LMFDB - Embedded newform 8027.2.a.f.1.19

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:	$0$
Dimension:	$176$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-2.32736 q^{2} -1.68164 q^{3} +3.41663 q^{4} +2.73432 q^{5} +3.91378 q^{6} +2.98551 q^{7} -3.29700 q^{8} -0.172094 q^{9} +O(q^{10})$	\(q-2.32736 q^{2} -1.68164 q^{3} +3.41663 q^{4} +2.73432 q^{5} +3.91378 q^{6} +2.98551 q^{7} -3.29700 q^{8} -0.172094 q^{9} -6.36375 q^{10} +5.81906 q^{11} -5.74553 q^{12} +4.09184 q^{13} -6.94837 q^{14} -4.59813 q^{15} +0.840077 q^{16} +1.41108 q^{17} +0.400526 q^{18} -0.843215 q^{19} +9.34213 q^{20} -5.02055 q^{21} -13.5431 q^{22} +1.00000 q^{23} +5.54436 q^{24} +2.47648 q^{25} -9.52320 q^{26} +5.33431 q^{27} +10.2004 q^{28} +7.07815 q^{29} +10.7015 q^{30} -2.42137 q^{31} +4.63884 q^{32} -9.78555 q^{33} -3.28410 q^{34} +8.16333 q^{35} -0.587981 q^{36} -5.17537 q^{37} +1.96247 q^{38} -6.88099 q^{39} -9.01505 q^{40} -1.45321 q^{41} +11.6846 q^{42} -8.03543 q^{43} +19.8815 q^{44} -0.470559 q^{45} -2.32736 q^{46} -0.879671 q^{47} -1.41271 q^{48} +1.91327 q^{49} -5.76368 q^{50} -2.37293 q^{51} +13.9803 q^{52} +0.713413 q^{53} -12.4149 q^{54} +15.9111 q^{55} -9.84324 q^{56} +1.41798 q^{57} -16.4734 q^{58} -12.5029 q^{59} -15.7101 q^{60} +8.18803 q^{61} +5.63540 q^{62} -0.513788 q^{63} -12.4764 q^{64} +11.1884 q^{65} +22.7745 q^{66} +7.32236 q^{67} +4.82114 q^{68} -1.68164 q^{69} -18.9990 q^{70} +3.98574 q^{71} +0.567395 q^{72} -12.0378 q^{73} +12.0450 q^{74} -4.16455 q^{75} -2.88095 q^{76} +17.3729 q^{77} +16.0146 q^{78} +6.86405 q^{79} +2.29704 q^{80} -8.45410 q^{81} +3.38215 q^{82} +2.00548 q^{83} -17.1533 q^{84} +3.85834 q^{85} +18.7014 q^{86} -11.9029 q^{87} -19.1855 q^{88} -6.63433 q^{89} +1.09516 q^{90} +12.2162 q^{91} +3.41663 q^{92} +4.07186 q^{93} +2.04732 q^{94} -2.30562 q^{95} -7.80085 q^{96} -7.59549 q^{97} -4.45288 q^{98} -1.00143 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) $ 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * 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 $

$2$	−2.32736	−1.64570	−0.822848	−	0.568262i	$-0.807616\pi$
$2$	−2.32736	−1.64570	−0.822848	+	0.568262i	$0.807616\pi$
$3$	−1.68164	−0.970894	−0.485447	−	0.874266i	$-0.661343\pi$
$3$	−1.68164	−0.970894	−0.485447	+	0.874266i	$0.661343\pi$
$4$	3.41663	1.70831
$5$	2.73432	1.22282	0.611412	−	0.791313i	$-0.290602\pi$
$5$	2.73432	1.22282	0.611412	+	0.791313i	$0.290602\pi$
$6$	3.91378	1.59780
$7$	2.98551	1.12842	0.564208	−	0.825632i	$-0.309181\pi$
$7$	2.98551	1.12842	0.564208	+	0.825632i	$0.309181\pi$
$8$	−3.29700	−1.16567
$9$	−0.172094	−0.0573647
$10$	−6.36375	−2.01239
$11$	5.81906	1.75451	0.877256	−	0.480022i	$-0.159371\pi$
$11$	5.81906	1.75451	0.877256	+	0.480022i	$0.159371\pi$
$12$	−5.74553	−1.65859
$13$	4.09184	1.13487	0.567436	−	0.823417i	$-0.307935\pi$
$13$	4.09184	1.13487	0.567436	+	0.823417i	$0.307935\pi$
$14$	−6.94837	−1.85703
$15$	−4.59813	−1.18723
$16$	0.840077	0.210019
$17$	1.41108	0.342238	0.171119	−	0.985250i	$-0.445262\pi$
$17$	1.41108	0.342238	0.171119	+	0.985250i	$0.445262\pi$
$18$	0.400526	0.0944048
$19$	−0.843215	−0.193447	−0.0967234	−	0.995311i	$-0.530836\pi$
$19$	−0.843215	−0.193447	−0.0967234	+	0.995311i	$0.530836\pi$
$20$	9.34213	2.08896
$21$	−5.02055	−1.09557
$22$	−13.5431	−2.88739
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	5.54436	1.13174
$25$	2.47648	0.495296
$26$	−9.52320	−1.86765
$27$	5.33431	1.02659
$28$	10.2004	1.92769
$29$	7.07815	1.31438	0.657189	−	0.753726i	$-0.271745\pi$
$29$	7.07815	1.31438	0.657189	+	0.753726i	$0.271745\pi$
$30$	10.7015	1.95382
$31$	−2.42137	−0.434890	−0.217445	−	0.976073i	$-0.569772\pi$
$31$	−2.42137	−0.434890	−0.217445	+	0.976073i	$0.569772\pi$
$32$	4.63884	0.820039
$33$	−9.78555	−1.70345
$34$	−3.28410	−0.563219
$35$	8.16333	1.37985
$36$	−0.587981	−0.0979968
$37$	−5.17537	−0.850825	−0.425413	−	0.904999i	$-0.639871\pi$
$37$	−5.17537	−0.850825	−0.425413	+	0.904999i	$0.639871\pi$
$38$	1.96247	0.318355
$39$	−6.88099	−1.10184
$40$	−9.01505	−1.42540
$41$	−1.45321	−0.226953	−0.113477	−	0.993541i	$-0.536199\pi$
$41$	−1.45321	−0.226953	−0.113477	+	0.993541i	$0.536199\pi$
$42$	11.6846	1.80298
$43$	−8.03543	−1.22539	−0.612696	−	0.790319i	$-0.709915\pi$
$43$	−8.03543	−1.22539	−0.612696	+	0.790319i	$0.709915\pi$
$44$	19.8815	2.99726
$45$	−0.470559	−0.0701469
$46$	−2.32736	−0.343151
$47$	−0.879671	−0.128313	−0.0641566	−	0.997940i	$-0.520436\pi$
$47$	−0.879671	−0.128313	−0.0641566	+	0.997940i	$0.520436\pi$
$48$	−1.41271	−0.203906
$49$	1.91327	0.273324
$50$	−5.76368	−0.815107
$51$	−2.37293	−0.332276
$52$	13.9803	1.93872
$53$	0.713413	0.0979948	0.0489974	−	0.998799i	$-0.484397\pi$
$53$	0.713413	0.0979948	0.0489974	+	0.998799i	$0.484397\pi$
$54$	−12.4149	−1.68945
$55$	15.9111	2.14546
$56$	−9.84324	−1.31536
$57$	1.41798	0.187816
$58$	−16.4734	−2.16307
$59$	−12.5029	−1.62774	−0.813869	−	0.581049i	$-0.802643\pi$
$59$	−12.5029	−1.62774	−0.813869	+	0.581049i	$0.802643\pi$
$60$	−15.7101	−2.02816
$61$	8.18803	1.04837	0.524185	−	0.851605i	$-0.324370\pi$
$61$	8.18803	1.04837	0.524185	+	0.851605i	$0.324370\pi$
$62$	5.63540	0.715696
$63$	−0.513788	−0.0647313
$64$	−12.4764	−1.55955
$65$	11.1884	1.38775
$66$	22.7745	2.80335
$67$	7.32236	0.894568	0.447284	−	0.894392i	$-0.352391\pi$
$67$	7.32236	0.894568	0.447284	+	0.894392i	$0.352391\pi$
$68$	4.82114	0.584649
$69$	−1.68164	−0.202445
$70$	−18.9990	−2.27082
$71$	3.98574	0.473020	0.236510	−	0.971629i	$-0.423996\pi$
$71$	3.98574	0.473020	0.236510	+	0.971629i	$0.423996\pi$
$72$	0.567395	0.0668681
$73$	−12.0378	−1.40891	−0.704457	−	0.709747i	$-0.748809\pi$
$73$	−12.0378	−1.40891	−0.704457	+	0.709747i	$0.748809\pi$
$74$	12.0450	1.40020
$75$	−4.16455	−0.480880
$76$	−2.88095	−0.330468
$77$	17.3729	1.97982
$78$	16.0146	1.81329
$79$	6.86405	0.772266	0.386133	−	0.922443i	$-0.373811\pi$
