LMFDB - Embedded newform 810.2.s.a.557.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(17,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([22, 9]))

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

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

chi := DirichletCharacter("810.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.s (of order $36$, degree $12$, not minimal)

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:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			557.11
Character	$\chi$	$=$	810.557
Dual form			810.2.s.a.413.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.91317 + 1.15748i) q^{5} +(-0.957323 - 2.05299i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.23108 - 0.149199i) q^{10} +(-3.39033 - 4.04043i) q^{11} +(-2.24888 - 3.21174i) q^{13} +(0.393351 - 2.23081i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.889884 - 3.32109i) q^{17} +(3.09115 - 1.78467i) q^{19} +(-1.74202 - 1.40191i) q^{20} +(-0.459695 - 5.25434i) q^{22} +(4.68275 + 2.18360i) q^{23} +(2.32048 - 4.42893i) q^{25} -3.92081i q^{26} +(1.60175 - 1.60175i) q^{28} +(0.136517 + 0.774225i) q^{29} +(-10.3110 + 3.75290i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(1.17595 - 3.23090i) q^{34} +(4.20782 + 2.81964i) q^{35} +(8.66041 - 2.32055i) q^{37} +(3.55576 + 0.311089i) q^{38} +(-0.622874 - 2.14756i) q^{40} +(-2.74726 - 0.484417i) q^{41} +(-0.583752 + 6.67232i) q^{43} +(2.63721 - 4.56777i) q^{44} +(2.58342 + 4.47461i) q^{46} +(-5.28675 + 2.46525i) q^{47} +(1.20123 - 1.43157i) q^{49} +(4.44115 - 2.29699i) q^{50} +(2.24888 - 3.21174i) q^{52} +(-9.14166 - 9.14166i) q^{53} +(11.1630 + 3.80582i) q^{55} +(2.23081 - 0.393351i) q^{56} +(-0.332249 + 0.712510i) q^{58} +(-8.39725 - 7.04613i) q^{59} +(1.73115 + 0.630087i) q^{61} +(-10.5989 - 2.83996i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(8.02003 + 3.54158i) q^{65} +(-2.63797 + 1.84712i) q^{67} +(2.81645 - 1.97210i) q^{68} +(1.82957 + 4.72322i) q^{70} +(-4.51486 - 2.60666i) q^{71} +(-3.63280 - 0.973406i) q^{73} +(8.42520 + 3.06652i) q^{74} +(2.73428 + 2.29433i) q^{76} +(-5.04932 + 10.8283i) q^{77} +(-6.60413 + 1.16449i) q^{79} +(0.721563 - 2.11645i) q^{80} +(-1.97258 - 1.97258i) q^{82} +(1.91102 - 2.72922i) q^{83} +(5.54661 + 5.32381i) q^{85} +(-4.30526 + 5.13081i) q^{86} +(4.78024 - 2.22906i) q^{88} +(-1.05755 - 1.83173i) q^{89} +(-4.44074 + 7.69159i) q^{91} +(-0.450320 + 5.14718i) q^{92} +(-5.74466 - 1.01294i) q^{94} +(-3.84818 + 6.99233i) q^{95} +(11.4669 + 1.00322i) q^{97} +(1.80510 - 0.483676i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$2$	0.819152	+	0.573576i	0.579228	+	0.405580i
$3$		0			0
$3$		0			0
$4$	0.342020	+	0.939693i	0.171010	+	0.469846i
$5$	−1.91317	+	1.15748i	−0.855598	+	0.517641i
$5$	−1.91317	+	1.15748i	−0.855598	+	0.517641i
$6$		0			0
$7$	−0.957323	−	2.05299i	−0.361834	−	0.775956i	−0.999982	−	0.00604179i	$-0.998077\pi$
$7$	−0.957323	−	2.05299i	−0.361834	−	0.775956i	0.638148	−	0.769914i	$-0.279701\pi$
$8$	−0.258819	+	0.965926i	−0.0915064	+	0.341506i
$9$		0			0
$10$	−2.23108	−	0.149199i	−0.705531	−	0.0471810i
$11$	−3.39033	−	4.04043i	−1.02222	−	1.21824i	−0.975653	−	0.219321i	$-0.929616\pi$
$11$	−3.39033	−	4.04043i	−1.02222	−	1.21824i	−0.0465691	−	0.998915i	$-0.514829\pi$
$12$		0			0
$13$	−2.24888	−	3.21174i	−0.623728	−	0.890775i	0.375624	−	0.926772i	$-0.377428\pi$
$13$	−2.24888	−	3.21174i	−0.623728	−	0.890775i	−0.999352	+	0.0359967i	$0.988539\pi$
$14$	0.393351	−	2.23081i	0.105128	−	0.596208i
$15$		0			0
$16$	−0.766044	+	0.642788i	−0.191511	+	0.160697i
$17$	−0.889884	−	3.32109i	−0.215829	−	0.805483i	−0.985873	−	0.167493i	$-0.946433\pi$
$17$	−0.889884	−	3.32109i	−0.215829	−	0.805483i	0.770045	−	0.637990i	$-0.220234\pi$
$18$		0			0
$19$	3.09115	−	1.78467i	0.709157	−	0.409432i	−0.101592	−	0.994826i	$-0.532393\pi$
$19$	3.09115	−	1.78467i	0.709157	−	0.409432i	0.810749	+	0.585394i	$0.199060\pi$
$20$	−1.74202	−	1.40191i	−0.389528	−	0.313478i
$21$		0			0
$22$	−0.459695	−	5.25434i	−0.0980073	−	1.12023i
$23$	4.68275	+	2.18360i	0.976420	+	0.455312i	0.844270	−	0.535918i	$-0.180034\pi$
$23$	4.68275	+	2.18360i	0.976420	+	0.455312i	0.132150	+	0.991230i	$0.457812\pi$
$24$		0			0
$25$	2.32048	−	4.42893i	0.464095	−	0.885785i
$26$		−	3.92081i		−	0.768933i
$27$		0			0
$28$	1.60175	−	1.60175i	0.302703	−	0.302703i
$29$	0.136517	+	0.774225i	0.0253505	+	0.143770i	0.994856	−	0.101300i	$-0.0323002\pi$
$29$	0.136517	+	0.774225i	0.0253505	+	0.143770i	−0.969505	+	0.245070i	$0.921189\pi$
$30$		0			0
$31$	−10.3110	+	3.75290i	−1.85191	+	0.674041i	−0.867690	+	0.497106i	$0.834396\pi$
$31$	−10.3110	+	3.75290i	−1.85191	+	0.674041i	−0.984222	+	0.176935i	$0.943382\pi$
$32$	−0.996195	+	0.0871557i	−0.176104	+	0.0154071i
$33$		0			0
$34$	1.17595	−	3.23090i	0.201674	−	0.554094i
$35$	4.20782	+	2.81964i	0.711251	+	0.476606i
$36$		0			0
$37$	8.66041	−	2.32055i	1.42376	−	0.381496i	0.536946	−	0.843617i	$-0.319578\pi$
$37$	8.66041	−	2.32055i	1.42376	−	0.381496i	0.886817	+	0.462121i	$0.152911\pi$
$38$	3.55576	+	0.311089i	0.576821	+	0.0504653i
$39$		0			0
$40$	−0.622874	−	2.14756i	−0.0984851	−	0.339560i
$41$	−2.74726	−	0.484417i	−0.429050	−	0.0756532i	−0.0450470	−	0.998985i	$-0.514344\pi$
$41$	−2.74726	−	0.484417i	−0.429050	−	0.0756532i	−0.384003	+	0.923332i	$0.625455\pi$
$42$		0			0
$43$	−0.583752	+	6.67232i	−0.0890213	+	1.01752i	0.811975	+	0.583692i	$0.198392\pi$
$43$	−0.583752	+	6.67232i	−0.0890213	+	1.01752i	−0.900996	+	0.433826i	$0.857163\pi$
$44$	2.63721	−	4.56777i	0.397574	−	0.688618i
$45$		0			0
$46$	2.58342	+	4.47461i	0.380904	+	0.659746i
$47$	−5.28675	+	2.46525i	−0.771152	+	0.359594i	−0.768041	−	0.640401i	$-0.778768\pi$
$47$	−5.28675	+	2.46525i	−0.771152	+	0.359594i	−0.00311126	+	0.999995i	$0.500990\pi$
$48$		0			0
$49$	1.20123	−	1.43157i	0.171604	−	0.204510i
$50$	4.44115	−	2.29699i	0.628074	−	0.324844i
$51$		0			0
$52$	2.24888	−	3.21174i	0.311864	−	0.445388i
$53$	−9.14166	−	9.14166i	−1.25570	−	1.25570i	−0.953124	−	0.302579i	$-0.902152\pi$
$53$	−9.14166	−	9.14166i	−1.25570	−	1.25570i	−0.302579	−	0.953124i	$-0.597848\pi$
$54$		0			0
$55$	11.1630	+	3.80582i	1.50522	+	0.513176i
$56$	2.23081	−	0.393351i	0.298104	−	0.0525638i
$57$		0			0
$58$	−0.332249	+	0.712510i	−0.0436264	+	0.0935572i
$59$	−8.39725	−	7.04613i	−1.09323	−	0.917328i	−0.0962781	−	0.995354i	$-0.530694\pi$
$59$	−8.39725	−	7.04613i	−1.09323	−	0.917328i	−0.996951	+	0.0780261i	$0.975138\pi$
$60$		0			0
$61$	1.73115	+	0.630087i	0.221651	+	0.0806744i	0.450459	−	0.892797i	$-0.351260\pi$
$61$	1.73115	+	0.630087i	0.221651	+	0.0806744i	−0.228808	+	0.973472i	$0.573483\pi$
$62$	−10.5989	−	2.83996i	−1.34606	−	0.360675i
$63$		0			0
$64$	−0.866025	−	0.500000i	−0.108253	−	0.0625000i
$65$	8.02003	+	3.54158i	0.994762	+	0.439278i
$66$		0			0
$67$	−2.63797	+	1.84712i	−0.322279	+	0.225662i	−0.723509	−	0.690315i	$-0.757472\pi$
$67$	−2.63797	+	1.84712i	−0.322279	+	0.225662i	0.401230	+	0.915977i	$0.368583\pi$
$68$	2.81645	−	1.97210i	0.341545	−	0.239152i
$69$		0			0
$70$	1.82957	+	4.72322i	0.218675	+	0.564533i
$71$	−4.51486	−	2.60666i	−0.535816	−	0.309353i	0.207566	−	0.978221i	$-0.433446\pi$
$71$	−4.51486	−	2.60666i	−0.535816	−	0.309353i	−0.743381	+	0.668868i	$0.766779\pi$
$72$		0			0
$73$	−3.63280	−	0.973406i	−0.425187	−	0.113929i	0.0398790	−	0.999205i	$-0.487303\pi$
$73$	−3.63280	−	0.973406i	−0.425187	−	0.113929i	−0.465066	+	0.885276i	$0.653969\pi$
$74$	8.42520	+	3.06652i	0.979410	+	0.356476i
$75$		0			0
$76$	2.73428	+	2.29433i	0.313643	+	0.263178i
$77$	−5.04932	+	10.8283i	−0.575423	+	1.23400i
$78$		0			0
$79$	−6.60413	+	1.16449i	−0.743023	+	0.131015i	−0.532329	−	0.846537i	$-0.678683\pi$
$79$	−6.60413	+	1.16449i	−0.743023	+	0.131015i	−0.210693	+	0.977552i	$0.567572\pi$
