LMFDB - Embedded newform 504.2.bs.a.257.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(257,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5, 5]))

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

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

chi := DirichletCharacter("504.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bs (of order $6$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			257.4
Character	$\chi$	$=$	504.257
Dual form			504.2.bs.a.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.54049 + 0.791772i) q^{3} +(-0.905867 - 1.56901i) q^{5} +(-2.60735 + 0.449161i) q^{7} +(1.74619 - 2.43943i) q^{9} +O(q^{10})$	\(q+(-1.54049 + 0.791772i) q^{3} +(-0.905867 - 1.56901i) q^{5} +(-2.60735 + 0.449161i) q^{7} +(1.74619 - 2.43943i) q^{9} +(-0.221585 - 0.127932i) q^{11} +(5.77765 + 3.33573i) q^{13} +(2.63777 + 1.69979i) q^{15} +(1.99857 + 3.46163i) q^{17} +(1.24687 + 0.719882i) q^{19} +(3.66095 - 2.75635i) q^{21} +(4.90746 - 2.83332i) q^{23} +(0.858809 - 1.48750i) q^{25} +(-0.758514 + 5.14049i) q^{27} +(-4.18486 + 2.41613i) q^{29} +10.1688i q^{31} +(0.442641 + 0.0216328i) q^{33} +(3.06665 + 3.68407i) q^{35} +(-1.65567 + 2.86771i) q^{37} +(-11.5415 - 0.564058i) q^{39} +(5.10089 - 8.83499i) q^{41} +(1.12248 + 1.94419i) q^{43} +(-5.40930 - 0.529993i) q^{45} +11.9418 q^{47} +(6.59651 - 2.34224i) q^{49} +(-5.81960 - 3.75018i) q^{51} +(3.97466 - 2.29477i) q^{53} +0.463558i q^{55} +(-2.49077 - 0.121729i) q^{57} -5.11151 q^{59} +9.93297i q^{61} +(-3.45723 + 7.14476i) q^{63} -12.0869i q^{65} +1.92427 q^{67} +(-5.31652 + 8.25028i) q^{69} -7.31241i q^{71} +(-2.47807 + 1.43071i) q^{73} +(-0.145221 + 2.97145i) q^{75} +(0.635210 + 0.234036i) q^{77} -3.66306 q^{79} +(-2.90162 - 8.51943i) q^{81} +(-2.68261 - 4.64642i) q^{83} +(3.62089 - 6.27156i) q^{85} +(4.53370 - 7.03548i) q^{87} +(0.378446 - 0.655488i) q^{89} +(-16.5626 - 6.10230i) q^{91} +(-8.05141 - 15.6650i) q^{93} -2.60847i q^{95} +(-4.21765 + 2.43506i) q^{97} +(-0.699011 + 0.317146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{9}+O(q^{10}) $ 48 * q - 4 * q^9	$ 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) $ 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$	−1.54049	+	0.791772i	−0.889400	+	0.457130i
$3$	−1.54049	+	0.791772i	−0.889400	+	0.457130i
$4$		0			0
$5$	−0.905867	−	1.56901i	−0.405116	−	0.701682i	0.589219	−	0.807974i	$-0.299436\pi$
$5$	−0.905867	−	1.56901i	−0.405116	−	0.701682i	−0.994335	+	0.106292i	$0.966102\pi$
$6$		0			0
$7$	−2.60735	+	0.449161i	−0.985484	+	0.169767i
$7$	−2.60735	+	0.449161i	−0.985484	+	0.169767i
$8$		0			0
$9$	1.74619	−	2.43943i	0.582064	−	0.813143i
$10$		0			0
$11$	−0.221585	−	0.127932i	−0.0668103	−	0.0385730i	0.466223	−	0.884667i	$-0.345615\pi$
$11$	−0.221585	−	0.127932i	−0.0668103	−	0.0385730i	−0.533033	+	0.846094i	$0.678948\pi$
$12$		0			0
$13$	5.77765	+	3.33573i	1.60243	+	0.925165i	0.990999	+	0.133869i	$0.0427400\pi$
$13$	5.77765	+	3.33573i	1.60243	+	0.925165i	0.611433	+	0.791296i	$0.290593\pi$
$14$		0			0
$15$	2.63777	+	1.69979i	0.681070	+	0.438885i
$16$		0			0
$17$	1.99857	+	3.46163i	0.484725	+	0.839569i	0.999846	−	0.0175487i	$-0.00558621\pi$
$17$	1.99857	+	3.46163i	0.484725	+	0.839569i	−0.515121	+	0.857118i	$0.672253\pi$
$18$		0			0
$19$	1.24687	+	0.719882i	0.286052	+	0.165152i	0.636160	−	0.771557i	$-0.280522\pi$
$19$	1.24687	+	0.719882i	0.286052	+	0.165152i	−0.350108	+	0.936709i	$0.613855\pi$
$20$		0			0
$21$	3.66095	−	2.75635i	0.798884	−	0.601485i
$22$		0			0
$23$	4.90746	−	2.83332i	1.02328	−	0.590789i	0.108225	−	0.994126i	$-0.465483\pi$
$23$	4.90746	−	2.83332i	1.02328	−	0.590789i	0.915051	+	0.403338i	$0.132150\pi$
$24$		0			0
$25$	0.858809	−	1.48750i	0.171762	−	0.297500i
$26$		0			0
$27$	−0.758514	+	5.14049i	−0.145976	+	0.989288i
$28$		0			0
$29$	−4.18486	+	2.41613i	−0.777110	+	0.448665i	−0.835405	−	0.549635i	$-0.814767\pi$
$29$	−4.18486	+	2.41613i	−0.777110	+	0.448665i	0.0582952	+	0.998299i	$0.481434\pi$
$30$		0			0
$31$			10.1688i			1.82638i	0.407536	+	0.913189i	$0.366388\pi$
$31$			10.1688i			1.82638i	−0.407536	+	0.913189i	$0.633612\pi$
$32$		0			0
$33$	0.442641	+	0.0216328i	0.0770540	+	0.00376579i
$34$		0			0
$35$	3.06665	+	3.68407i	0.518358	+	0.622721i
$36$		0			0
$37$	−1.65567	+	2.86771i	−0.272191	+	0.471448i	−0.969423	−	0.245398i	$-0.921082\pi$
$37$	−1.65567	+	2.86771i	−0.272191	+	0.471448i	0.697232	+	0.716846i	$0.254415\pi$
$38$		0			0
$39$	−11.5415	−	0.564058i	−1.84812	−	0.0903216i
$40$		0			0
$41$	5.10089	−	8.83499i	0.796624	−	1.37979i	−0.125178	−	0.992134i	$-0.539950\pi$
$41$	5.10089	−	8.83499i	0.796624	−	1.37979i	0.921803	−	0.387660i	$-0.126716\pi$
$42$		0			0
$43$	1.12248	+	1.94419i	0.171176	+	0.296486i	0.938831	−	0.344377i	$-0.111910\pi$
$43$	1.12248	+	1.94419i	0.171176	+	0.296486i	−0.767655	+	0.640863i	$0.778577\pi$
$44$		0			0
$45$	−5.40930	−	0.529993i	−0.806371	−	0.0790068i
$46$		0			0
$47$	11.9418			1.74190			0.870948	−	0.491375i	$-0.163505\pi$
$47$	11.9418			1.74190			0.870948	+	0.491375i	$0.163505\pi$
$48$		0			0
$49$	6.59651	−	2.34224i	0.942358	−	0.334605i
$50$		0			0
$51$	−5.81960	−	3.75018i	−0.814907	−	0.525130i
$52$		0			0
$53$	3.97466	−	2.29477i	0.545962	−	0.315211i	−0.201530	−	0.979482i	$-0.564591\pi$
$53$	3.97466	−	2.29477i	0.545962	−	0.315211i	0.747492	+	0.664271i	$0.231258\pi$
$54$		0			0
$55$			0.463558i			0.0625061i
$56$		0			0
$57$	−2.49077	−	0.121729i	−0.329911	−	0.0161234i
$58$		0			0
$59$	−5.11151			−0.665462			−0.332731	−	0.943022i	$-0.607970\pi$
$59$	−5.11151			−0.665462			−0.332731	+	0.943022i	$0.607970\pi$
$60$		0			0
$61$			9.93297i			1.27179i	0.771777	+	0.635893i	$0.219368\pi$
$61$			9.93297i			1.27179i	−0.771777	+	0.635893i	$0.780632\pi$
$62$		0			0
$63$	−3.45723	+	7.14476i	−0.435571	+	0.900155i
$64$		0			0
$65$		−	12.0869i		−	1.49920i
$66$		0			0
$67$	1.92427			0.235087			0.117544	−	0.993068i	$-0.462498\pi$
$67$	1.92427			0.235087			0.117544	+	0.993068i	$0.462498\pi$
$68$		0			0
$69$	−5.31652	+	8.25028i	−0.640034	+	0.993217i
$70$		0			0
$71$		−	7.31241i		−	0.867823i	−0.900955	−	0.433912i	$-0.857133\pi$
$71$		−	7.31241i		−	0.867823i	0.900955	−	0.433912i	$-0.142867\pi$
$72$		0			0
$73$	−2.47807	+	1.43071i	−0.290036	+	0.167452i	−0.637958	−	0.770071i	$-0.720221\pi$
$73$	−2.47807	+	1.43071i	−0.290036	+	0.167452i	0.347922	+	0.937523i	$0.386887\pi$
$74$		0			0
$75$	−0.145221	+	2.97145i	−0.0167687	+	0.343114i
$76$		0			0
$77$	0.635210	+	0.234036i	0.0723889	+	0.0266709i
$78$		0			0
$79$	−3.66306			−0.412127			−0.206063	−	0.978539i	$-0.566065\pi$
$79$	−3.66306			−0.412127			−0.206063	+	0.978539i	$0.566065\pi$
$80$		0			0
$81$	−2.90162	−	8.51943i	−0.322402	−	0.946603i
$82$		0			0