$79$	6.86405	0.772266	0.386133	+	0.922443i	$0.373811\pi$
$80$	2.29704	0.256816
$81$	−8.45410	−0.939345
$82$	3.38215	0.373496
$83$	2.00548	0.220130	0.110065	−	0.993924i	$-0.464894\pi$
$83$	2.00548	0.220130	0.110065	+	0.993924i	$0.464894\pi$
$84$	−17.1533	−1.87158
$85$	3.85834	0.418496
$86$	18.7014	2.01662
$87$	−11.9029	−1.27612
$88$	−19.1855	−2.04518
$89$	−6.63433	−0.703238	−0.351619	−	0.936143i	$-0.614369\pi$
$89$	−6.63433	−0.703238	−0.351619	+	0.936143i	$0.614369\pi$
$90$	1.09516	0.115440
$91$	12.2162	1.28061
$92$	3.41663	0.356208
$93$	4.07186	0.422232
$94$	2.04732	0.211165
$95$	−2.30562	−0.236551
$96$	−7.80085	−0.796171
$97$	−7.59549	−0.771205	−0.385603	−	0.922665i	$-0.626006\pi$
$97$	−7.59549	−0.771205	−0.385603	+	0.922665i	$0.626006\pi$
$98$	−4.45288	−0.449809
$99$	−1.00143	−0.100647
$100$	8.46121	0.846121
$101$	17.5517	1.74646	0.873231	−	0.487307i	$-0.162021\pi$
$101$	17.5517	1.74646	0.873231	+	0.487307i	$0.162021\pi$
$102$	5.52267	0.546826
$103$	14.1752	1.39673	0.698363	−	0.715744i	$-0.253912\pi$
$103$	14.1752	1.39673	0.698363	+	0.715744i	$0.253912\pi$
$104$	−13.4908	−1.32288
$105$	−13.7278	−1.33969
$106$	−1.66037	−0.161270
$107$	1.14586	0.110775	0.0553874	−	0.998465i	$-0.482361\pi$
$107$	1.14586	0.110775	0.0553874	+	0.998465i	$0.482361\pi$
$108$	18.2253	1.75374
$109$	20.2886	1.94329	0.971646	−	0.236442i	$-0.0759815\pi$
$109$	20.2886	1.94329	0.971646	+	0.236442i	$0.0759815\pi$
$110$	−37.0310	−3.53077
$111$	8.70310	0.826061
$112$	2.50806	0.236989
$113$	4.25824	0.400581	0.200291	−	0.979737i	$-0.435811\pi$
$113$	4.25824	0.400581	0.200291	+	0.979737i	$0.435811\pi$
$114$	−3.30016	−0.309089
$115$	2.73432	0.254976
$116$	24.1834	2.24537
$117$	−0.704181	−0.0651016
$118$	29.0988	2.67876
$119$	4.21280	0.386187
$120$	15.1600	1.38392
$121$	22.8615	2.07831
$122$	−19.0565	−1.72530
$123$	2.44377	0.220348
$124$	−8.27290	−0.742928
$125$	−6.90010	−0.617163
$126$	1.19577	0.106528
$127$	1.54916	0.137466	0.0687329	−	0.997635i	$-0.478104\pi$
$127$	1.54916	0.137466	0.0687329	+	0.997635i	$0.478104\pi$
$128$	19.7595	1.74651
$129$	13.5127	1.18973
$130$	−26.0394	−2.28381
$131$	−14.8765	−1.29977	−0.649883	−	0.760034i	$-0.725182\pi$
$131$	−14.8765	−1.29977	−0.649883	+	0.760034i	$0.725182\pi$
$132$	−33.4336	−2.91002
$133$	−2.51743	−0.218289
$134$	−17.0418	−1.47219
$135$	14.5857	1.25534
$136$	−4.65234	−0.398935
$137$	15.3396	1.31055	0.655276	−	0.755390i	$-0.272552\pi$
$137$	15.3396	1.31055	0.655276	+	0.755390i	$0.272552\pi$
$138$	3.91378	0.333163
$139$	14.1749	1.20230	0.601151	−	0.799136i	$-0.294709\pi$
$139$	14.1749	1.20230	0.601151	+	0.799136i	$0.294709\pi$
$140$	27.8910	2.35722
$141$	1.47929	0.124579
$142$	−9.27626	−0.778446
$143$	23.8107	1.99115
$144$	−0.144572	−0.0120477
$145$	19.3539	1.60725
$146$	28.0163	2.31864
$147$	−3.21743	−0.265369
$148$	−17.6823	−1.45348
$149$	−18.9209	−1.55006	−0.775028	−	0.631927i	$-0.782264\pi$
$149$	−18.9209	−1.55006	−0.775028	+	0.631927i	$0.782264\pi$
$150$	9.69242	0.791382
$151$	10.0386	0.816930	0.408465	−	0.912774i	$-0.366064\pi$
$151$	10.0386	0.816930	0.408465	+	0.912774i	$0.366064\pi$
$152$	2.78008	0.225495
$153$	−0.242839	−0.0196323
$154$	−40.4330	−3.25818
$155$	−6.62078	−0.531794
$156$	−23.5098	−1.88229
$157$	−20.3741	−1.62603	−0.813014	−	0.582244i	$-0.802175\pi$
$157$	−20.3741	−1.62603	−0.813014	+	0.582244i	$0.802175\pi$
$158$	−15.9752	−1.27091
$159$	−1.19970	−0.0951426
$160$	12.6841	1.00276
$161$	2.98551	0.235291
$162$	19.6758	1.54587
$163$	10.2711	0.804495	0.402248	−	0.915531i	$-0.368229\pi$
$163$	10.2711	0.804495	0.402248	+	0.915531i	$0.368229\pi$
$164$	−4.96507	−0.387707
$165$	−26.7568	−2.08301
$166$	−4.66747	−0.362266
$167$	7.65655	0.592482	0.296241	−	0.955113i	$-0.404267\pi$
$167$	7.65655	0.592482	0.296241	+	0.955113i	$0.404267\pi$
$168$	16.5528	1.27707
$169$	3.74316	0.287935
$170$	−8.97977	−0.688717
$171$	0.145112	0.0110970
$172$	−27.4540	−2.09335
$173$	−4.81599	−0.366153	−0.183076	−	0.983099i	$-0.558606\pi$
$173$	−4.81599	−0.366153	−0.183076	+	0.983099i	$0.558606\pi$
$174$	27.7023	2.10011
$175$	7.39356	0.558901
$176$	4.88846	0.368481
$177$	21.0253	1.58036
$178$	15.4405	1.15731
$179$	2.48395	0.185659	0.0928295	−	0.995682i	$-0.470409\pi$
$179$	2.48395	0.185659	0.0928295	+	0.995682i	$0.470409\pi$
$180$	−1.60773	−0.119833
$181$	10.7086	0.795964	0.397982	−	0.917393i	$-0.369711\pi$
$181$	10.7086	0.795964	0.397982	+	0.917393i	$0.369711\pi$
$182$	−28.4316	−2.10749
$183$	−13.7693	−1.01786
$184$	−3.29700	−0.243058
$185$	−14.1511	−1.04041
$186$	−9.47670	−0.694865
$187$	8.21117	0.600460
$188$	−3.00551	−0.219199
$189$	15.9256	1.15842
$190$	5.36601	0.389291
$191$	15.5937	1.12832	0.564160	−	0.825666i	$-0.309200\pi$
$191$	15.5937	1.12832	0.564160	+	0.825666i	$0.309200\pi$
$192$	20.9808	1.51416
$193$	16.5892	1.19411	0.597057	−	0.802199i	$-0.296337\pi$
$193$	16.5892	1.19411	0.597057	+	0.802199i	$0.296337\pi$
$194$	17.6775	1.26917
$195$	−18.8148	−1.34736
$196$	6.53693	0.466923
$197$	22.6011	1.61026	0.805132	−	0.593095i	$-0.202094\pi$
$197$	22.6011	1.61026	0.805132	+	0.593095i	$0.202094\pi$
$198$	2.33068	0.165634
$199$	−11.0208	−0.781244	−0.390622	−	0.920551i	$-0.627740\pi$
$199$	−11.0208	−0.781244	−0.390622	+	0.920551i	$0.627740\pi$
$200$	−8.16497	−0.577350
$201$	−12.3136	−0.868531
$202$	−40.8493	−2.87414
$203$	21.1319	1.48317
$204$	−8.10741	−0.567632
$205$	−3.97353	−0.277524
$206$	−32.9909	−2.29859
$207$	−0.172094	−0.0119614
$208$	3.43746	0.238345
$209$	−4.90672	−0.339405
$210$	31.9495	2.20472
$211$	−15.1655	−1.04404	−0.522018	−	0.852934i	$-0.674821\pi$
$211$	−15.1655	−1.04404	−0.522018	+	0.852934i	$0.674821\pi$
$212$	2.43746	0.167406
$213$	−6.70256	−0.459252
$214$	−2.66684	−0.182301
$215$	−21.9714	−1.49844
$216$	−17.5872	−1.19666
$217$	−7.22901	−0.490737
$218$	−47.2189	−3.19806
$219$	20.2432	1.36791
$220$	54.3624	3.66511