$80$	0.721563	−	2.11645i	0.0806732	−	0.236626i
$81$		0			0
$82$	−1.97258	−	1.97258i	−0.217835	−	0.217835i
$83$	1.91102	−	2.72922i	0.209762	−	0.299571i	−0.700460	−	0.713691i	$-0.747022\pi$
$83$	1.91102	−	2.72922i	0.209762	−	0.299571i	0.910222	+	0.414121i	$0.135911\pi$
$84$		0			0
$85$	5.54661	+	5.32381i	0.601614	+	0.577448i
$86$	−4.30526	+	5.13081i	−0.464249	+	0.553270i
$87$		0			0
$88$	4.78024	−	2.22906i	0.509575	−	0.237619i
$89$	−1.05755	−	1.83173i	−0.112100	−	0.194163i	0.804517	−	0.593930i	$-0.202424\pi$
$89$	−1.05755	−	1.83173i	−0.112100	−	0.194163i	−0.916617	+	0.399767i	$0.869091\pi$
$90$		0			0
$91$	−4.44074	+	7.69159i	−0.465516	+	0.806298i
$92$	−0.450320	+	5.14718i	−0.0469491	+	0.536630i
$93$		0			0
$94$	−5.74466	−	1.01294i	−0.592517	−	0.104477i
$95$	−3.84818	+	6.99233i	−0.394815	+	0.717398i
$96$		0			0
$97$	11.4669	+	1.00322i	1.16429	+	0.101862i	0.652869	−	0.757471i	$-0.273565\pi$
$97$	11.4669	+	1.00322i	1.16429	+	0.101862i	0.511417	+	0.859333i	$0.329121\pi$
$98$	1.80510	−	0.483676i	0.182343	−	0.0488586i
$99$		0			0
$100$	4.95548	+	0.665753i	0.495548	+	0.0665753i
$101$	−1.65735	+	4.55352i	−0.164912	+	0.453093i	−0.994431	−	0.105386i	$-0.966392\pi$
$101$	−1.65735	+	4.55352i	−0.164912	+	0.453093i	0.829519	+	0.558478i	$0.188615\pi$
$102$		0			0
$103$	0.938146	−	0.0820772i	0.0924383	−	0.00808730i	−0.0408427	−	0.999166i	$-0.513004\pi$
$103$	0.938146	−	0.0820772i	0.0924383	−	0.00808730i	0.133281	+	0.991078i	$0.457449\pi$
$104$	3.68435	−	1.34099i	0.361280	−	0.131495i
$105$		0			0
$106$	−2.24497	−	12.7318i	−0.218051	−	1.23663i
$107$	8.74026	−	8.74026i	0.844953	−	0.844953i	−0.144545	−	0.989498i	$-0.546172\pi$
$107$	8.74026	−	8.74026i	0.844953	−	0.844953i	0.989498	+	0.144545i	$0.0461719\pi$
$108$		0			0
$109$		−	2.48109i		−	0.237645i	−0.992915	−	0.118823i	$-0.962088\pi$
$109$		−	2.48109i		−	0.237645i	0.992915	−	0.118823i	$-0.0379120\pi$
$110$	6.96128	+	9.52038i	0.663732	+	0.907733i
$111$		0			0
$112$	2.05299	+	0.957323i	0.193989	+	0.0904585i
$113$	0.466860	+	5.33623i	0.0439185	+	0.501990i	0.986016	+	0.166651i	$0.0532954\pi$
$113$	0.466860	+	5.33623i	0.0439185	+	0.501990i	−0.942097	+	0.335339i	$0.891149\pi$
$114$		0			0
$115$	−11.4864	+	1.24258i	−1.07111	+	0.115871i
$116$	−0.680842	+	0.393084i	−0.0632146	+	0.0364969i
$117$		0			0
$118$	−2.83713	−	10.5883i	−0.261179	−	0.974734i
$119$	−5.96625	+	5.00628i	−0.546925	+	0.458925i
$120$		0			0
$121$	−2.92066	+	16.5639i	−0.265515	+	1.50581i
$122$	1.05667	+	1.50908i	0.0956666	+	0.136626i
$123$		0			0
$124$	−7.05315	−	8.40561i	−0.633391	−	0.754846i
$125$	0.686919	+	11.1592i	0.0614399	+	0.998111i
$126$		0			0
$127$	−2.83347	+	10.5746i	−0.251429	+	0.938347i	0.718613	+	0.695411i	$0.244777\pi$
$127$	−2.83347	+	10.5746i	−0.251429	+	0.938347i	−0.970042	+	0.242937i	$0.921889\pi$
$128$	−0.422618	−	0.906308i	−0.0373545	−	0.0801070i
$129$		0			0
$130$	4.53826	+	7.50119i	0.398031	+	0.657898i
$131$	0.984549	+	2.70503i	0.0860204	+	0.236339i	0.975243	−	0.221135i	$-0.0709763\pi$
$131$	0.984549	+	2.70503i	0.0860204	+	0.236339i	−0.889223	+	0.457475i	$0.848754\pi$
$132$		0			0
$133$	−6.62314	−	4.63757i	−0.574299	−	0.402128i
$134$	−3.22036			−0.278197
$135$		0			0
$136$	3.43825			0.294827
$137$	7.53427	+	5.27556i	0.643696	+	0.450721i	0.849297	−	0.527915i	$-0.177026\pi$
$137$	7.53427	+	5.27556i	0.643696	+	0.450721i	−0.205601	+	0.978636i	$0.565915\pi$
$138$		0			0
$139$	−4.65056	−	12.7773i	−0.394455	−	1.08376i	−0.964945	−	0.262452i	$-0.915469\pi$
$139$	−4.65056	−	12.7773i	−0.394455	−	1.08376i	0.570490	−	0.821305i	$-0.306753\pi$
$140$	−1.21043	+	4.91843i	−0.102300	+	0.415683i
$141$		0			0
$142$	−2.20324	−	4.72487i	−0.184892	−	0.396502i
$143$	−5.35236	+	19.9753i	−0.447587	+	1.67042i
$144$		0			0
$145$	−1.15733	−	1.32321i	−0.0961111	−	0.109887i
$146$	−2.41749	−	2.88106i	−0.200073	−	0.238438i
$147$		0			0
$148$	5.14264	+	7.34445i	0.422722	+	0.603710i
$149$	0.275686	−	1.56349i	0.0225851	−	0.128086i	−0.971431	−	0.237324i	$-0.923730\pi$
$149$	0.275686	−	1.56349i	0.0225851	−	0.128086i	0.994016	+	0.109237i	$0.0348409\pi$
$150$		0			0
$151$	5.05010	−	4.23754i	0.410971	−	0.344846i	−0.413745	−	0.910393i	$-0.635779\pi$
$151$	5.05010	−	4.23754i	0.410971	−	0.344846i	0.824716	+	0.565547i	$0.191335\pi$
$152$	0.923815	+	3.44772i	0.0749313	+	0.279647i
$153$		0			0
$154$	−10.3470	+	5.97385i	−0.833786	+	0.481387i
$155$	15.3829	−	19.1148i	1.23558	−	1.53533i
$156$		0			0
$157$	−1.36013	−	15.5463i	−0.108550	−	1.24073i	−0.833730	−	0.552172i	$-0.813799\pi$
$157$	−1.36013	−	15.5463i	−0.108550	−	1.24073i	0.725180	−	0.688559i	$-0.241756\pi$
$158$	−6.07771	−	2.83408i	−0.483516	−	0.225467i
$159$		0			0
$160$	1.80501	−	1.31982i	0.142699	−	0.104341i
$161$		−	11.7040i		−	0.922406i
$162$		0			0
$163$	4.17945	−	4.17945i	0.327360	−	0.327360i	−0.524222	−	0.851582i	$-0.675644\pi$
$163$	4.17945	−	4.17945i	0.327360	−	0.327360i	0.851582	+	0.524222i	$0.175644\pi$
$164$	−0.484417	−	2.74726i	−0.0378266	−	0.214525i
$165$		0			0
$166$	3.13083	−	1.13953i	0.242999	−	0.0884446i
$167$	16.6458	−	1.45632i	1.28809	−	0.112693i	0.577554	−	0.816352i	$-0.304007\pi$
$167$	16.6458	−	1.45632i	1.28809	−	0.112693i	0.710538	+	0.703659i	$0.248452\pi$
$168$		0			0
$169$	−0.811517	+	2.22962i	−0.0624244	+	0.171510i
$170$	1.48990	+	7.54241i	0.114270	+	0.578477i
$171$		0			0
$172$	−6.46958	+	1.73352i	−0.493301	+	0.132180i
$173$	16.6396	+	1.45577i	1.26508	+	0.110681i	0.699874	−	0.714266i	$-0.253240\pi$
$173$	16.6396	+	1.45577i	1.26508	+	0.110681i	0.565210	+	0.824947i	$0.308795\pi$
$174$		0			0
$175$	−11.3140	−	0.523993i	−0.855256	−	0.0396101i
$176$	5.19428	+	0.915892i	0.391534	+	0.0690379i
$177$		0			0
$178$	0.184343	−	2.10705i	0.0138171	−	0.157930i
$179$	8.82559	−	15.2864i	0.659655	−	1.14256i	−0.321050	−	0.947062i	$-0.604036\pi$
$179$	8.82559	−	15.2864i	0.659655	−	1.14256i	0.980705	−	0.195494i	$-0.0626310\pi$
$180$		0			0
$181$	4.29011	+	7.43069i	0.318881	+	0.552319i	0.980255	−	0.197738i	$-0.0633595\pi$
$181$	4.29011	+	7.43069i	0.318881	+	0.552319i	−0.661373	+	0.750057i	$0.730026\pi$
$182$	−8.04936	+	3.75348i	−0.596658	+	0.278226i
$183$		0			0
$184$	−3.32118	+	3.95803i	−0.244841	+	0.291790i
$185$	−13.8829	+	14.4639i	−1.02069	+	1.06341i
$186$		0			0
$187$	−10.4017	+	14.8551i	−0.760645	+	1.08631i
$188$	−4.12475	−	4.12475i	−0.300829	−	0.300829i
$189$		0			0
$190$	−7.16288	+	3.52056i	−0.519650	+	0.255408i
$191$	5.29919	−	0.934390i	0.383436	−	0.0676101i	0.0213920	−	0.999771i	$-0.493190\pi$
$191$	5.29919	−	0.934390i	0.383436	−	0.0676101i	0.362044	+	0.932161i	$0.382079\pi$
$192$		0			0
$193$	−10.0875	+	21.6328i	−0.726117	+	1.55716i	0.100843	+	0.994902i	$0.467846\pi$
$193$	−10.0875	+	21.6328i	−0.726117	+	1.55716i	−0.826960	+	0.562260i	$0.809932\pi$
$194$	8.81770	+	7.39893i	0.633074	+	0.531212i
$195$		0			0
$196$	1.75608	+	0.639160i	0.125434	+	0.0456543i
$197$	8.88605	+	2.38101i	0.633105	+	0.169640i	0.561078	−	0.827763i	$-0.310387\pi$
$197$	8.88605	+	2.38101i	0.633105	+	0.169640i	0.0720268	+	0.997403i	$0.477053\pi$
$198$		0			0
$199$	17.2165	+	9.93993i	1.22044	+	0.704623i	0.965012	−	0.262204i	$-0.0844495\pi$
$199$	17.2165	+	9.93993i	1.22044	+	0.704623i	0.255430	+	0.966827i	$0.417783\pi$
$200$	3.67743	+	3.38770i	0.260034	+	0.239546i
$201$		0			0
$202$	−3.96941	+	2.77941i	−0.279287	+	0.195559i
$203$	1.45878	−	1.02145i	0.102386	−	0.0716917i
$204$		0			0
$205$	5.81670	−	2.25313i	0.406256	−	0.157365i
$206$	0.815562	+	0.470865i	0.0568229	+	0.0328067i
$207$		0			0
$208$	3.78721	+	1.01478i	0.262596	+	0.0703623i
$209$	−17.6908	−	6.43894i	−1.22370	−	0.445391i
$210$		0			0
$211$	−8.47717	−	7.11319i	−0.583593	−	0.489692i	0.302532	−	0.953139i	$-0.402168\pi$
$211$	−8.47717	−	7.11319i	−0.583593	−	0.489692i	−0.886125	+	0.463447i	$0.846613\pi$