$83$	−2.68261	−	4.64642i	−0.294455	−	0.510011i	0.680403	−	0.732838i	$-0.261805\pi$
$83$	−2.68261	−	4.64642i	−0.294455	−	0.510011i	−0.974858	+	0.222827i	$0.928471\pi$
$84$		0			0
$85$	3.62089	−	6.27156i	0.392740	−	0.680246i
$86$		0			0
$87$	4.53370	−	7.03548i	0.486063	−	0.754282i
$88$		0			0
$89$	0.378446	−	0.655488i	0.0401152	−	0.0694815i	−0.845271	−	0.534338i	$-0.820561\pi$
$89$	0.378446	−	0.655488i	0.0401152	−	0.0694815i	0.885386	+	0.464857i	$0.153894\pi$
$90$		0			0
$91$	−16.5626	−	6.10230i	−1.73623	−	0.639695i
$92$		0			0
$93$	−8.05141	−	15.6650i	−0.834892	−	1.62438i
$94$		0			0
$95$		−	2.60847i		−	0.267624i
$96$		0			0
$97$	−4.21765	+	2.43506i	−0.428237	+	0.247243i	−0.698595	−	0.715517i	$-0.746191\pi$
$97$	−4.21765	+	2.43506i	−0.428237	+	0.247243i	0.270358	+	0.962760i	$0.412858\pi$
$98$		0			0
$99$	−0.699011	+	0.317146i	−0.0702532	+	0.0318744i
$100$		0			0
$101$	−8.20725	+	14.2154i	−0.816652	+	1.41448i	0.0914844	+	0.995807i	$0.470839\pi$
$101$	−8.20725	+	14.2154i	−0.816652	+	1.41448i	−0.908136	+	0.418675i	$0.862494\pi$
$102$		0			0
$103$	16.7999	−	9.69946i	1.65535	−	0.955716i	0.680528	−	0.732722i	$-0.261750\pi$
$103$	16.7999	−	9.69946i	1.65535	−	0.955716i	0.974820	−	0.222994i	$-0.0715830\pi$
$104$		0			0
$105$	−7.64107	−	3.24717i	−0.745692	−	0.316891i
$106$		0			0
$107$	6.47695	+	3.73947i	0.626150	+	0.361508i	0.779260	−	0.626701i	$-0.215595\pi$
$107$	6.47695	+	3.73947i	0.626150	+	0.361508i	−0.153109	+	0.988209i	$0.548929\pi$
$108$		0			0
$109$	4.26712	+	7.39087i	0.408716	+	0.707917i	0.994746	−	0.102372i	$-0.0326432\pi$
$109$	4.26712	+	7.39087i	0.408716	+	0.707917i	−0.586030	+	0.810289i	$0.699310\pi$
$110$		0			0
$111$	0.279968	−	5.72858i	0.0265733	−	0.543733i
$112$		0			0
$113$	1.22966	+	0.709943i	0.115676	+	0.0667858i	0.556722	−	0.830699i	$-0.312059\pi$
$113$	1.22966	+	0.709943i	0.115676	+	0.0667858i	−0.441045	+	0.897485i	$0.645392\pi$
$114$		0			0
$115$	−8.89101	−	5.13323i	−0.829091	−	0.478676i
$116$		0			0
$117$	18.2262	−	8.26934i	1.68501	−	0.764501i
$118$		0			0
$119$	−6.76580	−	8.12799i	−0.620220	−	0.745092i
$120$		0			0
$121$	−5.46727	−	9.46958i	−0.497024	−	0.860871i
$122$		0			0
$123$	−0.862539	+	17.6489i	−0.0777726	+	1.59135i
$124$		0			0
$125$	−12.1705			−1.08857
$126$		0			0
$127$	−5.17294			−0.459024			−0.229512	−	0.973306i	$-0.573713\pi$
$127$	−5.17294			−0.459024			−0.229512	+	0.973306i	$0.573713\pi$
$128$		0			0
$129$	−3.26851	−	2.10624i	−0.287776	−	0.185445i
$130$		0			0
$131$	−3.18262	−	5.51246i	−0.278067	−	0.481625i	0.692838	−	0.721094i	$-0.256360\pi$
$131$	−3.18262	−	5.51246i	−0.278067	−	0.481625i	−0.970904	+	0.239468i	$0.923027\pi$
$132$		0			0
$133$	−3.57437	−	1.31694i	−0.309937	−	0.114193i
$134$		0			0
$135$	8.75259	−	3.46649i	0.753303	−	0.298348i
$136$		0			0
$137$	−0.0421060	−	0.0243099i	−0.00359736	−	0.00207693i	0.498200	−	0.867062i	$-0.333994\pi$
$137$	−0.0421060	−	0.0243099i	−0.00359736	−	0.00207693i	−0.501798	+	0.864985i	$0.667328\pi$
$138$		0			0
$139$	−2.95962	−	1.70874i	−0.251032	−	0.144933i	0.369205	−	0.929348i	$-0.379630\pi$
$139$	−2.95962	−	1.70874i	−0.251032	−	0.144933i	−0.620237	+	0.784415i	$0.712963\pi$
$140$		0			0
$141$	−18.3962	+	9.45522i	−1.54924	+	0.796273i
$142$		0			0
$143$	−0.853493	−	1.47829i	−0.0713727	−	0.123621i
$144$		0			0
$145$	7.58186	+	4.37739i	0.629640	+	0.363523i
$146$		0			0
$147$	−8.30731	+	8.83111i	−0.685175	+	0.728378i
$148$		0			0
$149$	8.56669	−	4.94598i	0.701810	−	0.405190i	−0.106211	−	0.994344i	$-0.533872\pi$
$149$	8.56669	−	4.94598i	0.701810	−	0.405190i	0.808021	+	0.589153i	$0.200539\pi$
$150$		0			0
$151$	−4.24282	+	7.34878i	−0.345276	+	0.598035i	−0.985404	−	0.170233i	$-0.945548\pi$
$151$	−4.24282	+	7.34878i	−0.345276	+	0.598035i	0.640128	+	0.768268i	$0.278881\pi$
$152$		0			0
$153$	11.9343	+	1.16930i	0.964831	+	0.0945323i
$154$		0			0
$155$	15.9550	−	9.21163i	1.28154	−	0.739896i
$156$		0			0
$157$			18.4844i			1.47521i	0.675230	+	0.737607i	$0.264044\pi$
$157$			18.4844i			1.47521i	−0.675230	+	0.737607i	$0.735956\pi$
$158$		0			0
$159$	−4.30598	+	6.68210i	−0.341486	+	0.529925i
$160$		0			0
$161$	−11.5228	+	9.59169i	−0.908126	+	0.755931i
$162$		0			0
$163$	3.81360	−	6.60534i	0.298704	−	0.517370i	−0.677136	−	0.735858i	$-0.736779\pi$
$163$	3.81360	−	6.60534i	0.298704	−	0.517370i	0.975840	+	0.218488i	$0.0701124\pi$
$164$		0			0
$165$	−0.367032	−	0.714104i	−0.0285734	−	0.0555929i
$166$		0			0
$167$	−8.86874	+	15.3611i	−0.686284	+	1.18868i	0.286748	+	0.958006i	$0.407426\pi$
$167$	−8.86874	+	15.3611i	−0.686284	+	1.18868i	−0.973032	+	0.230672i	$0.925908\pi$
$168$		0			0
$169$	15.7542	+	27.2870i	1.21186	+	2.09900i
$170$		0			0
$171$	3.93338	−	1.78460i	0.300793	−	0.136472i
$172$		0			0
$173$	−14.0253			−1.06633			−0.533163	−	0.846013i	$-0.678997\pi$
$173$	−14.0253			−1.06633			−0.533163	+	0.846013i	$0.678997\pi$
$174$		0			0
$175$	−1.57108	+	4.26417i	−0.118763	+	0.322341i
$176$		0			0
$177$	7.87420	−	4.04715i	0.591861	−	0.304202i
$178$		0			0
$179$	8.29501	−	4.78913i	0.619998	−	0.357956i	−0.156870	−	0.987619i	$-0.550140\pi$
$179$	8.29501	−	4.78913i	0.619998	−	0.357956i	0.776868	+	0.629663i	$0.216807\pi$
$180$		0			0
$181$		−	1.57861i		−	0.117337i	−0.998278	−	0.0586687i	$-0.981314\pi$
$181$		−	1.57861i		−	0.117337i	0.998278	−	0.0586687i	$-0.0186856\pi$
$182$		0			0
$183$	−7.86465	−	15.3016i	−0.581372	−	1.13113i
$184$		0			0
$185$	5.99928			0.441076
$186$		0			0
$187$		−	1.02273i		−	0.0747892i
$188$		0			0
$189$	−0.331198	−	13.7437i	−0.0240911	−	0.999710i
$190$		0			0
$191$			17.4403i			1.26193i	0.775810	+	0.630967i	$0.217342\pi$
$191$			17.4403i			1.26193i	−0.775810	+	0.630967i	$0.782658\pi$
$192$		0			0
$193$	23.8526			1.71694			0.858472	−	0.512860i	$-0.171414\pi$
$193$	23.8526			1.71694			0.858472	+	0.512860i	$0.171414\pi$
$194$		0			0
$195$	9.57008	+	18.6197i	0.685328	+	1.33339i
$196$		0			0
$197$		−	19.1271i		−	1.36275i	−0.731935	−	0.681374i	$-0.761383\pi$
$197$		−	19.1271i		−	1.36275i	0.731935	−	0.681374i	$-0.238617\pi$
$198$		0			0
$199$	5.15196	−	2.97449i	0.365213	−	0.210856i	−0.306152	−	0.951983i	$-0.599042\pi$
$199$	5.15196	−	2.97449i	0.365213	−	0.210856i	0.671365	+	0.741127i	$0.265708\pi$
$200$		0			0
$201$	−2.96431	+	1.52358i	−0.209086	+	0.107465i
$202$		0			0
$203$	9.82616	−	8.17937i	0.689661	−	0.574079i
$204$		0			0
$205$	−18.4829			−1.29090
$206$		0			0
$207$	1.65768	−	16.9189i	0.115217	−	1.17595i
$208$		0			0
$209$	−0.184192	−	0.319030i	−0.0127408	−	0.0220678i
$210$		0			0
$211$	−5.86415	+	10.1570i	−0.403704	+	0.699237i	−0.994170	−	0.107826i	$-0.965611\pi$
$211$	−5.86415	+	10.1570i	−0.403704	+	0.699237i	0.590465	+	0.807063i	$0.298944\pi$
$212$		0			0
$213$	5.78976	+	11.2647i	0.396708	+	0.771842i
$214$		0			0
$215$	2.03363	−	3.52235i	0.138692	−	0.240222i
