LMFDB - Embedded newform 621.2.s.a.494.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [621,2,Mod(17,621)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("621.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(621, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 21])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 621 = 3^{3} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	621.s (of order $66$, degree $20$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.95870996552$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	no (minimal twist has level 207)
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			494.12
Character	$\chi$	$=$	621.494
Dual form			621.2.s.a.44.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.412156 - 0.0196334i) q^{2} +(-1.82146 + 0.173928i) q^{4} +(-2.81788 - 2.68684i) q^{5} +(0.539603 + 2.79973i) q^{7} +(-1.56416 + 0.224892i) q^{8} +(-1.21416 - 1.05207i) q^{10} +(1.68703 - 0.869723i) q^{11} +(2.45673 + 0.473497i) q^{13} +(0.277369 + 1.14333i) q^{14} +(2.95309 - 0.569162i) q^{16} +(2.19831 + 4.81363i) q^{17} +(2.26539 + 1.03457i) q^{19} +(5.59996 + 4.40386i) q^{20} +(0.678243 - 0.391584i) q^{22} +(-1.47338 + 4.56390i) q^{23} +(0.483411 + 10.1480i) q^{25} +(1.02185 + 0.146921i) q^{26} +(-1.46982 - 5.00573i) q^{28} +(-0.293166 + 3.07018i) q^{29} +(-7.06488 + 5.55588i) q^{31} +(4.27735 - 1.03767i) q^{32} +(1.00056 + 1.94081i) q^{34} +(6.00189 - 9.33912i) q^{35} +(1.48644 - 5.06234i) q^{37} +(0.954008 + 0.381927i) q^{38} +(5.01185 + 3.56892i) q^{40} +(3.86707 - 4.05566i) q^{41} +(-0.990237 + 1.25919i) q^{43} +(-2.92158 + 1.87758i) q^{44} +(-0.517659 + 1.90997i) q^{46} +(3.02178 + 1.74463i) q^{47} +(-1.04873 + 0.419849i) q^{49} +(0.398482 + 4.17309i) q^{50} +(-4.55719 - 0.435159i) q^{52} +(4.68343 + 5.40497i) q^{53} +(-7.09064 - 2.08200i) q^{55} +(-1.47366 - 4.25786i) q^{56} +(-0.0605523 + 1.27115i) q^{58} +(0.385512 - 2.00023i) q^{59} +(5.11063 - 12.7657i) q^{61} +(-2.80275 + 2.42860i) q^{62} +(-4.02867 + 1.18292i) q^{64} +(-5.65057 - 7.93511i) q^{65} +(-4.41270 + 8.55943i) q^{67} +(-4.84136 - 8.38547i) q^{68} +(2.29036 - 3.96701i) q^{70} +(0.382777 + 0.595613i) q^{71} +(-1.51265 + 3.31223i) q^{73} +(0.513254 - 2.11566i) q^{74} +(-4.30625 - 1.49041i) q^{76} +(3.34531 + 4.25391i) q^{77} +(-8.46405 + 2.92944i) q^{79} +(-9.85069 - 6.33066i) q^{80} +(1.51421 - 1.74749i) q^{82} +(-9.59700 + 9.15072i) q^{83} +(6.73889 - 19.4707i) q^{85} +(-0.383410 + 0.538424i) q^{86} +(-2.44318 + 1.73978i) q^{88} +(-2.44096 + 16.9773i) q^{89} +7.13369i q^{91} +(1.88991 - 8.56920i) q^{92} +(1.27970 + 0.659731i) q^{94} +(-3.60387 - 9.00204i) q^{95} +(17.4427 + 4.23155i) q^{97} +(-0.423998 + 0.193633i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) $ 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/621\mathbb{Z}\right)^\times$.

$n$	$28$	$461$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.412156	−	0.0196334i	0.291438	−	0.0138829i	0.0986464	−	0.995123i	$-0.468549\pi$
$2$	0.412156	−	0.0196334i	0.291438	−	0.0138829i	0.192792	+	0.981240i	$0.438246\pi$
$3$		0			0
$3$		0			0
$4$	−1.82146	+	0.173928i	−0.910728	+	0.0869640i
$5$	−2.81788	−	2.68684i	−1.26019	−	1.20159i	−0.969586	−	0.244749i	$-0.921294\pi$
$5$	−2.81788	−	2.68684i	−1.26019	−	1.20159i	−0.290607	−	0.956843i	$-0.593857\pi$
$6$		0			0
$7$	0.539603	+	2.79973i	0.203951	+	1.05820i	0.929162	+	0.369672i	$0.120530\pi$
$7$	0.539603	+	2.79973i	0.203951	+	1.05820i	−0.725212	+	0.688526i	$0.758258\pi$
$8$	−1.56416	+	0.224892i	−0.553013	+	0.0795113i
$9$		0			0
$10$	−1.21416	−	1.05207i	−0.383950	−	0.332695i
$11$	1.68703	−	0.869723i	0.508658	−	0.262231i	−0.184739	−	0.982788i	$-0.559144\pi$
$11$	1.68703	−	0.869723i	0.508658	−	0.262231i	0.693396	+	0.720556i	$0.256114\pi$
$12$		0			0
$13$	2.45673	+	0.473497i	0.681376	+	0.131324i	0.518183	−	0.855270i	$-0.326609\pi$
$13$	2.45673	+	0.473497i	0.681376	+	0.131324i	0.163193	+	0.986594i	$0.447821\pi$
$14$	0.277369	+	1.14333i	0.0741300	+	0.305568i
$15$		0			0
$16$	2.95309	−	0.569162i	0.738273	−	0.142290i
$17$	2.19831	+	4.81363i	0.533169	+	1.16748i	0.964209	+	0.265144i	$0.0854196\pi$
$17$	2.19831	+	4.81363i	0.533169	+	1.16748i	−0.431040	+	0.902333i	$0.641853\pi$
$18$		0			0
$19$	2.26539	+	1.03457i	0.519717	+	0.237347i	0.657962	−	0.753051i	$-0.271419\pi$
$19$	2.26539	+	1.03457i	0.519717	+	0.237347i	−0.138245	+	0.990398i	$0.544146\pi$
$20$	5.59996	+	4.40386i	1.25219	+	0.984732i
$21$		0			0
$22$	0.678243	−	0.391584i	0.144602	−	0.0834859i
$23$	−1.47338	+	4.56390i	−0.307221	+	0.951638i
$23$	−1.47338	+	4.56390i	−0.307221	+	0.951638i
$24$		0			0
$25$	0.483411	+	10.1480i	0.0966822	+	2.02961i
$26$	1.02185	+	0.146921i	0.200402	+	0.0288135i
$27$		0			0
$28$	−1.46982	−	5.00573i	−0.277769	−	0.945994i
$29$	−0.293166	+	3.07018i	−0.0544396	+	0.570118i	0.926565	+	0.376134i	$0.122747\pi$
$29$	−0.293166	+	3.07018i	−0.0544396	+	0.570118i	−0.981005	+	0.193983i	$0.937859\pi$
$30$		0			0
$31$	−7.06488	+	5.55588i	−1.26889	+	0.997866i	−0.269498	+	0.963001i	$0.586858\pi$
$31$	−7.06488	+	5.55588i	−1.26889	+	0.997866i	−0.999392	+	0.0348655i	$0.988900\pi$
$32$	4.27735	−	1.03767i	0.756137	−	0.183437i
$33$		0			0
$34$	1.00056	+	1.94081i	0.171594	+	0.332846i
$35$	6.00189	−	9.33912i	1.01450	−	1.57860i
$36$		0			0
$37$	1.48644	−	5.06234i	0.244369	−	0.832244i	−0.742378	−	0.669981i	$-0.766302\pi$
$37$	1.48644	−	5.06234i	0.244369	−	0.832244i	0.986747	−	0.162264i	$-0.0518795\pi$
$38$	0.954008	+	0.381927i	0.154760	+	0.0619568i
$39$		0			0
$40$	5.01185	+	3.56892i	0.792443	+	0.564296i
$41$	3.86707	−	4.05566i	0.603934	−	0.633388i	−0.348799	−	0.937198i	$-0.613410\pi$
$41$	3.86707	−	4.05566i	0.603934	−	0.633388i	0.952733	+	0.303810i	$0.0982588\pi$
$42$		0			0
$43$	−0.990237	+	1.25919i	−0.151010	+	0.192024i	−0.855672	−	0.517518i	$-0.826856\pi$
$43$	−0.990237	+	1.25919i	−0.151010	+	0.192024i	0.704663	+	0.709543i	$0.251098\pi$
$44$	−2.92158	+	1.87758i	−0.440444	+	0.283056i
$45$		0			0
$46$	−0.517659	+	1.90997i	−0.0763246	+	0.281609i
$47$	3.02178	+	1.74463i	0.440772	+	0.254480i	0.703925	−	0.710274i	$-0.251429\pi$
$47$	3.02178	+	1.74463i	0.440772	+	0.254480i	−0.263153	+	0.964754i	$0.584762\pi$
$48$		0			0
$49$	−1.04873	+	0.419849i	−0.149819	+	0.0599784i
$50$	0.398482	+	4.17309i	0.0563538	+	0.590164i
$51$		0			0
$52$	−4.55719	−	0.435159i	−0.631969	−	0.0603457i
$53$	4.68343	+	5.40497i	0.643319	+	0.742430i	0.979958	−	0.199204i	$-0.0638356\pi$
$53$	4.68343	+	5.40497i	0.643319	+	0.742430i	−0.336639	+	0.941634i	$0.609290\pi$
$54$		0			0
$55$	−7.09064	−	2.08200i	−0.956102	−	0.280737i
$56$	−1.47366	−	4.25786i	−0.196926	−	0.568981i
$57$		0			0
$58$	−0.0605523	+	1.27115i	−0.00795090	+	0.166910i
$59$	0.385512	−	2.00023i	0.0501894	−	0.260408i	−0.948163	−	0.317784i	$-0.897061\pi$
$59$	0.385512	−	2.00023i	0.0501894	−	0.260408i	0.998353	+	0.0573763i	$0.0182735\pi$
$60$		0			0
$61$	5.11063	−	12.7657i	0.654349	−	1.63448i	−0.113260	−	0.993565i	$-0.536129\pi$
$61$	5.11063	−	12.7657i	0.654349	−	1.63448i	0.767609	−	0.640919i	$-0.221446\pi$
$62$	−2.80275	+	2.42860i	−0.355950	+	0.308433i
$63$		0			0
$64$	−4.02867	+	1.18292i	−0.503583	+	0.147865i
$65$	−5.65057	−	7.93511i	−0.700867	−	0.984230i
$66$		0			0
$67$	−4.41270	+	8.55943i	−0.539097	+	1.04570i	0.449239	+	0.893411i	$0.351695\pi$
$67$	−4.41270	+	8.55943i	−0.539097	+	1.04570i	−0.988336	+	0.152290i	$0.951335\pi$
$68$	−4.84136	−	8.38547i	−0.587101	−	1.01689i
$69$		0			0
$70$	2.29036	−	3.96701i	0.273750	−	0.474149i
$71$	0.382777	+	0.595613i	0.0454273	+	0.0706863i	0.863224	−	0.504820i	$-0.168441\pi$
$71$	0.382777	+	0.595613i	0.0454273	+	0.0706863i	−0.817797	+	0.575507i	$0.804805\pi$
$72$		0			0
$73$	−1.51265	+	3.31223i	−0.177042	+	0.387668i	−0.977261	−	0.212040i	$-0.931989\pi$
$73$	−1.51265	+	3.31223i	−0.177042	+	0.387668i	0.800219	+	0.599708i	$0.204717\pi$
$74$	0.513254	−	2.11566i	0.0596645	−	0.245941i
$75$		0			0