$212$	5.46372	−	11.7170i	0.375250	−	0.804725i
$213$		0			0
$214$	12.1728	−	2.14640i	0.832116	−	0.146725i
$215$	−6.60626	−	13.4410i	−0.450543	−	0.916668i
$216$		0			0
$217$	17.5756	+	17.5756i	1.19311	+	1.19311i
$218$	1.42310	−	2.03239i	0.0963842	−	0.137651i
$219$		0			0
$220$	0.241675	+	11.7915i	0.0162937	+	0.794980i
$221$	−8.66523	+	10.3268i	−0.582886	+	0.694657i
$222$		0			0
$223$	−0.164952	+	0.0769186i	−0.0110460	+	0.00515085i	−0.428133	−	0.903716i	$-0.640829\pi$
$223$	−0.164952	+	0.0769186i	−0.0110460	+	0.00515085i	0.417087	+	0.908866i	$0.363051\pi$
$224$	1.13261	+	1.96174i	0.0756757	+	0.131074i
$225$		0			0
$226$	−2.67831	+	4.63896i	−0.178158	+	0.308579i
$227$	−0.206645	+	2.36196i	−0.0137155	+	0.156769i	−0.999964	−	0.00850120i	$-0.997294\pi$
$227$	−0.206645	+	2.36196i	−0.0137155	+	0.156769i	0.986248	+	0.165270i	$0.0528495\pi$
$228$		0			0
$229$	−4.67779	−	0.824820i	−0.309117	−	0.0545056i	0.0169378	−	0.999857i	$-0.494608\pi$
$229$	−4.67779	−	0.824820i	−0.309117	−	0.0545056i	−0.326055	+	0.945351i	$0.605719\pi$
$230$	−10.1218	−	5.57046i	−0.667412	−	0.367305i
$231$		0			0
$232$	−0.783177	−	0.0685191i	−0.0514181	−	0.00449850i
$233$	17.2623	−	4.62542i	1.13089	−	0.303021i	0.355608	−	0.934635i	$-0.384274\pi$
$233$	17.2623	−	4.62542i	1.13089	−	0.303021i	0.775283	+	0.631614i	$0.217607\pi$
$234$		0			0
$235$	7.26100	−	10.8358i	0.473655	−	0.706848i
$236$	3.74917	−	10.3008i	0.244050	−	0.670522i
$237$		0			0
$238$	−7.75875	+	0.678803i	−0.502925	+	0.0440002i
$239$	−8.36515	+	3.04466i	−0.541096	+	0.196943i	−0.598086	−	0.801432i	$-0.704072\pi$
$239$	−8.36515	+	3.04466i	−0.541096	+	0.196943i	0.0569898	+	0.998375i	$0.481850\pi$
$240$		0			0
$241$	0.820520	+	4.65340i	0.0528544	+	0.299752i	0.999763	−	0.0217495i	$-0.00692362\pi$
$241$	0.820520	+	4.65340i	0.0528544	+	0.299752i	−0.946909	+	0.321501i	$0.895813\pi$
$242$	−11.8931	+	11.8931i	−0.764519	+	0.764519i
$243$		0			0
$244$			1.84225i			0.117938i
$245$	−0.641148	+	4.12924i	−0.0409614	+	0.263807i
$246$		0			0
$247$	−12.6835	−	5.91442i	−0.807033	−	0.376326i
$248$	−0.956338	−	10.9310i	−0.0607275	−	0.694119i
$249$		0			0
$250$	−5.83797	+	9.53510i	−0.369226	+	0.603052i
$251$	−19.8423	+	11.4560i	−1.25243	+	0.723093i	−0.971592	−	0.236661i	$-0.923947\pi$
$251$	−19.8423	+	11.4560i	−1.25243	+	0.723093i	−0.280842	+	0.959754i	$0.590614\pi$
$252$		0			0
$253$	−7.05334	−	26.3234i	−0.443440	−	1.65494i
$254$	−8.38640	+	7.03703i	−0.526210	+	0.441542i
$255$		0			0
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	4.36842	+	6.23875i	0.272495	+	0.389163i	0.931953	−	0.362578i	$-0.118103\pi$
$257$	4.36842	+	6.23875i	0.272495	+	0.389163i	−0.659459	+	0.751741i	$0.729214\pi$
$258$		0			0
$259$	−13.0549	−	15.5582i	−0.811190	−	0.966738i
$260$	−0.584982	+	8.74765i	−0.0362790	+	0.542506i
$261$		0			0
$262$	−0.745044	+	2.78054i	−0.0460290	+	0.171782i
$263$	6.15555	+	13.2006i	0.379567	+	0.813985i	0.999568	+	0.0293837i	$0.00935447\pi$
$263$	6.15555	+	13.2006i	0.379567	+	0.813985i	−0.620001	+	0.784601i	$0.712868\pi$
$264$		0			0
$265$	28.0709	+	6.90830i	1.72438	+	0.424373i
$266$	−2.76535	−	7.59775i	−0.169555	−	0.465848i
$267$		0			0
$268$	−2.63797	−	1.84712i	−0.161139	−	0.112831i
$269$	16.8551			1.02767			0.513836	−	0.857889i	$-0.328224\pi$
$269$	16.8551			1.02767			0.513836	+	0.857889i	$0.328224\pi$
$270$		0			0
$271$	−28.2552			−1.71638			−0.858189	−	0.513334i	$-0.828410\pi$
$271$	−28.2552			−1.71638			−0.858189	+	0.513334i	$0.828410\pi$
$272$	2.81645	+	1.97210i	0.170772	+	0.119576i
$273$		0			0
$274$	3.14578	+	8.64296i	0.190044	+	0.522141i
$275$	−25.7620	+	5.63977i	−1.55350	+	0.340091i
$276$		0			0
$277$	7.58337	+	16.2626i	0.455640	+	0.977124i	0.991169	+	0.132607i	$0.0423347\pi$
$277$	7.58337	+	16.2626i	0.455640	+	0.977124i	−0.535529	+	0.844517i	$0.679888\pi$
$278$	3.51925	−	13.1340i	0.211070	−	0.787725i
$279$		0			0
$280$	−3.81263	+	3.33466i	−0.227848	+	0.199284i
$281$	−19.5894	−	23.3457i	−1.16860	−	1.39269i	−0.903566	−	0.428448i	$-0.859061\pi$
$281$	−19.5894	−	23.3457i	−1.16860	−	1.39269i	−0.265036	−	0.964238i	$-0.585384\pi$
$282$		0			0
$283$	−10.1611	−	14.5116i	−0.604015	−	0.862623i	0.394398	−	0.918940i	$-0.370953\pi$
$283$	−10.1611	−	14.5116i	−0.604015	−	0.862623i	−0.998413	+	0.0563170i	$0.982064\pi$
$284$	0.905283	−	5.13411i	0.0537186	−	0.304654i
$285$		0			0
$286$	−15.8418	+	13.2928i	−0.936743	+	0.786020i
$287$	1.63552	+	6.10384i	0.0965416	+	0.360298i
$288$		0			0
$289$	4.48467	−	2.58922i	0.263804	−	0.152307i
$290$	−0.189067	−	1.74773i	−0.0111024	−	0.102630i
$291$		0			0
$292$	−0.327789	−	3.74664i	−0.0191824	−	0.219256i
$293$	6.73139	+	3.13890i	0.393252	+	0.183376i	0.609178	−	0.793033i	$-0.291499\pi$
$293$	6.73139	+	3.13890i	0.393252	+	0.183376i	−0.215926	+	0.976410i	$0.569277\pi$
$294$		0			0
$295$	24.2212	+	3.76082i	1.41021	+	0.218964i
$296$			8.96591i			0.521133i
$297$		0			0
$298$	1.12261	−	1.12261i	0.0650312	−	0.0650312i
$299$	−3.51779	−	19.9504i	−0.203439	−	1.15376i
$300$		0			0
$301$	14.2570	−	5.18913i	0.821760	−	0.299096i
$302$	6.56735	−	0.574569i	0.377908	−	0.0330627i
$303$		0			0
$304$	−1.22079	+	3.35409i	−0.0700170	+	0.192370i
$305$	−4.04131	+	0.798306i	−0.231405	+	0.0457109i
$306$		0			0
$307$	2.71392	−	0.727192i	0.154892	−	0.0415031i	−0.180540	−	0.983568i	$-0.557785\pi$
$307$	2.71392	−	0.727192i	0.154892	−	0.0415031i	0.335432	+	0.942065i	$0.391118\pi$
$308$	−11.9022	−	1.04131i	−0.678193	−	0.0593342i
$309$		0			0
$310$	23.5647	−	6.83465i	1.33838	−	0.388182i
$311$	−21.4586	−	3.78374i	−1.21681	−	0.214556i	−0.471857	−	0.881675i	$-0.656416\pi$
$311$	−21.4586	−	3.78374i	−1.21681	−	0.214556i	−0.744951	+	0.667119i	$0.767527\pi$
$312$		0			0
$313$	2.03028	−	23.2062i	0.114758	−	1.31169i	−0.692466	−	0.721450i	$-0.743476\pi$
$313$	2.03028	−	23.2062i	0.114758	−	1.31169i	0.807225	−	0.590244i	$-0.200969\pi$
$314$	7.80285	−	13.5149i	0.440340	−	0.762692i
$315$		0			0
$316$	−3.35300	−	5.80757i	−0.188621	−	0.326702i
$317$	21.0704	−	9.82531i	1.18343	−	0.551844i	0.271603	−	0.962410i	$-0.412446\pi$
$317$	21.0704	−	9.82531i	1.18343	−	0.551844i	0.911831	+	0.410565i	$0.134669\pi$
$318$		0			0
$319$	2.66537	−	3.17646i	0.149232	−	0.177848i
$320$	2.23560	−	0.0458203i	0.124974	−	0.00256143i
$321$		0			0
$322$	6.71315	−	9.58737i	0.374109	−	0.534283i
$323$	−8.67783	−	8.67783i	−0.482847	−	0.482847i
$324$		0			0
$325$	−19.4430	+	2.50737i	−1.07850	+	0.139084i
$326$	5.82084	−	1.02637i	0.322386	−	0.0568454i
$327$		0			0
$328$	1.17895	−	2.52828i	0.0650969	−	0.139601i
$329$	10.1223	+	8.49358i	0.558058	+	0.468266i
$330$		0			0
$331$	−14.7666	−	5.37459i	−0.811644	−	0.295414i	−0.0973413	−	0.995251i	$-0.531034\pi$
$331$	−14.7666	−	5.37459i	−0.811644	−	0.295414i	−0.714303	+	0.699837i	$0.753256\pi$
$332$	3.21823	+	0.862323i	0.176623	+	0.0473261i
$333$		0			0
$334$	14.4708	+	8.35470i	0.791805	+	0.457149i
$335$	2.90888	−	6.58726i	0.158929	−	0.359901i
$336$		0			0
$337$	0.492730	−	0.345013i	0.0268407	−	0.0187941i	−0.560079	−	0.828439i	$-0.689229\pi$
$337$	0.492730	−	0.345013i	0.0268407	−	0.0187941i	0.586920	+	0.809645i	$0.300340\pi$
$338$	−1.94362	+	1.36093i	−0.105719	+	0.0740251i
$339$		0			0
$340$	−3.10569	+	7.03295i	−0.168430	+	0.381415i
$341$	50.1210	+	28.9374i	2.71421	+	1.56705i
$342$		0			0
$343$	−19.4052	−	5.19961i	−1.04778	−	0.280752i
$344$	−6.29388	−	2.29078i	−0.339343	−	0.123511i
$345$		0			0
$346$	12.7954	+	10.7366i	0.687882	+	0.577202i
$347$	7.99597	−	17.1474i	0.429246	−	0.920521i	−0.566116	−	0.824325i	$-0.691555\pi$
$347$	7.99597	−	17.1474i	0.429246	−	0.920521i	0.995362	−	0.0961959i	$-0.0306675\pi$
$348$		0			0
$349$	−15.8581	+	2.79621i	−0.848865	+	0.149678i	−0.581126	−	0.813814i	$-0.697388\pi$
$349$	−15.8581	+	2.79621i	−0.848865	+	0.149678i	−0.267739	+	0.963491i	$0.586277\pi$