$216$		0			0
$217$	−4.56745	−	26.5137i	−0.310059	−	1.79987i
$218$		0			0
$219$	2.68463	−	4.16606i	0.181411	−	0.281516i
$220$		0			0
$221$			26.6668i			1.79380i
$222$		0			0
$223$	16.0209	−	9.24969i	1.07284	−	0.619405i	0.143885	−	0.989594i	$-0.454040\pi$
$223$	16.0209	−	9.24969i	1.07284	−	0.619405i	0.928956	+	0.370189i	$0.120707\pi$
$224$		0			0
$225$	−2.12900	−	4.69246i	−0.141934	−	0.312831i
$226$		0			0
$227$	−0.338772	+	0.586771i	−0.0224851	+	0.0389454i	−0.877049	−	0.480401i	$-0.840491\pi$
$227$	−0.338772	+	0.586771i	−0.0224851	+	0.0389454i	0.854564	+	0.519346i	$0.173825\pi$
$228$		0			0
$229$	0.334692	−	0.193234i	0.0221171	−	0.0127693i	−0.488901	−	0.872339i	$-0.662602\pi$
$229$	0.334692	−	0.193234i	0.0221171	−	0.0127693i	0.511018	+	0.859570i	$0.329269\pi$
$230$		0			0
$231$	−1.16384	+	0.142413i	−0.0765748	+	0.00937009i
$232$		0			0
$233$	3.35520	+	1.93712i	0.219806	+	0.126905i	0.605861	−	0.795571i	$-0.292829\pi$
$233$	3.35520	+	1.93712i	0.219806	+	0.126905i	−0.386054	+	0.922476i	$0.626162\pi$
$234$		0			0
$235$	−10.8177	−	18.7368i	−0.705671	−	1.22226i
$236$		0			0
$237$	5.64290	−	2.90031i	0.366546	−	0.188395i
$238$		0			0
$239$	−9.97301	−	5.75792i	−0.645100	−	0.372449i	0.141476	−	0.989942i	$-0.454815\pi$
$239$	−9.97301	−	5.75792i	−0.645100	−	0.372449i	−0.786576	+	0.617493i	$0.788148\pi$
$240$		0			0
$241$	−10.2142	−	5.89716i	−0.657953	−	0.379869i	0.133544	−	0.991043i	$-0.457364\pi$
$241$	−10.2142	−	5.89716i	−0.657953	−	0.379869i	−0.791497	+	0.611174i	$0.790698\pi$
$242$		0			0
$243$	11.2153	+	10.8266i	0.719465	+	0.694529i
$244$		0			0
$245$	−9.65055	−	8.22822i	−0.616551	−	0.525682i
$246$		0			0
$247$	4.80267	+	8.31846i	0.305586	+	0.529291i
$248$		0			0
$249$	7.81143	+	5.03373i	0.495030	+	0.319000i
$250$		0			0
$251$	9.76523			0.616376			0.308188	−	0.951326i	$-0.400277\pi$
$251$	9.76523			0.616376			0.308188	+	0.951326i	$0.400277\pi$
$252$		0			0
$253$	−1.44989			−0.0911539
$254$		0			0
$255$	−0.612277	+	12.5282i	−0.0383423	+	0.784544i
$256$		0			0
$257$	7.07806	+	12.2596i	0.441517	+	0.764730i	0.997802	−	0.0662613i	$-0.0211071\pi$
$257$	7.07806	+	12.2596i	0.441517	+	0.764730i	−0.556285	+	0.830992i	$0.687774\pi$
$258$		0			0
$259$	3.02885	−	8.22077i	0.188203	−	0.510814i
$260$		0			0
$261$	−1.41360	+	14.4277i	−0.0874997	+	0.893053i
$262$		0			0
$263$	8.91828	+	5.14897i	0.549925	+	0.317499i	0.749092	−	0.662466i	$-0.230490\pi$
$263$	8.91828	+	5.14897i	0.549925	+	0.317499i	−0.199167	+	0.979966i	$0.563824\pi$
$264$		0			0
$265$	−7.20104	−	4.15752i	−0.442356	−	0.255395i
$266$		0			0
$267$	−0.0639937	+	1.30941i	−0.00391635	+	0.0801347i
$268$		0			0
$269$	3.95947	+	6.85801i	0.241413	+	0.418140i	0.961117	−	0.276141i	$-0.0890557\pi$
$269$	3.95947	+	6.85801i	0.241413	+	0.418140i	−0.719704	+	0.694281i	$0.755722\pi$
$270$		0			0
$271$	−9.45707	−	5.46004i	−0.574476	−	0.331674i	0.184459	−	0.982840i	$-0.440947\pi$
$271$	−9.45707	−	5.46004i	−0.574476	−	0.331674i	−0.758935	+	0.651166i	$0.774280\pi$
$272$		0			0
$273$	30.3461	−	3.71331i	1.83663	−	0.224740i
$274$		0			0
$275$	−0.380598	+	0.219738i	−0.0229509	+	0.0132507i
$276$		0			0
$277$	−6.41021	+	11.1028i	−0.385152	+	0.667103i	−0.991790	−	0.127875i	$-0.959184\pi$
$277$	−6.41021	+	11.1028i	−0.385152	+	0.667103i	0.606638	+	0.794978i	$0.292518\pi$
$278$		0			0
$279$	24.8062	+	17.7568i	1.48511	+	1.06307i
$280$		0			0
$281$	−18.3380	+	10.5874i	−1.09395	+	0.631593i	−0.934626	−	0.355633i	$-0.884265\pi$
$281$	−18.3380	+	10.5874i	−1.09395	+	0.631593i	−0.159326	+	0.987226i	$0.550932\pi$
$282$		0			0
$283$		−	25.6829i		−	1.52669i	−0.645991	−	0.763345i	$-0.723556\pi$
$283$		−	25.6829i		−	1.52669i	0.645991	−	0.763345i	$-0.276444\pi$
$284$		0			0
$285$	2.06532	+	4.01831i	0.122339	+	0.238024i
$286$		0			0
$287$	−9.33144	+	25.3270i	−0.550818	+	1.49501i
$288$		0			0
$289$	0.511404	−	0.885777i	0.0300826	−	0.0521046i
$290$		0			0
$291$	4.56922	−	7.09060i	0.267852	−	0.415658i
$292$		0			0
$293$	−14.4817	+	25.0831i	−0.846031	+	1.46537i	0.0386925	+	0.999251i	$0.487681\pi$
$293$	−14.4817	+	25.0831i	−0.846031	+	1.46537i	−0.884723	+	0.466117i	$0.845653\pi$
$294$		0			0
$295$	4.63035	+	8.02000i	0.269589	+	0.466942i
$296$		0			0
$297$	0.825709	−	1.04202i	0.0479125	−	0.0604639i
$298$		0			0
$299$	37.8048			2.18631
$300$		0			0
$301$	−3.79994	−	4.56499i	−0.219025	−	0.263122i
$302$		0			0
$303$	1.38781	−	28.3968i	0.0797277	−	1.63136i
$304$		0			0
$305$	15.5849	−	8.99795i	0.892389	−	0.515221i
$306$		0			0
$307$		−	28.0634i		−	1.60167i	−0.598888	−	0.800833i	$-0.704391\pi$
$307$		−	28.0634i		−	1.60167i	0.598888	−	0.800833i	$-0.295609\pi$
$308$		0			0
$309$	−18.2003	+	28.2436i	−1.03538	+	1.60672i
$310$		0			0
$311$	−7.91947			−0.449072			−0.224536	−	0.974466i	$-0.572087\pi$
$311$	−7.91947			−0.449072			−0.224536	+	0.974466i	$0.572087\pi$
$312$		0			0
$313$			11.7829i			0.666008i	0.942925	+	0.333004i	$0.108062\pi$
$313$			11.7829i			0.666008i	−0.942925	+	0.333004i	$0.891938\pi$
$314$		0			0
$315$	14.3420	−	1.04777i	0.808079	−	0.0590352i
$316$		0			0
$317$			16.5897i			0.931769i	0.884846	+	0.465884i	$0.154264\pi$
$317$			16.5897i			0.931769i	−0.884846	+	0.465884i	$0.845736\pi$
$318$		0			0
$319$	1.23640			0.0692253
$320$		0			0
$321$	−12.9385	−	0.632329i	−0.722154	−	0.0352932i
$322$		0			0
$323$			5.75495i			0.320214i
$324$		0			0
$325$	9.92379	−	5.72950i	0.550473	−	0.317816i
$326$		0			0
$327$	−12.4253	−	8.00695i	−0.687122	−	0.442785i
$328$		0			0
$329$	−31.1365	+	5.36381i	−1.71661	+	0.295716i
$330$		0			0
$331$	4.71712			0.259277			0.129638	−	0.991561i	$-0.458618\pi$
$331$	4.71712			0.259277			0.129638	+	0.991561i	$0.458618\pi$
$332$		0			0
$333$	4.10444	+	9.04646i	0.224922	+	0.495743i
$334$		0			0
$335$	−1.74313	−	3.01920i	−0.0952376	−	0.164956i
$336$		0			0
$337$	1.79195	−	3.10375i	0.0976138	−	0.169072i	−0.813083	−	0.582148i	$-0.802212\pi$
$337$	1.79195	−	3.10375i	0.0976138	−	0.169072i	0.910697	+	0.413076i	$0.135546\pi$
$338$		0			0
$339$	−2.45638	−	0.120048i	−0.133412	−	0.00652014i
$340$		0			0
$341$	1.30092	−	2.25326i	0.0704488	−	0.122021i
$342$		0			0
$343$	−16.1473	+	9.06992i	−0.871874	+	0.489729i
$344$		0			0
$345$	17.7608	+	0.868008i	0.956211	+	0.0467320i
$346$		0			0
$347$		−	18.1520i		−	0.974449i	−0.873277	−	0.487225i	$-0.838009\pi$
$347$		−	18.1520i		−	0.974449i	0.873277	−	0.487225i	$-0.161991\pi$
$348$		0			0
$349$	28.1608	−	16.2586i	1.50741	−	0.870304i	0.507448	−	0.861683i	$-0.330589\pi$
$349$	28.1608	−	16.2586i	1.50741	−	0.870304i	0.999963	−	0.00862123i	$-0.00274426\pi$
$350$		0			0
$351$	−21.5297	+	27.1698i	−1.14917	+	1.45022i
$352$		0			0
$353$	0.106030	−	0.183650i	0.00564343	−	0.00977471i	−0.863190	−	0.504879i	$-0.831537\pi$