$76$	−4.30625	−	1.49041i	−0.493961	−	0.170962i
$77$	3.34531	+	4.25391i	0.381234	+	0.484778i
$78$		0			0
$79$	−8.46405	+	2.92944i	−0.952280	+	0.329587i	−0.758658	−	0.651489i	$-0.774145\pi$
$79$	−8.46405	+	2.92944i	−0.952280	+	0.329587i	−0.193622	+	0.981076i	$0.562023\pi$
$80$	−9.85069	−	6.33066i	−1.10134	−	0.707789i
$81$		0			0
$82$	1.51421	−	1.74749i	0.167216	−	0.192978i
$83$	−9.59700	+	9.15072i	−1.05341	+	1.00442i	−0.0534245	+	0.998572i	$0.517014\pi$
$83$	−9.59700	+	9.15072i	−1.05341	+	1.00442i	−0.999983	+	0.00585005i	$0.998138\pi$
$84$		0			0
$85$	6.73889	−	19.4707i	0.730935	−	2.11190i
$86$	−0.383410	+	0.538424i	−0.0413442	+	0.0580598i
$87$		0			0
$88$	−2.44318	+	1.73978i	−0.260444	+	0.185461i
$89$	−2.44096	+	16.9773i	−0.258742	+	1.79959i	0.283083	+	0.959096i	$0.408643\pi$
$89$	−2.44096	+	16.9773i	−0.258742	+	1.79959i	−0.541824	+	0.840492i	$0.682266\pi$
$90$		0			0
$91$			7.13369i			0.747814i
$92$	1.88991	−	8.56920i	0.197037	−	0.893401i
$93$		0			0
$94$	1.27970	+	0.659731i	0.131991	+	0.0680460i
$95$	−3.60387	−	9.00204i	−0.369750	−	0.923590i
$96$		0			0
$97$	17.4427	+	4.23155i	1.77104	+	0.429649i	0.982641	−	0.185519i	$-0.0593968\pi$
$97$	17.4427	+	4.23155i	1.77104	+	0.429649i	0.788396	+	0.615168i	$0.210912\pi$
$98$	−0.423998	+	0.193633i	−0.0428303	+	0.0195599i
$99$		0			0
$100$	−2.64554	−	18.4001i	−0.264554	−	1.84001i
$101$	−6.88320	−	7.21890i	−0.684904	−	0.718307i	0.285879	−	0.958266i	$-0.407715\pi$
$101$	−6.88320	−	7.21890i	−0.684904	−	0.718307i	−0.970783	+	0.239959i	$0.922866\pi$
$102$		0			0
$103$	−5.40186	−	0.257322i	−0.532261	−	0.0253547i	−0.220269	−	0.975439i	$-0.570693\pi$
$103$	−5.40186	−	0.257322i	−0.532261	−	0.0253547i	−0.311993	+	0.950085i	$0.600996\pi$
$104$	−3.94920	−	0.188124i	−0.387251	−	0.0184471i
$105$		0			0
$106$	2.03642	+	2.13574i	0.197795	+	0.207441i
$107$	−0.313712	−	2.18191i	−0.0303277	−	0.210933i	0.969023	−	0.246971i	$-0.0794354\pi$
$107$	−0.313712	−	2.18191i	−0.0303277	−	0.210933i	−0.999350	+	0.0360379i	$0.988526\pi$
$108$		0			0
$109$	1.91450	−	0.874322i	0.183376	−	0.0837449i	−0.321611	−	0.946872i	$-0.604224\pi$
$109$	1.91450	−	0.874322i	0.183376	−	0.0837449i	0.504987	+	0.863127i	$0.331497\pi$
$110$	−2.96333	−	0.718896i	−0.282542	−	0.0685440i
$111$		0			0
$112$	3.18700	+	7.96073i	0.301143	+	0.752218i
$113$	8.00063	+	4.12461i	0.752636	+	0.388011i	0.791449	−	0.611236i	$-0.209327\pi$
$113$	8.00063	+	4.12461i	0.752636	+	0.388011i	−0.0388126	+	0.999247i	$0.512358\pi$
$114$		0			0
$115$	16.4143	−	8.90176i	1.53064	−	0.830093i
$116$		−	5.64319i		−	0.523957i
$117$		0			0
$118$	0.119620	−	0.831975i	0.0110119	−	0.0765895i
$119$	−12.2906	+	8.75213i	−1.12668	+	0.802306i
$120$		0			0
$121$	−4.29098	+	6.02584i	−0.390089	+	0.547804i
$122$	1.85574	−	5.36181i	0.168011	−	0.485436i
$123$		0			0
$124$	11.9021	−	11.3486i	1.06884	−	1.01913i
$125$	13.1554	−	15.1821i	1.17665	−	1.35793i
$126$		0			0
$127$	12.9965	+	8.35233i	1.15325	+	0.741150i	0.970284	−	0.241969i	$-0.0777933\pi$
$127$	12.9965	+	8.35233i	1.15325	+	0.741150i	0.182967	+	0.983119i	$0.441430\pi$
$128$	−9.95591	+	3.44577i	−0.879987	+	0.304566i
$129$		0			0
$130$	−2.48471	−	3.15957i	−0.217923	−	0.277112i
$131$	8.21538	+	2.84337i	0.717781	+	0.248426i	0.661454	−	0.749986i	$-0.269940\pi$
$131$	8.21538	+	2.84337i	0.717781	+	0.248426i	0.0563273	+	0.998412i	$0.482061\pi$
$132$		0			0
$133$	−1.67410	+	6.90074i	−0.145163	+	0.598370i
$134$	−1.65067	+	3.61446i	−0.142596	+	0.312242i
$135$		0			0
$136$	−4.52105	−	7.03490i	−0.387677	−	0.603237i
$137$	3.66836	−	6.35378i	0.313409	−	0.542840i	−0.665689	−	0.746229i	$-0.731862\pi$
$137$	3.66836	−	6.35378i	0.313409	−	0.542840i	0.979098	+	0.203389i	$0.0651956\pi$
$138$		0			0
$139$	−5.07885	−	8.79682i	−0.430782	−	0.746137i	0.566159	−	0.824296i	$-0.308429\pi$
$139$	−5.07885	−	8.79682i	−0.430782	−	0.746137i	−0.996941	+	0.0781594i	$0.975096\pi$
$140$	−9.30784	+	18.0547i	−0.786656	+	1.52590i
$141$		0			0
$142$	0.169458	+	0.237971i	0.0142206	+	0.0199700i
$143$	4.55639	−	1.33788i	0.381024	−	0.111879i
$144$		0			0
$145$	9.07519	−	7.86370i	0.753653	−	0.653044i
$146$	−0.558416	+	1.39486i	−0.0462149	+	0.115439i
$147$		0			0
$148$	−1.82700	+	9.47937i	−0.150178	+	0.779200i
$149$	−0.0190670	+	0.400267i	−0.00156203	+	0.0327911i	−0.999514	−	0.0311799i	$-0.990074\pi$
$149$	−0.0190670	+	0.400267i	−0.00156203	+	0.0327911i	0.997952	+	0.0639711i	$0.0203765\pi$
$150$		0			0
$151$	−2.85563	−	8.25080i	−0.232388	−	0.671441i	−0.999550	−	0.0299878i	$-0.990453\pi$
$151$	−2.85563	−	8.25080i	−0.232388	−	0.671441i	0.767162	−	0.641453i	$-0.221668\pi$
$152$	−3.77610	−	1.10876i	−0.306282	−	0.0899325i
$153$		0			0
$154$	1.46231	+	1.68760i	0.117836	+	0.135990i
$155$	34.8358	+	3.32641i	2.79808	+	0.267184i
$156$		0			0
$157$	0.561998	+	5.88551i	0.0448524	+	0.469715i	0.989797	+	0.142485i	$0.0455092\pi$
$157$	0.561998	+	5.88551i	0.0448524	+	0.469715i	−0.944945	+	0.327230i	$0.893885\pi$
$158$	−3.43100	+	1.37356i	−0.272955	+	0.109275i
$159$		0			0
$160$	−14.8411	−	8.56853i	−1.17329	−	0.677402i
$161$	−13.5727	−	1.66238i	−1.06968	−	0.131014i
$162$		0			0
$163$	−11.9294	+	7.66656i	−0.934383	+	0.600491i	−0.916797	−	0.399354i	$-0.869234\pi$
$163$	−11.9294	+	7.66656i	−0.934383	+	0.600491i	−0.0175860	+	0.999845i	$0.505598\pi$
$164$	−6.33830	+	8.05980i	−0.494938	+	0.629365i
$165$		0			0
$166$	−3.77580	+	3.95995i	−0.293059	+	0.307352i
$167$	0.456629	+	0.325164i	0.0353350	+	0.0251620i	0.597588	−	0.801803i	$-0.296126\pi$
$167$	0.456629	+	0.325164i	0.0353350	+	0.0251620i	−0.562253	+	0.826965i	$0.690065\pi$
$168$		0			0
$169$	−6.25744	−	2.50510i	−0.481341	−	0.192700i
$170$	2.39520	−	8.15730i	0.183703	−	0.625636i
$171$		0			0
$172$	1.58467	−	2.46579i	0.120830	−	0.188015i
$173$	0.0263099	+	0.0510341i	0.00200031	+	0.00388005i	0.889833	−	0.456285i	$-0.150820\pi$
$173$	0.0263099	+	0.0510341i	0.00200031	+	0.00388005i	−0.887833	+	0.460165i	$0.847790\pi$
$174$		0			0
$175$	−28.1509	+	6.82934i	−2.12801	+	0.516249i
$176$	4.48693	−	3.52856i	0.338215	−	0.265975i
$177$		0			0
$178$	−0.672736	+	7.04521i	−0.0504237	+	0.528061i
$179$	−0.0316032	−	0.107631i	−0.00236213	−	0.00804469i	0.958303	−	0.285752i	$-0.0922435\pi$
$179$	−0.0316032	−	0.107631i	−0.00236213	−	0.00804469i	−0.960666	+	0.277708i	$0.910425\pi$
$180$		0			0
$181$	14.9883	+	2.15499i	1.11407	+	0.160179i	0.674676	−	0.738114i	$-0.264283\pi$
$181$	14.9883	+	2.15499i	1.11407	+	0.160179i	0.439396	+	0.898293i	$0.355192\pi$
$182$	0.140059	+	2.94019i	0.0103818	+	0.217942i
$183$		0			0
$184$	1.27822	−	7.47000i	0.0942315	−	0.550696i
$185$	−17.7903	+	10.2712i	−1.30797	+	0.755157i
$186$		0			0
$187$	7.89514	+	6.20881i	0.577350	+	0.454033i
$188$	−5.80748	−	2.65219i	−0.423554	−	0.193431i
$189$		0			0
$190$	−1.66210	−	3.63949i	−0.120581	−	0.264036i
$191$	−3.04518	+	0.586910i	−0.220341	+	0.0424673i	−0.298227	−	0.954495i	$-0.596395\pi$
$191$	−3.04518	+	0.586910i	−0.220341	+	0.0424673i	0.0778856	+	0.996962i	$0.475183\pi$
$192$		0			0
$193$	−2.33717	−	9.63397i	−0.168234	−	0.693468i	−0.991968	−	0.126492i	$-0.959628\pi$
$193$	−2.33717	−	9.63397i	−0.168234	−	0.693468i	0.823734	−	0.566976i	$-0.191887\pi$
$194$	7.27219	+	1.40160i	0.522113	+	0.100629i
$195$		0			0
$196$	1.83719	−	0.947140i	0.131228	−	0.0676528i
$197$	−18.3799	−	15.9263i	−1.30952	−	1.13470i	−0.981798	−	0.189928i	$-0.939175\pi$
$197$	−18.3799	−	15.9263i	−1.30952	−	1.13470i	−0.327719	−	0.944775i	$-0.606280\pi$
$198$		0			0
$199$	−6.67327	+	0.959471i	−0.473055	+	0.0680151i	−0.374720	−	0.927138i	$-0.622261\pi$
$199$	−6.67327	+	0.959471i	−0.473055	+	0.0680151i	−0.0983357	+	0.995153i	$0.531352\pi$
$200$	−3.03834	−	15.7644i	−0.214843	−	1.11471i
$201$		0			0
$202$	−2.97869	−	2.84017i	−0.209580	−	0.199834i
$203$	−8.75386	+	0.835892i	−0.614400	+	0.0586681i
$204$		0			0
$205$	−21.7938	+	1.03817i	−1.52215	+	0.0725088i
$206$	−2.23146			−0.155473
$207$		0			0
$208$	7.52446			0.521727
$209$	4.72157	−	0.224916i	0.326598	−	0.0155578i