$221$	5.77392	0.388396
$222$	−20.2553	−1.35945
$223$	−9.58028	−0.641543	−0.320772	−	0.947157i	$-0.603942\pi$
$223$	−9.58028	−0.641543	−0.320772	+	0.947157i	$0.603942\pi$
$224$	13.8493	0.925346
$225$	−0.426188	−0.0284125
$226$	−9.91047	−0.659234
$227$	3.21564	0.213430	0.106715	−	0.994290i	$-0.465967\pi$
$227$	3.21564	0.213430	0.106715	+	0.994290i	$0.465967\pi$
$228$	4.84472	0.320849
$229$	14.8115	0.978772	0.489386	−	0.872067i	$-0.337221\pi$
$229$	14.8115	0.978772	0.489386	+	0.872067i	$0.337221\pi$
$230$	−6.36375	−0.419613
$231$	−29.2149	−1.92220
$232$	−23.3367	−1.53213
$233$	16.8961	1.10690	0.553451	−	0.832881i	$-0.313310\pi$
$233$	16.8961	1.10690	0.553451	+	0.832881i	$0.313310\pi$
$234$	1.63889	0.107137
$235$	−2.40530	−0.156904
$236$	−42.7177	−2.78069
$237$	−11.5428	−0.749789
$238$	−9.80472	−0.635545
$239$	−18.1942	−1.17689	−0.588444	−	0.808538i	$-0.700259\pi$
$239$	−18.1942	−1.17689	−0.588444	+	0.808538i	$0.700259\pi$
$240$	−3.86278	−0.249341
$241$	30.7883	1.98325	0.991625	−	0.129153i	$-0.0412258\pi$
$241$	30.7883	1.98325	0.991625	+	0.129153i	$0.0412258\pi$
$242$	−53.2069	−3.42027
$243$	−1.78620	−0.114585
$244$	27.9754	1.79094
$245$	5.23149	0.334227
$246$	−5.68755	−0.362625
$247$	−3.45030	−0.219538
$248$	7.98325	0.506937
$249$	−3.37248	−0.213722
$250$	16.0590	1.01566
$251$	−7.59537	−0.479416	−0.239708	−	0.970845i	$-0.577052\pi$
$251$	−7.59537	−0.479416	−0.239708	+	0.970845i	$0.577052\pi$
$252$	−1.75542	−0.110581
$253$	5.81906	0.365841
$254$	−3.60546	−0.226227
$255$	−6.48833	−0.406315
$256$	−21.0347	−1.31467
$257$	−24.6502	−1.53764	−0.768819	−	0.639467i	$-0.779155\pi$
$257$	−24.6502	−1.53764	−0.768819	+	0.639467i	$0.779155\pi$
$258$	−31.4489	−1.95792
$259$	−15.4511	−0.960086
$260$	38.2265	2.37071
$261$	−1.21811	−0.0753989
$262$	34.6230	2.13902
$263$	8.21180	0.506361	0.253181	−	0.967419i	$-0.418523\pi$
$263$	8.21180	0.506361	0.253181	+	0.967419i	$0.418523\pi$
$264$	32.2630	1.98565
$265$	1.95070	0.119830
$266$	5.85897	0.359237
$267$	11.1565	0.682769
$268$	25.0177	1.52820
$269$	−28.6451	−1.74652	−0.873262	−	0.487251i	$-0.838000\pi$
$269$	−28.6451	−1.74652	−0.873262	+	0.487251i	$0.838000\pi$
$270$	−33.9462	−2.06590
$271$	2.23336	0.135667	0.0678333	−	0.997697i	$-0.478391\pi$
$271$	2.23336	0.135667	0.0678333	+	0.997697i	$0.478391\pi$
$272$	1.18542	0.0718765
$273$	−20.5433	−1.24334
$274$	−35.7009	−2.15677
$275$	14.4108	0.869004
$276$	−5.74553	−0.345840
$277$	−2.57497	−0.154715	−0.0773574	−	0.997003i	$-0.524648\pi$
$277$	−2.57497	−0.154715	−0.0773574	+	0.997003i	$0.524648\pi$
$278$	−32.9902	−1.97862
$279$	0.416703	0.0249473
$280$	−26.9145	−1.60845
$281$	−15.4368	−0.920883	−0.460442	−	0.887690i	$-0.652309\pi$
$281$	−15.4368	−0.920883	−0.460442	+	0.887690i	$0.652309\pi$
$282$	−3.44284	−0.205018
$283$	13.1430	0.781269	0.390634	−	0.920546i	$-0.372256\pi$
$283$	13.1430	0.781269	0.390634	+	0.920546i	$0.372256\pi$
$284$	13.6178	0.808066
$285$	3.87721	0.229666
$286$	−55.4161	−3.27682
$287$	−4.33857	−0.256098
$288$	−0.798317	−0.0470413
$289$	−15.0088	−0.882873
$290$	−45.0435	−2.64505
$291$	12.7729	0.748759
$292$	−41.1285	−2.40686
$293$	2.65975	0.155384	0.0776920	−	0.996977i	$-0.475245\pi$
$293$	2.65975	0.155384	0.0776920	+	0.996977i	$0.475245\pi$
$294$	7.48813	0.436717
$295$	−34.1869	−1.99044
$296$	17.0632	0.991779
$297$	31.0407	1.80116
$298$	44.0357	2.55092
$299$	4.09184	0.236637
$300$	−14.2287	−0.821494
$301$	−23.9899	−1.38275
$302$	−23.3635	−1.34442
$303$	−29.5156	−1.69563
$304$	−0.708366	−0.0406276
$305$	22.3887	1.28197
$306$	0.565174	0.0323089
$307$	19.4171	1.10819	0.554097	−	0.832452i	$-0.313064\pi$
$307$	19.4171	1.10819	0.554097	+	0.832452i	$0.313064\pi$
$308$	59.3566	3.38215
$309$	−23.8376	−1.35607
$310$	15.4090	0.875170
$311$	−31.2179	−1.77021	−0.885104	−	0.465394i	$-0.845913\pi$
$311$	−31.2179	−1.77021	−0.885104	+	0.465394i	$0.845913\pi$
$312$	22.6867	1.28438
$313$	15.7129	0.888144	0.444072	−	0.895991i	$-0.353534\pi$
$313$	15.7129	0.888144	0.444072	+	0.895991i	$0.353534\pi$
$314$	47.4179	2.67595
$315$	−1.40486	−0.0791549
$316$	23.4519	1.31927
$317$	10.2980	0.578394	0.289197	−	0.957270i	$-0.406612\pi$
$317$	10.2980	0.578394	0.289197	+	0.957270i	$0.406612\pi$
$318$	2.79214	0.156576
$319$	41.1882	2.30609
$320$	−34.1145	−1.90706
$321$	−1.92693	−0.107551
$322$	−6.94837	−0.387218
$323$	−1.18985	−0.0662048
$324$	−28.8845	−1.60469
$325$	10.1334	0.562098
$326$	−23.9046	−1.32395
$327$	−34.1180	−1.88673
$328$	4.79124	0.264552
$329$	−2.62627	−0.144791
$330$	62.2728	3.42800
$331$	−8.49775	−0.467079	−0.233539	−	0.972347i	$-0.575031\pi$
$331$	−8.49775	−0.467079	−0.233539	+	0.972347i	$0.575031\pi$
$332$	6.85196	0.376050
$333$	0.890650	0.0488073
$334$	−17.8196	−0.975044
$335$	20.0216	1.09390
$336$	−4.21765	−0.230091
$337$	24.2853	1.32290	0.661452	−	0.749987i	$-0.269940\pi$
$337$	24.2853	1.32290	0.661452	+	0.749987i	$0.269940\pi$
$338$	−8.71169	−0.473853
$339$	−7.16081	−0.388922
$340$	13.1825	0.714922
$341$	−14.0901	−0.763020
$342$	−0.337729	−0.0182623
$343$	−15.1865	−0.819993
$344$	26.4928	1.42840
$345$	−4.59813	−0.247555
$346$	11.2086	0.602576
$347$	1.91315	0.102703	0.0513516	−	0.998681i	$-0.483647\pi$
$347$	1.91315	0.102703	0.0513516	+	0.998681i	$0.483647\pi$
$348$	−40.6677	−2.18002
$349$	−1.00000	−0.0535288
$349$	−1.00000	−0.0535288
$350$	−17.2075	−0.919780
$351$	21.8272	1.16505
$352$	26.9937	1.43877
$353$	29.5738	1.57405	0.787027	−	0.616919i	$-0.211619\pi$
$353$	29.5738	1.57405	0.787027	+	0.616919i	$0.211619\pi$
$354$	−48.9336	−2.60079
$355$	10.8983	0.578419
$356$	−22.6670	−1.20135
$357$	−7.08440	−0.374946
$358$	−5.78105	−0.305538
$359$	−12.7981	−0.675460	−0.337730	−	0.941243i	$-0.609659\pi$
$359$	−12.7981	−0.675460	−0.337730	+	0.941243i	$0.609659\pi$
$360$	1.55144	0.0817678
$361$	−18.2890	−0.962578
$362$	−24.9228	−1.30991
$363$	−38.4447	−2.01782
$364$	41.7383	2.18768
