753512
$571$	7.00879	0.293309	0.146654	−	0.989188i	$-0.453150\pi$
$571$	7.00879	0.293309	0.146654	+	0.989188i	$0.453150\pi$
$572$	−19.8515	−0.830034
$573$	−24.7106	−1.03230
$574$	86.1096	3.59414
$575$	30.7702	1.28321
$576$	−0.148568	−0.00619035
$577$	37.4969	1.56102	0.780508	−	0.625146i	$-0.214960\pi$
$577$	37.4969	1.56102	0.780508	+	0.625146i	$0.214960\pi$
$578$	−12.2127	−0.507981
$579$	28.5515	1.18656
$580$	2.15473	0.0894704
$581$	35.2720	1.46333
$582$	62.6528	2.59704
$583$	35.4241	1.46712
$584$	28.7241	1.18861
$585$	−0.00780237	−0.000322588 0
$586$	11.7408	0.485007
$587$	−22.3668	−0.923177	−0.461588	−	0.887094i	$-0.652720\pi$
$587$	−22.3668	−0.923177	−0.461588	+	0.887094i	$0.652720\pi$
$588$	49.4652	2.03991
$589$	11.0327	0.454594
$590$	4.51127	0.185726
$591$	−5.12095	−0.210648
$592$	−17.0375	−0.700238
$593$	0.411376	0.0168932	0.00844660	−	0.999964i	$-0.497311\pi$
$593$	0.411376	0.0168932	0.00844660	+	0.999964i	$0.497311\pi$
$594$	−48.0145	−1.97006
$595$	2.98935	0.122551
$596$	107.854	4.41786
$597$	−33.1866	−1.35824
$598$	19.1124	0.781566
$599$	12.0534	0.492490	0.246245	−	0.969208i	$-0.420803\pi$
$599$	12.0534	0.492490	0.246245	+	0.969208i	$0.420803\pi$
$600$	59.0784	2.41187
$601$	−8.42339	−0.343597	−0.171799	−	0.985132i	$-0.554958\pi$
$601$	−8.42339	−0.343597	−0.171799	+	0.985132i	$0.554958\pi$
$602$	−32.1687	−1.31110
$603$	0.00601734	0.000245045 0
$604$	39.6364	1.61278
$605$	0.290126	0.0117953
$606$	−16.2815	−0.661392
$607$	−15.1157	−0.613528	−0.306764	−	0.951786i	$-0.599246\pi$
$607$	−15.1157	−0.613528	−0.306764	+	0.951786i	$0.599246\pi$
$608$	−18.6086	−0.754677
$609$	16.2703	0.659306
$610$	1.79255	0.0725781
$611$	−11.2822	−0.456429
$612$	−0.804488	−0.0325195
$613$	19.9304	0.804981	0.402491	−	0.915424i	$-0.368145\pi$
$613$	19.9304	0.804981	0.402491	+	0.915424i	$0.368145\pi$
$614$	27.9301	1.12717
$615$	−2.79857	−0.112849
$616$	89.0491	3.58789
$617$	28.7206	1.15625	0.578124	−	0.815949i	$-0.303785\pi$
$617$	28.7206	1.15625	0.578124	+	0.815949i	$0.303785\pi$
$618$	−59.7168	−2.40216
$619$	3.95473	0.158954	0.0794771	−	0.996837i	$-0.474675\pi$
$619$	3.95473	0.158954	0.0794771	+	0.996837i	$0.474675\pi$
$620$	3.98705	0.160124
$621$	32.3736	1.29911
$622$	19.0490	0.763794
$623$	14.9181	0.597681
$624$	17.4730	0.699478
$625$	24.5318	0.981271
$626$	−8.01264	−0.320250
$627$	−13.9986	−0.559052
$628$	−34.0354	−1.35816
$629$	−9.34672	−0.372678
$630$	0.0611793	0.00243744
$631$	20.3908	0.811746	0.405873	−	0.913930i	$-0.366968\pi$
$631$	20.3908	0.811746	0.405873	+	0.913930i	$0.366968\pi$
$632$	58.7722	2.33783
$633$	24.8507	0.987728
$634$	22.5744	0.896544
$635$	2.29563	0.0910993
$636$	−80.1601	−3.17856