$210$		0			0
$211$	24.4711	−	2.33671i	1.68466	−	0.160866i	0.791674	−	0.610944i	$-0.209210\pi$
$211$	24.4711	−	2.33671i	1.68466	−	0.160866i	0.892989	+	0.450078i	$0.148604\pi$
$212$	−9.47075	−	9.03034i	−0.650454	−	0.620206i
$213$		0			0
$214$	−0.172137	−	0.893130i	−0.0117670	−	0.0610531i
$215$	6.17361	−	0.887631i	0.421036	−	0.0605359i
$216$		0			0
$217$	−19.3672	−	16.7818i	−1.31473	−	1.13922i
$218$	0.771906	−	0.397945i	0.0522801	−	0.0269523i
$219$		0			0
$220$	13.2774	+	2.55901i	0.895163	+	0.172529i
$221$	3.12143	+	12.8667i	0.209970	+	0.865509i
$222$		0			0
$223$	−13.1037	+	2.52554i	−0.877492	+	0.169123i	−0.608055	−	0.793895i	$-0.708050\pi$
$223$	−13.1037	+	2.52554i	−0.877492	+	0.169123i	−0.269437	+	0.963018i	$0.586838\pi$
$224$	5.21328	+	11.4155i	0.348327	+	0.762730i
$225$		0			0
$226$	3.37849	+	1.54290i	0.224734	+	0.102632i
$227$	3.28026	+	2.57962i	0.217718	+	0.171216i	0.721062	−	0.692871i	$-0.243654\pi$
$227$	3.28026	+	2.57962i	0.217718	+	0.171216i	−0.503343	+	0.864087i	$0.667897\pi$
$228$		0			0
$229$	0.135177	−	0.0780442i	0.00893272	−	0.00515731i	−0.495527	−	0.868593i	$-0.665025\pi$
$229$	0.135177	−	0.0780442i	0.00893272	−	0.00515731i	0.504460	+	0.863435i	$0.331692\pi$
$230$	6.59047	−	3.99118i	0.434563	−	0.263171i
$231$		0			0
$232$	−0.231900	−	4.86817i	−0.0152250	−	0.319611i
$233$	10.2631	+	1.47562i	0.672360	+	0.0966708i	0.470035	−	0.882648i	$-0.344241\pi$
$233$	10.2631	+	1.47562i	0.672360	+	0.0966708i	0.202325	+	0.979318i	$0.435150\pi$
$234$		0			0
$235$	−3.82748	−	13.0352i	−0.249677	−	0.850322i
$236$	−0.354298	+	3.71038i	−0.0230629	+	0.241525i
$237$		0			0
$238$	−4.89383	+	3.84855i	−0.317220	+	0.249465i
$239$	−8.54758	+	2.07362i	−0.552897	+	0.134131i	−0.502467	−	0.864596i	$-0.667574\pi$
$239$	−8.54758	+	2.07362i	−0.552897	+	0.134131i	−0.0504299	+	0.998728i	$0.516059\pi$
$240$		0			0
$241$	10.0070	+	19.4108i	0.644607	+	1.25036i	0.954108	+	0.299463i	$0.0968077\pi$
$241$	10.0070	+	19.4108i	0.644607	+	1.25036i	−0.309501	+	0.950899i	$0.600162\pi$
$242$	−1.65025	+	2.56784i	−0.106082	+	0.165067i
$243$		0			0
$244$	−7.08847	+	24.1411i	−0.453793	+	1.54548i
$245$	4.08326	+	1.63469i	0.260870	+	0.104437i
$246$		0			0
$247$	5.07560	+	3.61432i	0.322953	+	0.229974i
$248$	9.80111	−	10.2791i	0.622371	−	0.652724i
$249$		0			0
$250$	5.12400	−	6.51570i	0.324070	−	0.412089i
$251$	19.9712	−	12.8347i	1.26057	−	0.810119i	0.272207	−	0.962239i	$-0.412246\pi$
$251$	19.9712	−	12.8347i	1.26057	−	0.810119i	0.988362	+	0.152120i	$0.0486100\pi$
$252$		0			0
$253$	1.48369	+	8.98085i	0.0932787	+	0.564621i
$254$	5.52057	+	3.18730i	0.346391	+	0.199989i
$255$		0			0
$256$	3.76022	−	1.50537i	0.235014	−	0.0940854i
$257$	−2.02811	−	21.2393i	−0.126510	−	1.32487i	−0.806319	−	0.591481i	$-0.798543\pi$
$257$	−2.02811	−	21.2393i	−0.126510	−	1.32487i	0.679809	−	0.733389i	$-0.262063\pi$
$258$		0			0
$259$	14.9753	+	1.42997i	0.930518	+	0.0888537i
$260$	11.6724	+	13.4707i	0.723892	+	0.835416i
$261$		0			0
$262$	3.44185	+	1.01062i	0.212638	+	0.0624361i
$263$	−0.0103775	−	0.0299839i	−0.000639905	−	0.00184889i	0.944680	−	0.327992i	$-0.106372\pi$
$263$	−0.0103775	−	0.0299839i	−0.000639905	−	0.00184889i	−0.945320	+	0.326143i	$0.894251\pi$
$264$		0			0
$265$	1.32495	−	27.8142i	0.0813912	−	1.70861i
$266$	−0.554506	+	2.87705i	−0.0339990	+	0.176403i
$267$		0			0
$268$	6.54881	−	16.3581i	0.400032	−	0.999232i
$269$	6.25253	−	5.41785i	0.381224	−	0.330332i	−0.443078	−	0.896483i	$-0.646114\pi$
$269$	6.25253	−	5.41785i	0.381224	−	0.330332i	0.824302	+	0.566151i	$0.191568\pi$
$270$		0			0
$271$	20.7664	−	6.09758i	1.26147	−	0.370401i	0.418430	−	0.908249i	$-0.362581\pi$
$271$	20.7664	−	6.09758i	1.26147	−	0.370401i	0.843042	+	0.537848i	$0.180762\pi$
$272$	9.23155	+	12.9639i	0.559745	+	0.786052i
$273$		0			0
$274$	1.38719	−	2.69077i	0.0838032	−	0.162555i
$275$	9.64151	+	16.6996i	0.581405	+	1.00702i
$276$		0			0
$277$	−12.6723	+	21.9491i	−0.761405	+	1.31879i	0.180722	+	0.983534i	$0.442157\pi$
$277$	−12.6723	+	21.9491i	−0.761405	+	1.31879i	−0.942127	+	0.335257i	$0.891177\pi$
$278$	−2.26599	−	3.52595i	−0.135905	−	0.211472i
$279$		0			0
$280$	−7.28760	+	15.9576i	−0.435518	+	0.953651i
$281$	2.00902	−	8.28129i	0.119848	−	0.494020i	−0.879972	−	0.475026i	$-0.842439\pi$
$281$	2.00902	−	8.28129i	0.119848	−	0.494020i	0.999820	−	0.0189939i	$-0.00604630\pi$
$282$		0			0
$283$	17.6109	+	6.09521i	1.04686	+	0.362323i	0.795744	−	0.605634i	$-0.207080\pi$
$283$	17.6109	+	6.09521i	1.04686	+	0.362323i	0.251119	+	0.967956i	$0.419202\pi$
$284$	−0.800806	−	1.01831i	−0.0475191	−	0.0604255i
$285$		0			0
$286$	1.85168	−	0.640872i	0.109492	−	0.0378955i
$287$	13.4414	+	8.63828i	0.793423	+	0.509902i
$288$		0			0
$289$	−7.20585	+	8.31599i	−0.423873	+	0.489176i
$290$	3.58600	−	3.41925i	0.210577	−	0.200785i
$291$		0			0
$292$	2.17913	−	6.29618i	0.127524	−	0.368456i
$293$	−5.26116	+	7.38826i	−0.307360	+	0.431627i	−0.939147	−	0.343515i	$-0.888382\pi$
$293$	−5.26116	+	7.38826i	−0.307360	+	0.431627i	0.631787	+	0.775142i	$0.282322\pi$
$294$		0			0
$295$	−6.46062	+	4.60059i	−0.376152	+	0.267857i
$296$	−1.18654	+	8.25259i	−0.0689664	+	0.479672i
$297$		0			0
$298$			0.165347i			0.00957828i
$299$	−5.78070	+	10.5146i	−0.334307	+	0.608077i
$300$		0			0
$301$	−4.05972	−	2.09293i	−0.233998	−	0.120635i
$302$	−1.33896	−	3.34455i	−0.0770483	−	0.192457i
$303$		0			0
$304$	7.27875	+	1.76580i	0.417465	+	0.101276i
$305$	−48.7006	+	22.2408i	−2.78859	+	1.27351i
$306$		0			0
$307$	−0.383791	−	2.66932i	−0.0219041	−	0.152346i	0.975934	−	0.218066i	$-0.0699748\pi$
$307$	−0.383791	−	2.66932i	−0.0219041	−	0.152346i	−0.997838	+	0.0657196i	$0.979066\pi$
$308$	−6.83322	−	7.16647i	−0.389359	−	0.408348i
$309$		0			0
$310$	14.4231	+	0.687056i	0.819176	+	0.0390222i
$311$	8.84883	+	0.421522i	0.501771	+	0.0239023i	0.296942	−	0.954895i	$-0.404033\pi$
$311$	8.84883	+	0.421522i	0.501771	+	0.0239023i	0.204829	+	0.978798i	$0.434336\pi$
$312$		0			0
$313$	−1.56228	−	1.63847i	−0.0883052	−	0.0926118i	0.678099	−	0.734971i	$-0.262804\pi$
$313$	−1.56228	−	1.63847i	−0.0883052	−	0.0926118i	−0.766404	+	0.642359i	$0.777956\pi$
$314$	0.347184	+	2.41472i	0.0195927	+	0.136270i
$315$		0			0
$316$	14.9074	−	6.80797i	0.838606	−	0.382979i
$317$	−20.3384	−	4.93404i	−1.14232	−	0.277124i	−0.380416	−	0.924815i	$-0.624219\pi$
$317$	−20.3384	−	4.93404i	−1.14232	−	0.277124i	−0.761902	+	0.647692i	$0.775734\pi$
$318$		0			0
$319$	2.17562	+	5.43445i	0.121812	+	0.304271i
$320$	14.5306	+	7.49106i	0.812286	+	0.418763i
$321$		0			0
$322$	−5.62671	−	0.418680i	−0.313565	−	0.0233321i
$323$			13.1791i			0.733303i
$324$		0			0
$325$	−3.61745	+	25.1599i	−0.200660	+	1.39562i
$326$	−4.76626	+	3.39404i	−0.263978	+	0.187978i
$327$		0			0
$328$	−5.13661	+	7.21336i	−0.283622	+	0.398291i
$329$	−3.25392	+	9.40157i	−0.179394	+	0.518325i
$330$		0			0
$331$	−19.6691	+	18.7544i	−1.08111	+	1.03084i	−0.0816955	+	0.996657i	$0.526033\pi$
$331$	−19.6691	+	18.7544i	−1.08111	+	1.03084i	−0.999416	+	0.0341801i	$0.989118\pi$
$332$	15.8889	−	18.3368i	0.872019	−	1.00636i
$333$		0			0
$334$	0.194587	+	0.125053i	0.0106473	+	0.00684261i
$335$	35.4323	−	12.2632i	1.93587	−	0.670012i
$336$		0			0
$337$	8.98979	+	11.4314i	0.489705	+	0.622711i	0.966612	−	0.256243i	$-0.0824847\pi$
$337$	8.98979	+	11.4314i	0.489705	+	0.622711i	−0.476907	+	0.878954i	$0.658242\pi$
$338$	−2.62822	−	0.909637i	−0.142957	−	0.0494778i
$339$		0			0
$340$	−8.88809	+	36.6372i	−0.482024	+	1.98693i
$341$	−7.08657	+	15.5174i	−0.383759	+	0.840315i
$342$		0			0
$343$	9.04917	+	14.0808i	0.488609	+	0.760291i
$344$	1.26570	−	2.19226i	0.0682422	−	0.118199i
$345$		0			0
$346$	0.0118458	+	0.0205175i	0.000636833	+	0.00110303i
$347$	11.4236	−	22.1587i	0.613252	−	1.18954i	−0.353886	−	0.935289i	$-0.615140\pi$
$347$	11.4236	−	22.1587i	0.613252	−	1.18954i	0.967138	−	0.254254i	$-0.0818298\pi$
$348$		0			0
$349$	−9.09034	−	12.7656i	−0.486595	−	0.683327i	0.496162	−	0.868230i	$-0.334742\pi$