$350$	−8.96731	−	6.91866i	−0.479323	−	0.369818i
$351$		0			0
$352$	3.72957	+	3.72957i	0.198787	+	0.198787i
$353$	7.00086	−	9.99827i	0.372618	−	0.532154i	−0.588425	−	0.808552i	$-0.700252\pi$
$353$	7.00086	−	9.99827i	0.372618	−	0.532154i	0.961043	+	0.276398i	$0.0891407\pi$
$354$		0			0
$355$	11.6549	−	0.238876i	0.618577	−	0.0126782i
$356$	1.35956	−	1.62026i	0.0720564	−	0.0858734i
$357$		0			0
$358$	15.9974	−	7.45971i	0.845488	−	0.394258i
$359$	14.9022	+	25.8113i	0.786507	+	1.36227i	0.928094	+	0.372345i	$0.121446\pi$
$359$	14.9022	+	25.8113i	0.786507	+	1.36227i	−0.141587	+	0.989926i	$0.545220\pi$
$360$		0			0
$361$	−3.12988	+	5.42111i	−0.164731	+	0.285322i
$362$	−0.747816	+	8.54757i	−0.0393043	+	0.449250i
$363$		0			0
$364$	−8.74656	−	1.54225i	−0.458444	−	0.0808361i
$365$	8.07688	−	2.34260i	0.422763	−	0.122617i
$366$		0			0
$367$	15.4507	+	1.35176i	0.806520	+	0.0705613i	0.482955	−	0.875645i	$-0.339563\pi$
$367$	15.4507	+	1.35176i	0.806520	+	0.0705613i	0.323564	+	0.946206i	$0.395119\pi$
$368$	−4.99078	+	1.33728i	−0.260163	+	0.0697103i
$369$		0			0
$370$	−19.6683	+	3.88522i	−1.02251	+	0.201983i
$371$	−10.0162	+	27.5192i	−0.520014	+	1.42873i
$372$		0			0
$373$	28.2904	−	2.47509i	1.46482	−	0.128155i	0.673333	−	0.739339i	$-0.264862\pi$
$373$	28.2904	−	2.47509i	1.46482	−	0.128155i	0.791489	+	0.611184i	$0.209306\pi$
$374$	−17.0411	+	6.20245i	−0.881173	+	0.320721i
$375$		0			0
$376$	−1.01294	−	5.74466i	−0.0522383	−	0.296258i
$377$	2.17959	−	2.17959i	0.112255	−	0.112255i
$378$		0			0
$379$		−	15.8438i		−	0.813842i	−0.913463	−	0.406921i	$-0.866602\pi$
$379$		−	15.8438i		−	0.813842i	0.913463	−	0.406921i	$-0.133398\pi$
$380$	−7.88680	−	1.22458i	−0.404584	−	0.0628198i
$381$		0			0
$382$	4.87679	+	2.27408i	0.249518	+	0.116352i
$383$	−2.52368	−	28.8458i	−0.128954	−	1.47395i	−0.734754	−	0.678333i	$-0.762703\pi$
$383$	−2.52368	−	28.8458i	−0.128954	−	1.47395i	0.605800	−	0.795617i	$-0.292853\pi$
$384$		0			0
$385$	−2.87332	−	26.5609i	−0.146438	−	1.35367i
$386$	−20.6713	+	11.9346i	−1.05214	+	0.607454i
$387$		0			0
$388$	2.97919	+	11.1185i	0.151245	+	0.564455i
$389$	−2.09544	+	1.75828i	−0.106243	+	0.0891485i	−0.694362	−	0.719626i	$-0.744313\pi$
$389$	−2.09544	+	1.75828i	−0.106243	+	0.0891485i	0.588119	+	0.808775i	$0.299869\pi$
$390$		0			0
$391$	3.08484	−	17.4950i	0.156007	−	0.884759i
$392$	1.07189	+	1.53082i	0.0541385	+	0.0773178i
$393$		0			0
$394$	5.91334	+	7.04724i	0.297910	+	0.355035i
$395$	11.2870	−	9.87202i	0.567910	−	0.496715i
$396$		0			0
$397$	8.17298	−	30.5020i	0.410190	−	1.53085i	−0.384088	−	0.923296i	$-0.625484\pi$
$397$	8.17298	−	30.5020i	0.410190	−	1.53085i	0.794278	−	0.607554i	$-0.207849\pi$
$398$	8.40159	+	18.0173i	0.421134	+	0.903124i
$399$		0			0
$400$	1.06927	+	4.88433i	0.0534635	+	0.244216i
$401$	−1.65822	−	4.55593i	−0.0828077	−	0.227512i	0.891378	−	0.453261i	$-0.149739\pi$
$401$	−1.65822	−	4.55593i	−0.0828077	−	0.227512i	−0.974186	+	0.225749i	$0.927517\pi$
$402$		0			0
$403$	35.2416	+	24.6764i	1.75551	+	1.22922i
$404$	−4.84576			−0.241086
$405$		0			0
$406$	1.78084			0.0883818
$407$	−38.7376	−	27.1244i	−1.92015	−	1.34451i
$408$		0			0
$409$	−10.0536	−	27.6221i	−0.497119	−	1.36582i	−0.894047	−	0.447973i	$-0.852146\pi$
$409$	−10.0536	−	27.6221i	−0.497119	−	1.36582i	0.396928	−	0.917850i	$-0.370076\pi$
$410$	6.05710	+	1.49066i	0.299139	+	0.0736187i
$411$		0			0
$412$	0.397992	+	0.853497i	0.0196077	+	0.0420488i
$413$	−6.42673	+	23.9849i	−0.316239	+	1.18022i
$414$		0			0
$415$	−0.497096	+	7.43344i	−0.0244015	+	0.364893i
$416$	2.52025	+	3.00351i	0.123565	+	0.147259i
$417$		0			0
$418$	−10.7983	−	15.4215i	−0.528160	−	0.754291i
$419$	0.681601	−	3.86555i	0.0332984	−	0.188845i	−0.963622	−	0.267270i	$-0.913878\pi$
$419$	0.681601	−	3.86555i	0.0332984	−	0.188845i	0.996920	+	0.0784259i	$0.0249894\pi$
$420$		0			0
$421$	10.2416	−	8.59375i	0.499147	−	0.418834i	−0.358144	−	0.933666i	$-0.616590\pi$
$421$	10.2416	−	8.59375i	0.499147	−	0.418834i	0.857291	+	0.514832i	$0.172146\pi$
$422$	−2.86413	−	10.6891i	−0.139424	−	0.520337i
$423$		0			0
$424$	11.1962	−	6.46413i	0.543735	−	0.313926i
$425$	−16.7738	−	3.76529i	−0.813650	−	0.182643i
$426$		0			0
$427$	−0.363710	−	4.15723i	−0.0176012	−	0.201182i
$428$	11.2025	+	5.22381i	0.541494	+	0.252503i
$429$		0			0
$430$	2.29790	−	14.7994i	0.110815	−	0.713691i
$431$			6.91088i			0.332885i	0.986051	+	0.166443i	$0.0532281\pi$
$431$			6.91088i			0.332885i	−0.986051	+	0.166443i	$0.946772\pi$
$432$		0			0
$433$	11.4765	−	11.4765i	0.551527	−	0.551527i	−0.375355	−	0.926881i	$-0.622479\pi$
$433$	11.4765	−	11.4765i	0.551527	−	0.551527i	0.926881	+	0.375355i	$0.122479\pi$
$434$	4.31615	+	24.4781i	0.207182	+	1.17499i
$435$		0			0
$436$	2.33146	−	0.848583i	0.111657	−	0.0406398i
$437$	18.3721	−	1.60735i	0.878855	−	0.0768898i
$438$		0			0
$439$	−6.97074	+	19.1520i	−0.332695	+	0.914073i	0.654713	+	0.755878i	$0.272790\pi$
$439$	−6.97074	+	19.1520i	−0.332695	+	0.914073i	−0.987408	+	0.158195i	$0.949433\pi$
$440$	−6.56534	+	9.79762i	−0.312990	+	0.467083i
$441$		0			0
$442$	−13.0214	+	3.48906i	−0.619363	+	0.165958i
$443$	21.8255	+	1.90948i	1.03696	+	0.0907223i	0.592901	−	0.805275i	$-0.297982\pi$
$443$	21.8255	+	1.90948i	1.03696	+	0.0907223i	0.444059	+	0.895997i	$0.353538\pi$
$444$		0			0
$445$	4.14346	+	2.28032i	0.196419	+	0.108098i
$446$	−0.179240	−	0.0316048i	−0.00848725	−	0.00149653i
$447$		0			0
$448$	−0.197427	+	2.25660i	−0.00932754	+	0.106614i
$449$	12.5749	−	21.7804i	0.593447	−	1.02788i	−0.400317	−	0.916377i	$-0.631100\pi$
$449$	12.5749	−	21.7804i	0.593447	−	1.02788i	0.993764	−	0.111504i	$-0.0355668\pi$
$450$		0			0
$451$	7.35686	+	12.7425i	0.346421	+	0.600019i
$452$	−4.85474	+	2.26380i	−0.228348	+	0.106480i
$453$		0			0
$454$	−1.52404	+	1.81628i	−0.0715266	+	0.0852421i
$455$	−0.406952	−	19.8554i	−0.0190782	−	0.930837i
$456$		0			0
$457$	−19.9743	+	28.5262i	−0.934358	+	1.33440i	0.00806106	+	0.999968i	$0.497434\pi$
$457$	−19.9743	+	28.5262i	−0.934358	+	1.33440i	−0.942419	+	0.334434i	$0.891455\pi$
$458$	−3.35872	−	3.35872i	−0.156943	−	0.156943i
$459$		0			0
$460$	−5.09622	−	10.3687i	−0.237612	−	0.483442i
$461$	−37.9623	+	6.69377i	−1.76808	+	0.311760i	−0.960558	−	0.278080i	$-0.910302\pi$
$461$	−37.9623	+	6.69377i	−1.76808	+	0.311760i	−0.807520	+	0.589840i	$0.799191\pi$
$462$		0			0
$463$	−6.77038	+	14.5191i	−0.314646	+	0.674761i	−0.998494	−	0.0548637i	$-0.982528\pi$
$463$	−6.77038	+	14.5191i	−0.314646	+	0.674761i	0.683848	+	0.729625i	$0.260305\pi$
$464$	−0.602240	−	0.505339i	−0.0279583	−	0.0234598i
$465$		0			0
$466$	16.7935	+	6.11232i	0.777943	+	0.283148i
$467$	−36.4655	−	9.77089i	−1.68742	−	0.452143i	−0.717698	−	0.696355i	$-0.754804\pi$
$467$	−36.4655	−	9.77089i	−1.68742	−	0.452143i	−0.969722	+	0.244212i	$0.921471\pi$
$468$		0			0
$469$	6.31750	+	3.64741i	0.291715	+	0.168422i
$470$	12.1630	−	4.71141i	0.561038	−	0.217321i
$471$		0			0
$472$	8.97941	−	6.28745i	0.413311	−	0.289403i
$473$	28.9382	−	20.2627i	1.33058	−	0.931681i
$474$		0			0
$475$	−0.731258	−	17.8317i	−0.0335524	−	0.818177i
$476$	−6.74494	−	3.89419i	−0.309154	−	0.178490i
$477$		0			0
$478$	−8.59867	−	2.30401i	−0.393294	−	0.105383i
$479$	−11.1551	−	4.06013i	−0.509690	−	0.185512i	0.0743571	−	0.997232i	$-0.476310\pi$
$479$	−11.1551	−	4.06013i	−0.509690	−	0.185512i	−0.584047	+	0.811720i	$0.698532\pi$
$480$		0			0
$481$	−26.9292	−	22.5963i	−1.22787	−	1.03030i
$482$	−1.99695	+	4.28247i	−0.0909586	+	0.195061i
$483$		0			0
$484$	−16.5639	+	2.92066i	−0.752904	+	0.132757i
$485$	−23.0994	+	11.3534i	−1.04889	+	0.515530i
$486$		0			0
$487$	−4.60598	−	4.60598i	−0.208717	−	0.208717i	0.595005	−	0.803722i	$-0.297150\pi$
$487$	−4.60598	−	4.60598i	−0.208717	−	0.208717i	−0.803722	+	0.595005i	$0.797150\pi$