$637$	7.34520	0.291028
$638$	23.9417	0.947861
$639$	0.00739334	0.000292476 0
$640$	1.03946	0.0410881
$641$	−2.97985	−0.117697	−0.0588484	−	0.998267i	$-0.518743\pi$
$641$	−2.97985	−0.117697	−0.0588484	+	0.998267i	$0.518743\pi$
$642$	3.30884	0.130589
$643$	−25.5240	−1.00657	−0.503284	−	0.864121i	$-0.667875\pi$
$643$	−25.5240	−1.00657	−0.503284	+	0.864121i	$0.667875\pi$
$644$	−104.952	−4.13569
$645$	1.04549	0.0411661
$646$	−27.5439	−1.08370
$647$	42.5393	1.67239	0.836196	−	0.548430i	$-0.184774\pi$
$647$	42.5393	1.67239	0.836196	+	0.548430i	$0.184774\pi$
$648$	61.3918	2.41170
$649$	35.1040	1.37795
$650$	15.3347	0.601476
$651$	30.1061	1.17995
$652$	−91.7838	−3.59453
$653$	22.1322	0.866101	0.433051	−	0.901370i	$-0.357437\pi$
$653$	22.1322	0.866101	0.433051	+	0.901370i	$0.357437\pi$
$654$	38.6848	1.51270
$655$	−2.53516	−0.0990569
$656$	−78.1053	−3.04950
$657$	0.153560	0.00599096
$658$	88.4650	3.44873
$659$	1.35105	0.0526292	0.0263146	−	0.999654i	$-0.491623\pi$
$659$	1.35105	0.0526292	0.0263146	+	0.999654i	$0.491623\pi$
$660$	−5.05891	−0.196918
$661$	−13.5131	−0.525599	−0.262800	−	0.964850i	$-0.584646\pi$
$661$	−13.5131	−0.525599	−0.262800	+	0.964850i	$0.584646\pi$
$662$	−4.89675	−0.190318
$663$	9.58560	0.372274
$664$	−67.1904	−2.60749
$665$	1.46692	0.0568847
$666$	−0.191288	−0.00741226
$667$	−16.1426	−0.625045
$668$	−52.0333	−2.01323
$669$	1.09903	0.0424908
$670$	0.0744527	0.00287636
$671$	13.9485	0.538477
$672$	−50.7792	−1.95885
$673$	−16.6888	−0.643306	−0.321653	−	0.946858i	$-0.604238\pi$
$673$	−16.6888	−0.643306	−0.321653	+	0.946858i	$0.604238\pi$
$674$	−44.7647	−1.72427
$675$	25.9747	0.999766
$676$	−54.0888	−2.08034
$677$	−32.5222	−1.24993	−0.624965	−	0.780652i	$-0.714887\pi$
$677$	−32.5222	−1.24993	−0.624965	+	0.780652i	$0.714887\pi$
$678$	40.9643	1.57322
$679$	−51.0880	−1.96058
$680$	−5.69447	−0.218373
$681$	0.0917726	0.00351673
$682$	44.3010	1.69637
$683$	−14.7169	−0.563127	−0.281564	−	0.959543i	$-0.590853\pi$
$683$	−14.7169	−0.563127	−0.281564	+	0.959543i	$0.590853\pi$
$684$	−0.394775	−0.0150946
$685$	1.15298	0.0440530
$686$	7.97766	0.304588
$687$	−28.9536	−1.10465
$688$	29.1785	1.11242
$689$	−11.9032	−0.453474
$690$	4.87056	0.185419
$691$	−13.9788	−0.531778	−0.265889	−	0.964004i	$-0.585666\pi$
$691$	−13.9788	−0.531778	−0.265889	+	0.964004i	$0.585666\pi$
$692$	14.6633	0.557413
$693$	0.476061	0.0180841
$694$	−59.0825	−2.24274
$695$	1.14198	0.0433178
$696$	−30.9937	−1.17481
$697$	−42.8483	−1.62299
$698$	−36.5123	−1.38201
$699$	24.1757	0.914408
$700$	−84.2072	−3.18273
$701$	33.2233	1.25483	0.627413	−	0.778687i	$-0.284114\pi$
$701$	33.2233	1.25483	0.627413	+	0.778687i	$0.284114\pi$
$702$	16.1338	0.608930