$353$	0.106030	−	0.183650i	0.00564343	−	0.00977471i	0.868833	+	0.495105i	$0.164870\pi$
$354$		0			0
$355$	−11.4732	+	6.62407i	−0.608936	+	0.351569i
$356$		0			0
$357$	16.8581	+	7.16408i	0.892228	+	0.379163i
$358$		0			0
$359$	−28.7469	−	16.5970i	−1.51720	−	0.875958i	−0.999796	−	0.0202187i	$-0.993564\pi$
$359$	−28.7469	−	16.5970i	−1.51720	−	0.875958i	−0.517408	−	0.855739i	$-0.673103\pi$
$360$		0			0
$361$	−8.46354	−	14.6593i	−0.445449	−	0.771541i
$362$		0			0
$363$	15.9200	+	10.2589i	0.835583	+	0.538454i
$364$		0			0
$365$	4.48961	+	2.59208i	0.234997	+	0.135675i
$366$		0			0
$367$	0.200648	+	0.115844i	0.0104737	+	0.00604701i	0.505228	−	0.862986i	$-0.331408\pi$
$367$	0.200648	+	0.115844i	0.0104737	+	0.00604701i	−0.494754	+	0.869033i	$0.664742\pi$
$368$		0			0
$369$	−12.6452	−	27.8708i	−0.658283	−	1.45090i
$370$		0			0
$371$	−9.33260	+	7.76853i	−0.484525	+	0.403322i
$372$		0			0
$373$	−8.84776	−	15.3248i	−0.458119	−	0.793486i	0.540742	−	0.841188i	$-0.318143\pi$
$373$	−8.84776	−	15.3248i	−0.458119	−	0.793486i	−0.998862	+	0.0477023i	$0.984810\pi$
$374$		0			0
$375$	18.7485	−	9.63630i	0.968171	−	0.497616i
$376$		0			0
$377$	−32.2383			−1.66035
$378$		0			0
$379$	28.9131			1.48516			0.742582	−	0.669755i	$-0.233601\pi$
$379$	28.9131			1.48516			0.742582	+	0.669755i	$0.233601\pi$
$380$		0			0
$381$	7.96884	−	4.09579i	0.408256	−	0.209834i
$382$		0			0
$383$	−1.17792	−	2.04022i	−0.0601891	−	0.104250i	0.834361	−	0.551219i	$-0.185837\pi$
$383$	−1.17792	−	2.04022i	−0.0601891	−	0.104250i	−0.894550	+	0.446968i	$0.852504\pi$
$384$		0			0
$385$	−0.208212	−	1.20866i	−0.0106115	−	0.0615988i
$386$		0			0
$387$	6.70276	+	0.656724i	0.340720	+	0.0333832i
$388$		0			0
$389$	9.61347	+	5.55034i	0.487422	+	0.281413i	0.723505	−	0.690320i	$-0.242530\pi$
$389$	9.61347	+	5.55034i	0.487422	+	0.281413i	−0.236082	+	0.971733i	$0.575863\pi$
$390$		0			0
$391$	19.6158	+	11.3252i	0.992016	+	0.572740i
$392$		0			0
$393$	9.26739	+	5.97195i	0.467478	+	0.301245i
$394$		0			0
$395$	3.31825	+	5.74738i	0.166959	+	0.289182i
$396$		0			0
$397$	−4.59168	−	2.65101i	−0.230450	−	0.133050i	0.380330	−	0.924851i	$-0.375810\pi$
$397$	−4.59168	−	2.65101i	−0.230450	−	0.133050i	−0.610780	+	0.791801i	$0.709144\pi$
$398$		0			0
$399$	6.54898	−	0.801368i	0.327859	−	0.0401186i
$400$		0			0
$401$	28.4117	−	16.4035i	1.41881	−	0.819151i	0.422617	−	0.906309i	$-0.361112\pi$
$401$	28.4117	−	16.4035i	1.41881	−	0.819151i	0.996195	+	0.0871576i	$0.0277784\pi$
$402$		0			0
$403$	−33.9205	+	58.7520i	−1.68970	+	2.92665i
$404$		0			0
$405$	−10.7386	+	12.2701i	−0.533604	+	0.609708i
$406$		0			0
$407$	0.733744	−	0.423627i	0.0363703	−	0.0209984i
$408$		0			0
$409$			15.2257i			0.752862i	0.926445	+	0.376431i	$0.122849\pi$
$409$			15.2257i			0.752862i	−0.926445	+	0.376431i	$0.877151\pi$
$410$		0			0
$411$	0.0841116	+	0.00411071i	0.00414892	+	0.000202766i
$412$		0			0
$413$	13.3275	−	2.29589i	0.655802	−	0.112973i
$414$		0			0
$415$	−4.86018	+	8.41808i	−0.238577	+	0.413227i
$416$		0			0
$417$	5.91219	+	0.288941i	0.289521	+	0.0141495i
$418$		0			0
$419$	−6.32224	+	10.9504i	−0.308861	+	0.534964i	−0.978114	−	0.208072i	$-0.933281\pi$
$419$	−6.32224	+	10.9504i	−0.308861	+	0.534964i	0.669252	+	0.743035i	$0.266615\pi$
$420$		0			0
$421$	−14.4841	−	25.0872i	−0.705911	−	1.22267i	−0.966362	−	0.257187i	$-0.917204\pi$
$421$	−14.4841	−	25.0872i	−0.705911	−	1.22267i	0.260451	−	0.965487i	$-0.416129\pi$
$422$		0			0
$423$	20.8528	−	29.1313i	1.01390	−	1.41641i
$424$		0			0
$425$	6.86557			0.333029
$426$		0			0
$427$	−4.46150	−	25.8987i	−0.215907	−	1.25333i
$428$		0			0
$429$	2.48527	+	1.60152i	0.119990	+	0.0773220i
$430$		0			0
$431$	−31.6662	+	18.2825i	−1.52531	+	0.880638i	−0.525760	+	0.850633i	$0.676219\pi$
$431$	−31.6662	+	18.2825i	−1.52531	+	0.880638i	−0.999550	+	0.0300048i	$0.990448\pi$
$432$		0			0
$433$		−	29.3243i		−	1.40924i	−0.709586	−	0.704619i	$-0.751118\pi$
$433$		−	29.3243i		−	1.40924i	0.709586	−	0.704619i	$-0.248882\pi$
$434$		0			0
$435$	−15.1457	−	0.740199i	−0.726178	−	0.0354898i
$436$		0			0
$437$	8.15864			0.390281
$438$		0			0
$439$		−	16.5850i		−	0.791557i	−0.918346	−	0.395778i	$-0.870475\pi$
$439$		−	16.5850i		−	0.791557i	0.918346	−	0.395778i	$-0.129525\pi$
$440$		0			0
$441$	5.80506	−	20.1817i	0.276432	−	0.961034i
$442$		0			0
$443$			15.3392i			0.728788i	0.931245	+	0.364394i	$0.118724\pi$
$443$			15.3392i			0.728788i	−0.931245	+	0.364394i	$0.881276\pi$
$444$		0			0
$445$	−1.37129			−0.0650052
$446$		0			0
$447$	−9.28077	+	14.4021i	−0.438965	+	0.681195i
$448$		0			0
$449$		−	22.9580i		−	1.08346i	−0.840554	−	0.541728i	$-0.817770\pi$
$449$		−	22.9580i		−	1.08346i	0.840554	−	0.541728i	$-0.182230\pi$
$450$		0			0
$451$	−2.26056	+	1.30513i	−0.106445	+	0.0614563i
$452$		0			0
$453$	0.717444	−	14.6800i	0.0337085	−	0.689729i
$454$		0			0
$455$	5.42897	+	31.5148i	0.254514	+	1.47743i
$456$		0			0
$457$	−21.8251			−1.02094			−0.510468	−	0.859897i	$-0.670528\pi$
$457$	−21.8251			−1.02094			−0.510468	+	0.859897i	$0.670528\pi$
$458$		0			0
$459$	−19.3104	+	7.64796i	−0.901334	+	0.356976i
$460$		0			0
$461$	−16.9154	−	29.2984i	−0.787830	−	1.36456i	−0.927294	−	0.374335i	$-0.877871\pi$
$461$	−16.9154	−	29.2984i	−0.787830	−	1.36456i	0.139463	−	0.990227i	$-0.455462\pi$
$462$		0			0
$463$	−1.82082	+	3.15375i	−0.0846206	+	0.146567i	−0.905229	−	0.424923i	$-0.860301\pi$
$463$	−1.82082	+	3.15375i	−0.0846206	+	0.146567i	0.820609	+	0.571490i	$0.193634\pi$
$464$		0			0
$465$	−17.2849	+	26.8231i	−0.801570	+	1.24389i
$466$		0			0
$467$	−12.1438	+	21.0337i	−0.561948	+	0.973322i	0.435378	+	0.900248i	$0.356615\pi$
$467$	−12.1438	+	21.0337i	−0.561948	+	0.973322i	−0.997326	+	0.0730749i	$0.976719\pi$
$468$		0			0
$469$	−5.01724	+	0.864307i	−0.231675	+	0.0399100i
$470$		0			0
$471$	−14.6354	−	28.4749i	−0.674365	−	1.31206i
$472$		0			0
$473$		−	0.574403i		−	0.0264111i
$474$		0			0
$475$	2.14165	−	1.23648i	0.0982657	−	0.0567337i
$476$		0			0
$477$	1.34260	−	13.7030i	0.0614733	−	0.627419i
$478$		0			0
$479$	15.1100	−	26.1713i	0.690393	−	1.19580i	−0.281316	−	0.959615i	$-0.590771\pi$
$479$	15.1100	−	26.1713i	0.690393	−	1.19580i	0.971709	−	0.236181i	$-0.0758959\pi$
$480$		0			0
$481$	−19.1318	+	11.0457i	−0.872335	+	0.503643i
$482$		0			0
$483$	10.1563	−	23.8993i	0.462128	−	1.08746i
$484$		0			0
$485$	7.64126	+	4.41169i	0.346972	+	0.200324i
$486$		0			0
$487$	2.84999	+	4.93634i	0.129146	+	0.223687i	0.923346	−	0.383969i	$-0.125443\pi$
$487$	2.84999	+	4.93634i	0.129146	+	0.223687i	−0.794200	+	0.607656i	$0.792110\pi$
$488$		0			0
$489$	−0.644864	+	13.1949i	−0.0291618	+	0.596696i
$490$		0			0
$491$	−28.3275	−	16.3549i	−1.27840	−	0.738086i	−0.301848	−	0.953356i	$-0.597604\pi$
$491$	−28.3275	−	16.3549i	−1.27840	−	0.738086i	−0.976555	+	0.215270i	$0.930937\pi$