$349$	−9.09034	−	12.7656i	−0.486595	−	0.683327i	−0.982757	+	0.184903i	$0.940803\pi$
$350$	−11.4685	+	3.36745i	−0.613017	+	0.179998i
$351$		0			0
$352$	6.31352	−	5.47070i	0.336512	−	0.291589i
$353$	12.5218	−	31.2779i	0.666467	−	1.66476i	−0.0778800	−	0.996963i	$-0.524815\pi$
$353$	12.5218	−	31.2779i	0.666467	−	1.66476i	0.744347	−	0.667793i	$-0.232761\pi$
$354$		0			0
$355$	0.521698	−	2.70683i	0.0276889	−	0.143664i
$356$	1.49329	−	31.3479i	0.0791440	−	1.66144i
$357$		0			0
$358$	−0.0151386	−	0.0437401i	−0.000800100	−	0.00231174i
$359$	−22.5665	−	6.62612i	−1.19101	−	0.349713i	−0.374604	−	0.927185i	$-0.622221\pi$
$359$	−22.5665	−	6.62612i	−1.19101	−	0.349713i	−0.816411	+	0.577472i	$0.804039\pi$
$360$		0			0
$361$	−8.38069	−	9.67183i	−0.441089	−	0.509044i
$362$	6.21984	+	0.593922i	0.326907	+	0.0312159i
$363$		0			0
$364$	−1.24075	−	12.9937i	−0.0650329	−	0.681055i
$365$	13.1619	−	5.26923i	0.688925	−	0.275804i
$366$		0			0
$367$	3.18377	+	1.83815i	0.166192	+	0.0959508i	0.580789	−	0.814054i	$-0.302744\pi$
$367$	3.18377	+	1.83815i	0.166192	+	0.0959508i	−0.414597	+	0.910005i	$0.636078\pi$
$368$	−1.75344	+	14.3162i	−0.0914043	+	0.746283i
$369$		0			0
$370$	−7.13073	+	4.58264i	−0.370709	+	0.238240i
$371$	−12.6053	+	16.0289i	−0.654432	+	0.832178i
$372$		0			0
$373$	−6.53697	+	6.85578i	−0.338471	+	0.354979i	−0.870868	−	0.491516i	$-0.836443\pi$
$373$	−6.53697	+	6.85578i	−0.338471	+	0.354979i	0.532397	+	0.846495i	$0.321291\pi$
$374$	3.37593	+	2.40399i	0.174565	+	0.124307i
$375$		0			0
$376$	−5.11889	−	2.04930i	−0.263987	−	0.105684i
$377$	−2.17395	+	7.40380i	−0.111964	+	0.381315i
$378$		0			0
$379$	−10.7972	+	16.8008i	−0.554614	+	0.862997i	−0.999468	−	0.0326062i	$-0.989619\pi$
$379$	−10.7972	+	16.8008i	−0.554614	+	0.862997i	0.444854	+	0.895603i	$0.353256\pi$
$380$	8.13001	+	15.7700i	0.417061	+	0.808985i
$381$		0			0
$382$	−1.24357	+	0.301686i	−0.0636264	+	0.0154356i
$383$	5.59403	−	4.39920i	0.285842	−	0.224788i	−0.464934	−	0.885345i	$-0.653922\pi$
$383$	5.59403	−	4.39920i	0.285842	−	0.224788i	0.750776	+	0.660557i	$0.229680\pi$
$384$		0			0
$385$	2.00290	−	20.9753i	0.102077	−	1.06900i
$386$	−1.15243	−	3.92481i	−0.0586571	−	0.199768i
$387$		0			0
$388$	−32.5071	−	4.67381i	−1.65030	−	0.237277i
$389$	0.0213200	+	0.447561i	0.00108097	+	0.0226923i	0.999343	−	0.0362327i	$-0.0115358\pi$
$389$	0.0213200	+	0.447561i	0.00108097	+	0.0226923i	−0.998262	+	0.0589250i	$0.981233\pi$
$390$		0			0
$391$	−25.2079	+	2.94055i	−1.27482	+	0.148710i
$392$	1.54596	−	0.892560i	0.0780827	−	0.0450811i
$393$		0			0
$394$	−7.88810	−	6.20327i	−0.397397	−	0.312516i
$395$	31.7216	+	14.4868i	1.59609	+	0.728908i
$396$		0			0
$397$	−1.36108	−	2.98036i	−0.0683108	−	0.149580i	0.872397	−	0.488798i	$-0.162565\pi$
$397$	−1.36108	−	2.98036i	−0.0683108	−	0.149580i	−0.940708	+	0.339219i	$0.889837\pi$
$398$	−2.73159	+	0.526471i	−0.136922	+	0.0263896i
$399$		0			0
$400$	7.20343	+	29.6930i	0.360172	+	1.48465i
$401$	−23.8778	−	4.60208i	−1.19240	−	0.229817i	−0.445828	−	0.895119i	$-0.647091\pi$
$401$	−23.8778	−	4.60208i	−1.19240	−	0.229817i	−0.746574	+	0.665302i	$0.768303\pi$
$402$		0			0
$403$	−19.9872	+	10.3041i	−0.995635	+	0.513286i
$404$	13.7930	+	11.9517i	0.686229	+	0.594621i
$405$		0			0
$406$	−3.59155	+	0.516386i	−0.178245	+	0.0256278i
$407$	−1.89518	−	9.83310i	−0.0939403	−	0.487409i
$408$		0			0
$409$	−11.1809	−	10.6610i	−0.552860	−	0.527151i	0.361329	−	0.932438i	$-0.382323\pi$
$409$	−11.1809	−	10.6610i	−0.552860	−	0.527151i	−0.914189	+	0.405287i	$0.867172\pi$
$410$	−8.96208	+	0.855775i	−0.442606	+	0.0422637i
$411$		0			0
$412$	9.88401	−	0.470834i	0.486950	−	0.0231963i
$413$	5.80812			0.285799
$414$		0			0
$415$	51.6297			2.53440
$416$	10.9997	−	0.523978i	0.539303	−	0.0256902i
$417$		0			0
$418$	1.94161	−	0.185401i	0.0949671	−	0.00906826i
$419$	6.46416	+	6.16356i	0.315795	+	0.301110i	0.831353	−	0.555745i	$-0.187567\pi$
$419$	6.46416	+	6.16356i	0.315795	+	0.301110i	−0.515558	+	0.856855i	$0.672415\pi$
$420$		0			0
$421$	−2.53056	−	13.1298i	−0.123332	−	0.639906i	−0.990005	−	0.141030i	$-0.954959\pi$
$421$	−2.53056	−	13.1298i	−0.123332	−	0.639906i	0.866674	−	0.498876i	$-0.166254\pi$
$422$	10.0401	−	1.44354i	0.488742	−	0.0702705i
$423$		0			0
$424$	−8.54116	−	7.40096i	−0.414795	−	0.359422i
$425$	−47.7863	+	24.6355i	−2.31797	+	1.19500i
$426$		0			0
$427$	38.4983	+	7.41994i	1.86306	+	0.359076i
$428$	0.950908	+	3.91970i	0.0459639	+	0.189466i
$429$		0			0
$430$	2.52706	−	0.487051i	0.121866	−	0.0234877i
$431$	−2.98287	−	6.53158i	−0.143680	−	0.314615i	0.824087	−	0.566464i	$-0.191689\pi$
$431$	−2.98287	−	6.53158i	−0.143680	−	0.314615i	−0.967767	+	0.251848i	$0.918962\pi$
$432$		0			0
$433$	22.6057	+	10.3237i	1.08636	+	0.496124i	0.876399	−	0.481586i	$-0.159939\pi$
$433$	22.6057	+	10.3237i	1.08636	+	0.496124i	0.209961	+	0.977710i	$0.432666\pi$
$434$	−8.31180	−	6.53647i	−0.398979	−	0.313761i
$435$		0			0
$436$	−3.33511	+	1.92552i	−0.159723	+	0.0922159i
$437$	−8.05946	+	8.81470i	−0.385536	+	0.421664i
$438$		0			0
$439$	−1.19517	−	25.0897i	−0.0570424	−	1.19747i	−0.828055	−	0.560648i	$-0.810552\pi$
$439$	−1.19517	−	25.0897i	−0.0570424	−	1.19747i	0.771012	−	0.636821i	$-0.219751\pi$
$440$	11.5591	+	1.66195i	0.551059	+	0.0792303i
$441$		0			0
$442$	1.53913	+	5.24181i	0.0732092	+	0.249328i
$443$	1.59548	−	16.7087i	0.0758038	−	0.793853i	−0.875013	−	0.484099i	$-0.839147\pi$
$443$	1.59548	−	16.7087i	0.0758038	−	0.793853i	0.950817	−	0.309754i	$-0.100247\pi$
$444$		0			0
$445$	52.4936	−	41.2814i	2.48843	−	1.95693i
$446$	−5.35121	+	1.29819i	−0.253387	+	0.0614710i
$447$		0			0
$448$	−5.48575	−	10.6409i	−0.259177	−	0.502734i
$449$	−0.530935	+	0.826150i	−0.0250563	+	0.0389884i	−0.853556	−	0.521001i	$-0.825559\pi$
$449$	−0.530935	+	0.826150i	−0.0250563	+	0.0389884i	0.828499	+	0.559990i	$0.189195\pi$
$450$		0			0
$451$	2.99654	−	10.2053i	0.141102	−	0.480548i
$452$	−15.2902	−	6.12127i	−0.719190	−	0.287920i
$453$		0			0
$454$	1.40263	+	0.998806i	0.0658285	+	0.0468763i
$455$	19.1671	−	20.1019i	0.898567	−	0.942390i
$456$		0			0
$457$	12.3735	−	15.7342i	0.578808	−	0.736015i	−0.405182	−	0.914236i	$-0.632792\pi$
$457$	12.3735	−	15.7342i	0.578808	−	0.736015i	0.983990	+	0.178221i	$0.0570343\pi$
$458$	0.0541816	−	0.0348204i	0.00253174	−	0.00162705i
$459$		0			0
$460$	−28.3496	+	19.0691i	−1.32181	+	0.889100i
$461$	25.6915	+	14.8330i	1.19657	+	0.690842i	0.959790	−	0.280720i	$-0.0905733\pi$
$461$	25.6915	+	14.8330i	1.19657	+	0.690842i	0.236784	+	0.971562i	$0.423907\pi$
$462$		0			0
$463$	−7.88481	+	3.15660i	−0.366438	+	0.146700i	−0.547572	−	0.836759i	$-0.684448\pi$
$463$	−7.88481	+	3.15660i	−0.366438	+	0.146700i	0.181134	+	0.983459i	$0.442023\pi$
$464$	0.881680	+	9.23337i	0.0409310	+	0.428649i
$465$		0			0
$466$	4.25898	+	0.406684i	0.197294	+	0.0188393i
$467$	−0.996120	−	1.14958i	−0.0460949	−	0.0531964i	0.732234	−	0.681053i	$-0.238478\pi$
$467$	−0.996120	−	1.14958i	−0.0460949	−	0.0531964i	−0.778329	+	0.627857i	$0.783932\pi$
$468$		0			0
$469$	−26.3452	−	7.73565i	−1.21651	−	0.357199i
$470$	−1.83344	−	5.29739i	−0.0845704	−	0.244350i
$471$		0			0
$472$	−0.153167	+	3.21537i	−0.00705008	+	0.147999i
$473$	−0.575411	+	2.98552i	−0.0264574	+	0.137274i
$474$		0			0
$475$	−9.40375	+	23.4894i	−0.431474	+	1.07777i
$476$	20.8646	−	18.0793i	0.956329	−	0.828664i
$477$		0			0
$478$	−3.48223	+	1.02247i	−0.159273	+	0.0467669i
$479$	7.76122	+	10.8991i	0.354619	+	0.497993i	0.952896	−	0.303296i	$-0.0980872\pi$
$479$	7.76122	+	10.8991i	0.354619	+	0.497993i	−0.598277	+	0.801289i	$0.704148\pi$
$480$		0			0
$481$	6.04879	−	11.7330i	0.275801	−	0.534979i
$482$	4.50554	+	7.80383i	0.205222	+	0.355455i
$483$		0			0
$484$	6.76778	−	11.7221i	0.307626	−	0.532824i
$485$	−37.7819	−	58.7897i	−1.71559	−	2.66950i
$486$		0			0
$487$	13.8495	−	30.3262i	0.627580	−	1.37421i	−0.282295	−	0.959328i	$-0.591096\pi$
