LMFDB - Embedded newform 504.2.bm.c.107.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(107,504)]

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([3, 3, 3, 2]))

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

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

chi := DirichletCharacter("504.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.bm (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			107.12
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.c.179.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0218210 - 1.41405i) q^{2} +(-1.99905 + 0.0617118i) q^{4} +(-0.317795 + 0.550436i) q^{5} +(2.11900 + 1.58425i) q^{7} +(0.130884 + 2.82540i) q^{8} +O(q^{10})$	\(q+(-0.0218210 - 1.41405i) q^{2} +(-1.99905 + 0.0617118i) q^{4} +(-0.317795 + 0.550436i) q^{5} +(2.11900 + 1.58425i) q^{7} +(0.130884 + 2.82540i) q^{8} +(0.785276 + 0.437365i) q^{10} +(-3.16457 + 1.82707i) q^{11} +4.15869i q^{13} +(2.19396 - 3.03093i) q^{14} +(3.99238 - 0.246730i) q^{16} +(-3.01908 + 1.74306i) q^{17} +(-1.99238 + 3.45090i) q^{19} +(0.601318 - 1.11996i) q^{20} +(2.65261 + 4.43498i) q^{22} +(1.47015 - 2.54638i) q^{23} +(2.29801 + 3.98028i) q^{25} +(5.88058 - 0.0907468i) q^{26} +(-4.33375 - 3.03622i) q^{28} +6.35746 q^{29} +(5.20467 - 3.00492i) q^{31} +(-0.436004 - 5.64003i) q^{32} +(2.53065 + 4.23107i) q^{34} +(-1.54543 + 0.662908i) q^{35} +(1.59870 + 0.923007i) q^{37} +(4.92321 + 2.74201i) q^{38} +(-1.59680 - 0.825852i) q^{40} -10.4931i q^{41} -2.83895 q^{43} +(6.21338 - 3.84768i) q^{44} +(-3.63278 - 2.02330i) q^{46} +(-4.61494 + 7.99332i) q^{47} +(1.98031 + 6.71404i) q^{49} +(5.57814 - 3.33635i) q^{50} +(-0.256640 - 8.31342i) q^{52} +(2.99666 + 5.19038i) q^{53} -2.32253i q^{55} +(-4.19879 + 6.19437i) q^{56} +(-0.138726 - 8.98974i) q^{58} +(-9.10070 + 5.25429i) q^{59} +(1.72447 + 0.995622i) q^{61} +(-4.36266 - 7.29407i) q^{62} +(-7.96574 + 0.739601i) q^{64} +(-2.28909 - 1.32161i) q^{65} +(-8.01122 - 13.8758i) q^{67} +(5.92771 - 3.67078i) q^{68} +(0.971104 + 2.17085i) q^{70} +0.737952 q^{71} +(2.13696 + 3.70132i) q^{73} +(1.27029 - 2.28077i) q^{74} +(3.76990 - 7.02147i) q^{76} +(-9.60025 - 1.14192i) q^{77} +(-7.74900 - 4.47389i) q^{79} +(-1.13295 + 2.27596i) q^{80} +(-14.8377 + 0.228970i) q^{82} +3.67740i q^{83} -2.21574i q^{85} +(0.0619487 + 4.01440i) q^{86} +(-5.57638 - 8.70204i) q^{88} +(4.63483 + 2.67592i) q^{89} +(-6.58841 + 8.81226i) q^{91} +(-2.78177 + 5.18107i) q^{92} +(11.4036 + 6.35132i) q^{94} +(-1.26633 - 2.19335i) q^{95} +17.6696 q^{97} +(9.45075 - 2.94675i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) $ 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−0.0218210	−	1.41405i	−0.0154298	−	0.999881i
$2$	−0.0218210	−	1.41405i	−0.0154298	−	0.999881i
$3$		0			0