$492$		0			0
$493$	−16.7275	−	9.65764i	−0.753370	−	0.434958i
$494$		0			0
$495$	1.13082	+	0.809462i	0.0508264	+	0.0363826i
$496$		0			0
$497$	3.28445	+	19.0660i	0.147328	+	0.855226i
$498$		0			0
$499$	−3.73643	−	6.47169i	−0.167266	−	0.289712i	0.770192	−	0.637812i	$-0.220160\pi$
$499$	−3.73643	−	6.47169i	−0.167266	−	0.289712i	−0.937458	+	0.348100i	$0.886827\pi$
$500$		0			0
$501$	1.49967	−	30.6856i	0.0670002	−	1.37093i
$502$		0			0
$503$	−29.2765			−1.30537			−0.652686	−	0.757628i	$-0.726358\pi$
$503$	−29.2765			−1.30537			−0.652686	+	0.757628i	$0.726358\pi$
$504$		0			0
$505$	29.7387			1.32336
$506$		0			0
$507$	−45.8742	−	29.5616i	−2.03734	−	1.31287i
$508$		0			0
$509$	−9.56925	−	16.5744i	−0.424150	−	0.734649i	0.572191	−	0.820120i	$-0.306094\pi$
$509$	−9.56925	−	16.5744i	−0.424150	−	0.734649i	−0.996341	+	0.0854717i	$0.972760\pi$
$510$		0			0
$511$	5.81857	−	4.84342i	0.257398	−	0.214260i
$512$		0			0
$513$	−4.64632	+	5.86350i	−0.205140	+	0.258880i
$514$		0			0
$515$	−30.4371	−	17.5728i	−1.34122	−	0.774352i
$516$		0			0
$517$	−2.64613	−	1.52774i	−0.116377	−	0.0671901i
$518$		0			0
$519$	21.6058	−	11.1049i	0.948390	−	0.487449i
$520$		0			0
$521$	−12.0228	−	20.8241i	−0.526727	−	0.912318i	−0.999515	−	0.0311420i	$-0.990086\pi$
$521$	−12.0228	−	20.8241i	−0.526727	−	0.912318i	0.472788	−	0.881176i	$-0.343248\pi$
$522$		0			0
$523$	22.2119	+	12.8241i	0.971259	+	0.560757i	0.899620	−	0.436674i	$-0.143844\pi$
$523$	22.2119	+	12.8241i	0.971259	+	0.560757i	0.0716394	+	0.997431i	$0.477177\pi$
$524$		0			0
$525$	−0.956019	−	7.81284i	−0.0417241	−	0.340980i
$526$		0			0
$527$	−35.2008	+	20.3232i	−1.53337	+	0.885292i
$528$		0			0
$529$	4.55543	−	7.89024i	0.198062	−	0.343054i
$530$		0			0
$531$	−8.92568	+	12.4692i	−0.387341	+	0.541115i
$532$		0			0
$533$	58.9423	−	34.0303i	2.55307	−	1.47402i
$534$		0			0
$535$		−	13.5499i		−	0.585811i
$536$		0			0
$537$	−8.98645	+	13.9453i	−0.387794	+	0.601786i
$538$		0			0
$539$	−1.76133	−	0.324901i	−0.0758660	−	0.0139945i
$540$		0			0
$541$	−10.4700	+	18.1346i	−0.450141	+	0.779667i	−0.998394	−	0.0566455i	$-0.981960\pi$
$541$	−10.4700	+	18.1346i	−0.450141	+	0.779667i	0.548254	+	0.836312i	$0.315293\pi$
$542$		0			0
$543$	1.24990	+	2.43183i	0.0536384	+	0.104360i
$544$		0			0
$545$	7.73089	−	13.3903i	0.331155	−	0.573578i
$546$		0			0
$547$	6.53210	+	11.3139i	0.279292	+	0.483748i	0.971209	−	0.238229i	$-0.0765668\pi$
$547$	6.53210	+	11.3139i	0.279292	+	0.483748i	−0.691917	+	0.721977i	$0.743234\pi$
$548$		0			0
$549$	24.2308	+	17.3449i	1.03414	+	0.740262i
$550$		0			0
$551$	−6.95733			−0.296392
$552$		0			0
$553$	9.55087	−	1.64531i	0.406144	−	0.0699655i
$554$		0			0
$555$	−9.24180	+	4.75006i	−0.392293	+	0.201629i
$556$		0			0
$557$	32.5390	−	18.7864i	1.37872	−	0.796006i	0.386717	−	0.922198i	$-0.373609\pi$
$557$	32.5390	−	18.7864i	1.37872	−	0.796006i	0.992006	+	0.126193i	$0.0402757\pi$
$558$		0			0
$559$			14.9771i			0.633464i
$560$		0			0
$561$	0.809767	+	1.57550i	0.0341884	+	0.0665175i
$562$		0			0
$563$	11.0734			0.466689			0.233344	−	0.972394i	$-0.425033\pi$
$563$	11.0734			0.466689			0.233344	+	0.972394i	$0.425033\pi$
$564$		0			0
$565$		−	2.57246i		−	0.108224i
$566$		0			0
$567$	11.3921	+	20.9098i	0.478424	+	0.878129i
$568$		0			0
$569$			21.4724i			0.900170i	0.892986	+	0.450085i	$0.148606\pi$
$569$			21.4724i			0.900170i	−0.892986	+	0.450085i	$0.851394\pi$
$570$		0			0
$571$	−14.9138			−0.624122			−0.312061	−	0.950062i	$-0.601019\pi$
$571$	−14.9138			−0.624122			−0.312061	+	0.950062i	$0.601019\pi$
$572$		0			0
$573$	−13.8087	−	26.8665i	−0.576868	−	1.12236i
$574$		0			0
$575$		−	9.73313i		−	0.405899i
$576$		0			0
$577$	−28.0634	+	16.2024i	−1.16829	+	0.674515i	−0.953278	−	0.302095i	$-0.902314\pi$
$577$	−28.0634	+	16.2024i	−1.16829	+	0.674515i	−0.215017	+	0.976610i	$0.568981\pi$
$578$		0			0
$579$	−36.7445	+	18.8858i	−1.52705	+	0.784867i
$580$		0			0
$581$	9.08149	+	10.9099i	0.376764	+	0.452619i
$582$		0			0
$583$	−1.17430			−0.0486346
$584$		0			0
$585$	−29.4851	−	21.1061i	−1.21906	−	0.872629i
$586$		0			0
$587$	−9.88731	−	17.1253i	−0.408093	−	0.706838i	0.586583	−	0.809889i	$-0.300473\pi$
$587$	−9.88731	−	17.1253i	−0.408093	−	0.706838i	−0.994676	+	0.103051i	$0.967139\pi$
$588$		0			0
$589$	−7.32037	+	12.6793i	−0.301631	+	0.522440i
$590$		0			0
$591$	15.1443	+	29.4650i	0.622953	+	1.21203i
$592$		0			0
$593$	4.41904	−	7.65401i	0.181468	−	0.314312i	−0.760912	−	0.648855i	$-0.775248\pi$
$593$	4.41904	−	7.65401i	0.181468	−	0.314312i	0.942381	+	0.334542i	$0.108582\pi$
$594$		0			0
$595$	−6.62396	+	17.9785i	−0.271556	+	0.737046i
$596$		0			0
$597$	−5.58141	+	8.66134i	−0.228432	+	0.354485i
$598$		0			0
$599$		−	37.8583i		−	1.54685i	−0.633890	−	0.773423i	$-0.718543\pi$
$599$		−	37.8583i		−	1.54685i	0.633890	−	0.773423i	$-0.281457\pi$
$600$		0			0
$601$	30.5662	−	17.6474i	1.24682	−	0.719853i	0.276347	−	0.961058i	$-0.410876\pi$
$601$	30.5662	−	17.6474i	1.24682	−	0.719853i	0.970474	+	0.241205i	$0.0775426\pi$
$602$		0			0
$603$	3.36015	−	4.69412i	0.136836	−	0.191159i
$604$		0			0
$605$	−9.90524	+	17.1564i	−0.402705	+	0.697506i
$606$		0			0
$607$	6.37903	−	3.68294i	0.258917	−	0.149486i	−0.364924	−	0.931038i	$-0.618905\pi$
$607$	6.37903	−	3.68294i	0.258917	−	0.149486i	0.623840	+	0.781552i	$0.285572\pi$
$608$		0			0
$609$	−8.66086	+	20.3803i	−0.350956	+	0.825851i
$610$		0			0
$611$	68.9958	+	39.8347i	2.79127	+	1.61154i
$612$		0			0
$613$	−9.39378	−	16.2705i	−0.379411	−	0.657159i	0.611566	−	0.791194i	$-0.290540\pi$
$613$	−9.39378	−	16.2705i	−0.379411	−	0.657159i	−0.990977	+	0.134034i	$0.957207\pi$
$614$		0			0
$615$	28.4727	−	14.6343i	1.14813	−	0.590110i
$616$		0			0
$617$	3.17209	+	1.83141i	0.127703	+	0.0737296i	0.562491	−	0.826804i	$-0.309843\pi$
$617$	3.17209	+	1.83141i	0.127703	+	0.0737296i	−0.434787	+	0.900533i	$0.643176\pi$
$618$		0			0
$619$	−4.00077	−	2.30984i	−0.160804	−	0.0928405i	0.417438	−	0.908705i	$-0.362928\pi$
$619$	−4.00077	−	2.30984i	−0.160804	−	0.0928405i	−0.578243	+	0.815865i	$0.696261\pi$
$620$		0			0
$621$	10.8423	+	27.3759i	0.435086	+	1.09856i
$622$		0			0
$623$	−0.692320	+	1.87907i	−0.0277372	+	0.0752832i
$624$		0			0
$625$	6.73085	+	11.6582i	0.269234	+	0.466327i
$626$		0			0
$627$	0.536344	+	0.345623i	0.0214195	+	0.0138029i
$628$		0			0
$629$	−13.2359			−0.527751
$630$		0			0
$631$	40.5302			1.61348			0.806740	−	0.590906i	$-0.201230\pi$
$631$	40.5302			1.61348			0.806740	+	0.590906i	$0.201230\pi$
$632$		0			0
$633$	0.991604	−	20.2898i	0.0394127	−	0.806446i
$634$		0			0
$635$	4.68600	+	8.11639i	0.185958	+	0.322089i
$636$		0			0
$637$	45.9254	+	8.47154i	1.81963	+	0.335655i
$638$		0			0
$639$	−17.8381	−	12.7689i	−0.705664	−	0.505129i