$487$	13.8495	−	30.3262i	0.627580	−	1.37421i	0.909875	−	0.414882i	$-0.136177\pi$
$488$	−5.12292	+	21.1169i	−0.231903	+	0.955919i
$489$		0			0
$490$	1.71504	+	0.593580i	0.0774774	+	0.0268152i
$491$	22.9830	+	29.2253i	1.03721	+	1.31892i	0.946381	+	0.323053i	$0.104709\pi$
$491$	22.9830	+	29.2253i	1.03721	+	1.31892i	0.0908291	+	0.995866i	$0.471048\pi$
$492$		0			0
$493$	−15.4232	+	5.33802i	−0.694625	+	0.240412i
$494$	2.16290	+	1.39001i	0.0973136	+	0.0625396i
$495$		0			0
$496$	−17.7010	+	20.4281i	−0.794800	+	0.917248i
$497$	−1.46101	+	1.39307i	−0.0655351	+	0.0624876i
$498$		0			0
$499$	6.52021	−	18.8389i	0.291885	−	0.843346i	−0.699764	−	0.714375i	$-0.746711\pi$
$499$	6.52021	−	18.8389i	0.291885	−	0.843346i	0.991648	−	0.128971i	$-0.0411675\pi$
$500$	−21.3214	+	29.9417i	−0.953522	+	1.33903i
$501$		0			0
$502$	7.97925	−	5.68200i	0.356132	−	0.253600i
$503$	1.17664	−	8.18371i	0.0524638	−	0.364894i	−0.946630	−	0.322323i	$-0.895536\pi$
$503$	1.17664	−	8.18371i	0.0524638	−	0.364894i	0.999093	−	0.0425704i	$-0.0135547\pi$
$504$		0			0
$505$			38.8360i			1.72818i
$506$	0.787836	+	3.67238i	0.0350236	+	0.163257i
$507$		0			0
$508$	−25.1252	−	12.9530i	−1.11475	−	0.574695i
$509$	−1.81341	−	4.52968i	−0.0803780	−	0.200775i	0.882735	−	0.469870i	$-0.155699\pi$
$509$	−1.81341	−	4.52968i	−0.0803780	−	0.200775i	−0.963113	+	0.269096i	$0.913275\pi$
$510$		0			0
$511$	−10.0896	−	2.44771i	−0.446337	−	0.108280i
$512$	20.6868	−	9.44736i	0.914237	−	0.417518i
$513$		0			0
$514$	−1.25290	−	8.71409i	−0.0552629	−	0.384362i
$515$	14.5304	+	15.2391i	0.640286	+	0.671513i
$516$		0			0
$517$	6.61517	+	0.315119i	0.290935	+	0.0138589i
$518$	6.20023	+	0.295353i	0.272422	+	0.0129771i
$519$		0			0
$520$	10.6229	+	11.1410i	0.465846	+	0.488565i
$521$	3.73147	+	25.9530i	0.163479	+	1.13702i	0.892013	+	0.452010i	$0.149293\pi$
$521$	3.73147	+	25.9530i	0.163479	+	1.13702i	−0.728534	+	0.685009i	$0.759798\pi$
$522$		0			0
$523$	31.7130	−	14.4828i	1.38671	−	0.633290i	0.424459	−	0.905447i	$-0.360464\pi$
$523$	31.7130	−	14.4828i	1.38671	−	0.633290i	0.962253	+	0.272157i	$0.0877370\pi$
$524$	−15.4585	−	3.75019i	−0.675308	−	0.163828i
$525$		0			0
$526$	−0.00486585	−	0.0121543i	−0.000212161	−	0.000529953i
$527$	−42.2748	−	21.7942i	−1.84152	−	0.949369i
$528$		0			0
$529$	−18.6583	−	13.4487i	−0.811230	−	0.584727i
$530$		−	11.4898i		−	0.499085i
$531$		0			0
$532$	1.84907	−	12.8606i	0.0801674	−	0.557577i
$533$	11.4207	−	8.13264i	0.494685	−	0.352264i
$534$		0			0
$535$	−4.97845	+	6.99126i	−0.215237	+	0.302258i
$536$	4.97720	−	14.3807i	0.214982	−	0.621151i
$537$		0			0
$538$	2.47065	−	2.35576i	0.106517	−	0.101564i
$539$	−1.40409	+	1.62040i	−0.0604782	+	0.0697956i
$540$		0			0
$541$	0.354224	+	0.227646i	0.0152293	+	0.00978727i	0.548233	−	0.836325i	$-0.315301\pi$
$541$	0.354224	+	0.227646i	0.0152293	+	0.00978727i	−0.533004	+	0.846113i	$0.678937\pi$
$542$	8.43930	−	2.92087i	0.362499	−	0.125462i
$543$		0			0
$544$	14.3979	+	18.3085i	0.617307	+	0.784970i
$545$	−7.74399	−	2.68022i	−0.331716	−	0.114808i
$546$		0			0
$547$	1.80228	−	7.42910i	0.0770599	−	0.317645i	−0.920216	−	0.391412i	$-0.871987\pi$
$547$	1.80228	−	7.42910i	0.0770599	−	0.317645i	0.997276	+	0.0737665i	$0.0235020\pi$
$548$	−5.57665	+	12.2112i	−0.238223	+	0.521635i
$549$		0			0
$550$	4.30168	+	6.69354i	0.183424	+	0.285414i
$551$	−3.84045	+	6.65186i	−0.163609	+	0.283379i
$552$		0			0
$553$	−12.7689	−	22.1163i	−0.542987	−	0.940481i
$554$	−4.79203	+	9.29524i	−0.203594	+	0.394917i
$555$		0			0
$556$	10.7809	+	15.1397i	0.457213	+	0.642065i
$557$	5.83299	−	1.71272i	0.247152	−	0.0725702i	−0.155810	−	0.987787i	$-0.549799\pi$
$557$	5.83299	−	1.71272i	0.247152	−	0.0725702i	0.402962	+	0.915217i	$0.367981\pi$
$558$		0			0
$559$	−3.02897	+	2.62462i	−0.128112	+	0.111010i
$560$	12.4087	−	30.9953i	0.524361	−	1.30979i
$561$		0			0
$562$	0.665439	−	3.45263i	0.0280699	−	0.145640i
$563$	−1.09539	+	22.9951i	−0.0461653	+	0.969128i	0.850378	+	0.526172i	$0.176373\pi$
$563$	−1.09539	+	22.9951i	−0.0461653	+	0.969128i	−0.896543	+	0.442956i	$0.853930\pi$
$564$		0			0
$565$	−11.4626	−	33.1191i	−0.482236	−	1.39333i
$566$	7.37813	+	2.16641i	0.310126	+	0.0910612i
$567$		0			0
$568$	−0.732673	−	0.845549i	−0.0307423	−	0.0354785i
$569$	−41.1183	−	3.92633i	−1.72377	−	0.164600i	−0.814321	−	0.580415i	$-0.802891\pi$
$569$	−41.1183	−	3.92633i	−1.72377	−	0.164600i	−0.909450	+	0.415814i	$0.863497\pi$
$570$		0			0
$571$	−0.640264	−	6.70515i	−0.0267942	−	0.280602i	−0.998933	−	0.0461937i	$-0.985291\pi$
$571$	−0.640264	−	6.70515i	−0.0267942	−	0.280602i	0.972138	−	0.234408i	$-0.0753152\pi$
$572$	−8.06657	+	3.22937i	−0.337280	+	0.135027i
$573$		0			0
$574$	5.70957	+	3.29642i	0.238313	+	0.137590i
$575$	−47.0269	−	12.7457i	−1.96116	−	0.531533i
$576$		0			0
$577$	−6.71023	+	4.31240i	−0.279350	+	0.179528i	−0.672812	−	0.739813i	$-0.734914\pi$
$577$	−6.71023	+	4.31240i	−0.279350	+	0.179528i	0.393462	+	0.919341i	$0.371277\pi$
$578$	−2.80666	+	3.56896i	−0.116742	+	0.148449i
$579$		0			0
$580$	−15.1623	+	15.9018i	−0.629582	+	0.660287i
$581$	−30.7981	−	21.9312i	−1.27772	−	0.909861i
$582$		0			0
$583$	12.6019	+	5.04504i	0.521918	+	0.208944i
$584$	1.62112	−	5.52104i	0.0670825	−	0.228462i
$585$		0			0
$586$	−2.02336	+	3.14841i	−0.0835843	+	0.130060i
$587$	3.92604	+	7.61546i	0.162045	+	0.314324i	0.955853	−	0.293845i	$-0.0949348\pi$
$587$	3.92604	+	7.61546i	0.162045	+	0.314324i	−0.793808	+	0.608168i	$0.791905\pi$
$588$		0			0
$589$	−21.7527	+	5.27714i	−0.896304	+	0.217441i
$590$	−2.57246	+	2.02301i	−0.105907	+	0.0832858i
$591$		0			0
$592$	1.50830	−	15.7956i	0.0619906	−	0.649195i
$593$	−6.00060	−	20.4362i	−0.246415	−	0.839212i	−0.986085	−	0.166242i	$-0.946837\pi$
$593$	−6.00060	−	20.4362i	−0.246415	−	0.839212i	0.739670	−	0.672970i	$-0.234982\pi$
$594$		0			0
$595$	58.1491	+	8.36058i	2.38388	+	0.342750i
$596$	−0.0348878	−	0.732384i	−0.00142906	−	0.0299996i
$597$		0			0
$598$	−2.17611	+	4.44717i	−0.0889879	+	0.181858i
$599$	−28.0149	+	16.1744i	−1.14466	+	0.660868i	−0.947580	−	0.319520i	$-0.896478\pi$
$599$	−28.0149	+	16.1744i	−1.14466	+	0.660868i	−0.197077	+	0.980388i	$0.563145\pi$
$600$		0			0
$601$	−22.2969	−	17.5345i	−0.909510	−	0.715246i	0.0494537	−	0.998776i	$-0.484252\pi$
$601$	−22.2969	−	17.5345i	−0.909510	−	0.715246i	−0.958963	+	0.283530i	$0.908494\pi$
$602$	−1.71433	−	0.782909i	−0.0698709	−	0.0319090i
$603$		0			0
$604$	6.63645	+	14.5318i	0.270033	+	0.591291i
$605$	28.2820	−	5.45090i	1.14982	−	0.221611i
$606$		0			0
$607$	−4.11960	−	16.9812i	−0.167210	−	0.689247i	−0.992259	−	0.124186i	$-0.960368\pi$
$607$	−4.11960	−	16.9812i	−0.167210	−	0.689247i	0.825049	−	0.565061i	$-0.191147\pi$
$608$	10.7634	+	2.07448i	0.436515	+	0.0841313i
$609$		0			0
$610$	−19.6356	+	10.1229i	−0.795022	+	0.409862i
$611$	6.59764	+	5.71689i	0.266912	+	0.231281i
$612$		0			0
$613$	−40.2352	+	5.78495i	−1.62508	+	0.233652i	−0.893815	−	0.448436i	$-0.851981\pi$
$613$	−40.2352	+	5.78495i	−1.62508	+	0.233652i	−0.731270	+	0.682088i	$0.761072\pi$
$614$	−0.210590	−	1.09264i	−0.00849871	−	0.0440955i
$615$		0			0
$616$	−6.18927	−	5.90145i	−0.249373	−	0.237776i
$617$	29.3860	−	2.80602i	1.18303	−	0.112966i	0.515062	−	0.857153i	$-0.327769\pi$
$617$	29.3860	−	2.80602i	1.18303	−	0.112966i	0.667972	+	0.744187i	$0.267163\pi$
$618$		0			0
$619$	17.4812	−	0.832733i	0.702630	−	0.0334704i	0.306773	−	0.951783i	$-0.400751\pi$
$619$	17.4812	−	0.832733i	0.702630	−	0.0334704i	0.395857	+	0.918312i	$0.370448\pi$
$620$	−64.0304			−2.57152
$621$		0			0
$622$	3.65538			0.146567
$623$	−48.8489	+	2.32696i	−1.95709	+	0.0932277i
$624$		0			0
$625$	−27.2946	+	2.60632i	−1.09178	+	0.104253i
$626$	−0.676071	−	0.644633i	−0.0270212	−	0.0257647i
$627$		0			0
$628$	−2.04731	−	10.6225i	−0.0816966	−	0.423882i
$629$	27.6359	−	3.97345i	1.10192	−	0.158432i
$630$		0			0
$631$	0.744832	+	0.645401i	0.0296513	+	0.0256930i	0.669560	−	0.742758i	$-0.266483\pi$