$3$		0			0
$4$	−1.99905	+	0.0617118i	−0.999524	+	0.0308559i
$5$	−0.317795	+	0.550436i	−0.142122	+	0.246163i	−0.928296	−	0.371843i	$-0.878726\pi$
$5$	−0.317795	+	0.550436i	−0.142122	+	0.246163i	0.786173	+	0.618006i	$0.212059\pi$
$6$		0			0
$7$	2.11900	+	1.58425i	0.800906	+	0.598790i
$7$	2.11900	+	1.58425i	0.800906	+	0.598790i
$8$	0.130884	+	2.82540i	0.0462746	+	0.998929i
$9$		0			0
$10$	0.785276	+	0.437365i	0.248326	+	0.138307i
$11$	−3.16457	+	1.82707i	−0.954155	+	0.550881i	−0.894369	−	0.447330i	$-0.852375\pi$
$11$	−3.16457	+	1.82707i	−0.954155	+	0.550881i	−0.0597855	+	0.998211i	$0.519042\pi$
$12$		0			0
$13$			4.15869i			1.15341i	0.816951	+	0.576707i	$0.195662\pi$
$13$			4.15869i			1.15341i	−0.816951	+	0.576707i	$0.804338\pi$
$14$	2.19396	−	3.03093i	0.586361	−	0.810050i
$15$		0			0
$16$	3.99238	−	0.246730i	0.998096	−	0.0616824i
$17$	−3.01908	+	1.74306i	−0.732233	+	0.422755i	−0.819239	−	0.573453i	$-0.805604\pi$
$17$	−3.01908	+	1.74306i	−0.732233	+	0.422755i	0.0870053	+	0.996208i	$0.472270\pi$
$18$		0			0
$19$	−1.99238	+	3.45090i	−0.457083	+	0.791691i	−0.998805	−	0.0488665i	$-0.984439\pi$
$19$	−1.99238	+	3.45090i	−0.457083	+	0.791691i	0.541722	+	0.840558i	$0.317772\pi$
$20$	0.601318	−	1.11996i	0.134459	−	0.250431i
$21$		0			0
$22$	2.65261	+	4.43498i	0.565538	+	0.945541i
$23$	1.47015	−	2.54638i	0.306548	−	0.530957i	−0.671056	−	0.741406i	$-0.734159\pi$
$23$	1.47015	−	2.54638i	0.306548	−	0.530957i	0.977605	+	0.210449i	$0.0674925\pi$
$24$		0			0
$25$	2.29801	+	3.98028i	0.459603	+	0.796055i
$26$	5.88058	−	0.0907468i	1.15328	−	0.0177969i
$27$		0			0
$28$	−4.33375	−	3.03622i	−0.819001	−	0.573792i
$29$	6.35746			1.18055			0.590275	−	0.807202i	$-0.299019\pi$
$29$	6.35746			1.18055			0.590275	+	0.807202i	$0.299019\pi$
$30$		0			0
$31$	5.20467	−	3.00492i	0.934787	−	0.539699i	0.0464645	−	0.998920i	$-0.485205\pi$
$31$	5.20467	−	3.00492i	0.934787	−	0.539699i	0.888322	+	0.459221i	$0.151871\pi$
$32$	−0.436004	−	5.64003i	−0.0770754	−	0.997025i
$33$		0			0
$34$	2.53065	+	4.23107i	0.434003	+	0.725623i
$35$	−1.54543	+	0.662908i	−0.261226	+	0.112052i
$36$		0			0
$37$	1.59870	+	0.923007i	0.262824	+	0.151741i	0.625622	−	0.780126i	$-0.284845\pi$
$37$	1.59870	+	0.923007i	0.262824	+	0.151741i	−0.362798	+	0.931868i	$0.618179\pi$
$38$	4.92321	+	2.74201i	0.798649	+	0.444813i
$39$		0			0
$40$	−1.59680	−	0.825852i	−0.252476	−	0.130579i
$41$		−	10.4931i		−	1.63874i	−0.573262	−	0.819372i	$-0.694322\pi$
$41$		−	10.4931i		−	1.63874i	0.573262	−	0.819372i	$-0.305678\pi$
$42$		0			0
$43$	−2.83895			−0.432935			−0.216468	−	0.976290i	$-0.569454\pi$
$43$	−2.83895			−0.432935			−0.216468	+	0.976290i	$0.569454\pi$
$44$	6.21338	−	3.84768i	0.936702	−	0.580060i
$45$		0			0
$46$	−3.63278	−	2.02330i	−0.535624	−	0.298319i