$640$		0			0
$641$	13.5303	+	7.81170i	0.534413	+	0.308544i	0.742812	−	0.669500i	$-0.233492\pi$
$641$	13.5303	+	7.81170i	0.534413	+	0.308544i	−0.208398	+	0.978044i	$0.566825\pi$
$642$		0			0
$643$	−13.9719	−	8.06670i	−0.550999	−	0.318120i	0.198526	−	0.980096i	$-0.436385\pi$
$643$	−13.9719	−	8.06670i	−0.550999	−	0.318120i	−0.749525	+	0.661976i	$0.769718\pi$
$644$		0			0
$645$	−0.343879	+	7.03630i	−0.0135402	+	0.277054i
$646$		0			0
$647$	17.2365	+	29.8545i	0.677637	+	1.17370i	0.975691	+	0.219152i	$0.0703292\pi$
$647$	17.2365	+	29.8545i	0.677637	+	1.17370i	−0.298054	+	0.954549i	$0.596337\pi$
$648$		0			0
$649$	1.13263	+	0.653926i	0.0444597	+	0.0256688i
$650$		0			0
$651$	28.0289	+	37.2276i	1.09854	+	1.45906i
$652$		0			0
$653$	11.1709	−	6.44950i	0.437150	−	0.252388i	−0.265238	−	0.964183i	$-0.585451\pi$
$653$	11.1709	−	6.44950i	0.437150	−	0.252388i	0.702388	+	0.711794i	$0.252117\pi$
$654$		0			0
$655$	−5.76606	+	9.98711i	−0.225299	+	0.390229i
$656$		0			0
$657$	−0.837064	+	8.54338i	−0.0326570	+	0.333309i
$658$		0			0
$659$	−9.60396	+	5.54485i	−0.374117	+	0.215997i	−0.675256	−	0.737584i	$-0.735967\pi$
$659$	−9.60396	+	5.54485i	−0.374117	+	0.215997i	0.301138	+	0.953580i	$0.402633\pi$
$660$		0			0
$661$		−	5.03083i		−	0.195677i	−0.995202	−	0.0978383i	$-0.968807\pi$
$661$		−	5.03083i		−	0.195677i	0.995202	−	0.0978383i	$-0.0311928\pi$
$662$		0			0
$663$	−21.1140	−	41.0798i	−0.820001	−	1.59541i
$664$		0			0
$665$	1.17162	+	6.80119i	0.0454336	+	0.263739i
$666$		0			0
$667$	−13.6914	+	23.7141i	−0.530132	+	0.918215i
$668$		0			0
$669$	−17.3564	+	26.9340i	−0.671036	+	1.04133i
$670$		0			0
$671$	1.27074	−	2.20099i	0.0490566	−	0.0849685i
$672$		0			0
$673$	−2.50713	−	4.34248i	−0.0966428	−	0.167390i	0.813650	−	0.581355i	$-0.197477\pi$
$673$	−2.50713	−	4.34248i	−0.0966428	−	0.167390i	−0.910293	+	0.413964i	$0.864144\pi$
$674$		0			0
$675$	6.99506	+	5.54299i	0.269240	+	0.213350i
$676$		0			0
$677$	−37.5456			−1.44300			−0.721498	−	0.692417i	$-0.756546\pi$
$677$	−37.5456			−1.44300			−0.721498	+	0.692417i	$0.756546\pi$
$678$		0			0
$679$	9.90314	−	8.24345i	0.380048	−	0.316355i
$680$		0			0
$681$	0.0572851	−	1.17214i	0.00219517	−	0.0449166i
$682$		0			0
$683$	20.4810	−	11.8247i	0.783684	−	0.452460i	−0.0540503	−	0.998538i	$-0.517213\pi$
$683$	20.4810	−	11.8247i	0.783684	−	0.452460i	0.837734	+	0.546078i	$0.183880\pi$
$684$		0			0
$685$			0.0880862i			0.00336560i
$686$		0			0
$687$	−0.362590	+	0.562675i	−0.0138337	+	0.0214674i
$688$		0			0
$689$	30.6190			1.16649
$690$		0			0
$691$		−	24.0857i		−	0.916264i	−0.888884	−	0.458132i	$-0.848519\pi$
$691$		−	24.0857i		−	0.916264i	0.888884	−	0.458132i	$-0.151481\pi$
$692$		0			0
$693$	1.68011	−	1.14088i	0.0638222	−	0.0433384i
$694$		0			0
$695$			6.19157i			0.234859i
$696$		0			0
$697$	40.7780			1.54458
$698$		0			0
$699$	−6.70239	−	0.327560i	−0.253508	−	0.0123894i
$700$		0			0
$701$		−	15.6261i		−	0.590190i	−0.955468	−	0.295095i	$-0.904649\pi$
$701$		−	15.6261i		−	0.590190i	0.955468	−	0.295095i	$-0.0953513\pi$
$702$		0			0
$703$	−4.12883	+	2.38378i	−0.155722	+	0.0899059i
$704$		0			0
$705$	31.4999	+	20.2987i	1.18635	+	0.764492i
$706$		0			0
$707$	15.0141	−	40.7508i	0.564665	−	1.53259i
$708$		0			0
$709$	14.4101			0.541182			0.270591	−	0.962694i	$-0.412781\pi$
$709$	14.4101			0.541182			0.270591	+	0.962694i	$0.412781\pi$
$710$		0			0
$711$	−6.39642	+	8.93578i	−0.239884	+	0.335118i
$712$		0			0
$713$	28.8116	+	49.9032i	1.07900	+	1.86889i
$714$		0			0
$715$	−1.54630	+	2.67828i	−0.0578285	+	0.100162i
$716$		0			0
$717$	19.9222	+	0.973641i	0.744010	+	0.0363613i
$718$		0			0
$719$	−7.49770	+	12.9864i	−0.279617	+	0.484311i	−0.971290	−	0.237900i	$-0.923541\pi$
$719$	−7.49770	+	12.9864i	−0.279617	+	0.484311i	0.691673	+	0.722211i	$0.256874\pi$
$720$		0			0
$721$	−39.4467	+	32.8357i	−1.46907	+	1.22287i
$722$		0			0
$723$	20.4040	+	0.997186i	0.758833	+	0.0370857i
$724$		0			0
$725$			8.29998i			0.308254i
$726$		0			0
$727$	17.9806	−	10.3811i	0.666862	−	0.385013i	−0.128025	−	0.991771i	$-0.540864\pi$
$727$	17.9806	−	10.3811i	0.666862	−	0.385013i	0.794887	+	0.606758i	$0.207530\pi$
$728$		0			0
$729$	−25.8493	−	7.79827i	−0.957382	−	0.288825i
$730$		0			0
$731$	−4.48670	+	7.77120i	−0.165947	+	0.287428i
$732$		0			0
$733$	−21.1373	+	12.2036i	−0.780724	+	0.450751i	−0.836687	−	0.547682i	$-0.815510\pi$
$733$	−21.1373	+	12.2036i	−0.780724	+	0.450751i	0.0559630	+	0.998433i	$0.482177\pi$
$734$		0			0
$735$	21.3814	+	5.03442i	0.788665	+	0.185697i
$736$		0			0
$737$	−0.426389	−	0.246176i	−0.0157062	−	0.00906800i
$738$		0			0
$739$	0.295124	+	0.511169i	0.0108563	+	0.0188037i	0.871403	−	0.490569i	$-0.163211\pi$
$739$	0.295124	+	0.511169i	0.0108563	+	0.0188037i	−0.860546	+	0.509372i	$0.829878\pi$
$740$		0			0
$741$	−13.9848	−	9.01185i	−0.513743	−	0.331059i
$742$		0			0
$743$	33.2573	+	19.2011i	1.22009	+	0.704421i	0.964938	−	0.262479i	$-0.0845401\pi$
$743$	33.2573	+	19.2011i	1.22009	+	0.704421i	0.255155	+	0.966900i	$0.417873\pi$
$744$		0			0
$745$	−15.5206	−	8.96080i	−0.568629	−	0.328298i
$746$		0			0
$747$	−16.0190	−	1.56951i	−0.586104	−	0.0574253i
$748$		0			0
$749$	−18.5673	−	6.84090i	−0.678433	−	0.249961i
$750$		0			0
$751$	22.8587	+	39.5923i	0.834124	+	1.44475i	0.894742	+	0.446584i	$0.147360\pi$
$751$	22.8587	+	39.5923i	0.834124	+	1.44475i	−0.0606175	+	0.998161i	$0.519307\pi$
$752$		0			0
$753$	−15.0432	+	7.73184i	−0.548204	+	0.281764i
$754$		0			0
$755$	15.3737			0.559507
$756$		0			0
$757$	−7.42071			−0.269710			−0.134855	−	0.990865i	$-0.543057\pi$
$757$	−7.42071			−0.269710			−0.134855	+	0.990865i	$0.543057\pi$
$758$		0			0
$759$	2.23354	−	1.14798i	0.0810722	−	0.0416692i
$760$		0			0
$761$	−23.6521	−	40.9666i	−0.857387	−	1.48504i	−0.874413	−	0.485183i	$-0.838753\pi$
$761$	−23.6521	−	40.9666i	−0.857387	−	1.48504i	0.0170257	−	0.999855i	$-0.494580\pi$
$762$		0			0
$763$	−14.4456	−	17.3539i	−0.522964	−	0.628255i
$764$		0			0
$765$	−8.97625	−	19.7842i	−0.324537	−	0.715301i
$766$		0			0
$767$	−29.5325	−	17.0506i	−1.06636	−	0.615662i
$768$		0			0
$769$	−42.3251	−	24.4364i	−1.52628	−	0.881199i	−0.999513	−	0.0311905i	$-0.990070\pi$
$769$	−42.3251	−	24.4364i	−1.52628	−	0.881199i	−0.526769	−	0.850009i	$-0.676597\pi$
$770$		0			0
$771$	−20.6104	−	13.2815i	−0.742266	−	0.478320i
$772$		0			0
$773$	11.4374	+	19.8101i	0.411374	+	0.712521i	0.995040	−	0.0994731i	$-0.0317157\pi$
$773$	11.4374	+	19.8101i	0.411374	+	0.712521i	−0.583666	+	0.811994i	$0.698382\pi$
$774$		0			0
$775$	15.1262	+	8.73309i	0.543348	+	0.313702i
$776$		0			0
$777$	1.84308	+	15.0621i	0.0661202	+	0.540351i
$778$		0			0
$779$	12.7203	−	7.34408i	0.455753	−	0.263129i
$780$		0			0
$781$	−0.935491	+	1.62032i	−0.0334745	+	0.0579795i