$631$	0.744832	+	0.645401i	0.0296513	+	0.0256930i	−0.639909	+	0.768451i	$0.721028\pi$
$632$	12.5803	−	6.48559i	0.500417	−	0.257983i
$633$		0			0
$634$	−8.47947	−	1.63428i	−0.336763	−	0.0649057i
$635$	−14.1811	−	58.4553i	−0.562760	−	2.31973i
$636$		0			0
$637$	−2.77525	+	0.534886i	−0.109959	+	0.0211929i
$638$	1.00339	+	2.19713i	0.0397247	+	0.0869851i
$639$		0			0
$640$	37.3128	+	17.0402i	1.47492	+	0.673572i
$641$	3.84013	+	3.01991i	0.151676	+	0.119279i	0.691113	−	0.722747i	$-0.257121\pi$
$641$	3.84013	+	3.01991i	0.151676	+	0.119279i	−0.539437	+	0.842026i	$0.681363\pi$
$642$		0			0
$643$	5.96974	−	3.44663i	0.235424	−	0.135922i	−0.377648	−	0.925949i	$-0.623267\pi$
$643$	5.96974	−	3.44663i	0.235424	−	0.135922i	0.613072	+	0.790027i	$0.289934\pi$
$644$	25.0112	+	0.667273i	0.985581	+	0.0262942i
$645$		0			0
$646$	0.258750	+	5.43184i	0.0101804	+	0.213713i
$647$	−37.3999	−	5.37729i	−1.47034	−	0.211403i	−0.639878	−	0.768477i	$-0.721015\pi$
$647$	−37.3999	−	5.37729i	−1.47034	−	0.211403i	−0.830463	+	0.557074i	$0.811924\pi$
$648$		0			0
$649$	−1.08927	−	3.70973i	−0.0427578	−	0.145620i
$650$	−0.996980	+	10.4409i	−0.0391048	+	0.409524i
$651$		0			0
$652$	20.3955	−	16.0392i	0.798748	−	0.628142i
$653$	23.8169	−	5.77791i	0.932026	−	0.226107i	0.259128	−	0.965843i	$-0.416565\pi$
$653$	23.8169	−	5.77791i	0.932026	−	0.226107i	0.672897	+	0.739736i	$0.265050\pi$
$654$		0			0
$655$	−15.5103	−	30.0857i	−0.606036	−	1.17555i
$656$	9.11147	−	14.1777i	0.355743	−	0.553547i
$657$		0			0
$658$	−1.15654	+	3.93880i	−0.0450865	+	0.153550i
$659$	−27.7656	−	11.1157i	−1.08159	−	0.433005i	−0.238705	−	0.971092i	$-0.576723\pi$
$659$	−27.7656	−	11.1157i	−1.08159	−	0.433005i	−0.842889	+	0.538088i	$0.819147\pi$
$660$		0			0
$661$	−13.3217	−	9.48635i	−0.518155	−	0.368976i	0.290859	−	0.956766i	$-0.406059\pi$
$661$	−13.3217	−	9.48635i	−0.518155	−	0.368976i	−0.809014	+	0.587790i	$0.799998\pi$
$662$	−7.73853	+	8.11593i	−0.300766	+	0.315435i
$663$		0			0
$664$	12.9533	−	16.4714i	0.502685	−	0.639216i
$665$	23.2586	−	14.9474i	0.901930	−	0.579635i
$666$		0			0
$667$	−13.5800	−	5.86153i	−0.525821	−	0.226959i
$668$	−0.888285	−	0.512852i	−0.0343688	−	0.0198428i
$669$		0			0
$670$	14.3629	−	5.75002i	0.554886	−	0.222143i
$671$	−2.48088	−	25.9810i	−0.0957733	−	1.00298i
$672$		0			0
$673$	47.3961	+	4.52578i	1.82699	+	0.174456i	0.951268	−	0.308366i	$-0.0997823\pi$
$673$	47.3961	+	4.52578i	1.82699	+	0.174456i	0.875718	+	0.482822i	$0.160388\pi$
$674$	3.92964	+	4.53504i	0.151364	+	0.174683i
$675$		0			0
$676$	11.8334	+	3.47459i	0.455129	+	0.133638i
$677$	2.89337	+	8.35984i	0.111201	+	0.321295i	0.986847	−	0.161660i	$-0.0516848\pi$
$677$	2.89337	+	8.35984i	0.111201	+	0.321295i	−0.875645	+	0.482955i	$0.839564\pi$
$678$		0			0
$679$	−2.43506	+	51.1181i	−0.0934489	+	1.96173i
$680$	−6.16187	+	31.9708i	−0.236297	+	1.22603i
$681$		0			0
$682$	−2.61611	+	6.53473i	−0.100176	+	0.250228i
$683$	10.4612	−	9.06468i	0.400287	−	0.346850i	−0.431336	−	0.902191i	$-0.641958\pi$
$683$	10.4612	−	9.06468i	0.400287	−	0.346850i	0.831623	+	0.555341i	$0.187412\pi$
$684$		0			0
$685$	−27.4086	+	8.04788i	−1.04723	+	0.307494i
$686$	4.00613	+	5.62582i	0.152955	+	0.214795i
$687$		0			0
$688$	−2.20758	+	4.28210i	−0.0841631	+	0.163254i
$689$	8.94672	+	15.4962i	0.340843	+	0.590357i
$690$		0			0
$691$	−24.9509	+	43.2162i	−0.949177	+	1.64402i	−0.202013	+	0.979383i	$0.564748\pi$
$691$	−24.9509	+	43.2162i	−0.949177	+	1.64402i	−0.747164	+	0.664639i	$0.768585\pi$
$692$	−0.0567986	−	0.0883804i	−0.00215916	−	0.00335972i
$693$		0			0
$694$	4.27326	−	9.35714i	0.162211	−	0.355192i
$695$	−9.32409	+	38.4344i	−0.353683	+	1.45790i
$696$		0			0
$697$	28.0235	+	9.69902i	1.06146	+	0.367377i
$698$	−3.99727	−	5.08295i	−0.151299	−	0.192392i
$699$		0			0
$700$	50.0879	−	17.3356i	1.89314	−	0.655223i
$701$	29.6207	+	19.0361i	1.11876	+	0.718982i	0.963184	−	0.268842i	$-0.0866411\pi$
$701$	29.6207	+	19.0361i	1.11876	+	0.718982i	0.155574	+	0.987824i	$0.450277\pi$
$702$		0			0
$703$	8.60472	−	9.93037i	0.324533	−	0.374531i
$704$	−5.76766	+	5.49945i	−0.217377	+	0.207268i
$705$		0			0
$706$	4.54684	−	13.1372i	0.171123	−	0.494426i
$707$	16.4967	−	23.1664i	0.620424	−	0.871264i
$708$		0			0
$709$	−6.12034	+	4.35828i	−0.229854	+	0.163679i	−0.689182	−	0.724588i	$-0.742030\pi$
$709$	−6.12034	+	4.35828i	−0.229854	+	0.163679i	0.459327	+	0.888267i	$0.348090\pi$
$710$	0.161877	−	1.12588i	0.00607513	−	0.0422535i
$711$		0			0
$712$		−	27.1041i		−	1.01577i
$713$	−14.9472	−	40.4293i	−0.559777	−	1.51409i
$714$		0			0
$715$	−16.4340	−	8.47232i	−0.614597	−	0.316847i
$716$	0.0762838	+	0.190548i	0.00285086	+	0.00712110i
$717$		0			0
$718$	−9.43102	−	2.28794i	−0.351963	−	0.0853852i
$719$	30.9786	−	14.1474i	1.15531	−	0.527610i	0.256753	−	0.966477i	$-0.417347\pi$
$719$	30.9786	−	14.1474i	1.15531	−	0.527610i	0.898552	+	0.438867i	$0.144620\pi$
$720$		0			0
$721$	−2.19443	−	15.2626i	−0.0817249	−	0.568409i
$722$	−3.64404	−	3.82176i	−0.135617	−	0.142231i
$723$		0			0
$724$	−27.6754	−	1.31834i	−1.02855	−	0.0489958i
$725$	−31.2980	−	1.49091i	−1.16238	−	0.0553710i
$726$		0			0
$727$	26.1822	+	27.4591i	0.971043	+	1.01840i	0.999823	+	0.0188149i	$0.00598933\pi$
$727$	26.1822	+	27.4591i	0.971043	+	1.01840i	−0.0287799	+	0.999586i	$0.509162\pi$
$728$	−1.60431	−	11.1582i	−0.0594596	−	0.413551i
$729$		0			0
$730$	5.32131	−	2.43016i	0.196950	−	0.0899442i
$731$	−8.23812	−	1.99855i	−0.304698	−	0.0739189i
$732$		0			0
$733$	−2.91125	−	7.27196i	−0.107530	−	0.268596i	0.864838	−	0.502051i	$-0.167421\pi$
$733$	−2.91125	−	7.27196i	−0.107530	−	0.268596i	−0.972368	+	0.233455i	$0.924997\pi$
$734$	1.34830	+	0.695097i	0.0497667	+	0.0256565i
$735$		0			0
$736$	−1.56634	+	21.0503i	−0.0577360	+	0.775924i
$737$			18.2778i			0.673272i
$738$		0			0
$739$	0.0759584	−	0.528302i	0.00279417	−	0.0194339i	−0.988377	−	0.152025i	$-0.951421\pi$
$739$	0.0759584	−	0.528302i	0.00279417	−	0.0194339i	0.991171	+	0.132591i	$0.0423297\pi$
$740$	30.6178	−	21.8029i	1.12553	−	0.801489i
$741$		0			0
$742$	−4.88063	+	6.85389i	−0.179174	+	0.251614i
$743$	−13.0343	+	37.6600i	−0.478181	+	1.38161i	0.405745	+	0.913986i	$0.367012\pi$
$743$	−13.0343	+	37.6600i	−0.478181	+	1.38161i	−0.883926	+	0.467627i	$0.845109\pi$
$744$		0			0
$745$	1.12918	−	1.07667i	0.0413700	−	0.0394462i
$746$	−2.55965	+	2.95399i	−0.0937155	+	0.108153i
$747$		0			0
$748$	−15.4605	−	9.93588i	−0.565293	−	0.363292i
$749$	5.93948	−	2.05568i	0.217024	−	0.0751127i
$750$		0			0
$751$	−17.9707	−	22.8516i	−0.655759	−	0.833866i	0.338488	−	0.940971i	$-0.390084\pi$
$751$	−17.9707	−	22.8516i	−0.655759	−	0.833866i	−0.994248	+	0.107105i	$0.965842\pi$
$752$	9.91657	+	3.43216i	0.361620	+	0.125158i
$753$		0			0
$754$	−0.750646	+	3.09420i	−0.0273369	+	0.112684i
$755$	−14.1218	+	30.9224i	−0.513944	+	1.12538i
$756$		0			0
$757$	−15.4754	−	24.0802i	−0.562463	−	0.875209i	0.437246	−	0.899342i	$-0.355954\pi$
$757$	−15.4754	−	24.0802i	−0.562463	−	0.875209i	−0.999709	+	0.0241331i	$0.992317\pi$
$758$	−4.12027	+	7.13652i	−0.149655	+	0.259210i
$759$		0			0
$760$	7.66151	+	13.2701i	0.277912	+	0.481358i
$761$	−13.8824	+	26.9282i	−0.503238	+	0.976146i	0.491222	+	0.871034i	$0.336550\pi$
$761$	−13.8824	+	26.9282i	−0.503238	+	0.976146i	−0.994460	+	0.105111i	$0.966480\pi$
$762$		0			0
$763$	3.48093	+	4.88829i	0.126018	+	0.176968i
$764$	5.44458	−	1.59867i	0.196978	−	0.0578379i
$765$		0			0
$766$	2.21924	−	1.92299i	0.0801846	−	0.0694803i
$767$	1.89420	−	4.73149i	0.0683957	−	0.170844i
$768$		0			0
$769$	3.14775	−	16.3321i	0.113511	−	0.588950i	−0.879977	−	0.475016i	$-0.842442\pi$
$769$	3.14775	−	16.3321i	0.113511	−	0.588950i	0.993488	−	0.113935i	$-0.0363454\pi$
$770$	0.413691	−	8.68444i	0.0149084	−	0.312965i
$771$		0			0
$772$	5.93268	+	17.1414i	0.213522	+	0.616931i
$773$	−1.21930	−	0.358019i	−0.0438553	−	0.0128771i	0.259731	−	0.965681i	$-0.416366\pi$
$773$	−1.21930	−	0.358019i	−0.0438553	−	0.0128771i	−0.303587	+	0.952804i	$0.598184\pi$