$488$	−1.05667	+	1.50908i	−0.0478333	+	0.0683130i
$489$		0			0
$490$	−2.89363	+	3.01473i	−0.130721	+	0.136192i
$491$	14.0210	−	16.7096i	0.632759	−	0.754093i	−0.350449	−	0.936582i	$-0.613971\pi$
$491$	14.0210	−	16.7096i	0.632759	−	0.754093i	0.983208	+	0.182489i	$0.0584153\pi$
$492$		0			0
$493$	2.44979	−	1.14235i	0.110333	−	0.0514491i
$494$	−6.99736	−	12.1198i	−0.314826	−	0.545295i
$495$		0			0
$496$	5.48638	−	9.50268i	0.246346	−	0.426683i
$497$	−1.02925	+	11.7644i	−0.0461681	+	0.527704i
$498$		0			0
$499$	37.8964	+	6.68215i	1.69647	+	0.299134i	0.936461	−	0.350772i	$-0.114081\pi$
$499$	37.8964	+	6.68215i	1.69647	+	0.299134i	0.760014	+	0.649907i	$0.225192\pi$
$500$	−10.2513	+	4.46217i	−0.458452	+	0.199554i
$501$		0			0
$502$	−22.8247	−	1.99690i	−1.01872	−	0.0891262i
$503$	−32.4623	+	8.69825i	−1.44742	+	0.387836i	−0.895126	−	0.445813i	$-0.852915\pi$
$503$	−32.4623	+	8.69825i	−1.44742	+	0.387836i	−0.552296	+	0.833648i	$0.686248\pi$
$504$		0			0
$505$	−2.09982	−	10.6300i	−0.0934408	−	0.473030i
$506$	9.32074	−	25.6085i	0.414358	−	1.13844i
$507$		0			0
$508$	−10.9060	+	0.954152i	−0.483876	+	0.0423337i
$509$	31.2904	−	11.3888i	1.38692	−	0.504798i	0.462653	−	0.886540i	$-0.346898\pi$
$509$	31.2904	−	11.3888i	1.38692	−	0.504798i	0.924269	+	0.381741i	$0.124676\pi$
$510$		0			0
$511$	1.47938	+	8.38995i	0.0654437	+	0.371150i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			7.61611i			0.335932i
$515$	−1.69984	+	1.24291i	−0.0749037	+	0.0547694i
$516$		0			0
$517$	27.8845	+	13.0028i	1.22636	+	0.571860i
$518$	−1.77011	−	20.2325i	−0.0777743	−	0.888964i
$519$		0			0
$520$	−5.49663	+	6.83012i	−0.241043	+	0.299521i
$521$	21.7156	−	12.5375i	0.951376	−	0.549277i	0.0578681	−	0.998324i	$-0.481570\pi$
$521$	21.7156	−	12.5375i	0.951376	−	0.549277i	0.893508	+	0.449047i	$0.148236\pi$
$522$		0			0
$523$	−0.121127	−	0.452053i	−0.00529653	−	0.0197669i	0.963227	−	0.268689i	$-0.0865904\pi$
$523$	−0.121127	−	0.452053i	−0.00529653	−	0.0197669i	−0.968524	+	0.248922i	$0.919924\pi$
$524$	−2.20516	+	1.85035i	−0.0963327	+	0.0808328i
$525$		0			0
$526$	−2.52923	+	14.3440i	−0.110280	+	0.625428i
$527$	21.6393	+	30.9042i	0.942625	+	1.34621i
$528$		0			0
$529$	2.37588	+	2.83147i	0.103299	+	0.123107i
$530$	19.0319	+	21.7597i	0.826692	+	0.945183i
$531$		0			0
$532$	2.09264	−	7.80985i	0.0907276	−	0.338600i
$533$	4.62245	+	9.91288i	0.200221	+	0.429374i
$534$		0			0
$535$	−6.60497	+	26.8383i	−0.285558	+	1.16032i
$536$	−1.10143	−	3.02615i	−0.0475745	−	0.130710i
$537$		0			0
$538$	13.8069	+	9.66766i	0.595256	+	0.416803i
$539$	−9.85671			−0.424559
$540$		0			0
$541$	−34.4459			−1.48095			−0.740473	−	0.672086i	$-0.765398\pi$
$541$	−34.4459			−1.48095			−0.740473	+	0.672086i	$0.765398\pi$
$542$	−23.1453	−	16.2065i	−0.994174	−	0.696128i
$543$		0			0
$544$	1.17595	+	3.23090i	0.0504185	+	0.138524i
$545$	2.87182	+	4.74676i	0.123015	+	0.203329i
$546$		0			0
$547$	−10.3667	−	22.2316i	−0.443250	−	0.950552i	−0.993315	−	0.115431i	$-0.963175\pi$
$547$	−10.3667	−	22.2316i	−0.443250	−	0.950552i	0.550066	−	0.835121i	$-0.314603\pi$
$548$	−2.38053	+	8.88425i	−0.101691	+	0.379516i
$549$		0			0
$550$	−24.3378	−	10.1566i	−1.03777	−	0.433080i
$551$	1.80373	+	2.14960i	0.0768415	+	0.0915762i
$552$		0			0
$553$	8.71296	+	12.4434i	0.370513	+	0.529147i
$554$	−3.11590	+	17.6712i	−0.132382	+	0.750776i
$555$		0			0
$556$	10.4162	−	8.74019i	0.441743	−	0.370667i
$557$	−2.17970	−	8.13474i	−0.0923567	−	0.344680i	0.904249	−	0.427006i	$-0.140432\pi$
$557$	−2.17970	−	8.13474i	−0.0923567	−	0.344680i	−0.996605	+	0.0823262i	$0.973765\pi$
$558$		0			0
$559$	22.7425	−	13.1304i	0.961905	−	0.555356i
$560$	−5.03580	+	0.544765i	−0.212802	+	0.0230205i
$561$		0			0
$562$	−2.65613	−	30.3597i	−0.112042	−	1.28064i
$563$	−19.1477	−	8.92870i	−0.806978	−	0.376300i	−0.0250634	−	0.999686i	$-0.507979\pi$
$563$	−19.1477	−	8.92870i	−0.806978	−	0.376300i	−0.781914	+	0.623386i	$0.785757\pi$
$564$		0			0
$565$	−7.06977	−	9.66876i	−0.297427	−	0.406768i
$566$		−	17.7153i		−	0.744631i
$567$		0			0
$568$	3.68637	−	3.68637i	0.154677	−	0.154677i
$569$	4.48927	+	25.4599i	0.188200	+	1.06733i	0.921775	+	0.387726i	$0.126739\pi$
$569$	4.48927	+	25.4599i	0.188200	+	1.06733i	−0.733575	+	0.679609i	$0.762150\pi$
$570$		0			0
$571$	34.0373	−	12.3886i	1.42442	−	0.518446i	0.489091	−	0.872233i	$-0.337328\pi$
$571$	34.0373	−	12.3886i	1.42442	−	0.518446i	0.935326	+	0.353787i	$0.115106\pi$
$572$	−20.6012	+	1.80238i	−0.861381	+	0.0753611i
$573$		0			0
$574$	−2.16128	+	5.93806i	−0.0902100	+	0.247850i
$575$	20.5372	−	15.6725i	0.856461	−	0.653590i
$576$		0			0
$577$	4.33109	−	1.16051i	0.180305	−	0.0483127i	−0.167537	−	0.985866i	$-0.553581\pi$
$577$	4.33109	−	1.16051i	0.180305	−	0.0483127i	0.347842	+	0.937553i	$0.386915\pi$
$578$	5.15874	+	0.451331i	0.214575	+	0.0187729i
$579$		0			0
$580$	0.847582	−	1.54010i	0.0351939	−	0.0639492i
$581$	−7.43251	−	1.31055i	−0.308352	−	0.0543708i
$582$		0			0
$583$	−5.94306	+	67.9295i	−0.246136	+	2.81335i
$584$	1.88048	−	3.25708i	0.0778146	−	0.134779i
$585$		0			0
$586$	3.71363	+	6.43220i	0.153409	+	0.265712i
$587$	24.3374	−	11.3487i	1.00451	−	0.468412i	0.150470	−	0.988615i	$-0.451921\pi$
$587$	24.3374	−	11.3487i	1.00451	−	0.468412i	0.854043	+	0.520203i	$0.174144\pi$
$588$		0			0
$589$	−25.1751	+	30.0026i	−1.03732	+	1.23623i
$590$	17.6837	+	16.9734i	0.728027	+	0.698783i
$591$		0			0
$592$	−5.14264	+	7.34445i	−0.211361	+	0.301855i
$593$	−20.2128	−	20.2128i	−0.830041	−	0.830041i	0.157481	−	0.987522i	$-0.449663\pi$
$593$	−20.2128	−	20.2128i	−0.830041	−	0.830041i	−0.987522	+	0.157481i	$0.949663\pi$
$594$		0			0
$595$	5.61981	−	16.4837i	0.230390	−	0.675766i
$596$	1.56349	−	0.275686i	0.0640432	−	0.0112925i
$597$		0			0
$598$	8.56147	−	18.3601i	0.350105	−	0.750802i
$599$	−3.67565	−	3.08424i	−0.150183	−	0.126019i	0.564600	−	0.825364i	$-0.309030\pi$
$599$	−3.67565	−	3.08424i	−0.150183	−	0.126019i	−0.714783	+	0.699346i	$0.753475\pi$
$600$		0			0
$601$	1.68112	+	0.611877i	0.0685742	+	0.0249590i	0.376080	−	0.926587i	$-0.377272\pi$
$601$	1.68112	+	0.611877i	0.0685742	+	0.0249590i	−0.307505	+	0.951546i	$0.599494\pi$
$602$	14.6550	+	3.92680i	0.597294	+	0.160044i
$603$		0			0
$604$	5.70922	+	3.29622i	0.232305	+	0.134121i
$605$	−13.5846	−	35.0702i	−0.552294	−	1.42581i
$606$		0			0
$607$	−4.87081	+	3.41057i	−0.197700	+	0.138431i	−0.668235	−	0.743950i	$-0.732950\pi$
$607$	−4.87081	+	3.41057i	−0.197700	+	0.138431i	0.470535	+	0.882381i	$0.344061\pi$
$608$	−2.92384	+	2.04729i	−0.118577	+	0.0830287i
$609$		0			0
$610$	−3.76833	−	1.66406i	−0.152575	−	0.0673760i
$611$	19.8070	+	11.4356i	0.801306	+	0.462634i
$612$		0			0
$613$	−6.91743	−	1.85352i	−0.279392	−	0.0748629i	0.116402	−	0.993202i	$-0.462864\pi$
$613$	−6.91743	−	1.85352i	−0.279392	−	0.0748629i	−0.395794	+	0.918339i	$0.629531\pi$
$614$	2.64021	+	0.960959i	0.106550	+	0.0387811i
$615$		0			0
$616$	−9.15247	−	7.67983i	−0.368763	−	0.309429i
$617$	−1.05695	+	2.26664i	−0.0425512	+	0.0912513i	−0.926434	−	0.376457i	$-0.877142\pi$
$617$	−1.05695	+	2.26664i	−0.0425512	+	0.0912513i	0.883883	+	0.467708i	$0.154920\pi$
$618$		0			0
$619$	−27.4374	+	4.83795i	−1.10280	+	0.194454i	−0.695278	−	0.718741i	$-0.744719\pi$
$619$	−27.4374	+	4.83795i	−1.10280	+	0.194454i	−0.407523	+	0.913195i	$0.633608\pi$
$620$	23.2232	+	7.91753i	0.932668	+	0.317976i
$621$		0			0
$622$	−15.4076	−	15.4076i	−0.617790	−	0.617790i
$623$	−2.74809	+	3.92468i	−0.110100	+	0.157239i
$624$		0			0
$625$	−14.2308	−	20.5544i	−0.569231	−	0.822178i
$626$	14.9737	−	17.8449i	0.598468	−	0.713227i
$627$		0			0
$628$	14.1436	−	6.59525i	0.564390	−	0.263179i
$629$	−15.4135	−	26.6970i	−0.614577	−	1.06448i
$630$		0			0
$631$	2.60673	−	4.51500i	0.103772	−	0.179739i	−0.809464	−	0.587170i	$-0.800242\pi$