$365$	−32.9150	−1.72285
$366$	32.0462	1.67508
$367$	3.44465	0.179809	0.0899047	−	0.995950i	$-0.471344\pi$
$367$	3.44465	0.179809	0.0899047	+	0.995950i	$0.471344\pi$
$368$	0.840077	0.0437920
$369$	0.250089	0.0130191
$370$	32.9347	1.71220
$371$	2.12990	0.110579
$372$	13.9120	0.721305
$373$	0.144165	0.00746457	0.00373228	−	0.999993i	$-0.498812\pi$
$373$	0.144165	0.00746457	0.00373228	+	0.999993i	$0.498812\pi$
$374$	−19.1104	−0.988174
$375$	11.6035	0.599200
$376$	2.90028	0.149570
$377$	28.9626	1.49165
$378$	−37.0648	−1.90641
$379$	2.99289	0.153735	0.0768673	−	0.997041i	$-0.475508\pi$
$379$	2.99289	0.153735	0.0768673	+	0.997041i	$0.475508\pi$
$380$	−7.87743	−0.404104
$381$	−2.60513	−0.133465
$382$	−36.2922	−1.85687
$383$	−35.1189	−1.79449	−0.897245	−	0.441533i	$-0.854435\pi$
$383$	−35.1189	−1.79449	−0.897245	+	0.441533i	$0.854435\pi$
$384$	−33.2283	−1.69568
$385$	47.5029	2.42097
$386$	−38.6090	−1.96515
$387$	1.38285	0.0702942
$388$	−25.9510	−1.31746
$389$	−7.35037	−0.372678	−0.186339	−	0.982485i	$-0.559662\pi$
$389$	−7.35037	−0.372678	−0.186339	+	0.982485i	$0.559662\pi$
$390$	43.7889	2.21734
$391$	1.41108	0.0713615
$392$	−6.30806	−0.318605
$393$	25.0169	1.26194
$394$	−52.6011	−2.65000
$395$	18.7685	0.944345
$396$	−3.42150	−0.171937
$397$	−24.4397	−1.22659	−0.613295	−	0.789854i	$-0.710156\pi$
$397$	−24.4397	−1.22659	−0.613295	+	0.789854i	$0.710156\pi$
$398$	25.6494	1.28569
$399$	4.23340	0.211935
$400$	2.08044	0.104022
$401$	−26.9732	−1.34698	−0.673488	−	0.739198i	$-0.735205\pi$
$401$	−26.9732	−1.34698	−0.673488	+	0.739198i	$0.735205\pi$
$402$	28.6581	1.42934
$403$	−9.90784	−0.493545
$404$	59.9677	2.98350
$405$	−23.1162	−1.14865
$406$	−49.1816	−2.44084
$407$	−30.1158	−1.49278
$408$	7.82355	0.387323
$409$	−11.1449	−0.551078	−0.275539	−	0.961290i	$-0.588856\pi$
$409$	−11.1449	−0.551078	−0.275539	+	0.961290i	$0.588856\pi$
$410$	9.24786	0.456719
$411$	−25.7957	−1.27241
$412$	48.4314	2.38605
$413$	−37.3275	−1.83677
$414$	0.400526	0.0196848
$415$	5.48360	0.269179
$416$	18.9814	0.930639
$417$	−23.8371	−1.16731
$418$	11.4197	0.558557
$419$	−22.2672	−1.08783	−0.543913	−	0.839142i	$-0.683058\pi$
$419$	−22.2672	−1.08783	−0.543913	+	0.839142i	$0.683058\pi$
$420$	−46.9026	−2.28861
$421$	9.66366	0.470978	0.235489	−	0.971877i	$-0.424331\pi$
$421$	9.66366	0.470978	0.235489	+	0.971877i	$0.424331\pi$
$422$	35.2956	1.71816
$423$	0.151386	0.00736065
$424$	−2.35212	−0.114229
$425$	3.49452	0.169509
$426$	15.5993	0.755789
$427$	24.4454	1.18300
$428$	3.91498	0.189238
$429$	−40.0409	−1.93319
$430$	51.1354	2.46597
$431$	23.3189	1.12323	0.561616	−	0.827398i	$-0.310180\pi$
$431$	23.3189	1.12323	0.561616	+	0.827398i	$0.310180\pi$
$432$	4.48123	0.215603
$433$	−3.76269	−0.180824	−0.0904118	−	0.995904i	$-0.528818\pi$
$433$	−3.76269	−0.180824	−0.0904118	+	0.995904i	$0.528818\pi$
$434$	16.8245	0.807604
$435$	−32.5462	−1.56047
$436$	69.3184	3.31975
$437$	−0.843215	−0.0403365
$438$	−47.1132	−2.25116
$439$	37.5563	1.79246	0.896232	−	0.443585i	$-0.146294\pi$
$439$	37.5563	1.79246	0.896232	+	0.443585i	$0.146294\pi$
$440$	−52.4591	−2.50089
$441$	−0.329262	−0.0156792
$442$	−13.4380	−0.639181
$443$	25.1894	1.19679	0.598393	−	0.801203i	$-0.295806\pi$
$443$	25.1894	1.19679	0.598393	+	0.801203i	$0.295806\pi$
$444$	29.7352	1.41117
$445$	−18.1404	−0.859935
$446$	22.2968	1.05578
$447$	31.8180	1.50494
$448$	−37.2485	−1.75983
$449$	21.2411	1.00243	0.501215	−	0.865323i	$-0.332886\pi$
$449$	21.2411	1.00243	0.501215	+	0.865323i	$0.332886\pi$
$450$	0.991894	0.0467583
$451$	−8.45632	−0.398192
$452$	14.5488	0.684318
$453$	−16.8813	−0.793152
$454$	−7.48398	−0.351240
$455$	33.4030	1.56596
$456$	−4.67509	−0.218931
$457$	−18.5327	−0.866924	−0.433462	−	0.901172i	$-0.642708\pi$
$457$	−18.5327	−0.866924	−0.433462	+	0.901172i	$0.642708\pi$
$458$	−34.4718	−1.61076
$459$	7.52715	0.351337
$460$	9.34213	0.435579
$461$	23.3608	1.08802	0.544011	−	0.839078i	$-0.316905\pi$
$461$	23.3608	1.08802	0.544011	+	0.839078i	$0.316905\pi$
$462$	67.9936	3.16335
$463$	6.62455	0.307869	0.153935	−	0.988081i	$-0.450806\pi$
$463$	6.62455	0.307869	0.153935	+	0.988081i	$0.450806\pi$
$464$	5.94619	0.276045
$465$	11.1337	0.516315
$466$	−39.3235	−1.82162
$467$	−40.4788	−1.87314	−0.936568	−	0.350487i	$-0.886016\pi$
$467$	−40.4788	−1.87314	−0.936568	+	0.350487i	$0.886016\pi$
$468$	−2.40592	−0.111214
$469$	21.8610	1.00945
$470$	5.59801	0.258217
$471$	34.2618	1.57870
$472$	41.2221	1.89740
$473$	−46.7586	−2.14996
$474$	26.8644	1.23392
$475$	−2.08821	−0.0958135
$476$	14.3936	0.659727
$477$	−0.122774	−0.00562144
$478$	42.3446	1.93680
$479$	−38.5423	−1.76104	−0.880521	−	0.474007i	$-0.842807\pi$
$479$	−38.5423	−1.76104	−0.880521	+	0.474007i	$0.842807\pi$
$480$	−21.3300	−0.973576
$481$	−21.1768	−0.965578
$482$	−71.6556	−3.26382
$483$	−5.02055	−0.228443
$484$	78.1090	3.55041
$485$	−20.7685	−0.943048
$486$	4.15715	0.188572
$487$	37.0798	1.68025	0.840124	−	0.542395i	$-0.182482\pi$
$487$	37.0798	1.68025	0.840124	+	0.542395i	$0.182482\pi$
$488$	−26.9959	−1.22205
$489$	−17.2723	−0.781080
$490$	−12.1756	−0.550036
$491$	−16.6178	−0.749952	−0.374976	−	0.927034i	$-0.622349\pi$
$491$	−16.6178	−0.749952	−0.374976	+	0.927034i	$0.622349\pi$
$492$	8.34946	0.376423
$493$	9.98784	0.449830
$494$	8.03011	0.361292
$495$	−2.73821	−0.123074
$496$	−2.03413	−0.0913353
$497$	11.8995	0.533763
$498$	7.84900	0.351722
$499$	3.04495	0.136311	0.0681553	−	0.997675i	$-0.478289\pi$
$499$	3.04495	0.136311	0.0681553	+	0.997675i	$0.478289\pi$
$500$	−23.5750	−1.05431
$501$	−12.8755	−0.575237
$502$	17.6772	0.788972
$503$	−12.3013	−0.548487	−0.274244	−	0.961660i	$-0.588427\pi$
$503$	−12.3013	−0.548487	−0.274244	+	0.961660i	$0.588427\pi$
$504$	1.69396	0.0754551
$505$	47.9919	2.13561
$506$	−13.5431	−0.602063
$507$	−6.29463	−0.279554
$508$	5.29290	0.234835