$774$		0			0
$775$	−59.7966	−	69.0090i	−2.14796	−	2.47887i
$776$	−28.2347	−	2.69609i	−1.01357	−	0.0967840i
$777$		0			0
$778$	0.0175743	+	0.184047i	0.000630070	+	0.00659839i
$779$	12.9563	−	5.18691i	0.464207	−	0.185840i
$780$		0			0
$781$	1.16377	+	0.671906i	0.0416431	+	0.0240427i
$782$	−10.3318	+	1.70688i	−0.369466	+	0.0610379i
$783$		0			0
$784$	−2.85804	+	1.83675i	−0.102073	+	0.0655981i
$785$	14.2298	−	18.0947i	0.507883	−	0.645826i
$786$		0			0
$787$	−12.1248	+	12.7161i	−0.432202	+	0.453280i	−0.903433	−	0.428730i	$-0.858961\pi$
$787$	−12.1248	+	12.7161i	−0.432202	+	0.453280i	0.471231	+	0.882010i	$0.343810\pi$
$788$	36.2483	+	25.8123i	1.29129	+	0.919525i
$789$		0			0
$790$	13.3587	+	5.34801i	0.475280	+	0.190273i
$791$	−7.23062	+	24.6252i	−0.257091	+	0.875573i
$792$		0			0
$793$	18.6000	−	28.9421i	0.660505	−	1.02777i
$794$	−0.619494	−	1.20165i	−0.0219850	−	0.0426450i
$795$		0			0
$796$	11.9882	−	2.90830i	0.424910	−	0.103082i
$797$	36.2559	−	28.5119i	1.28425	−	1.00995i	0.285581	−	0.958354i	$-0.407813\pi$
$797$	36.2559	−	28.5119i	1.28425	−	1.00995i	0.998668	−	0.0515906i	$-0.0164291\pi$
$798$		0			0
$799$	−1.75517	+	18.3810i	−0.0620935	+	0.650272i
$800$	12.5981	+	42.9052i	0.445410	+	1.51693i
$801$		0			0
$802$	−9.93175	−	1.42797i	−0.350702	−	0.0504234i
$803$	0.328850	+	6.90341i	0.0116049	+	0.243616i
$804$		0			0
$805$	33.7797	+	41.1521i	1.19058	+	1.45042i
$806$	−8.03556	+	4.63933i	−0.283040	+	0.163413i
$807$		0			0
$808$	12.3899	+	9.74351i	0.435875	+	0.342776i
$809$	−7.99865	−	3.65286i	−0.281218	−	0.128428i	0.269813	−	0.962913i	$-0.413038\pi$
$809$	−7.99865	−	3.65286i	−0.281218	−	0.128428i	−0.551031	+	0.834485i	$0.685765\pi$
$810$		0			0
$811$	10.4674	+	22.9204i	0.367560	+	0.804844i	0.999554	+	0.0298704i	$0.00950945\pi$
$811$	10.4674	+	22.9204i	0.367560	+	0.804844i	−0.631994	+	0.774973i	$0.717763\pi$
$812$	15.7994	−	3.04508i	0.554450	−	0.106861i
$813$		0			0
$814$	−0.974166	−	4.01557i	−0.0341445	−	0.140745i
$815$	54.2144	+	10.4490i	1.89905	+	0.366012i
$816$		0			0
$817$	−3.54599	+	1.82809i	−0.124059	+	0.0639567i
$818$	−4.81759	−	4.17447i	−0.168443	−	0.145957i
$819$		0			0
$820$	39.5160	−	5.68154i	1.37996	−	0.198408i
$821$	−7.84044	−	40.6801i	−0.273633	−	1.41974i	−0.815245	−	0.579116i	$-0.803398\pi$
$821$	−7.84044	−	40.6801i	−0.273633	−	1.41974i	0.541612	−	0.840629i	$-0.317814\pi$
$822$		0			0
$823$	−34.6777	−	33.0652i	−1.20879	−	1.15258i	−0.983999	−	0.178172i	$-0.942982\pi$
$823$	−34.6777	−	33.0652i	−1.20879	−	1.15258i	−0.224791	−	0.974407i	$-0.572170\pi$
$824$	8.50723	−	0.812342i	0.296363	−	0.0282993i
$825$		0			0
$826$	2.39385	−	0.114033i	0.0832928	−	0.00396772i
$827$	−23.7876			−0.827177			−0.413588	−	0.910464i	$-0.635725\pi$
$827$	−23.7876			−0.827177			−0.413588	+	0.910464i	$0.635725\pi$
$828$		0			0
$829$	10.6534			0.370006			0.185003	−	0.982738i	$-0.440770\pi$
$829$	10.6534			0.370006			0.185003	+	0.982738i	$0.440770\pi$
$830$	21.2795	−	1.01367i	0.738622	−	0.0351849i
$831$		0			0
$832$	−10.4575	+	0.998568i	−0.362548	+	0.0346191i
$833$	−4.32643	−	4.12525i	−0.149902	−	0.142931i
$834$		0			0
$835$	−0.413061	−	2.14316i	−0.0142946	−	0.0741672i
$836$	−8.56101	+	1.23089i	−0.296089	+	0.0425711i
$837$		0			0
$838$	2.78525	+	2.41344i	0.0962150	+	0.0833708i
$839$	−14.9245	+	7.69412i	−0.515252	+	0.265631i	−0.696182	−	0.717865i	$-0.745119\pi$
$839$	−14.9245	+	7.69412i	−0.515252	+	0.265631i	0.180931	+	0.983496i	$0.442089\pi$
$840$		0			0
$841$	19.1359	+	3.68814i	0.659858	+	0.127177i
$842$	−1.30077	−	5.36183i	−0.0448274	−	0.184781i
$843$		0			0
$844$	−44.1667	+	8.51244i	−1.52028	+	0.293010i
$845$	10.9019	+	23.8718i	0.375036	+	0.821215i
$846$		0			0
$847$	−19.1862	−	8.76202i	−0.659244	−	0.301067i
$848$	16.9069	+	13.2957i	0.580586	+	0.456578i
$849$		0			0
$850$	−19.2117	+	11.0919i	−0.658957	+	0.380449i
$851$	20.9139	+	14.2427i	0.716920	+	0.488234i
$852$		0			0
$853$	−0.880891	−	18.4922i	−0.0301611	−	0.633160i	−0.962452	−	0.271451i	$-0.912496\pi$
$853$	−0.880891	−	18.4922i	−0.0301611	−	0.633160i	0.932291	−	0.361709i	$-0.117807\pi$
$854$	16.0130	+	2.30232i	0.547953	+	0.0787838i
$855$		0			0
$856$	0.981389	+	3.34230i	0.0335432	+	0.114238i
$857$	0.140114	−	1.46734i	0.00478621	−	0.0501235i	−0.992763	−	0.120088i	$-0.961682\pi$
$857$	0.140114	−	1.46734i	0.00478621	−	0.0501235i	0.997550	+	0.0699642i	$0.0222885\pi$
$858$		0			0
$859$	−27.9384	+	21.9710i	−0.953245	+	0.749641i	−0.968182	−	0.250248i	$-0.919488\pi$
$859$	−27.9384	+	21.9710i	−0.953245	+	0.749641i	0.0149363	+	0.999888i	$0.495245\pi$
$860$	−11.0906	+	2.69054i	−0.378185	+	0.0917468i
$861$		0			0
$862$	−1.35765	−	2.63347i	−0.0462416	−	0.0896963i
$863$	−0.570000	+	0.886937i	−0.0194030	+	0.0301917i	−0.850820	−	0.525458i	$-0.823894\pi$
$863$	−0.570000	+	0.886937i	−0.0194030	+	0.0301917i	0.831417	+	0.555650i	$0.187530\pi$
$864$		0			0
$865$	0.0629825	−	0.214499i	0.00214147	−	0.00729317i
$866$	9.51976	+	3.81114i	0.323495	+	0.129508i
$867$		0			0
$868$	38.1953	+	27.1988i	1.29643	+	0.923187i
$869$	−11.7313	+	12.3034i	−0.397956	+	0.417365i
$870$		0			0
$871$	−14.8937	+	18.9389i	−0.504653	+	0.641719i
$872$	−2.79795	+	1.79813i	−0.0947505	+	0.0608924i
$873$		0			0
$874$	−3.14869	+	3.79127i	−0.106506	+	0.128242i
$875$	49.6046	+	28.6392i	1.67694	+	0.968182i
$876$		0			0
$877$	−16.0329	+	6.41862i	−0.541394	+	0.216741i	−0.626209	−	0.779655i	$-0.715394\pi$
$877$	−16.0329	+	6.41862i	−0.541394	+	0.216741i	0.0848150	+	0.996397i	$0.472970\pi$
$878$	−0.985195	−	10.3174i	−0.0332487	−	0.348196i
$879$		0			0
$880$	−22.1243	−	2.11261i	−0.745810	−	0.0712162i
$881$	29.7522	+	34.3359i	1.00238	+	1.15681i	0.987612	+	0.156915i	$0.0501550\pi$
$881$	29.7522	+	34.3359i	1.00238	+	1.15681i	0.0147663	+	0.999891i	$0.495300\pi$
$882$		0			0
$883$	−4.39522	−	1.29055i	−0.147911	−	0.0434306i	0.206939	−	0.978354i	$-0.433650\pi$
$883$	−4.39522	−	1.29055i	−0.147911	−	0.0434306i	−0.354850	+	0.934923i	$0.615468\pi$
$884$	−7.92343	−	22.8933i	−0.266494	−	0.769983i
$885$		0			0
$886$	0.329541	−	6.91791i	0.0110711	−	0.232412i
$887$	0.119055	−	0.617717i	0.00399748	−	0.0207409i	−0.979875	−	0.199611i	$-0.936032\pi$
$887$	0.119055	−	0.617717i	0.00399748	−	0.0207409i	0.983873	+	0.178870i	$0.0572442\pi$
$888$		0			0
$889$	−16.3713	+	40.8936i	−0.549076	+	1.37153i
$890$	20.8251	−	18.0450i	0.698057	−	0.604870i
$891$		0			0
$892$	23.4286	−	6.87927i	0.784449	−	0.230335i
$893$	5.04058	+	7.07851i	0.168677	+	0.236873i
$894$		0			0
$895$	−0.200132	+	0.388203i	−0.00668969	+	0.0129762i
$896$	−15.0195	−	26.0145i	−0.501766	−	0.869083i
$897$		0			0
$898$	−0.202608	+	0.350927i	−0.00676111	+	0.0117106i
$899$	−14.9864	−	23.3192i	−0.499823	−	0.777740i
$900$		0			0
$901$	−15.7219	+	34.4261i	−0.523772	+	1.14690i
$902$	1.03468	−	4.26500i	0.0344510	−	0.142009i
$903$		0			0
$904$	−13.4418	−	4.65226i	−0.447069	−	0.154732i
$905$	−36.4451	−	46.3437i	−1.21148	−	1.54052i
$906$		0			0
$907$	8.02706	−	2.77819i	0.266534	−	0.0922484i	−0.190532	−	0.981681i	$-0.561021\pi$
$907$	8.02706	−	2.77819i	0.266534	−	0.0922484i	0.457066	+	0.889433i	$0.348900\pi$
$908$	−6.42352	−	4.12815i	−0.213172	−	0.136997i
$909$		0			0
$910$	7.50517	−	8.66143i	0.248794	−	0.287123i
$911$	−15.7883	+	15.0541i	−0.523090	+	0.498765i	−0.904987	−	0.425440i	$-0.860119\pi$
$911$	−15.7883	+	15.0541i	−0.523090	+	0.498765i	0.381897	+	0.924205i	$0.375271\pi$
$912$		0			0
$913$	−8.23181	+	23.7842i	−0.272433	+	0.787143i
$914$	4.79090	−	6.72788i	0.158469	−	0.222539i
$915$		0			0
$916$	−0.232644	+	0.165665i	−0.00768678	+	0.00547373i
$917$	−3.52762	+	24.5351i	−0.116492	+	0.810221i
$918$		0			0
$919$			46.3980i			1.53053i	0.643715	+	0.765265i	$0.277392\pi$
$919$			46.3980i			1.53053i	−0.643715	+	0.765265i	$0.722608\pi$
$920$	−23.6726	+	17.6152i	−0.780462	+	0.580755i
$921$		0			0
$922$	10.8801	+	5.60910i	0.358318	+	0.184726i
$923$	0.658362	+	1.64451i	0.0216702	+	0.0541296i
$924$		0			0
$925$	52.0915	+	12.6373i	1.71276	+	0.415510i