$703$	−4.58658	−0.172986
$704$	−14.3041	−0.539106
$705$	−2.87512	−0.108283
$706$	24.9390	0.938593
$707$	13.2762	0.499303
$708$	−79.4359	−2.98538
$709$	37.3012	1.40088	0.700438	−	0.713713i	$-0.252988\pi$
$709$	37.3012	1.40088	0.700438	+	0.713713i	$0.252988\pi$
$710$	0.0914779	0.00343311
$711$	0.314199	0.0117834
$712$	−28.4178	−1.06500
$713$	−29.8698	−1.11863
$714$	−75.1618	−2.81286
$715$	−0.751209	−0.0280936
$716$	31.1258	1.16323
$717$	−31.6025	−1.18022
$718$	71.7072	2.67609
$719$	10.5420	0.393149	0.196575	−	0.980489i	$-0.437018\pi$
$719$	10.5420	0.393149	0.196575	+	0.980489i	$0.437018\pi$
$720$	−0.0554924	−0.00206808
$721$	48.6939	1.81346
$722$	35.5678	1.32370
$723$	5.44794	0.202611
$724$	−80.8129	−3.00339
$725$	−12.9519	−0.481021
$726$	−7.29471	−0.270732
$727$	−24.6101	−0.912739	−0.456369	−	0.889790i	$-0.650850\pi$
$727$	−24.6101	−0.912739	−0.456369	+	0.889790i	$0.650850\pi$
$728$	−29.9222	−1.10899
$729$	27.3241	1.01200
$730$	1.90001	0.0703224
$731$	16.0072	0.592049
$732$	−31.5637	−1.16663
$733$	−13.6172	−0.502962	−0.251481	−	0.967862i	$-0.580918\pi$
$733$	−13.6172	−0.502962	−0.251481	+	0.967862i	$0.580918\pi$
$734$	−36.3948	−1.34336
$735$	1.87183	0.0690436
$736$	50.3807	1.85706
$737$	0.579347	0.0213405
$738$	−0.876924	−0.0322800
$739$	−1.58326	−0.0582410	−0.0291205	−	0.999576i	$-0.509271\pi$
$739$	−1.58326	−0.0582410	−0.0291205	+	0.999576i	$0.509271\pi$
$740$	−1.65752	−0.0609318
$741$	4.70381	0.172799
$742$	93.3341	3.42640
$743$	26.4827	0.971557	0.485779	−	0.874082i	$-0.338536\pi$
$743$	26.4827	0.971557	0.485779	+	0.874082i	$0.338536\pi$
$744$	−57.3497	−2.10254
$745$	4.08133	0.149528
$746$	76.8583	2.81398
$747$	−0.359203	−0.0131426
$748$	−77.4557	−2.83206
$749$	−2.69808	−0.0985855
$750$	7.84030	0.286287
$751$	−30.1530	−1.10030	−0.550149	−	0.835066i	$-0.685429\pi$
$751$	−30.1530	−1.10030	−0.550149	+	0.835066i	$0.685429\pi$
$752$	−80.2418	−2.92612
$753$	−10.2604	−0.373911
$754$	−8.04486	−0.292977
$755$	1.49990	0.0545869
$756$	−88.5953	−3.22218
$757$	−37.1512	−1.35028	−0.675142	−	0.737687i	$-0.735918\pi$
$757$	−37.1512	−1.35028	−0.675142	+	0.737687i	$0.735918\pi$
$758$	−27.2058	−0.988160
$759$	37.8998	1.37568
$760$	−2.79437	−0.101362
$761$	−14.5782	−0.528458	−0.264229	−	0.964460i	$-0.585118\pi$
$761$	−14.5782	−0.528458	−0.264229	+	0.964460i	$0.585118\pi$
$762$	−57.7196	−2.09096
$763$	−31.5442	−1.14197
$764$	−67.0936	−2.42736
$765$	−0.0304429	−0.00110067
$766$	−1.52998	−0.0552805
$767$	−11.7956	−0.425915
$768$	−39.9863	−1.44288
$769$	−36.2972	−1.30891	−0.654454	−	0.756101i	$-0.727102\pi$
$769$	−36.2972	−1.30891	−0.654454	+	0.756101i	$0.727102\pi$
$770$	5.89032	0.212272
$771$	40.9555	1.47498