$509$	−6.68287	−0.296213	−0.148106	−	0.988971i	$-0.547318\pi$
$509$	−6.68287	−0.296213	−0.148106	+	0.988971i	$0.547318\pi$
$510$	15.1007	0.668671
$511$	−35.9389	−1.58984
$512$	9.43645	0.417036
$513$	−4.49798	−0.198590
$514$	57.3700	2.53048
$515$	38.7595	1.70795
$516$	46.1678	2.03242
$517$	−5.11886	−0.225127
$518$	35.9604	1.58001
$519$	8.09875	0.355496
$520$	−36.8881	−1.61765
$521$	−12.6902	−0.555966	−0.277983	−	0.960586i	$-0.589666\pi$
$521$	−12.6902	−0.555966	−0.277983	+	0.960586i	$0.589666\pi$
$522$	2.83498	0.124084
$523$	−23.9052	−1.04530	−0.522650	−	0.852548i	$-0.675056\pi$
$523$	−23.9052	−1.04530	−0.522650	+	0.852548i	$0.675056\pi$
$524$	−50.8274	−2.22041
$525$	−12.4333	−0.542633
$526$	−19.1119	−0.833316
$527$	−3.41674	−0.148836
$528$	−8.22062	−0.357756
$529$	1.00000	0.0434783
$530$	−4.53998	−0.197204
$531$	2.15167	0.0933747
$532$	−8.60111	−0.372905
$533$	−5.94630	−0.257563
$534$	−25.9653	−1.12363
$535$	3.13315	0.135458
$536$	−24.1418	−1.04277
$537$	−4.17710	−0.180255
$538$	66.6677	2.87425
$539$	11.1334	0.479551
$540$	49.8339	2.14451
$541$	−28.9264	−1.24364	−0.621821	−	0.783159i	$-0.713607\pi$
$541$	−28.9264	−1.24364	−0.621821	+	0.783159i	$0.713607\pi$
$542$	−5.19783	−0.223266
$543$	−18.0080	−0.772797
$544$	6.54578	0.280648
$545$	55.4753	2.37630
$546$	47.8117	2.04615
$547$	2.80933	0.120118	0.0600592	−	0.998195i	$-0.480871\pi$
$547$	2.80933	0.120118	0.0600592	+	0.998195i	$0.480871\pi$
$548$	52.4097	2.23883
$549$	−1.40911	−0.0601394
$550$	−33.5392	−1.43012
$551$	−5.96840	−0.254262
$552$	5.54436	0.235984
$553$	20.4927	0.871438
$554$	5.99289	0.254613
$555$	23.7970	1.01013
$556$	48.4304	2.05391
$557$	30.3427	1.28566	0.642830	−	0.766009i	$-0.277760\pi$
$557$	30.3427	1.28566	0.642830	+	0.766009i	$0.277760\pi$
$558$	−0.969819	−0.0410557
$559$	−32.8797	−1.39066
$560$	6.85782	0.289796
$561$	−13.8082	−0.582983
$562$	35.9271	1.51549
$563$	−1.18456	−0.0499232	−0.0249616	−	0.999688i	$-0.507946\pi$
$563$	−1.18456	−0.0499232	−0.0249616	+	0.999688i	$0.507946\pi$
$564$	5.05418	0.212819
$565$	11.6434	0.489840
$566$	−30.5885	−1.28573
$567$	−25.2398	−1.05997
$568$	−13.1410	−0.551383
$569$	38.9487	1.63282	0.816408	−	0.577475i	$-0.195962\pi$
$569$	38.9487	1.63282	0.816408	+	0.577475i	$0.195962\pi$
$570$	−9.02369	−0.377961
$571$	−13.6586	−0.571594	−0.285797	−	0.958290i	$-0.592258\pi$
$571$	−13.6586	−0.571594	−0.285797	+	0.958290i	$0.592258\pi$
$572$	81.3521	3.40150
$573$	−26.2229	−1.09548
$574$	10.0974	0.421459
$575$	2.47648	0.103276
$576$	2.14712	0.0894633
$577$	−4.23214	−0.176186	−0.0880931	−	0.996112i	$-0.528077\pi$
$577$	−4.23214	−0.176186	−0.0880931	+	0.996112i	$0.528077\pi$
$578$	34.9311	1.45294
$579$	−27.8970	−1.15936
$580$	66.1250	2.74569
$581$	5.98737	0.248398
$582$	−29.7271	−1.23223
$583$	4.15139	0.171933
$584$	39.6885	1.64232
$585$	−1.92545	−0.0796077
$586$	−6.19020	−0.255715
$587$	−31.4840	−1.29948	−0.649742	−	0.760155i	$-0.725123\pi$
$587$	−31.4840	−1.29948	−0.649742	+	0.760155i	$0.725123\pi$
$588$	−10.9927	−0.453333
$589$	2.04173	0.0841281
$590$	79.5653	3.27565
$591$	−38.0069	−1.56340
$592$	−4.34771	−0.178690
$593$	4.69966	0.192992	0.0964959	−	0.995333i	$-0.469237\pi$
$593$	4.69966	0.192992	0.0964959	+	0.995333i	$0.469237\pi$
$594$	−72.2430	−2.96417
$595$	11.5191	0.472238
$596$	−64.6455	−2.64798
$597$	18.5330	0.758505
$598$	−9.52320	−0.389433
$599$	11.1541	0.455744	0.227872	−	0.973691i	$-0.426823\pi$
$599$	11.1541	0.455744	0.227872	+	0.973691i	$0.426823\pi$
$600$	13.7305	0.560546
$601$	−35.5308	−1.44933	−0.724667	−	0.689100i	$-0.758006\pi$
$601$	−35.5308	−1.44933	−0.724667	+	0.689100i	$0.758006\pi$
$602$	55.8331	2.27559
$603$	−1.26013	−0.0513166
$604$	34.2981	1.39557
$605$	62.5104	2.54141
$606$	68.6936	2.79049
$607$	44.2640	1.79662	0.898310	−	0.439363i	$-0.144796\pi$
$607$	44.2640	1.79662	0.898310	+	0.439363i	$0.144796\pi$
$608$	−3.91154	−0.158634
$609$	−35.5362	−1.44000
$610$	−52.1065	−2.10973
$611$	−3.59947	−0.145619
$612$	−0.829689	−0.0335382
$613$	−5.50730	−0.222438	−0.111219	−	0.993796i	$-0.535475\pi$
$613$	−5.50730	−0.222438	−0.111219	+	0.993796i	$0.535475\pi$
$614$	−45.1907	−1.82375
$615$	6.68205	0.269446
$616$	−57.2784	−2.30781
$617$	−10.7057	−0.430995	−0.215498	−	0.976504i	$-0.569137\pi$
$617$	−10.7057	−0.430995	−0.215498	+	0.976504i	$0.569137\pi$
$618$	55.4788	2.23168
$619$	−6.23190	−0.250481	−0.125241	−	0.992126i	$-0.539970\pi$
$619$	−6.23190	−0.250481	−0.125241	+	0.992126i	$0.539970\pi$
$620$	−22.6207	−0.908470
$621$	5.33431	0.214059
$622$	72.6555	2.91322
$623$	−19.8069	−0.793545
$624$	−5.78056	−0.231408
$625$	−31.2494	−1.24998
$626$	−36.5696	−1.46161
$627$	8.25133	0.329526
$628$	−69.6106	−2.77777
$629$	−7.30287	−0.291184
$630$	3.26962	0.130265
$631$	−18.1344	−0.721919	−0.360959	−	0.932582i	$-0.617551\pi$
$631$	−18.1344	−0.721919	−0.360959	+	0.932582i	$0.617551\pi$
$632$	−22.6308	−0.900205
$633$	25.5029	1.01365
$634$	−23.9672	−0.951861
$635$	4.23590	0.168096
$636$	−4.09893	−0.162533
$637$	7.82880	0.310188
$638$	−95.8598	−3.79513
$639$	−0.685921	−0.0271346
$640$	54.0287	2.13567
$641$	50.5887	1.99813	0.999066	−	0.0432072i	$-0.0137575\pi$
$641$	50.5887	1.99813	0.999066	+	0.0432072i	$0.0137575\pi$
$642$	4.48466	0.176995
$643$	6.78845	0.267710	0.133855	−	0.991001i	$-0.457264\pi$
$643$	6.78845	0.267710	0.133855	+	0.991001i	$0.457264\pi$
$644$	10.2004	0.401951
$645$	36.9479	1.45482
$646$	2.76920	0.108953
$647$	41.5726	1.63439	0.817193	−	0.576364i	$-0.195529\pi$
$647$	41.5726	1.63439	0.817193	+	0.576364i	$0.195529\pi$
$648$	27.8732	1.09496
$649$	−72.7551	−2.85589
$650$	−23.5840	−0.925042
$651$	12.1566	0.476454
$652$	35.0925	1.37433
$653$	−27.1592	−1.06282	−0.531411	−	0.847114i	$-0.678338\pi$
$653$	−27.1592	−1.06282	−0.531411	+	0.847114i	$0.678338\pi$
$654$	79.4050	3.10498
$655$	−40.6771	−1.58938
$656$	−1.22081	−0.0476645
$657$	2.07163	0.0808219
$658$	6.11228	0.238282