$782$		0			0
$783$	−9.24583	−	23.3449i	−0.330419	−	0.834280i
$784$		0			0
$785$	29.0021	−	16.7444i	1.03513	−	0.597633i
$786$		0			0
$787$			26.3671i			0.939886i	0.882697	+	0.469943i	$0.155726\pi$
$787$			26.3671i			0.939886i	−0.882697	+	0.469943i	$0.844274\pi$
$788$		0			0
$789$	−17.8153	−	0.870670i	−0.634241	−	0.0309967i
$790$		0			0
$791$	−3.52502	−	1.29875i	−0.125335	−	0.0461783i
$792$		0			0
$793$	−33.1337	+	57.3892i	−1.17661	+	2.03795i
$794$		0			0
$795$	14.3849	+	0.703020i	0.510180	+	0.0249336i
$796$		0			0
$797$	8.16906	−	14.1492i	0.289363	−	0.501191i	−0.684295	−	0.729205i	$-0.739890\pi$
$797$	8.16906	−	14.1492i	0.289363	−	0.501191i	0.973658	+	0.228014i	$0.0732232\pi$
$798$		0			0
$799$	23.8667	+	41.3383i	0.844342	+	1.46244i
$800$		0			0
$801$	−0.938175	−	2.06780i	−0.0331488	−	0.0730621i
$802$		0			0
$803$	0.732137			0.0258366
$804$		0			0
$805$	25.4876	+	9.39061i	0.898320	+	0.330975i
$806$		0			0
$807$	−11.5295	−	7.42966i	−0.405857	−	0.261536i
$808$		0			0
$809$	−11.1321	+	6.42711i	−0.391383	+	0.225965i	−0.682759	−	0.730643i	$-0.739220\pi$
$809$	−11.1321	+	6.42711i	−0.391383	+	0.225965i	0.291376	+	0.956609i	$0.405887\pi$
$810$		0			0
$811$			38.3887i			1.34801i	0.738727	+	0.674005i	$0.235427\pi$
$811$			38.3887i			1.34801i	−0.738727	+	0.674005i	$0.764573\pi$
$812$		0			0
$813$	18.8916	+	0.923271i	0.662557	+	0.0323805i
$814$		0			0
$815$	−13.8184			−0.484039
$816$		0			0
$817$			3.23220i			0.113080i
$818$		0			0
$819$	−43.8077	+	29.7475i	−1.53076	+	1.03946i
$820$		0			0
$821$		−	22.2429i		−	0.776284i	−0.921600	−	0.388142i	$-0.873117\pi$
$821$		−	22.2429i		−	0.776284i	0.921600	−	0.388142i	$-0.126883\pi$
$822$		0			0
$823$	35.1570			1.22550			0.612748	−	0.790278i	$-0.290064\pi$
$823$	35.1570			1.22550			0.612748	+	0.790278i	$0.290064\pi$
$824$		0			0
$825$	0.412323	−	0.639851i	0.0143552	−	0.0222767i
$826$		0			0
$827$		−	42.3779i		−	1.47362i	−0.676098	−	0.736812i	$-0.736330\pi$
$827$		−	42.3779i		−	1.47362i	0.676098	−	0.736812i	$-0.263670\pi$
$828$		0			0
$829$	46.8574	−	27.0531i	1.62742	−	0.939593i	0.642565	−	0.766231i	$-0.277870\pi$
$829$	46.8574	−	27.0531i	1.62742	−	0.939593i	0.984858	−	0.173362i	$-0.0554630\pi$
$830$		0			0
$831$	1.08394	−	22.1791i	0.0376015	−	0.769386i
$832$		0			0
$833$	21.2916	+	18.1536i	0.737709	+	0.628983i
$834$		0			0
$835$	32.1356			1.11210
$836$		0			0
$837$	−52.2729	−	7.71322i	−1.80681	−	0.266608i
$838$		0			0
$839$	−20.1561	−	34.9114i	−0.695866	−	1.20528i	−0.969888	−	0.243552i	$-0.921687\pi$
$839$	−20.1561	−	34.9114i	−0.695866	−	1.20528i	0.274022	−	0.961724i	$-0.411646\pi$
$840$		0			0
$841$	−2.82461	+	4.89236i	−0.0974002	+	0.168702i
$842$		0			0
$843$	19.8665	−	30.8293i	0.684240	−	1.06182i
$844$		0			0
$845$	28.5424	−	49.4369i	0.981888	−	1.70068i
$846$		0			0
$847$	18.5084	+	22.2348i	0.635957	+	0.763997i
$848$		0			0
$849$	20.3350	+	39.5642i	0.697896	+	1.35784i
$850$		0			0
$851$			18.7642i			0.643229i
$852$		0			0
$853$	8.81155	−	5.08735i	0.301702	−	0.174188i	−0.341505	−	0.939880i	$-0.610937\pi$
$853$	8.81155	−	5.08735i	0.301702	−	0.174188i	0.643207	+	0.765692i	$0.277603\pi$
$854$		0			0
$855$	−6.36318	−	4.55490i	−0.217616	−	0.155774i
$856$		0			0
$857$	7.22141	−	12.5078i	0.246679	−	0.427260i	−0.715924	−	0.698179i	$-0.753994\pi$
$857$	7.22141	−	12.5078i	0.246679	−	0.427260i	0.962602	+	0.270919i	$0.0873275\pi$
$858$		0			0
$859$	−14.9939	+	8.65674i	−0.511585	+	0.295364i	−0.733485	−	0.679706i	$-0.762108\pi$
$859$	−14.9939	+	8.65674i	−0.511585	+	0.295364i	0.221900	+	0.975070i	$0.428774\pi$
$860$		0			0
$861$	−5.67827	−	46.4043i	−0.193515	−	1.58145i
$862$		0			0
$863$	24.1380	+	13.9361i	0.821667	+	0.474390i	0.850991	−	0.525180i	$-0.176002\pi$
$863$	24.1380	+	13.9361i	0.821667	+	0.474390i	−0.0293239	+	0.999570i	$0.509335\pi$
$864$		0			0
$865$	12.7051	+	22.0059i	0.431986	+	0.748221i
$866$		0			0
$867$	−0.0864763	+	1.76944i	−0.00293689	+	0.0600934i
$868$		0			0
$869$	0.811679	+	0.468623i	0.0275343	+	0.0158970i
$870$		0			0
$871$	11.1178	+	6.41884i	0.376711	+	0.217494i
$872$		0			0
$873$	−1.42468	+	14.5407i	−0.0482179	+	0.492130i
$874$		0			0
$875$	31.7328	−	5.46653i	1.07276	−	0.184803i
$876$		0			0
$877$	−5.15433	−	8.92756i	−0.174049	−	0.301462i	0.765783	−	0.643100i	$-0.222352\pi$
$877$	−5.15433	−	8.92756i	−0.174049	−	0.301462i	−0.939832	+	0.341637i	$0.889019\pi$
$878$		0			0
$879$	2.44880	−	50.1063i	0.0825960	−	1.69004i
$880$		0			0
$881$	2.48707			0.0837914			0.0418957	−	0.999122i	$-0.486660\pi$
$881$	2.48707			0.0837914			0.0418957	+	0.999122i	$0.486660\pi$
$882$		0			0
$883$	7.98895			0.268850			0.134425	−	0.990924i	$-0.457081\pi$
$883$	7.98895			0.268850			0.134425	+	0.990924i	$0.457081\pi$
$884$		0			0
$885$	−13.4830	−	8.68851i	−0.453226	−	0.292061i
$886$		0			0
$887$	−0.807224	−	1.39815i	−0.0271039	−	0.0469454i	0.852155	−	0.523289i	$-0.175295\pi$
$887$	−0.807224	−	1.39815i	−0.0271039	−	0.0469454i	−0.879259	+	0.476344i	$0.841962\pi$
$888$		0			0
$889$	13.4877	−	2.32348i	0.452361	−	0.0779271i
$890$		0			0
$891$	−0.446953	+	2.25899i	−0.0149735	+	0.0756789i
$892$		0			0
$893$	14.8900	+	8.59672i	0.498274	+	0.287678i
$894$		0			0
$895$	−15.0284	−	8.67663i	−0.502343	−	0.290028i
$896$		0			0
$897$	−58.2377	+	29.9328i	−1.94450	+	0.999426i
$898$		0			0
$899$	−24.5693	−	42.5552i	−0.819431	−	1.41930i
$900$		0			0
$901$	15.8873	+	9.17255i	0.529283	+	0.305582i
$902$		0			0
$903$	9.46818	+	4.02362i	0.315081	+	0.133898i
$904$		0			0
$905$	−2.47686	+	1.43001i	−0.0823335	+	0.0475353i
$906$		0			0
$907$	−0.809565	+	1.40221i	−0.0268812	+	0.0465595i	−0.879153	−	0.476540i	$-0.841891\pi$
$907$	−0.809565	+	1.40221i	−0.0268812	+	0.0465595i	0.852272	+	0.523099i	$0.175224\pi$
$908$		0			0
$909$	20.3459	+	44.8438i	0.674832	+	1.48737i
$910$		0			0
$911$	−20.1759	+	11.6485i	−0.668456	+	0.385933i	−0.795492	−	0.605965i	$-0.792787\pi$
$911$	−20.1759	+	11.6485i	−0.668456	+	0.385933i	0.127035	+	0.991898i	$0.459454\pi$
$912$		0			0
$913$			1.37277i			0.0454320i
$914$		0			0
$915$	−16.8840	+	26.2009i	−0.558168	+	0.866176i
$916$		0			0
$917$	10.7742	+	12.9434i	0.355794	+	0.427428i
$918$		0			0
$919$	−0.928631	+	1.60844i	−0.0306327	+	0.0530574i	−0.880935	−	0.473237i	$-0.843086\pi$
$919$	−0.928631	+	1.60844i	−0.0306327	+	0.0530574i	0.850303	+	0.526294i	$0.176419\pi$
$920$		0			0
$921$	22.2199	+	43.2313i	0.732169	+	1.42452i
$922$		0			0
$923$	24.3922	−	42.2485i	0.802879	−	1.39063i
$924$		0			0
$925$	2.84381	+	4.92562i	0.0935039	+	0.161954i
$926$		0			0
$927$	5.67484	−	57.9194i	0.186386	−	1.90232i
$928$		0			0
$929$	−46.0664			−1.51139			−0.755695	−	0.654923i	$-0.772701\pi$
$929$	−46.0664			−1.51139			−0.755695	+	0.654923i	$0.772701\pi$
$930$		0			0
$931$	9.91114	+	1.82824i	0.324825	+	0.0599181i