$772$	77.5223	2.79009
$773$	−23.3317	−0.839183	−0.419592	−	0.907713i	$-0.637827\pi$
$773$	−23.3317	−0.839183	−0.419592	+	0.907713i	$0.637827\pi$
$774$	0.327601	0.0117754
$775$	−23.9658	−0.860876
$776$	97.3187	3.49354
$777$	−12.5159	−0.449005
$778$	−47.1437	−1.69019
$779$	−21.0263	−0.753347
$780$	1.69989	0.0608658
$781$	0.711827	0.0254712
$782$	74.5720	2.66669
$783$	−13.6268	−0.486982
$784$	52.2409	1.86575
$785$	−1.28795	−0.0459687
$786$	63.7422	2.27361
$787$	33.6453	1.19932	0.599662	−	0.800253i	$-0.295302\pi$
$787$	33.6453	1.19932	0.599662	+	0.800253i	$0.295302\pi$
$788$	−13.9043	−0.495319
$789$	36.7213	1.30731
$790$	3.88760	0.138314
$791$	−33.4029	−1.18767
$792$	−0.906860	−0.0322239
$793$	−4.68697	−0.166439
$794$	−15.3142	−0.543481
$795$	−3.03337	−0.107583
$796$	−90.1073	−3.19377
$797$	−40.7334	−1.44285	−0.721426	−	0.692491i	$-0.756513\pi$
$797$	−40.7334	−1.44285	−0.721426	+	0.692491i	$0.756513\pi$
$798$	−36.8831	−1.30565
$799$	−44.0204	−1.55733
$800$	40.4225	1.42915
$801$	−0.151923	−0.00536794
$802$	87.3263	3.08360
$803$	14.7847	0.521742
$804$	−1.31099	−0.0462350
$805$	−3.97153	−0.139978
$806$	−14.8860	−0.524336
$807$	−7.65350	−0.269416
$808$	−25.2901	−0.889703
$809$	−38.5014	−1.35364	−0.676819	−	0.736149i	$-0.736642\pi$
$809$	−38.5014	−1.35364	−0.676819	+	0.736149i	$0.736642\pi$
$810$	4.06087	0.142684
$811$	−11.9088	−0.418174	−0.209087	−	0.977897i	$-0.567049\pi$
$811$	−11.9088	−0.418174	−0.209087	+	0.977897i	$0.567049\pi$
$812$	44.1767	1.55030
$813$	38.8750	1.36340
$814$	−18.4171	−0.645520
$815$	−3.47322	−0.121662
$816$	68.1752	2.38661
$817$	7.85500	0.274812
$818$	−23.2790	−0.813933
$819$	−0.159966	−0.00558965
$820$	−7.59861	−0.265355
$821$	52.0101	1.81517	0.907583	−	0.419872i	$-0.137925\pi$
$821$	52.0101	1.81517	0.907583	+	0.419872i	$0.137925\pi$
$822$	−28.9896	−1.01113
$823$	27.5810	0.961414	0.480707	−	0.876881i	$-0.340380\pi$
$823$	27.5810	0.961414	0.480707	+	0.876881i	$0.340380\pi$
$824$	−92.7581	−3.23138
$825$	30.4086	1.05869
$826$	92.4908	3.21817
$827$	−3.16853	−0.110181	−0.0550903	−	0.998481i	$-0.517545\pi$
$827$	−3.16853	−0.110181	−0.0550903	+	0.998481i	$0.517545\pi$
$828$	1.06881	0.0371438
$829$	−44.2496	−1.53685	−0.768427	−	0.639938i	$-0.778960\pi$
$829$	−44.2496	−1.53685	−0.768427	+	0.639938i	$0.778960\pi$
$830$	−4.44443	−0.154269
$831$	30.2802	1.05041
$832$	4.80644	0.166633
$833$	28.6592	0.992982
$834$	−28.7131	−0.994253
$835$	−1.96901	−0.0681405
$836$	−38.0088	−1.31456
$837$	−25.2146	−0.871545
$838$	−52.7223	−1.82126
$839$	−2.42543	−0.0837352	−0.0418676	−	0.999123i	$-0.513331\pi$
$839$	−2.42543	−0.0837352	−0.0418676	+	0.999123i	$0.513331\pi$
$840$	−7.62529	−0.263097