$659$	−28.8138	−1.12242	−0.561212	−	0.827672i	$-0.689665\pi$
$659$	−28.8138	−1.12242	−0.561212	+	0.827672i	$0.689665\pi$
$660$	−91.4179	−3.55844
$661$	4.26191	0.165769	0.0828846	−	0.996559i	$-0.473587\pi$
$661$	4.26191	0.165769	0.0828846	+	0.996559i	$0.473587\pi$
$662$	19.7774	0.768669
$663$	−9.70964	−0.377091
$664$	−6.61206	−0.256598
$665$	−6.88344	−0.266928
$666$	−2.07287	−0.0803220
$667$	7.07815	0.274067
$668$	26.1596	1.01214
$669$	16.1106	0.622870
$670$	−46.5976	−1.80022
$671$	47.6466	1.83938
$672$	−23.2895	−0.898413
$673$	39.6915	1.52999	0.764997	−	0.644034i	$-0.222741\pi$
$673$	39.6915	1.52999	0.764997	+	0.644034i	$0.222741\pi$
$674$	−56.5207	−2.17710
$675$	13.2103	0.508466
$676$	12.7890	0.491883
$677$	−5.65899	−0.217493	−0.108746	−	0.994070i	$-0.534684\pi$
$677$	−5.65899	−0.217493	−0.108746	+	0.994070i	$0.534684\pi$
$678$	16.6658	0.640047
$679$	−22.6764	−0.870241
$680$	−12.7210	−0.487827
$681$	−5.40755	−0.207218
$682$	32.7927	1.25570
$683$	40.2392	1.53971	0.769855	−	0.638219i	$-0.220329\pi$
$683$	40.2392	1.53971	0.769855	+	0.638219i	$0.220329\pi$
$684$	0.495794	0.0189572
$685$	41.9434	1.60257
$686$	35.3445	1.34946
$687$	−24.9076	−0.950284
$688$	−6.75038	−0.257356
$689$	2.91917	0.111212
$690$	10.7015	0.407400
$691$	−13.1813	−0.501441	−0.250720	−	0.968060i	$-0.580667\pi$
$691$	−13.1813	−0.501441	−0.250720	+	0.968060i	$0.580667\pi$
$692$	−16.4544	−0.625503
$693$	−2.98977	−0.113572
$694$	−4.45260	−0.169018
$695$	38.7587	1.47020
$696$	39.2438	1.48753
$697$	−2.05060	−0.0776719
$698$	2.32736	0.0880920
$699$	−28.4132	−1.07469
$700$	25.2610	0.954777
$701$	10.4621	0.395146	0.197573	−	0.980288i	$-0.436694\pi$
$701$	10.4621	0.395146	0.197573	+	0.980288i	$0.436694\pi$
$702$	−50.7998	−1.91731
$703$	4.36395	0.164590
$704$	−72.6011	−2.73626
$705$	4.04484	0.152338
$706$	−68.8290	−2.59041
$707$	52.4008	1.97074
$708$	71.8357	2.69975
$709$	−26.0586	−0.978650	−0.489325	−	0.872101i	$-0.662757\pi$
$709$	−26.0586	−0.978650	−0.489325	+	0.872101i	$0.662757\pi$
$710$	−25.3642	−0.951902
$711$	−1.18126	−0.0443008
$712$	21.8734	0.819740
$713$	−2.42137	−0.0906808
$714$	16.4880	0.617047
$715$	65.1059	2.43482
$716$	8.48672	0.317164
$717$	30.5961	1.14263
$718$	29.7860	1.11160
$719$	−20.7378	−0.773391	−0.386695	−	0.922208i	$-0.626383\pi$
$719$	−20.7378	−0.773391	−0.386695	+	0.922208i	$0.626383\pi$
$720$	−0.395306	−0.0147322
$721$	42.3203	1.57609
$722$	42.5651	1.58411
$723$	−51.7748	−1.92553
$724$	36.5873	1.35976
$725$	17.5289	0.651007
$726$	89.4748	3.32072
$727$	9.92499	0.368098	0.184049	−	0.982917i	$-0.441080\pi$
$727$	9.92499	0.368098	0.184049	+	0.982917i	$0.441080\pi$
$728$	−40.2769	−1.49276
$729$	28.3661	1.05059
$730$	76.6053	2.83529
$731$	−11.3386	−0.419375
$732$	−47.0445	−1.73882
$733$	39.6999	1.46635	0.733175	−	0.680040i	$-0.238038\pi$
$733$	39.6999	1.46635	0.733175	+	0.680040i	$0.238038\pi$
$734$	−8.01697	−0.295912
$735$	−8.79747	−0.324499
$736$	4.63884	0.170990
$737$	42.6092	1.56953
$738$	−0.582048	−0.0214255
$739$	−33.4660	−1.23107	−0.615534	−	0.788110i	$-0.711060\pi$
$739$	−33.4660	−1.23107	−0.615534	+	0.788110i	$0.711060\pi$
$740$	−48.3490	−1.77734
$741$	5.80216	0.213148
$742$	−4.95706	−0.181979
$743$	1.61372	0.0592017	0.0296009	−	0.999562i	$-0.490576\pi$
$743$	1.61372	0.0592017	0.0296009	+	0.999562i	$0.490576\pi$
$744$	−13.4249	−0.492182
$745$	−51.7356	−1.89544
$746$	−0.335524	−0.0122844
$747$	−0.345130	−0.0126277
$748$	28.0545	1.02577
$749$	3.42098	0.125000
$750$	−27.0055	−0.986101
$751$	−11.3562	−0.414395	−0.207198	−	0.978299i	$-0.566434\pi$
$751$	−11.3562	−0.414395	−0.207198	+	0.978299i	$0.566434\pi$
$752$	−0.738992	−0.0269483
$753$	12.7727	0.465462
$754$	−67.4066	−2.45480
$755$	27.4487	0.998960
$756$	54.4120	1.97894
$757$	21.3892	0.777404	0.388702	−	0.921364i	$-0.372924\pi$
$757$	21.3892	0.777404	0.388702	+	0.921364i	$0.372924\pi$
$758$	−6.96555	−0.253000
$759$	−9.78555	−0.355193
$760$	7.60163	0.275740
$761$	42.2649	1.53210	0.766050	−	0.642781i	$-0.222219\pi$
$761$	42.2649	1.53210	0.766050	+	0.642781i	$0.222219\pi$
$762$	6.06308	0.219642
$763$	60.5717	2.19284
$764$	53.2778	1.92752
$765$	−0.663998	−0.0240069
$766$	81.7344	2.95318
$767$	−51.1598	−1.84727
$768$	35.3728	1.27641
$769$	7.99723	0.288388	0.144194	−	0.989549i	$-0.453941\pi$
$769$	7.99723	0.288388	0.144194	+	0.989549i	$0.453941\pi$
$770$	−110.557	−3.98418
$771$	41.4527	1.49288
$772$	56.6790	2.03992
$773$	19.4827	0.700744	0.350372	−	0.936611i	$-0.386055\pi$
$773$	19.4827	0.700744	0.350372	+	0.936611i	$0.386055\pi$
$774$	−3.21839	−0.115683
$775$	−5.99647	−0.215399
$776$	25.0424	0.898968
$777$	25.9832	0.932141
$778$	17.1070	0.613315
$779$	1.22537	0.0439034
$780$	−64.2831	−2.30171
$781$	23.1932	0.829919
$782$	−3.28410	−0.117439
$783$	37.7571	1.34933
$784$	1.60729	0.0574034
$785$	−55.7092	−1.98835
$786$	−58.2234	−2.07676
$787$	39.3136	1.40138	0.700690	−	0.713466i	$-0.252876\pi$
$787$	39.3136	1.40138	0.700690	+	0.713466i	$0.252876\pi$
$788$	77.2196	2.75083
$789$	−13.8093	−0.491623
$790$	−43.6811	−1.55410
$791$	12.7130	0.452022
$792$	3.30170	0.117321
$793$	33.5041	1.18977
$794$	56.8800	2.01859
$795$	−3.28036	−0.116343
$796$	−37.6540	−1.33461
$797$	19.0338	0.674213	0.337107	−	0.941466i	$-0.390552\pi$
$797$	19.0338	0.674213	0.337107	+	0.941466i	$0.390552\pi$
$798$	−9.85267	−0.348781
$799$	−1.24129	−0.0439136
$800$	11.4880	0.406162
$801$	1.14173	0.0403410
$802$	62.7764	2.21671
$803$	−70.0485	−2.47196
$804$	−42.0708	−1.48372
$805$	8.16333	0.287719
$806$	23.0592	0.812224
$807$	48.1707	1.69569
$808$	−57.8681	−2.03579
$809$	14.8212	0.521085	0.260542	−	0.965462i	$-0.416099\pi$
$809$	14.8212	0.521085	0.260542	+	0.965462i	$0.416099\pi$
$810$	53.7998	1.89033
$811$	45.1684	1.58608	0.793038	−	0.609172i	$-0.208498\pi$
$811$	45.1684	1.58608	0.793038	+	0.609172i	$0.208498\pi$
$812$	72.1997	2.53371