$926$	−3.18780	+	1.45582i	−0.104758	+	0.0478412i
$927$		0			0
$928$	1.93187	+	13.4365i	0.0634167	+	0.441073i
$929$	10.2684	+	10.7692i	0.336895	+	0.353325i	0.870289	−	0.492542i	$-0.163932\pi$
$929$	10.2684	+	10.7692i	0.336895	+	0.353325i	−0.533394	+	0.845867i	$0.679084\pi$
$930$		0			0
$931$	−2.81015	−	0.133864i	−0.0920989	−	0.00438721i
$932$	−18.9505	−	0.902723i	−0.620744	−	0.0295697i
$933$		0			0
$934$	−0.433127	−	0.454251i	−0.0141724	−	0.0148635i
$935$	−5.56546	−	38.7086i	−0.182010	−	1.26591i
$936$		0			0
$937$	−7.36347	+	3.36278i	−0.240554	+	0.109857i	−0.532045	−	0.846716i	$-0.678576\pi$
$937$	−7.36347	+	3.36278i	−0.240554	+	0.109857i	0.291490	+	0.956574i	$0.405849\pi$
$938$	−11.0102	−	2.67105i	−0.359496	−	0.0872128i
$939$		0			0
$940$	9.23877	+	23.0773i	0.301335	+	0.752699i
$941$	7.56439	+	3.89972i	0.246592	+	0.127127i	0.577093	−	0.816679i	$-0.304187\pi$
$941$	7.56439	+	3.89972i	0.246592	+	0.127127i	−0.330500	+	0.943806i	$0.607217\pi$
$942$		0			0
$943$	12.8119	+	23.6244i	0.417214	+	0.769317i
$944$		−	6.12627i		−	0.199393i
$945$		0			0
$946$	−0.178543	+	1.24180i	−0.00580495	+	0.0403743i
$947$	34.6828	−	24.6975i	1.12704	−	0.802561i	0.144664	−	0.989481i	$-0.453790\pi$
$947$	34.6828	−	24.6975i	1.12704	−	0.802561i	0.982375	+	0.186920i	$0.0598505\pi$
$948$		0			0
$949$	−5.28450	+	7.42105i	−0.171542	+	0.240897i
$950$	−3.41464	+	9.86594i	−0.110785	+	0.320093i
$951$		0			0
$952$	17.2562	−	16.4538i	0.559277	−	0.533270i
$953$	−13.6947	+	15.8045i	−0.443615	+	0.511960i	−0.932886	−	0.360173i	$-0.882718\pi$
$953$	−13.6947	+	15.8045i	−0.443615	+	0.511960i	0.489270	+	0.872132i	$0.337263\pi$
$954$		0			0
$955$	10.1579	+	6.52807i	0.328701	+	0.211243i
$956$	15.2084	−	5.26368i	0.491875	−	0.170239i
$957$		0			0
$958$	3.41282	+	4.33975i	0.110263	+	0.140211i
$959$	19.7683	+	6.84188i	0.638352	+	0.220936i
$960$		0			0
$961$	11.7362	−	48.3772i	0.378586	−	1.56055i
$962$	2.26269	−	4.95459i	0.0729520	−	0.159742i
$963$		0			0
$964$	−21.6034	−	33.6155i	−0.695798	−	1.08268i
$965$	−19.2991	+	33.4270i	−0.621259	+	1.07605i
$966$		0			0
$967$	16.7702	+	29.0469i	0.539295	+	0.934086i	0.998942	+	0.0459843i	$0.0146424\pi$
$967$	16.7702	+	29.0469i	0.539295	+	0.934086i	−0.459648	+	0.888101i	$0.652024\pi$
$968$	5.35661	−	10.3904i	0.172168	−	0.333959i
$969$		0			0
$970$	−16.7263	−	23.4888i	−0.537048	−	0.754179i
$971$	−13.7785	+	4.04573i	−0.442173	+	0.129834i	−0.495238	−	0.868757i	$-0.664919\pi$
$971$	−13.7785	+	4.04573i	−0.442173	+	0.129834i	0.0530649	+	0.998591i	$0.483101\pi$
$972$		0			0
$973$	21.8882	−	18.9662i	0.701702	−	0.608028i
$974$	5.11275	−	12.7710i	0.163823	−	0.409210i
$975$		0			0
$976$	7.82638	−	40.6071i	0.250516	−	1.29980i
$977$	2.15010	−	45.1362i	0.0687878	−	1.44403i	−0.655843	−	0.754897i	$-0.727687\pi$
$977$	2.15010	−	45.1362i	0.0687878	−	1.44403i	0.724631	−	0.689137i	$-0.242010\pi$
$978$		0			0
$979$	10.6476	+	30.7641i	0.340297	+	0.983224i
$980$	−7.72180	−	2.26733i	−0.246664	−	0.0724271i
$981$		0			0
$982$	10.0464	+	11.5942i	0.320593	+	0.369984i
$983$	56.8866	+	5.43201i	1.81440	+	0.173254i	0.946333	−	0.323192i	$-0.104756\pi$
$983$	56.8866	+	5.43201i	1.81440	+	0.173254i	0.868067	+	0.496447i	$0.165362\pi$
$984$		0			0
$985$	9.00097	+	94.2624i	0.286795	+	3.00345i
$986$	−6.25196	+	2.50291i	−0.199103	+	0.0797088i
$987$		0			0
$988$	−9.87362	−	5.70054i	−0.314122	−	0.181358i
$989$	−4.28781	−	6.37460i	−0.136344	−	0.202701i
$990$		0			0
$991$	10.5824	−	6.80090i	0.336161	−	0.216038i	−0.361659	−	0.932310i	$-0.617790\pi$
$991$	10.5824	−	6.80090i	0.336161	−	0.216038i	0.697821	+	0.716273i	$0.254153\pi$
$992$	−24.4538	+	31.0955i	−0.776409	+	0.987284i
$993$		0			0
$994$	−0.574813	+	0.602846i	−0.0182319	+	0.0191211i
$995$	21.3824	+	15.2263i	0.677867	+	0.482707i
$996$		0			0
$997$	−9.81201	−	3.92814i	−0.310749	−	0.124405i	0.211046	−	0.977476i	$-0.432313\pi$
$997$	−9.81201	−	3.92814i	−0.310749	−	0.124405i	−0.521795	+	0.853071i	$0.674737\pi$
$998$	2.31747	−	7.89259i	0.0733583	−	0.249836i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	621.2.s.a.494.12		440
3.2	odd	2		207.2.o.a.11.11	✓	440
9.4	even	3		207.2.o.a.149.11	yes	440
9.5	odd	6	inner	621.2.s.a.287.12		440
23.21	odd	22	inner	621.2.s.a.251.12		440
69.44	even	22		207.2.o.a.182.11	yes	440
207.67	odd	66		207.2.o.a.113.11	yes	440
207.113	even	66	inner	621.2.s.a.44.12		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.11	✓	440	3.2	odd	2
207.2.o.a.113.11	yes	440	207.67	odd	66
207.2.o.a.149.11	yes	440	9.4	even	3
207.2.o.a.182.11	yes	440	69.44	even	22
621.2.s.a.44.12		440	207.113	even	66	inner
621.2.s.a.251.12		440	23.21	odd	22	inner
621.2.s.a.287.12		440	9.5	odd	6	inner
621.2.s.a.494.12		440	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 621 = 3^{3} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	621.s (of order \(66\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.412156 - 0.0196334i) q^{2} +(-1.82146 + 0.173928i) q^{4} +(-2.81788 - 2.68684i) q^{5} +(0.539603 + 2.79973i) q^{7} +(-1.56416 + 0.224892i) q^{8} +(-1.21416 - 1.05207i) q^{10} +(1.68703 - 0.869723i) q^{11} +(2.45673 + 0.473497i) q^{13} +(0.277369 + 1.14333i) q^{14} +(2.95309 - 0.569162i) q^{16} +(2.19831 + 4.81363i) q^{17} +(2.26539 + 1.03457i) q^{19} +(5.59996 + 4.40386i) q^{20} +(0.678243 - 0.391584i) q^{22} +(-1.47338 + 4.56390i) q^{23} +(0.483411 + 10.1480i) q^{25} +(1.02185 + 0.146921i) q^{26} +(-1.46982 - 5.00573i) q^{28} +(-0.293166 + 3.07018i) q^{29} +(-7.06488 + 5.55588i) q^{31} +(4.27735 - 1.03767i) q^{32} +(1.00056 + 1.94081i) q^{34} +(6.00189 - 9.33912i) q^{35} +(1.48644 - 5.06234i) q^{37} +(0.954008 + 0.381927i) q^{38} +(5.01185 + 3.56892i) q^{40} +(3.86707 - 4.05566i) q^{41} +(-0.990237 + 1.25919i) q^{43} +(-2.92158 + 1.87758i) q^{44} +(-0.517659 + 1.90997i) q^{46} +(3.02178 + 1.74463i) q^{47} +(-1.04873 + 0.419849i) q^{49} +(0.398482 + 4.17309i) q^{50} +(-4.55719 - 0.435159i) q^{52} +(4.68343 + 5.40497i) q^{53} +(-7.09064 - 2.08200i) q^{55} +(-1.47366 - 4.25786i) q^{56} +(-0.0605523 + 1.27115i) q^{58} +(0.385512 - 2.00023i) q^{59} +(5.11063 - 12.7657i) q^{61} +(-2.80275 + 2.42860i) q^{62} +(-4.02867 + 1.18292i) q^{64} +(-5.65057 - 7.93511i) q^{65} +(-4.41270 + 8.55943i) q^{67} +(-4.84136 - 8.38547i) q^{68} +(2.29036 - 3.96701i) q^{70} +(0.382777 + 0.595613i) q^{71} +(-1.51265 + 3.31223i) q^{73} +(0.513254 - 2.11566i) q^{74} +(-4.30625 - 1.49041i) q^{76} +(3.34531 + 4.25391i) q^{77} +(-8.46405 + 2.92944i) q^{79} +(-9.85069 - 6.33066i) q^{80} +(1.51421 - 1.74749i) q^{82} +(-9.59700 + 9.15072i) q^{83} +(6.73889 - 19.4707i) q^{85} +(-0.383410 + 0.538424i) q^{86} +(-2.44318 + 1.73978i) q^{88} +(-2.44096 + 16.9773i) q^{89} +7.13369i q^{91} +(1.88991 - 8.56920i) q^{92} +(1.27970 + 0.659731i) q^{94} +(-3.60387 - 9.00204i) q^{95} +(17.4427 + 4.23155i) q^{97} +(-0.423998 + 0.193633i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q + 27 q^{2} - 29 q^{4} + 33 q^{5} - 11 q^{7} - 44 q^{10} + 33 q^{11} - 9 q^{13} + 33 q^{14} + 3 q^{16} - 44 q^{19} + 33 q^{20} + 27 q^{23} + 11 q^{25} - 44 q^{28} - 27 q^{29} - 3 q^{31} + 33 q^{32}+ \cdots + 22 q^{97}+O(q^{100}) \) 440 * q + 27 * q^2 - 29 * q^4 + 33 * q^5 - 11 * q^7 - 44 * q^10 + 33 * q^11 - 9 * q^13 + 33 * q^14 + 3 * q^16 - 44 * q^19 + 33 * q^20 + 27 * q^23 + 11 * q^25 - 44 * q^28 - 27 * q^29 - 3 * q^31 + 33 * q^32 - 11 * q^34 - 44 * q^37 + 33 * q^38 - 77 * q^40 - 9 * q^41 - 11 * q^43 - 36 * q^46 + 120 * q^47 + 35 * q^49 + 3 * q^50 - 38 * q^52 - 44 * q^55 - 165 * q^56 - 10 * q^58 + 9 * q^59 - 11 * q^61 - 22 * q^64 - 198 * q^65 - 11 * q^67 - 70 * q^70 - 36 * q^73 - 231 * q^74 - 11 * q^76 - 39 * q^77 - 11 * q^79 - 10 * q^82 - 66 * q^83 + q^85 + 33 * q^86 - 99 * q^88 - 63 * q^92 - 42 * q^94 + 93 * q^95 + 22 * q^97

Introduction

L-functions

Modular forms

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Database

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