$932$		0			0
$933$	12.1998	−	6.27042i	0.399405	−	0.205284i
$934$		0			0
$935$	−1.60467	+	0.926455i	−0.0524782	+	0.0302983i
$936$		0			0
$937$			19.2806i			0.629871i	0.949113	+	0.314935i	$0.101983\pi$
$937$			19.2806i			0.629871i	−0.949113	+	0.314935i	$0.898017\pi$
$938$		0			0
$939$	−9.32937	−	18.1514i	−0.304452	−	0.592348i
$940$		0			0
$941$	16.6260			0.541991			0.270995	−	0.962581i	$-0.412647\pi$
$941$	16.6260			0.541991			0.270995	+	0.962581i	$0.412647\pi$
$942$		0			0
$943$		−	57.8098i		−	1.88255i
$944$		0			0
$945$	−21.2640	+	12.9697i	−0.691718	+	0.421903i
$946$		0			0
$947$			12.5702i			0.408477i	0.978921	+	0.204238i	$0.0654718\pi$
$947$			12.5702i			0.408477i	−0.978921	+	0.204238i	$0.934528\pi$
$948$		0			0
$949$	−19.0899			−0.619684
$950$		0			0
$951$	−13.1352	−	25.5562i	−0.425940	−	0.828715i
$952$		0			0
$953$			47.3870i			1.53502i	0.641040	+	0.767508i	$0.278503\pi$
$953$			47.3870i			1.53502i	−0.641040	+	0.767508i	$0.721497\pi$
$954$		0			0
$955$	27.3639	−	15.7986i	0.885476	−	0.511230i
$956$		0			0
$957$	−1.90466	+	0.978950i	−0.0615690	+	0.0316450i
$958$		0			0
$959$	0.120704	+	0.0444719i	0.00389773	+	0.00143607i
$960$		0			0
$961$	−72.4054			−2.33566
$962$		0			0
$963$	20.4322	−	9.27022i	0.658417	−	0.298729i
$964$		0			0
$965$	−21.6073	−	37.4249i	−0.695562	−	1.20475i
$966$		0			0
$967$	−11.6171	+	20.1215i	−0.373582	+	0.647063i	−0.990114	−	0.140267i	$-0.955204\pi$
$967$	−11.6171	+	20.1215i	−0.373582	+	0.647063i	0.616532	+	0.787330i	$0.288537\pi$
$968$		0			0
$969$	−4.55661	−	8.86542i	−0.146379	−	0.284798i
$970$		0			0
$971$	−21.1024	+	36.5504i	−0.677208	+	1.17296i	0.298610	+	0.954375i	$0.403477\pi$
$971$	−21.1024	+	36.5504i	−0.677208	+	1.17296i	−0.975818	+	0.218583i	$0.929856\pi$
$972$		0			0
$973$	8.48426	+	3.12593i	0.271993	+	0.100213i
$974$		0			0
$975$	−10.7510	+	16.6836i	−0.344308	+	0.534303i
$976$		0			0
$977$		−	29.7413i		−	0.951510i	−0.879578	−	0.475755i	$-0.842175\pi$
$977$		−	29.7413i		−	0.951510i	0.879578	−	0.475755i	$-0.157825\pi$
$978$		0			0
$979$	−0.167716	+	0.0968307i	−0.00536022	+	0.00309472i
$980$		0			0
$981$	25.4807	+	2.49655i	0.813537	+	0.0797089i
$982$		0			0
$983$	−8.79843	+	15.2393i	−0.280626	+	0.486059i	−0.971539	−	0.236879i	$-0.923876\pi$
$983$	−8.79843	+	15.2393i	−0.280626	+	0.486059i	0.690913	+	0.722938i	$0.257209\pi$
$984$		0			0
$985$	−30.0105	+	17.3266i	−0.956215	+	0.552071i
$986$		0			0
$987$	43.7184	−	32.9159i	1.39157	−	1.04772i
$988$		0			0
$989$	11.0170	+	6.36067i	0.350321	+	0.202258i
$990$		0			0
$991$	8.84717	+	15.3238i	0.281040	+	0.486775i	0.971641	−	0.236461i	$-0.0759874\pi$
$991$	8.84717	+	15.3238i	0.281040	+	0.486775i	−0.690601	+	0.723236i	$0.742654\pi$
$992$		0			0
$993$	−7.26666	+	3.73489i	−0.230601	+	0.118523i
$994$		0			0
$995$	−9.33399	−	5.38898i	−0.295907	−	0.170842i
$996$		0			0
$997$	−31.5932	−	18.2403i	−1.00057	−	0.577677i	−0.0921505	−	0.995745i	$-0.529374\pi$
$997$	−31.5932	−	18.2403i	−1.00057	−	0.577677i	−0.908416	+	0.418068i	$0.862707\pi$
$998$		0			0
$999$	−13.4856	−	10.6862i	−0.426665	−	0.338095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bs.a.257.4	✓	48
3.2	odd	2		1512.2.bs.a.1097.19		48
4.3	odd	2		1008.2.ca.e.257.21		48
7.3	odd	6		504.2.cx.a.185.5	yes	48
9.2	odd	6		504.2.cx.a.425.5	yes	48
9.7	even	3		1512.2.cx.a.89.19		48
12.11	even	2		3024.2.ca.e.2609.19		48
21.17	even	6		1512.2.cx.a.17.19		48
28.3	even	6		1008.2.df.e.689.20		48
36.7	odd	6		3024.2.df.e.1601.19		48
36.11	even	6		1008.2.df.e.929.20		48
63.38	even	6	inner	504.2.bs.a.353.4	yes	48
63.52	odd	6		1512.2.bs.a.521.19		48
84.59	odd	6		3024.2.df.e.17.19		48
252.115	even	6		3024.2.ca.e.2033.19		48
252.227	odd	6		1008.2.ca.e.353.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.4	✓	48	1.1	even	1	trivial
504.2.bs.a.353.4	yes	48	63.38	even	6	inner
504.2.cx.a.185.5	yes	48	7.3	odd	6
504.2.cx.a.425.5	yes	48	9.2	odd	6
1008.2.ca.e.257.21		48	4.3	odd	2
1008.2.ca.e.353.21		48	252.227	odd	6
1008.2.df.e.689.20		48	28.3	even	6
1008.2.df.e.929.20		48	36.11	even	6
1512.2.bs.a.521.19		48	63.52	odd	6
1512.2.bs.a.1097.19		48	3.2	odd	2
1512.2.cx.a.17.19		48	21.17	even	6
1512.2.cx.a.89.19		48	9.7	even	3
3024.2.ca.e.2033.19		48	252.115	even	6
3024.2.ca.e.2609.19		48	12.11	even	2
3024.2.df.e.17.19		48	84.59	odd	6
3024.2.df.e.1601.19		48	36.7	odd	6

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.54049 + 0.791772i) q^{3} +(-0.905867 - 1.56901i) q^{5} +(-2.60735 + 0.449161i) q^{7} +(1.74619 - 2.43943i) q^{9} +O(q^{10})\)	\(q+(-1.54049 + 0.791772i) q^{3} +(-0.905867 - 1.56901i) q^{5} +(-2.60735 + 0.449161i) q^{7} +(1.74619 - 2.43943i) q^{9} +(-0.221585 - 0.127932i) q^{11} +(5.77765 + 3.33573i) q^{13} +(2.63777 + 1.69979i) q^{15} +(1.99857 + 3.46163i) q^{17} +(1.24687 + 0.719882i) q^{19} +(3.66095 - 2.75635i) q^{21} +(4.90746 - 2.83332i) q^{23} +(0.858809 - 1.48750i) q^{25} +(-0.758514 + 5.14049i) q^{27} +(-4.18486 + 2.41613i) q^{29} +10.1688i q^{31} +(0.442641 + 0.0216328i) q^{33} +(3.06665 + 3.68407i) q^{35} +(-1.65567 + 2.86771i) q^{37} +(-11.5415 - 0.564058i) q^{39} +(5.10089 - 8.83499i) q^{41} +(1.12248 + 1.94419i) q^{43} +(-5.40930 - 0.529993i) q^{45} +11.9418 q^{47} +(6.59651 - 2.34224i) q^{49} +(-5.81960 - 3.75018i) q^{51} +(3.97466 - 2.29477i) q^{53} +0.463558i q^{55} +(-2.49077 - 0.121729i) q^{57} -5.11151 q^{59} +9.93297i q^{61} +(-3.45723 + 7.14476i) q^{63} -12.0869i q^{65} +1.92427 q^{67} +(-5.31652 + 8.25028i) q^{69} -7.31241i q^{71} +(-2.47807 + 1.43071i) q^{73} +(-0.145221 + 2.97145i) q^{75} +(0.635210 + 0.234036i) q^{77} -3.66306 q^{79} +(-2.90162 - 8.51943i) q^{81} +(-2.68261 - 4.64642i) q^{83} +(3.62089 - 6.27156i) q^{85} +(4.53370 - 7.03548i) q^{87} +(0.378446 - 0.655488i) q^{89} +(-16.5626 - 6.10230i) q^{91} +(-8.05141 - 15.6650i) q^{93} -2.60847i q^{95} +(-4.21765 + 2.43506i) q^{97} +(-0.699011 + 0.317146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{9}+O(q^{10}) \) 48 * q - 4 * q^9	\( 48 q - 4 q^{9} + 8 q^{15} + 8 q^{21} - 12 q^{23} - 24 q^{25} - 18 q^{27} + 18 q^{29} - 10 q^{39} + 6 q^{41} - 6 q^{43} + 6 q^{45} + 36 q^{47} + 6 q^{49} - 12 q^{51} + 12 q^{53} + 4 q^{57} + 46 q^{63} - 54 q^{75} - 36 q^{77} - 12 q^{79} - 24 q^{87} + 18 q^{89} + 6 q^{91} + 16 q^{93} - 64 q^{99}+O(q^{100}) \) 48 * q - 4 * q^9 + 8 * q^15 + 8 * q^21 - 12 * q^23 - 24 * q^25 - 18 * q^27 + 18 * q^29 - 10 * q^39 + 6 * q^41 - 6 * q^43 + 6 * q^45 + 36 * q^47 + 6 * q^49 - 12 * q^51 + 12 * q^53 + 4 * q^57 + 46 * q^63 - 54 * q^75 - 36 * q^77 - 12 * q^79 - 24 * q^87 + 18 * q^89 + 6 * q^91 + 16 * q^93 - 64 * q^99

Introduction

L-functions

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Database

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