$841$	−22.2052	−0.765696
$842$	−45.2913	−1.56084
$843$	−31.3128	−1.07847
$844$	67.4741	2.32255
$845$	−2.04679	−0.0704118
$846$	−0.900911	−0.0309740
$847$	5.94821	0.204383
$848$	−84.6583	−2.90718
$849$	−48.8392	−1.67616
$850$	59.8322	2.05223
$851$	12.4177	0.425673
$852$	−1.61077	−0.0551842
$853$	−43.4722	−1.48846	−0.744229	−	0.667925i	$-0.767183\pi$
$853$	−43.4722	−1.48846	−0.744229	+	0.667925i	$0.767183\pi$
$854$	36.7511	1.25760
$855$	−0.0149388	−0.000510897 0
$856$	5.13962	0.175669
$857$	−24.0817	−0.822615	−0.411308	−	0.911497i	$-0.634928\pi$
$857$	−24.0817	−0.822615	−0.411308	+	0.911497i	$0.634928\pi$
$858$	18.8878	0.644820
$859$	−55.9261	−1.90817	−0.954087	−	0.299531i	$-0.903170\pi$
$859$	−55.9261	−1.90817	−0.954087	+	0.299531i	$0.903170\pi$
$860$	2.83868	0.0967983
$861$	−57.3768	−1.95540
$862$	24.8766	0.847300
$863$	−9.06313	−0.308513	−0.154256	−	0.988031i	$-0.549298\pi$
$863$	−9.06313	−0.308513	−0.154256	+	0.988031i	$0.549298\pi$
$864$	42.5289	1.44686
$865$	0.554878	0.0188664
$866$	−43.5094	−1.47851
$867$	8.13759	0.276367
$868$	81.7432	2.77455
$869$	30.2510	1.02619
$870$	−2.05013	−0.0695060
$871$	−0.194672	−0.00659619
$872$	60.0892	2.03488
$873$	0.520271	0.0176085
$874$	36.5937	1.23780
$875$	−6.39310	−0.216126
$876$	−33.4559	−1.13037
$877$	29.2319	0.987093	0.493546	−	0.869720i	$-0.335700\pi$
$877$	29.2319	0.987093	0.493546	+	0.869720i	$0.335700\pi$
$878$	−27.4673	−0.926975
$879$	−7.82316	−0.263869
$880$	−5.34279	−0.180105
$881$	0.500057	0.0168473	0.00842367	−	0.999965i	$-0.497319\pi$
$881$	0.500057	0.0168473	0.00842367	+	0.999965i	$0.497319\pi$
$882$	0.586533	0.0197496
$883$	17.1044	0.575609	0.287804	−	0.957689i	$-0.407075\pi$
$883$	17.1044	0.575609	0.287804	+	0.957689i	$0.407075\pi$
$884$	26.0266	0.875369
$885$	−3.00596	−0.101044
$886$	38.0114	1.27702
$887$	−16.9753	−0.569974	−0.284987	−	0.958531i	$-0.591989\pi$
$887$	−16.9753	−0.569974	−0.284987	+	0.958531i	$0.591989\pi$
$888$	23.8418	0.800079
$889$	47.0654	1.57852
$890$	−1.87975	−0.0630093
$891$	31.5993	1.05862
$892$	2.98405	0.0999133
$893$	−21.6015	−0.722866
$894$	−102.618	−3.43206
$895$	1.17784	0.0393710
$896$	21.3111	0.711954
$897$	−12.7351	−0.425211
$898$	−38.1045	−1.27156
$899$	12.5729	0.419329
$900$	0.857551	0.0285850
$901$	−46.4432	−1.54725
$902$	−84.4298	−2.81121
$903$	21.4348	0.713305
$904$	63.6299	2.11630
$905$	−3.05807	−0.101654
$906$	−37.7123	−1.25291
$907$	6.83731	0.227029	0.113515	−	0.993536i	$-0.463789\pi$
$907$	6.83731	0.227029	0.113515	+	0.993536i	$0.463789\pi$
$908$	0.249179	0.00826929
$909$	−0.135202	−0.00448438
$910$	−1.97926	−0.0656117
$911$	−20.0234	−0.663406	−0.331703	−	0.943384i	$-0.607623\pi$