$47$	−4.61494	+	7.99332i	−0.673159	+	1.16595i	0.303845	+	0.952722i	$0.401730\pi$
$47$	−4.61494	+	7.99332i	−0.673159	+	1.16595i	−0.977003	+	0.213224i	$0.931604\pi$
$48$		0			0
$49$	1.98031	+	6.71404i	0.282901	+	0.959149i
$50$	5.57814	−	3.33635i	0.788869	−	0.471831i
$51$		0			0
$52$	−0.256640	−	8.31342i	−0.0355896	−	1.15286i
$53$	2.99666	+	5.19038i	0.411624	+	0.712953i	0.995067	−	0.0992005i	$-0.0316285\pi$
$53$	2.99666	+	5.19038i	0.411624	+	0.712953i	−0.583444	+	0.812153i	$0.698295\pi$
$54$		0			0
$55$		−	2.32253i		−	0.313170i
$56$	−4.19879	+	6.19437i	−0.561087	+	0.827757i
$57$		0			0
$58$	−0.138726	−	8.98974i	−0.0182156	−	1.18041i
$59$	−9.10070	+	5.25429i	−1.18481	+	0.684050i	−0.957122	−	0.289684i	$-0.906450\pi$
$59$	−9.10070	+	5.25429i	−1.18481	+	0.684050i	−0.227688	+	0.973734i	$0.573117\pi$
$60$		0			0
$61$	1.72447	+	0.995622i	0.220795	+	0.127476i	0.606319	−	0.795222i	$-0.292646\pi$
$61$	1.72447	+	0.995622i	0.220795	+	0.127476i	−0.385523	+	0.922698i	$0.625979\pi$
$62$	−4.36266	−	7.29407i	−0.554059	−	0.926348i
$63$		0			0
$64$	−7.96574	+	0.739601i	−0.995717	+	0.0924501i
$65$	−2.28909	−	1.32161i	−0.283927	−	0.163925i
$66$		0			0
$67$	−8.01122	−	13.8758i	−0.978726	−	1.69520i	−0.667048	−	0.745015i	$-0.732442\pi$
$67$	−8.01122	−	13.8758i	−0.978726	−	1.69520i	−0.311678	−	0.950188i	$-0.600891\pi$
$68$	5.92771	−	3.67078i	0.718840	−	0.445147i
$69$		0			0
$70$	0.971104	+	2.17085i	0.116069	+	0.259466i
$71$	0.737952			0.0875788			0.0437894	−	0.999041i	$-0.486057\pi$
$71$	0.737952			0.0875788			0.0437894	+	0.999041i	$0.486057\pi$
$72$		0			0
$73$	2.13696	+	3.70132i	0.250112	+	0.433207i	0.963557	−	0.267505i	$-0.0861991\pi$
$73$	2.13696	+	3.70132i	0.250112	+	0.433207i	−0.713444	+	0.700712i	$0.752866\pi$
$74$	1.27029	−	2.28077i	0.147668	−	0.265134i
$75$		0			0
$76$	3.76990	−	7.02147i	0.432437	−	0.805418i
$77$	−9.60025	−	1.14192i	−1.09405	−	0.130134i
$78$		0			0
$79$	−7.74900	−	4.47389i	−0.871830	−	0.503351i	−0.00387425	−	0.999992i	$-0.501233\pi$
$79$	−7.74900	−	4.47389i	−0.871830	−	0.503351i	−0.867956	+	0.496641i	$0.834567\pi$
$80$	−1.13295	+	2.27596i	−0.126668	+	0.254460i
$81$		0			0
$82$	−14.8377	+	0.228970i	−1.63855	+	0.0252855i
$83$			3.67740i			0.403647i	0.979422	+	0.201823i	$0.0646867\pi$
$83$			3.67740i			0.403647i	−0.979422	+	0.201823i	$0.935313\pi$
$84$		0			0
$85$		−	2.21574i		−	0.240331i
$86$	0.0619487	+	4.01440i	0.00668010	+	0.432884i
$87$		0			0
$88$	−5.57638	−	8.70204i	−0.594444	−	0.927641i
$89$	4.63483	+	2.67592i	0.491291	+	0.283647i	0.725110	−	0.688633i	$-0.241789\pi$
$89$	4.63483	+	2.67592i	0.491291	+	0.283647i	−0.233819	+	0.972280i	$0.575122\pi$
$90$		0			0
$91$	−6.58841	+	8.81226i	−0.690653	+	0.923776i
$92$	−2.78177	+	5.18107i	−0.290019	+	0.540163i
$93$		0			0
$94$	11.4036	+	6.35132i	1.17619	+	0.655088i