$813$	−3.75569	−0.131718
$814$	70.0904	2.45667
$815$	28.0845	0.983756
$816$	−1.99344	−0.0697844
$817$	6.77560	0.237048
$818$	25.9381	0.906906
$819$	−2.10234	−0.0734617
$820$	−13.5761	−0.474097
$821$	27.9727	0.976253	0.488126	−	0.872773i	$-0.337680\pi$
$821$	27.9727	0.976253	0.488126	+	0.872773i	$0.337680\pi$
$822$	60.0360	2.09399
$823$	1.30171	0.0453746	0.0226873	−	0.999743i	$-0.492778\pi$
$823$	1.30171	0.0453746	0.0226873	+	0.999743i	$0.492778\pi$
$824$	−46.7358	−1.62812
$825$	−24.2337	−0.843711
$826$	86.8747	3.02276
$827$	2.97183	0.103341	0.0516703	−	0.998664i	$-0.483546\pi$
$827$	2.97183	0.103341	0.0516703	+	0.998664i	$0.483546\pi$
$828$	−0.587981	−0.0204337
$829$	6.79264	0.235918	0.117959	−	0.993018i	$-0.462365\pi$
$829$	6.79264	0.235918	0.117959	+	0.993018i	$0.462365\pi$
$830$	−12.7623	−0.442987
$831$	4.33016	0.150212
$832$	−51.0515	−1.76989
$833$	2.69978	0.0935419
$834$	55.4776	1.92103
$835$	20.9354	0.724500
$836$	−16.7644	−0.579810
$837$	−12.9163	−0.446453
$838$	51.8240	1.79023
$839$	−18.5299	−0.639723	−0.319861	−	0.947464i	$-0.603636\pi$
$839$	−18.5299	−0.639723	−0.319861	+	0.947464i	$0.603636\pi$
$840$	45.2605	1.56163
$841$	21.1002	0.727591
$842$	−22.4909	−0.775086
$843$	25.9591	0.894080
$844$	−51.8148	−1.78354
$845$	10.2350	0.352094
$846$	−0.352331	−0.0121134
$847$	68.2531	2.34520
$848$	0.599322	0.0205808
$849$	−22.1017	−0.758529
$850$	−8.13302	−0.278960
$851$	−5.17537	−0.177409
$852$	−22.9001	−0.784546
$853$	−12.9502	−0.443407	−0.221704	−	0.975114i	$-0.571162\pi$
$853$	−12.9502	−0.443407	−0.221704	+	0.975114i	$0.571162\pi$
$854$	−56.8934	−1.94685
$855$	0.396783	0.0135697
$856$	−3.77791	−0.129126
$857$	42.0953	1.43795	0.718973	−	0.695038i	$-0.244612\pi$
$857$	42.0953	1.43795	0.718973	+	0.695038i	$0.244612\pi$
$858$	93.1898	3.18145
$859$	20.9662	0.715356	0.357678	−	0.933845i	$-0.383569\pi$
$859$	20.9662	0.715356	0.357678	+	0.933845i	$0.383569\pi$
$860$	−75.0680	−2.55980
$861$	7.29591	0.248644
$862$	−54.2716	−1.84850
$863$	47.5313	1.61798	0.808991	−	0.587821i	$-0.200014\pi$
$863$	47.5313	1.61798	0.808991	+	0.587821i	$0.200014\pi$
$864$	24.7450	0.841843
$865$	−13.1684	−0.447740
$866$	8.75716	0.297580
$867$	25.2394	0.857177
$868$	−24.6988	−0.838333
$869$	39.9423	1.35495
$870$	75.7469	2.56806
$871$	29.9619	1.01522
$872$	−66.8914	−2.26523
$873$	1.30714	0.0442400
$874$	1.96247	0.0663815
$875$	−20.6003	−0.696417
$876$	69.1633	2.33681
$877$	14.3308	0.483915	0.241958	−	0.970287i	$-0.422210\pi$
$877$	14.3308	0.483915	0.241958	+	0.970287i	$0.422210\pi$
$878$	−87.4072	−2.94985
$879$	−4.47273	−0.150861
$880$	13.3666	0.450588
$881$	38.5566	1.29900	0.649502	−	0.760360i	$-0.274977\pi$
$881$	38.5566	1.29900	0.649502	+	0.760360i	$0.274977\pi$
$882$	0.766314	0.0258031
$883$	−18.3587	−0.617818	−0.308909	−	0.951092i	$-0.599964\pi$
$883$	−18.3587	−0.617818	−0.308909	+	0.951092i	$0.599964\pi$
$884$	19.7273	0.663502
$885$	57.4899	1.93250
$886$	−58.6250	−1.96955
$887$	−22.2031	−0.745509	−0.372754	−	0.927930i	$-0.621587\pi$
$887$	−22.2031	−0.745509	−0.372754	+	0.927930i	$0.621587\pi$
$888$	−28.6941	−0.962912
$889$	4.62504	0.155119
$890$	42.2192	1.41519
$891$	−49.1949	−1.64809
$892$	−32.7322	−1.09596
$893$	0.741752	0.0248218
$894$	−74.0521	−2.47667
$895$	6.79190	0.227028
$896$	58.9922	1.97079
$897$	−6.88099	−0.229750
$898$	−49.4358	−1.64970
$899$	−17.1388	−0.571610
$900$	−1.45612	−0.0485375
$901$	1.00668	0.0335375
$902$	19.6809	0.655303
$903$	40.3422	1.34251
$904$	−14.0394	−0.466944
$905$	29.2807	0.973324
$906$	39.2889	1.30529
$907$	−52.4764	−1.74245	−0.871225	−	0.490884i	$-0.836674\pi$
$907$	−52.4764	−1.74245	−0.871225	+	0.490884i	$0.836674\pi$
$908$	10.9867	0.364605
$909$	−3.02055	−0.100185
$910$	−77.7410	−2.57709
$911$	17.4259	0.577347	0.288674	−	0.957428i	$-0.406786\pi$
$911$	17.4259	0.577347	0.288674	+	0.957428i	$0.406786\pi$
$912$	1.19121	0.0394451
$913$	11.6700	0.386220
$914$	43.1324	1.42669
$915$	−37.6496	−1.24466
$916$	50.6054	1.67205
$917$	−44.4139	−1.46668
$918$	−17.5184	−0.578194
$919$	−30.2110	−0.996569	−0.498284	−	0.867014i	$-0.666036\pi$
$919$	−30.2110	−0.996569	−0.498284	+	0.867014i	$0.666036\pi$
$920$	−9.01505	−0.297217
$921$	−32.6526	−1.07594
$922$	−54.3691	−1.79055
$923$	16.3090	0.536817
$924$	−99.8162	−3.28371
$925$	−12.8167	−0.421411
$926$	−15.4177	−0.506659
$927$	−2.43947	−0.0801228
$928$	32.8344	1.07784
$929$	−39.8728	−1.30818	−0.654092	−	0.756415i	$-0.726949\pi$
$929$	−39.8728	−1.30818	−0.654092	+	0.756415i	$0.726949\pi$
$930$	−25.9123	−0.849698
$931$	−1.61330	−0.0528738
$932$	57.7278	1.89094
$933$	52.4973	1.71868
$934$	94.2089	3.08261
$935$	22.4519	0.734256
$936$	2.32169	0.0758867
$937$	41.9966	1.37197	0.685985	−	0.727616i	$-0.259372\pi$
$937$	41.9966	1.37197	0.685985	+	0.727616i	$0.259372\pi$
$938$	−50.8784	−1.66124
$939$	−26.4233	−0.862293
$940$	−8.21801	−0.268042
$941$	36.2933	1.18313	0.591564	−	0.806258i	$-0.298511\pi$
$941$	36.2933	1.18313	0.591564	+	0.806258i	$0.298511\pi$
$942$	−79.7398	−2.59806
$943$	−1.45321	−0.0473230
$944$	−10.5034	−0.341856
$945$	43.5457	1.41654
$946$	108.824	3.53819
$947$	−29.4432	−0.956774	−0.478387	−	0.878149i	$-0.658778\pi$
$947$	−29.4432	−0.956774	−0.478387	+	0.878149i	$0.658778\pi$
$948$	−39.4376	−1.28087
$949$	−49.2566	−1.59894
$950$	4.86002	0.157680
$951$	−17.3175	−0.561560
$952$	−13.8896	−0.450165
$953$	−25.0974	−0.812986	−0.406493	−	0.913654i	$-0.633248\pi$
$953$	−25.0974	−0.812986	−0.406493	+	0.913654i	$0.633248\pi$
$954$	0.285740	0.00925118
$955$	42.6381	1.37974
$956$	−62.1629	−2.01049
$957$	−69.2636	−2.23897
$958$	89.7019	2.89814
$959$	45.7966	1.47885
$960$	57.3682	1.85155
$961$	−25.1370	−0.810871
$962$	49.2861	1.58905
$963$	−0.197196	−0.00635456
$964$	105.192	3.38801
$965$	45.3600	1.46019
$966$	11.6846	0.375947
$967$	47.8759	1.53958	0.769792	−	0.638294i	$-0.220360\pi$
$967$	47.8759	1.53958	0.769792	+	0.638294i	$0.220360\pi$