$911$	−20.0234	−0.663406	−0.331703	+	0.943384i	$0.607623\pi$
$912$	33.4547	1.10779
$913$	−34.5839	−1.14456
$914$	38.3130	1.26728
$915$	−1.19441	−0.0394861
$916$	−78.6142	−2.59748
$917$	−51.9763	−1.71641
$918$	62.9500	2.07766
$919$	36.3529	1.19917	0.599586	−	0.800311i	$-0.295332\pi$
$919$	36.3529	1.19917	0.599586	+	0.800311i	$0.295332\pi$
$920$	7.56545	0.249426
$921$	−18.6105	−0.613236
$922$	−7.06251	−0.232592
$923$	−0.239187	−0.00787295
$924$	−103.719	−3.41209
$925$	9.96321	0.327588
$926$	−29.8589	−0.981223
$927$	−0.495890	−0.0162872
$928$	−21.2064	−0.696134
$929$	35.4759	1.16393	0.581964	−	0.813215i	$-0.302285\pi$
$929$	35.4759	1.16393	0.581964	+	0.813215i	$0.302285\pi$
$930$	−3.79350	−0.124394
$931$	14.0635	0.460913
$932$	65.6412	2.15015
$933$	−12.6928	−0.415543
$934$	4.80473	0.157216
$935$	−2.93103	−0.0958550
$936$	0.304722	0.00996015
$937$	9.18749	0.300142	0.150071	−	0.988675i	$-0.452050\pi$
$937$	9.18749	0.300142	0.150071	+	0.988675i	$0.452050\pi$
$938$	1.52644	0.0498401
$939$	5.33901	0.174232
$940$	−7.80647	−0.254619
$941$	−50.2677	−1.63868	−0.819339	−	0.573309i	$-0.805660\pi$
$941$	−50.2677	−1.63868	−0.819339	+	0.573309i	$0.805660\pi$
$942$	32.3831	1.05510
$943$	56.9266	1.85378
$944$	−83.8934	−2.73050
$945$	−3.35257	−0.109059
$946$	31.5412	1.02549
$947$	−34.8160	−1.13137	−0.565684	−	0.824622i	$-0.691388\pi$
$947$	−34.8160	−1.13137	−0.565684	+	0.824622i	$0.691388\pi$
$948$	−68.4540	−2.22328
$949$	−4.96795	−0.161266
$950$	29.3606	0.952584
$951$	−15.0419	−0.487766
$952$	−116.749	−3.78386
$953$	−50.3081	−1.62964	−0.814820	−	0.579714i	$-0.803164\pi$
$953$	−50.3081	−1.62964	−0.814820	+	0.579714i	$0.803164\pi$
$954$	−0.950497	−0.0307735
$955$	−2.53891	−0.0821573
$956$	−85.8063	−2.77518
$957$	−15.9529	−0.515684
$958$	−94.2528	−3.04517
$959$	23.6385	0.763328
$960$	1.22486	0.0395322
$961$	−7.73551	−0.249533
$962$	6.18850	0.199525
$963$	0.0274767	0.000885424 0
$964$	14.7921	0.476422
$965$	2.93355	0.0944343
$966$	99.8571	3.21285
$967$	3.47960	0.111896	0.0559481	−	0.998434i	$-0.482182\pi$
$967$	3.47960	0.111896	0.0559481	+	0.998434i	$0.482182\pi$
$968$	−11.3309	−0.364188
$969$	18.3531	0.589587
$970$	6.43732	0.206690
$971$	−49.1228	−1.57643	−0.788213	−	0.615402i	$-0.788994\pi$
$971$	−49.1228	−1.57643	−0.788213	+	0.615402i	$0.788994\pi$
$972$	1.79350	0.0575267
$973$	23.4131	0.750588
$974$	−41.0701	−1.31597
$975$	−10.2179	−0.327233
$976$	−33.3349	−1.06702
$977$	28.6975	0.918114	0.459057	−	0.888407i	$-0.348187\pi$
$977$	28.6975	0.918114	0.459057	+	0.888407i	$0.348187\pi$
$978$	87.3281	2.79245
$979$	−14.6271	−0.467484
$980$	5.08235	0.162350
$981$	0.321240	0.0102564
$982$	−30.9058	−0.986243
$983$	−13.0839	−0.417311	−0.208656	−	0.977989i	$-0.566909\pi$