$631$	2.60673	−	4.51500i	0.103772	−	0.179739i	0.913236	+	0.407431i	$0.133575\pi$
$632$	0.584467	−	6.68049i	0.0232489	−	0.265736i
$633$		0			0
$634$	22.8955	+	4.03709i	0.909295	+	0.160333i
$635$	−6.81902	−	23.5108i	−0.270605	−	0.932998i
$636$		0			0
$637$	−7.29924	−	0.638601i	−0.289206	−	0.0253023i
$638$	4.00528	−	1.07321i	0.158571	−	0.0424889i
$639$		0			0
$640$	1.85758	+	1.24475i	0.0734272	+	0.0492032i
$641$	−0.875297	+	2.40486i	−0.0345722	+	0.0949862i	−0.955778	−	0.294090i	$-0.904983\pi$
$641$	−0.875297	+	2.40486i	−0.0345722	+	0.0949862i	0.921206	+	0.389076i	$0.127206\pi$
$642$		0			0
$643$	−36.3704	+	3.18199i	−1.43431	+	0.125486i	−0.777647	−	0.628701i	$-0.783587\pi$
$643$	−36.3704	+	3.18199i	−1.43431	+	0.125486i	−0.656660	+	0.754187i	$0.728031\pi$
$644$	10.9982	−	4.00301i	0.433389	−	0.157741i
$645$		0			0
$646$	−2.13106	−	12.0859i	−0.0838456	−	0.475512i
$647$	−2.18876	+	2.18876i	−0.0860490	+	0.0860490i	−0.748821	−	0.662772i	$-0.769380\pi$
$647$	−2.18876	+	2.18876i	−0.0860490	+	0.0860490i	0.662772	+	0.748821i	$0.269380\pi$
$648$		0			0
$649$			57.8172i			2.26952i
$650$	−17.3650	−	9.09814i	−0.681110	−	0.356858i
$651$		0			0
$652$	5.35685	+	2.49794i	0.209791	+	0.0978269i
$653$	−0.607544	−	6.94426i	−0.0237750	−	0.271750i	−0.998772	−	0.0495336i	$-0.984227\pi$
$653$	−0.607544	−	6.94426i	−0.0237750	−	0.271750i	0.974997	−	0.222216i	$-0.0713291\pi$
$654$		0			0
$655$	−5.01463	−	4.03559i	−0.195938	−	0.157684i
$656$	2.41590	−	1.39482i	0.0943251	−	0.0544586i
$657$		0			0
$658$	3.41995	+	12.7634i	0.133324	+	0.497570i
$659$	3.29307	−	2.76322i	0.128280	−	0.107640i	−0.576391	−	0.817174i	$-0.695539\pi$
$659$	3.29307	−	2.76322i	0.128280	−	0.107640i	0.704670	+	0.709535i	$0.251095\pi$
$660$		0			0
$661$	2.43780	−	13.8255i	0.0948196	−	0.537748i	−0.899983	−	0.435925i	$-0.856421\pi$
$661$	2.43780	−	13.8255i	0.0948196	−	0.537748i	0.994802	−	0.101823i	$-0.0324676\pi$
$662$	−9.01333	−	12.8724i	−0.350313	−	0.500299i
$663$		0			0
$664$	2.14161	+	2.55228i	0.0831107	+	0.0990475i
$665$	18.0391	+	1.20633i	0.699527	+	0.0467795i
$666$		0			0
$667$	−1.05132	+	3.92359i	−0.0407074	+	0.151922i
$668$	7.06170	+	15.1439i	0.273225	+	0.585933i
$669$		0			0
$670$	6.16111	−	3.72751i	0.238025	−	0.144006i
$671$	−3.32334	−	9.13080i	−0.128296	−	0.352491i
$672$		0			0
$673$	16.5854	+	11.6132i	0.639321	+	0.447657i	0.847761	−	0.530378i	$-0.177950\pi$
$673$	16.5854	+	11.6132i	0.639321	+	0.447657i	−0.208441	+	0.978035i	$0.566839\pi$
$674$	0.601512			0.0231694
$675$		0			0
$676$	−2.37272			−0.0912583
$677$	−6.24019	−	4.36943i	−0.239830	−	0.167931i	0.447482	−	0.894293i	$-0.352321\pi$
$677$	−6.24019	−	4.36943i	−0.239830	−	0.167931i	−0.687312	+	0.726362i	$0.741210\pi$
$678$		0			0
$679$	−8.91792	−	24.5018i	−0.342238	−	0.940292i
$680$	−6.57797	+	3.97971i	−0.252254	+	0.152615i
$681$		0			0
$682$	24.4589	+	52.4524i	0.936581	+	2.00851i
$683$	−7.31689	+	27.3070i	−0.279973	+	1.04487i	0.672462	+	0.740132i	$0.265237\pi$
$683$	−7.31689	+	27.3070i	−0.279973	+	1.04487i	−0.952435	+	0.304742i	$0.901430\pi$
$684$		0			0
$685$	−20.5207	−	1.37228i	−0.784057	−	0.0524322i
$686$	−12.9134	−	15.3896i	−0.493037	−	0.587579i
$687$		0			0
$688$	−3.84170	−	5.48652i	−0.146463	−	0.209172i
$689$	−8.80208	+	49.9191i	−0.335333	+	1.90177i
$690$		0			0
$691$	−23.0914	+	19.3760i	−0.878438	+	0.737097i	−0.965857	−	0.259075i	$-0.916582\pi$
$691$	−23.0914	+	19.3760i	−0.878438	+	0.737097i	0.0874193	+	0.996172i	$0.472138\pi$
$692$	4.32309	+	16.1340i	0.164339	+	0.613323i
$693$		0			0
$694$	16.3853	−	9.46004i	0.621976	−	0.359098i
$695$	23.6868	+	19.0623i	0.898492	+	0.723074i
$696$		0			0
$697$	0.835953	+	9.55499i	0.0316640	+	0.361921i
$698$	−14.5940	−	6.80532i	−0.552393	−	0.257585i
$699$		0			0
$700$	−3.37721	−	10.8109i	−0.127647	−	0.408612i
$701$			24.3339i			0.919079i	0.888157	+	0.459539i	$0.151986\pi$
$701$			24.3339i			0.919079i	−0.888157	+	0.459539i	$0.848014\pi$
$702$		0			0
$703$	22.6292	−	22.6292i	0.853475	−	0.853475i
$704$	0.915892	+	5.19428i	0.0345190	+	0.195767i
$705$		0			0
$706$	11.4695	−	4.17457i	0.431662	−	0.157112i
$707$	10.9349	−	0.956683i	0.411251	−	0.0359798i
$708$		0			0
$709$	5.51749	−	15.1592i	0.207214	−	0.569315i	−0.791934	−	0.610607i	$-0.790925\pi$
$709$	5.51749	−	15.1592i	0.207214	−	0.569315i	0.999147	+	0.0412927i	$0.0131476\pi$
$710$	9.68413	+	6.48929i	0.363439	+	0.243539i
$711$		0			0
$712$	2.04302	−	0.547427i	0.0765656	−	0.0205157i
$713$	−56.4787	−	4.94124i	−2.11514	−	0.185051i
$714$		0			0
$715$	−12.8810	−	44.4115i	−0.481722	−	1.66090i
$716$	17.3830	+	3.06509i	0.649634	+	0.114548i
$717$		0			0
$718$	−2.59762	+	29.6910i	−0.0969424	+	1.10806i
$719$	−20.0698	+	34.7619i	−0.748478	+	1.29640i	0.200074	+	0.979781i	$0.435882\pi$
$719$	−20.0698	+	34.7619i	−0.748478	+	1.29640i	−0.948552	+	0.316621i	$0.897452\pi$
$720$		0			0
$721$	−1.06661	−	1.84743i	−0.0397227	−	0.0688018i
$722$	−5.67327	+	2.64549i	−0.211137	+	0.0984549i
$723$		0			0
$724$	−5.51526	+	6.57283i	−0.204973	+	0.244277i
$725$	3.74577	+	1.19195i	0.139114	+	0.0442678i
$726$		0			0
$727$	−1.85205	+	2.64500i	−0.0686887	+	0.0980977i	−0.852027	−	0.523498i	$-0.824627\pi$
$727$	−1.85205	+	2.64500i	−0.0686887	+	0.0980977i	0.783338	+	0.621596i	$0.213515\pi$
$728$	−6.28016	−	6.28016i	−0.232758	−	0.232758i
$729$		0			0
$730$	7.95985	+	2.71376i	0.294607	+	0.100441i
$731$	22.6789	−	3.99889i	0.838808	−	0.147904i
$732$		0			0
$733$	−2.74347	+	5.88338i	−0.101332	+	0.217308i	−0.950437	−	0.310916i	$-0.899364\pi$
$733$	−2.74347	+	5.88338i	−0.101332	+	0.217308i	0.849105	+	0.528224i	$0.177142\pi$
$734$	11.8811	+	9.96945i	0.438541	+	0.367979i
$735$		0			0
$736$	−4.85524	−	1.76716i	−0.178967	−	0.0651385i
$737$	16.4067	+	4.39617i	0.604350	+	0.161935i
$738$		0			0
$739$	−33.8397	−	19.5374i	−1.24481	−	0.718693i	−0.274743	−	0.961518i	$-0.588593\pi$
$739$	−33.8397	−	19.5374i	−1.24481	−	0.718693i	−0.970070	+	0.242825i	$0.921926\pi$
$740$	−18.3398	−	8.09871i	−0.674185	−	0.297714i
$741$		0			0
$742$	−23.9891	+	16.7974i	−0.880669	+	0.616651i
$743$	5.05580	−	3.54011i	0.185479	−	0.129874i	−0.477149	−	0.878822i	$-0.658330\pi$
$743$	5.05580	−	3.54011i	0.185479	−	0.129874i	0.662628	+	0.748948i	$0.269441\pi$
$744$		0			0
$745$	1.28228	+	3.31034i	0.0469790	+	0.121281i
$746$	24.5938	+	14.1992i	0.900443	+	0.519871i
$747$		0			0
$748$	−17.5168	−	4.69362i	−0.640478	−	0.171616i
$749$	−26.3109	−	9.57638i	−0.961379	−	0.349913i
$750$		0			0
$751$	0.718971	+	0.603288i	0.0262356	+	0.0220143i	0.655811	−	0.754925i	$-0.272327\pi$
$751$	0.718971	+	0.603288i	0.0262356	+	0.0220143i	−0.629576	+	0.776939i	$0.716771\pi$
$752$	2.46525	−	5.28675i	0.0898985	−	0.192788i
$753$		0			0
$754$	3.03558	−	0.535255i	0.110549	−	0.0194929i
$755$	−4.75686	+	13.9525i	−0.173120	+	0.507785i
$756$		0			0
$757$	−3.26714	−	3.26714i	−0.118746	−	0.118746i	0.645237	−	0.763983i	$-0.276759\pi$
$757$	−3.26714	−	3.26714i	−0.118746	−	0.118746i	−0.763983	+	0.645237i	$0.776759\pi$
$758$	9.08764	−	12.9785i	0.330078	−	0.471400i
$759$		0			0
$760$	−5.75809	−	5.52680i	−0.208868	−	0.200478i
$761$	−9.10126	+	10.8465i	−0.329920	+	0.393184i	−0.905349	−	0.424668i	$-0.860391\pi$
$761$	−9.10126	+	10.8465i	−0.329920	+	0.393184i	0.575429	+	0.817852i	$0.304835\pi$
$762$		0			0
$763$	−5.09365	+	2.37521i	−0.184402	+	0.0859883i
$764$	2.69047	+	4.66003i	0.0973377	+	0.168594i
$765$		0			0
$766$	14.4780	−	25.0766i	0.523111	−	0.906054i
$767$	−3.74589	+	42.8157i	−0.135256	+	1.54598i
$768$		0			0
$769$	28.6310	+	5.04841i	1.03246	+	0.182050i	0.664108	−	0.747636i	$-0.268811\pi$
$769$	28.6310	+	5.04841i	1.03246	+	0.182050i	0.368351	+	0.929687i	$0.379923\pi$
$770$	12.8810	−	23.4055i	0.464200	−	0.843475i
$771$		0			0
$772$	−23.7783	−	2.08033i	−0.855800	−	0.0748728i