$968$	−75.3743	−2.42262
$969$	2.00089	0.0642778
$970$	48.3358	1.55197
$971$	−21.6509	−0.694811	−0.347406	−	0.937715i	$-0.612937\pi$
$971$	−21.6509	−0.694811	−0.347406	+	0.937715i	$0.612937\pi$
$972$	−6.10279	−0.195747
$973$	42.3194	1.35670
$974$	−86.2983	−2.76517
$975$	−17.0407	−0.545738
$976$	6.87857	0.220178
$977$	−21.1515	−0.676696	−0.338348	−	0.941021i	$-0.609868\pi$
$977$	−21.1515	−0.676696	−0.338348	+	0.941021i	$0.609868\pi$
$978$	40.1989	1.28542
$979$	−38.6056	−1.23384
$980$	17.8740	0.570965
$981$	−3.49154	−0.111476
$982$	38.6758	1.23419
$983$	−28.6150	−0.912676	−0.456338	−	0.889806i	$-0.650839\pi$
$983$	−28.6150	−0.912676	−0.456338	+	0.889806i	$0.650839\pi$
$984$	−8.05713	−0.256852
$985$	61.7986	1.96907
$986$	−23.2453	−0.740283
$987$	4.41643	0.140577
$988$	−11.7884	−0.375039
$989$	−8.03543	−0.255512
$990$	6.37282	0.202542
$991$	33.9697	1.07908	0.539541	−	0.841959i	$-0.318598\pi$
$991$	33.9697	1.07908	0.539541	+	0.841959i	$0.318598\pi$
$992$	−11.2323	−0.356627
$993$	14.2901	0.453484
$994$	−27.6944	−0.878412
$995$	−30.1344	−0.955324
$996$	−11.5225	−0.365105
$997$	47.1250	1.49246	0.746232	−	0.665686i	$-0.231861\pi$
$997$	47.1250	1.49246	0.746232	+	0.665686i	$0.231861\pi$
$998$	−7.08670	−0.224326
$999$	−27.6070	−0.873448

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.f.1.19	✓	176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.f.1.19	✓	176	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)

\(f(q)\)	\(=\)	\(q-2.32736 q^{2} -1.68164 q^{3} +3.41663 q^{4} +2.73432 q^{5} +3.91378 q^{6} +2.98551 q^{7} -3.29700 q^{8} -0.172094 q^{9} +O(q^{10})\)	\(q-2.32736 q^{2} -1.68164 q^{3} +3.41663 q^{4} +2.73432 q^{5} +3.91378 q^{6} +2.98551 q^{7} -3.29700 q^{8} -0.172094 q^{9} -6.36375 q^{10} +5.81906 q^{11} -5.74553 q^{12} +4.09184 q^{13} -6.94837 q^{14} -4.59813 q^{15} +0.840077 q^{16} +1.41108 q^{17} +0.400526 q^{18} -0.843215 q^{19} +9.34213 q^{20} -5.02055 q^{21} -13.5431 q^{22} +1.00000 q^{23} +5.54436 q^{24} +2.47648 q^{25} -9.52320 q^{26} +5.33431 q^{27} +10.2004 q^{28} +7.07815 q^{29} +10.7015 q^{30} -2.42137 q^{31} +4.63884 q^{32} -9.78555 q^{33} -3.28410 q^{34} +8.16333 q^{35} -0.587981 q^{36} -5.17537 q^{37} +1.96247 q^{38} -6.88099 q^{39} -9.01505 q^{40} -1.45321 q^{41} +11.6846 q^{42} -8.03543 q^{43} +19.8815 q^{44} -0.470559 q^{45} -2.32736 q^{46} -0.879671 q^{47} -1.41271 q^{48} +1.91327 q^{49} -5.76368 q^{50} -2.37293 q^{51} +13.9803 q^{52} +0.713413 q^{53} -12.4149 q^{54} +15.9111 q^{55} -9.84324 q^{56} +1.41798 q^{57} -16.4734 q^{58} -12.5029 q^{59} -15.7101 q^{60} +8.18803 q^{61} +5.63540 q^{62} -0.513788 q^{63} -12.4764 q^{64} +11.1884 q^{65} +22.7745 q^{66} +7.32236 q^{67} +4.82114 q^{68} -1.68164 q^{69} -18.9990 q^{70} +3.98574 q^{71} +0.567395 q^{72} -12.0378 q^{73} +12.0450 q^{74} -4.16455 q^{75} -2.88095 q^{76} +17.3729 q^{77} +16.0146 q^{78} +6.86405 q^{79} +2.29704 q^{80} -8.45410 q^{81} +3.38215 q^{82} +2.00548 q^{83} -17.1533 q^{84} +3.85834 q^{85} +18.7014 q^{86} -11.9029 q^{87} -19.1855 q^{88} -6.63433 q^{89} +1.09516 q^{90} +12.2162 q^{91} +3.41663 q^{92} +4.07186 q^{93} +2.04732 q^{94} -2.30562 q^{95} -7.80085 q^{96} -7.59549 q^{97} -4.45288 q^{98} -1.00143 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9}+O(q^{10}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9	\( 176 q + 19 q^{2} + 22 q^{3} + 203 q^{4} + 28 q^{5} + 9 q^{6} + 30 q^{7} + 51 q^{8} + 204 q^{9} + 18 q^{10} + 11 q^{11} + 46 q^{12} + 87 q^{13} - 6 q^{14} + 29 q^{15} + 257 q^{16} + 14 q^{17} + 72 q^{18} + 34 q^{19} + 45 q^{20} + 23 q^{21} + 62 q^{22} + 176 q^{23} + 33 q^{24} + 272 q^{25} + 31 q^{26} + 82 q^{27} + 80 q^{28} + 75 q^{29} - 30 q^{30} + 73 q^{31} + 71 q^{32} + 30 q^{33} + 23 q^{34} + 44 q^{35} + 264 q^{36} + 236 q^{37} - 21 q^{38} + 17 q^{39} + 43 q^{40} + 51 q^{41} + 38 q^{42} + 51 q^{43} + 12 q^{44} + 127 q^{45} + 19 q^{46} + 45 q^{47} + 61 q^{48} + 268 q^{49} + 55 q^{50} - 3 q^{51} + 166 q^{52} + 63 q^{53} - 32 q^{54} + 11 q^{55} - 9 q^{56} + 72 q^{57} + 98 q^{58} + 95 q^{59} - 7 q^{60} + 73 q^{61} + 12 q^{62} + 19 q^{63} + 365 q^{64} + 19 q^{65} - 28 q^{66} + 138 q^{67} + 16 q^{68} + 22 q^{69} + 100 q^{70} + 85 q^{71} + 129 q^{72} + 118 q^{73} - 21 q^{74} - 12 q^{75} + 52 q^{76} + 75 q^{77} + 97 q^{78} + 74 q^{79} + 8 q^{80} + 280 q^{81} + 67 q^{82} + 10 q^{83} - 51 q^{84} + 169 q^{85} - 39 q^{86} - 6 q^{87} + 159 q^{88} + 38 q^{89} + 22 q^{90} + 90 q^{91} + 203 q^{92} + 230 q^{93} + 63 q^{94} + 30 q^{95} + 107 q^{96} + 161 q^{97} + 58 q^{98} + 7 q^{99}+O(q^{100}) \) 176 * q + 19 * q^2 + 22 * q^3 + 203 * q^4 + 28 * q^5 + 9 * q^6 + 30 * q^7 + 51 * q^8 + 204 * q^9 + 18 * q^10 + 11 * q^11 + 46 * q^12 + 87 * q^13 - 6 * q^14 + 29 * q^15 + 257 * q^16 + 14 * q^17 + 72 * q^18 + 34 * q^19 + 45 * q^20 + 23 * q^21 + 62 * q^22 + 176 * q^23 + 33 * q^24 + 272 * q^25 + 31 * q^26 + 82 * q^27 + 80 * q^28 + 75 * q^29 - 30 * q^30 + 73 * q^31 + 71 * q^32 + 30 * q^33 + 23 * q^34 + 44 * q^35 + 264 * q^36 + 236 * q^37 - 21 * q^38 + 17 * q^39 + 43 * q^40 + 51 * q^41 + 38 * q^42 + 51 * q^43 + 12 * q^44 + 127 * q^45 + 19 * q^46 + 45 * q^47 + 61 * q^48 + 268 * q^49 + 55 * q^50 - 3 * q^51 + 166 * q^52 + 63 * q^53 - 32 * q^54 + 11 * q^55 - 9 * q^56 + 72 * q^57 + 98 * q^58 + 95 * q^59 - 7 * q^60 + 73 * q^61 + 12 * q^62 + 19 * q^63 + 365 * q^64 + 19 * q^65 - 28 * q^66 + 138 * q^67 + 16 * q^68 + 22 * q^69 + 100 * q^70 + 85 * q^71 + 129 * q^72 + 118 * q^73 - 21 * q^74 - 12 * q^75 + 52 * q^76 + 75 * q^77 + 97 * q^78 + 74 * q^79 + 8 * q^80 + 280 * q^81 + 67 * q^82 + 10 * q^83 - 51 * q^84 + 169 * q^85 - 39 * q^86 - 6 * q^87 + 159 * q^88 + 38 * q^89 + 22 * q^90 + 90 * q^91 + 203 * q^92 + 230 * q^93 + 63 * q^94 + 30 * q^95 + 107 * q^96 + 161 * q^97 + 58 * q^98 + 7 * q^99

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