$983$	−13.0839	−0.417311	−0.208656	+	0.977989i	$0.566909\pi$
$984$	109.298	3.48430
$985$	−0.526157	−0.0167648
$986$	−31.3891	−0.999632
$987$	−58.9463	−1.87628
$988$	12.7717	0.406321
$989$	−21.2666	−0.676238
$990$	−0.0599859	−0.00190648
$991$	19.3942	0.616077	0.308039	−	0.951374i	$-0.400327\pi$
$991$	19.3942	0.616077	0.308039	+	0.951374i	$0.400327\pi$
$992$	−39.2397	−1.24586
$993$	3.26282	0.103542
$994$	1.87550	0.0594871
$995$	−3.40979	−0.108097
$996$	78.2590	2.47973
$997$	51.1682	1.62051	0.810257	−	0.586075i	$-0.199328\pi$
$997$	51.1682	1.62051	0.810257	+	0.586075i	$0.199328\pi$
$998$	39.1520	1.23934
$999$	10.4824	0.331648

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.20	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.20	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58337 q^{2} +1.72136 q^{3} +4.67379 q^{4} +0.176863 q^{5} -4.44690 q^{6} +3.62607 q^{7} -6.90738 q^{8} -0.0369272 q^{9} +O(q^{10})\)	\(q-2.58337 q^{2} +1.72136 q^{3} +4.67379 q^{4} +0.176863 q^{5} -4.44690 q^{6} +3.62607 q^{7} -6.90738 q^{8} -0.0369272 q^{9} -0.456901 q^{10} -3.55533 q^{11} +8.04526 q^{12} +1.19466 q^{13} -9.36747 q^{14} +0.304444 q^{15} +8.49672 q^{16} +4.66127 q^{17} +0.0953965 q^{18} +2.28736 q^{19} +0.826618 q^{20} +6.24176 q^{21} +9.18474 q^{22} -6.19278 q^{23} -11.8901 q^{24} -4.96872 q^{25} -3.08624 q^{26} -5.22764 q^{27} +16.9475 q^{28} +2.60668 q^{29} -0.786490 q^{30} +4.82333 q^{31} -8.13539 q^{32} -6.12000 q^{33} -12.0418 q^{34} +0.641316 q^{35} -0.172590 q^{36} -2.00519 q^{37} -5.90909 q^{38} +2.05644 q^{39} -1.22166 q^{40} -9.19241 q^{41} -16.1248 q^{42} +3.43409 q^{43} -16.6169 q^{44} -0.00653104 q^{45} +15.9982 q^{46} -9.44386 q^{47} +14.6259 q^{48} +6.14837 q^{49} +12.8360 q^{50} +8.02371 q^{51} +5.58359 q^{52} -9.96364 q^{53} +13.5049 q^{54} -0.628806 q^{55} -25.0466 q^{56} +3.93736 q^{57} -6.73402 q^{58} -9.87362 q^{59} +1.42291 q^{60} -3.92327 q^{61} -12.4604 q^{62} -0.133901 q^{63} +4.02327 q^{64} +0.211291 q^{65} +15.8102 q^{66} -0.162951 q^{67} +21.7858 q^{68} -10.6600 q^{69} -1.65675 q^{70} -0.200214 q^{71} +0.255070 q^{72} -4.15846 q^{73} +5.18014 q^{74} -8.55294 q^{75} +10.6906 q^{76} -12.8919 q^{77} -5.31253 q^{78} -8.50861 q^{79} +1.50275 q^{80} -8.88785 q^{81} +23.7474 q^{82} +9.72734 q^{83} +29.1727 q^{84} +0.824404 q^{85} -8.87152 q^{86} +4.48704 q^{87} +24.5580 q^{88} +4.11413 q^{89} +0.0168721 q^{90} +4.33192 q^{91} -28.9437 q^{92} +8.30267 q^{93} +24.3970 q^{94} +0.404548 q^{95} -14.0039 q^{96} -14.0891 q^{97} -15.8835 q^{98} +0.131289 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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