$773$	−13.7334	+	3.67985i	−0.493956	+	0.132355i	−0.497193	−	0.867640i	$-0.665636\pi$
$773$	−13.7334	+	3.67985i	−0.493956	+	0.132355i	0.00323767	+	0.999995i	$0.498969\pi$
$774$		0			0
$775$	−7.30514	+	54.3752i	−0.262408	+	1.95322i
$776$	−3.93689	+	10.8165i	−0.141326	+	0.388290i
$777$		0			0
$778$	−2.72499	+	0.238406i	−0.0976958	+	0.00854727i
$779$	−9.35671	+	3.40557i	−0.335239	+	0.122017i
$780$		0			0
$781$	4.77483	+	27.0794i	0.170857	+	0.968978i
$782$	12.5617	−	12.5617i	0.449204	−	0.449204i
$783$		0			0
$784$			1.86878i			0.0667421i
$785$	20.5967	+	28.1685i	0.735129	+	1.00538i
$786$		0			0
$787$	−2.85030	−	1.32912i	−0.101602	−	0.0473779i	0.371153	−	0.928572i	$-0.378963\pi$
$787$	−2.85030	−	1.32912i	−0.101602	−	0.0473779i	−0.472755	+	0.881194i	$0.656740\pi$
$788$	0.801791	+	9.16451i	0.0285626	+	0.326472i
$789$		0			0
$790$	14.9081	−	1.61274i	0.530407	−	0.0573786i
$791$	10.5083	−	6.06695i	0.373631	−	0.215716i
$792$		0			0
$793$	−1.86948	−	6.97699i	−0.0663871	−	0.247760i
$794$	24.1901	−	20.2979i	0.858475	−	0.720346i
$795$		0			0
$796$	−3.45210	+	19.5778i	−0.122356	+	0.693918i
$797$	−4.68030	−	6.68416i	−0.165785	−	0.236765i	0.727660	−	0.685938i	$-0.240608\pi$
$797$	−4.68030	−	6.68416i	−0.165785	−	0.236765i	−0.893445	+	0.449173i	$0.851719\pi$
$798$		0			0
$799$	12.8919	+	15.3640i	0.456084	+	0.543539i
$800$	−1.92564	+	4.61432i	−0.0680817	+	0.163141i
$801$		0			0
$802$	1.25484	−	4.68312i	0.0443099	−	0.165367i
$803$	8.38340	+	17.9783i	0.295844	+	0.634439i
$804$		0			0
$805$	13.5472	+	22.3918i	0.477475	+	0.789209i
$806$	14.7144	+	40.4275i	0.518293	+	1.42400i
$807$		0			0
$808$	−3.96941	−	2.77941i	−0.139643	−	0.0977794i
$809$	11.1588			0.392323			0.196161	−	0.980572i	$-0.437152\pi$
$809$	11.1588			0.392323			0.196161	+	0.980572i	$0.437152\pi$
$810$		0			0
$811$	40.8224			1.43347			0.716734	−	0.697346i	$-0.245636\pi$
$811$	40.8224			1.43347			0.716734	+	0.697346i	$0.245636\pi$
$812$	1.45878	+	1.02145i	0.0511932	+	0.0358459i
$813$		0			0
$814$	−16.1741	−	44.4380i	−0.566902	−	1.55755i
$815$	−3.15839	+	12.8336i	−0.110633	+	0.449543i
$816$		0			0
$817$	10.1034	+	21.6669i	0.353475	+	0.758029i
$818$	7.60793	−	28.3932i	0.266005	−	0.992744i
$819$		0			0
$820$	4.10668	+	4.69529i	0.143411	+	0.163967i
$821$	22.2863	+	26.5597i	0.777796	+	0.926941i	0.998832	−	0.0483244i	$-0.0153881\pi$
$821$	22.2863	+	26.5597i	0.777796	+	0.926941i	−0.221036	+	0.975266i	$0.570944\pi$
$822$		0			0
$823$	13.7385	+	19.6207i	0.478895	+	0.683933i	0.983806	−	0.179239i	$-0.0573634\pi$
$823$	13.7385	+	19.6207i	0.478895	+	0.683933i	−0.504911	+	0.863172i	$0.668475\pi$
$824$	−0.163530	+	0.927423i	−0.00569683	+	0.0323083i
$825$		0			0
$826$	−19.0216	+	15.9610i	−0.661847	+	0.555356i
$827$	5.67676	+	21.1860i	0.197400	+	0.736708i	0.991632	+	0.129094i	$0.0412068\pi$
$827$	5.67676	+	21.1860i	0.197400	+	0.736708i	−0.794232	+	0.607615i	$0.792127\pi$
$828$		0			0
$829$	−43.4213	+	25.0693i	−1.50808	+	0.870692i	−0.508127	+	0.861282i	$0.669662\pi$
$829$	−43.4213	+	25.0693i	−1.50808	+	0.870692i	−0.999956	+	0.00940960i	$0.997005\pi$
$830$	−4.67084	+	5.80399i	−0.162127	+	0.201460i
$831$		0			0
$832$	0.341721	+	3.90589i	0.0118470	+	0.135412i
$833$	−5.82333	−	2.71546i	−0.201766	−	0.0940852i
$834$		0			0
$835$	−30.1607	+	22.0534i	−1.04375	+	0.763190i
$836$		−	18.8262i		−	0.651118i
$837$		0			0
$838$	2.77552	−	2.77552i	0.0958789	−	0.0958789i
$839$	7.44054	+	42.1974i	0.256876	+	1.45682i	0.791211	+	0.611543i	$0.209451\pi$
$839$	7.44054	+	42.1974i	0.256876	+	1.45682i	−0.534335	+	0.845273i	$0.679438\pi$
$840$		0			0
$841$	26.6703	−	9.70720i	0.919665	−	0.334731i
$842$	13.3186	−	1.16523i	0.458990	−	0.0401565i
$843$		0			0
$844$	3.78485	−	10.3988i	0.130280	−	0.357941i
$845$	−1.02817	−	5.20498i	−0.0353702	−	0.179057i
$846$		0			0
$847$	36.8014	−	9.86092i	1.26451	−	0.338825i
$848$	12.8791	+	1.12677i	0.442269	+	0.0386935i
$849$		0			0
$850$	−11.5806	−	12.7054i	−0.397213	−	0.435792i
$851$	45.6216	+	8.04433i	1.56389	+	0.275756i
$852$		0			0
$853$	3.20547	−	36.6387i	0.109753	−	1.25449i	−0.719055	−	0.694953i	$-0.755425\pi$
$853$	3.20547	−	36.6387i	0.109753	−	1.25449i	0.828808	−	0.559533i	$-0.189019\pi$
$854$	2.08655	−	3.61401i	0.0714004	−	0.123669i
$855$		0			0
$856$	6.18030	+	10.7046i	0.211238	+	0.365875i
$857$	−30.3972	+	14.1744i	−1.03835	+	0.484189i	−0.865579	−	0.500773i	$-0.833049\pi$
$857$	−30.3972	+	14.1744i	−1.03835	+	0.484189i	−0.172769	+	0.984962i	$0.555271\pi$
$858$		0			0
$859$	−10.7965	+	12.8668i	−0.368372	+	0.439009i	−0.918108	−	0.396329i	$-0.870284\pi$
$859$	−10.7965	+	12.8668i	−0.368372	+	0.439009i	0.549736	+	0.835338i	$0.314728\pi$
$860$	10.3709	−	10.8049i	0.353646	−	0.368445i
$861$		0			0
$862$	−3.96392	+	5.66106i	−0.135012	+	0.192817i
$863$	11.9401	+	11.9401i	0.406445	+	0.406445i	0.880497	−	0.474052i	$-0.157209\pi$
$863$	11.9401	+	11.9401i	0.406445	+	0.406445i	−0.474052	+	0.880497i	$0.657209\pi$
$864$		0			0
$865$	−33.5195	+	16.4748i	−1.13970	+	0.560162i
$866$	15.9837	−	2.81835i	0.543148	−	0.0957716i
$867$		0			0
$868$	−10.5045	+	22.5269i	−0.356545	+	0.764613i
$869$	27.0952	+	22.7356i	0.919141	+	0.771251i
$870$		0			0
$871$	11.8649	+	4.31849i	0.402028	+	0.146326i
$872$	2.39655	+	0.642154i	0.0811574	+	0.0217461i
$873$		0			0
$874$	15.9714	+	9.22112i	0.540242	+	0.311909i
$875$	22.2521	−	12.0932i	0.752259	−	0.408825i
$876$		0			0
$877$	−10.6094	+	7.42880i	−0.358255	+	0.250853i	−0.738822	−	0.673901i	$-0.764618\pi$
$877$	−10.6094	+	7.42880i	−0.358255	+	0.250853i	0.380567	+	0.924753i	$0.375729\pi$
$878$	−16.6952	+	11.6901i	−0.563436	+	0.394522i
$879$		0			0
$880$	−10.9977	+	4.26002i	−0.370732	+	0.143605i
$881$	−40.4376	−	23.3467i	−1.36238	−	0.786569i	−0.372438	−	0.928057i	$-0.621478\pi$
$881$	−40.4376	−	23.3467i	−1.36238	−	0.786569i	−0.989940	+	0.141488i	$0.954811\pi$
$882$		0			0
$883$	−4.73050	−	1.26753i	−0.159194	−	0.0426559i	0.178342	−	0.983969i	$-0.442927\pi$
$883$	−4.73050	−	1.26753i	−0.159194	−	0.0426559i	−0.337536	+	0.941313i	$0.609593\pi$
$884$	−12.6677	−	4.61067i	−0.426061	−	0.155074i
$885$		0			0
$886$	16.7832	+	14.0827i	0.563841	+	0.473119i
$887$	−6.11970	+	13.1237i	−0.205479	+	0.440652i	−0.981859	−	0.189614i	$-0.939276\pi$
$887$	−6.11970	+	13.1237i	−0.205479	+	0.440652i	0.776379	+	0.630266i	$0.217054\pi$
$888$		0			0
$889$	24.4221	−	4.30628i	0.819092	−	0.144428i
$890$	2.08619	+	4.24452i	0.0699291	+	0.142277i
$891$		0			0
$892$	−0.128697	−	0.128697i	−0.00430909	−	0.00430909i
$893$	−11.9424	+	17.0556i	−0.399639	+	0.570743i
$894$		0			0
$895$	0.808782	+	39.4609i	0.0270346	+	1.31903i
$896$	−1.45606	+	1.73526i	−0.0486434	+	0.0579709i
$897$		0			0
$898$	22.7935	−	10.6288i	0.760629	−	0.354687i
$899$	−4.31321	−	7.47071i	−0.143854	−	0.249162i
$900$		0			0
$901$	−22.2253	+	38.4953i	−0.740431	+	1.28246i
$902$	−1.28239	+	14.6577i	−0.0426988	+	0.488049i
$903$		0			0
$904$	−5.27523	−	0.930166i	−0.175452	−	0.0309369i
$905$	−16.8086	−	9.25049i	−0.558737	−	0.307497i
$906$		0			0
$907$	27.9883	+	2.44866i	0.929336	+	0.0813063i	0.541762	−	0.840532i	$-0.317758\pi$
$907$	27.9883	+	2.44866i	0.929336	+	0.0813063i	0.387574	+	0.921839i	$0.373313\pi$
$908$	−2.29019	+	0.613655i	−0.0760027	+	0.0203649i
$909$		0			0
$910$	11.0553	−	16.4980i	0.366478	−	0.546905i
$911$	2.71846	−	7.46890i	0.0900665	−	0.247456i	−0.886478	−	0.462770i	$-0.846855\pi$
$911$	2.71846	−	7.46890i	0.0900665	−	0.247456i	0.976545	+	0.215315i	$0.0690777\pi$
$912$		0			0
$913$	−17.5062	+	1.53159i	−0.579370	+	0.0506884i
$914$	−32.7240	+	11.9106i	−1.08241	+	0.393966i
$915$		0			0
$916$	−0.824820	−	4.67779i	−0.0272528	−	0.154558i
$917$	4.61085	−	4.61085i	0.152264	−	0.152264i
$918$		0			0
$919$		−	45.0659i		−	1.48659i	−0.668965	−	0.743294i	$-0.733263\pi$
$919$		−	45.0659i		−	1.48659i	0.668965	−	0.743294i	$-0.266737\pi$
$920$	1.77266	−	11.4166i	0.0584428	−	0.376394i
$921$		0			0
$922$	−34.9362	−	16.2910i	−1.15056	−	0.536517i
$923$	1.78150	+	20.3626i	0.0586387	+	0.670244i
$924$		0			0
$925$	9.81873	−	43.7411i	0.322838	−	1.43820i
$926$	−13.8738	+	8.01004i	−0.455921	+	0.263226i
$927$		0			0
$928$	−0.203475	−	0.759380i	−0.00667940	−	0.0249279i
$929$	1.75991	−	1.47674i	0.0577408	−	0.0484503i	−0.613461	−	0.789725i	$-0.710223\pi$
$929$	1.75991	−	1.47674i	0.0577408	−	0.0484503i	0.671201	+	0.741275i	$0.265779\pi$
$930$		0			0
$931$	1.15829	−	6.56899i	0.0379614	−	0.215290i
$932$	10.2505	+	14.6393i	0.335767	+	0.479525i
$933$		0			0
$934$	−24.2664	−	28.9196i	−0.794021	−	0.946277i
$935$	2.70569	−	40.4601i	0.0884855	−	1.32319i
$936$		0			0
$937$	1.77392	−	6.62037i	0.0579515	−	0.216278i	−0.930878	−	0.365331i	$-0.880956\pi$
$937$	1.77392	−	6.62037i	0.0579515	−	0.216278i	0.988829	+	0.149053i	$0.0476225\pi$
$938$	3.08293	+	6.61136i	0.100661	+	0.215868i
$939$		0			0
$940$	12.6657	+	3.11705i	0.413110	+	0.101667i
$941$	−0.277721	−	0.763032i	−0.00905344	−	0.0248741i	0.935084	−	0.354427i	$-0.115324\pi$
$941$	−0.277721	−	0.763032i	−0.00905344	−	0.0248741i	−0.944137	+	0.329553i	$0.893102\pi$
$942$		0			0
$943$	−11.8070	−	8.26732i	−0.384488	−	0.269221i
$944$	10.9618			0.356777
$945$		0			0
$946$	35.3270			1.14858
$947$	7.48508	+	5.24111i	0.243232	+	0.170313i	0.688836	−	0.724917i	$-0.258122\pi$
$947$	7.48508	+	5.24111i	0.243232	+	0.170313i	−0.445604	+	0.895230i	$0.647011\pi$
$948$		0			0
$949$	5.04342	+	13.8567i	0.163716	+	0.449807i
$950$	9.62886	−	15.0263i	0.312401	−	0.487519i
$951$		0			0
$952$	−3.29152	−	7.05868i	−0.106679	−	0.228773i
$953$	−5.49003	+	20.4891i	−0.177840	+	0.663706i	0.818211	+	0.574918i	$0.194966\pi$
$953$	−5.49003	+	20.4891i	−0.177840	+	0.663706i	−0.996051	+	0.0887881i	$0.971701\pi$
$954$		0			0
$955$	−9.05674	+	7.92136i	−0.293069	+	0.256329i
$956$	−5.72210	−	6.81933i	−0.185066	−	0.220553i
$957$		0			0
$958$	−6.80894	−	9.72417i	−0.219987	−	0.314174i
$959$	3.61791	−	20.5182i	0.116828	−	0.662566i
$960$		0			0
$961$	68.4853	−	57.4660i	2.20920	−	1.85374i
$962$	−9.09842	−	33.9558i	−0.293345	−	1.09478i
$963$		0			0
$964$	−4.09213	+	2.36259i	−0.131799	+	0.0760940i
$965$	−5.74032	−	53.0635i	−0.184787	−	1.70817i
$966$		0			0
$967$	−1.84703	−	21.1117i	−0.0593966	−	0.678906i	−0.966275	−	0.257513i	$-0.917097\pi$
$967$	−1.84703	−	21.1117i	−0.0593966	−	0.678906i	0.906878	−	0.421393i	$-0.138459\pi$
$968$	−15.2436	−	7.10819i	−0.489947	−	0.228466i
$969$		0			0
$970$	−25.4339	−	3.94913i	−0.816634	−	0.126799i
$971$		−	6.63914i		−	0.213060i	−0.994309	−	0.106530i	$-0.966026\pi$
$971$		−	6.63914i		−	0.213060i	0.994309	−	0.106530i	$-0.0339741\pi$
$972$		0			0
$973$	−21.7795	+	21.7795i	−0.698220	+	0.698220i
$974$	−1.13112	−	6.41488i	−0.0362433	−	0.205546i
$975$		0			0
$976$	−1.73115	+	0.630087i	−0.0554128	+	0.0201686i
$977$	−30.5859	+	2.67592i	−0.978529	+	0.0856102i	−0.565185	−	0.824964i	$-0.691195\pi$
$977$	−30.5859	+	2.67592i	−0.978529	+	0.0856102i	−0.413345	+	0.910575i	$0.635640\pi$
$978$		0			0
$979$	−3.81554	+	10.4831i	−0.121945	+	0.335041i
$980$	−4.09950	+	0.809802i	−0.130954	+	0.0258682i
$981$		0			0
$982$	21.0696	−	5.64557i	0.672357	−	0.180157i
$983$	−5.80945	−	0.508261i	−0.185293	−	0.0162110i	−0.00586834	−	0.999983i	$-0.501868\pi$
$983$	−5.80945	−	0.508261i	−0.185293	−	0.0162110i	−0.179424	+	0.983772i	$0.557424\pi$
$984$		0			0
$985$	−19.7566	+	5.73015i	−0.629496	+	0.182578i
$986$	2.66198	+	0.469378i	0.0847746	+	0.0149480i
$987$		0			0
$988$	1.21972	−	13.9415i	0.0388045	−	0.443537i
$989$	−17.3032	+	29.9701i	−0.550211	+	0.952993i
$990$		0			0
$991$	−3.57818	−	6.19759i	−0.113665	−	0.196873i	0.803581	−	0.595196i	$-0.202926\pi$
$991$	−3.57818	−	6.19759i	−0.113665	−	0.196873i	−0.917245	+	0.398323i	$0.869592\pi$
$992$	9.94469	−	4.63728i	0.315744	−	0.147234i
$993$		0			0
$994$	−7.59087	+	9.04645i	−0.240768	+	0.286936i
$995$	−44.4434	+	0.910901i	−1.40895	+	0.0288775i
$996$		0			0
$997$	25.6591	−	36.6449i	0.812631	−	1.16056i	−0.171860	−	0.985121i	$-0.554978\pi$
$997$	25.6591	−	36.6449i	0.812631	−	1.16056i	0.984491	−	0.175436i	$-0.0561334\pi$
$998$	27.2102	+	27.2102i	0.861323	+	0.861323i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.s.a.557.11		216
3.2	odd	2		270.2.r.a.257.6	yes	216
5.3	odd	4	inner	810.2.s.a.233.13		216
15.8	even	4		270.2.r.a.203.9	yes	216
27.2	odd	18	inner	810.2.s.a.737.13		216
27.25	even	9		270.2.r.a.137.9	yes	216
135.83	even	36	inner	810.2.s.a.413.11		216
135.133	odd	36		270.2.r.a.83.6	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.83.6	✓	216	135.133	odd	36
270.2.r.a.137.9	yes	216	27.25	even	9
270.2.r.a.203.9	yes	216	15.8	even	4
270.2.r.a.257.6	yes	216	3.2	odd	2
810.2.s.a.233.13		216	5.3	odd	4	inner
810.2.s.a.413.11		216	135.83	even	36	inner
810.2.s.a.557.11		216	1.1	even	1	trivial
810.2.s.a.737.13		216	27.2	odd	18	inner

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:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.s (of order \(36\), degree \(12\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.819152 + 0.573576i) q^{2} +(0.342020 + 0.939693i) q^{4} +(-1.91317 + 1.15748i) q^{5} +(-0.957323 - 2.05299i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(-2.23108 - 0.149199i) q^{10} +(-3.39033 - 4.04043i) q^{11} +(-2.24888 - 3.21174i) q^{13} +(0.393351 - 2.23081i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(-0.889884 - 3.32109i) q^{17} +(3.09115 - 1.78467i) q^{19} +(-1.74202 - 1.40191i) q^{20} +(-0.459695 - 5.25434i) q^{22} +(4.68275 + 2.18360i) q^{23} +(2.32048 - 4.42893i) q^{25} -3.92081i q^{26} +(1.60175 - 1.60175i) q^{28} +(0.136517 + 0.774225i) q^{29} +(-10.3110 + 3.75290i) q^{31} +(-0.996195 + 0.0871557i) q^{32} +(1.17595 - 3.23090i) q^{34} +(4.20782 + 2.81964i) q^{35} +(8.66041 - 2.32055i) q^{37} +(3.55576 + 0.311089i) q^{38} +(-0.622874 - 2.14756i) q^{40} +(-2.74726 - 0.484417i) q^{41} +(-0.583752 + 6.67232i) q^{43} +(2.63721 - 4.56777i) q^{44} +(2.58342 + 4.47461i) q^{46} +(-5.28675 + 2.46525i) q^{47} +(1.20123 - 1.43157i) q^{49} +(4.44115 - 2.29699i) q^{50} +(2.24888 - 3.21174i) q^{52} +(-9.14166 - 9.14166i) q^{53} +(11.1630 + 3.80582i) q^{55} +(2.23081 - 0.393351i) q^{56} +(-0.332249 + 0.712510i) q^{58} +(-8.39725 - 7.04613i) q^{59} +(1.73115 + 0.630087i) q^{61} +(-10.5989 - 2.83996i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(8.02003 + 3.54158i) q^{65} +(-2.63797 + 1.84712i) q^{67} +(2.81645 - 1.97210i) q^{68} +(1.82957 + 4.72322i) q^{70} +(-4.51486 - 2.60666i) q^{71} +(-3.63280 - 0.973406i) q^{73} +(8.42520 + 3.06652i) q^{74} +(2.73428 + 2.29433i) q^{76} +(-5.04932 + 10.8283i) q^{77} +(-6.60413 + 1.16449i) q^{79} +(0.721563 - 2.11645i) q^{80} +(-1.97258 - 1.97258i) q^{82} +(1.91102 - 2.72922i) q^{83} +(5.54661 + 5.32381i) q^{85} +(-4.30526 + 5.13081i) q^{86} +(4.78024 - 2.22906i) q^{88} +(-1.05755 - 1.83173i) q^{89} +(-4.44074 + 7.69159i) q^{91} +(-0.450320 + 5.14718i) q^{92} +(-5.74466 - 1.01294i) q^{94} +(-3.84818 + 6.99233i) q^{95} +(11.4669 + 1.00322i) q^{97} +(1.80510 - 0.483676i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 24 q^{11} + 24 q^{20} - 24 q^{23} + 36 q^{25} + 108 q^{35} + 36 q^{38} + 72 q^{41} + 48 q^{47} + 48 q^{50} + 12 q^{56} + 36 q^{61} - 24 q^{65} - 72 q^{67} - 36 q^{68} + 240 q^{77} + 60 q^{83} - 72 q^{86}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q - 24 * q^11 + 24 * q^20 - 24 * q^23 + 36 * q^25 + 108 * q^35 + 36 * q^38 + 72 * q^41 + 48 * q^47 + 48 * q^50 + 12 * q^56 + 36 * q^61 - 24 * q^65 - 72 * q^67 - 36 * q^68 + 240 * q^77 + 60 * q^83 - 72 * q^86 + 48 * q^92 + 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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