$95$	−1.26633	−	2.19335i	−0.129923	−	0.225033i
$96$		0			0
$97$	17.6696			1.79407			0.897036	−	0.441958i	$-0.145716\pi$
$97$	17.6696			1.79407			0.897036	+	0.441958i	$0.145716\pi$
$98$	9.45075	−	2.94675i	0.954670	−	0.297667i
$99$		0			0
$100$	−4.83947	−	7.81495i	−0.483947	−	0.781495i
$101$	6.12560	+	10.6099i	0.609520	+	1.05572i	0.991320	+	0.131475i	$0.0419712\pi$
$101$	6.12560	+	10.6099i	0.609520	+	1.05572i	−0.381799	+	0.924245i	$0.624695\pi$
$102$		0			0
$103$	2.71030	+	1.56479i	0.267054	+	0.154184i	0.627548	−	0.778578i	$-0.284059\pi$
$103$	2.71030	+	1.56479i	0.267054	+	0.154184i	−0.360494	+	0.932761i	$0.617392\pi$
$104$	−11.7500	+	0.544308i	−1.15218	+	0.0533738i
$105$		0			0
$106$	7.27404	−	4.35068i	0.706517	−	0.422575i
$107$	−5.64238	−	3.25763i	−0.545470	−	0.314927i	0.201823	−	0.979422i	$-0.435313\pi$
$107$	−5.64238	−	3.25763i	−0.545470	−	0.314927i	−0.747293	+	0.664495i	$0.768647\pi$
$108$		0			0
$109$	−1.23586	+	0.713527i	−0.118374	+	0.0683435i	−0.558018	−	0.829829i	$-0.688438\pi$
$109$	−1.23586	+	0.713527i	−0.118374	+	0.0683435i	0.439644	+	0.898172i	$0.355105\pi$
$110$	−3.28416	+	0.0506799i	−0.313132	+	0.00483214i
$111$		0			0
$112$	8.85073	+	5.80211i	0.836316	+	0.548248i
$113$		−	3.27992i		−	0.308549i	−0.988028	−	0.154275i	$-0.950696\pi$
$113$		−	3.27992i		−	0.308549i	0.988028	−	0.154275i	$-0.0493040\pi$
$114$		0			0
$115$	0.934414	+	1.61845i	0.0871346	+	0.150922i
$116$	−12.7089	+	0.392330i	−1.17999	+	0.0364269i
$117$		0			0
$118$	7.62839	+	12.7541i	0.702250	+	1.17411i
$119$	−9.15886	−	1.08942i	−0.839592	−	0.0998669i
$120$		0			0
$121$	1.17635	−	2.03749i	0.106941	−	0.185226i
$122$	1.37022	−	2.46020i	0.124054	−	0.222736i
$123$		0			0
$124$	−10.2189	+	6.32817i	−0.917689	+	0.568286i
$125$	−6.09913			−0.545523
$126$		0			0
$127$		−	19.0629i		−	1.69156i	−0.533535	−	0.845778i	$-0.679137\pi$
$127$		−	19.0629i		−	1.69156i	0.533535	−	0.845778i	$-0.320863\pi$
$128$	1.21965	+	11.2478i	0.107803	+	0.994172i
$129$		0			0
$130$	−1.81887	+	3.26572i	−0.159525	+	0.286423i
$131$	11.2577	+	6.49965i	0.983591	+	0.567877i	0.903352	−	0.428899i	$-0.141098\pi$
$131$	11.2577	+	6.49965i	0.983591	+	0.567877i	0.0802388	+	0.996776i	$0.474432\pi$
$132$		0			0
$133$	−9.68893	+	4.15603i	−0.840137	+	0.360373i
$134$	−19.4462	+	11.6310i	−1.67990	+	1.00477i
$135$		0			0
$136$	−5.32000	−	8.30195i	−0.456186	−	0.711886i
$137$	1.17651	−	0.679257i	0.100516	−	0.0580329i	−0.448899	−	0.893582i	$-0.648184\pi$
$137$	1.17651	−	0.679257i	0.100516	−	0.0580329i	0.549415	+	0.835549i	$0.314851\pi$
$138$		0			0
$139$	−3.06037			−0.259577			−0.129788	−	0.991542i	$-0.541430\pi$
$139$	−3.06037			−0.259577			−0.129788	+	0.991542i	$0.541430\pi$
$140$	3.04849	−	1.42056i	0.257644	−	0.120059i
$141$		0			0
$142$	−0.0161029	−	1.04350i	−0.00135132	−	0.0875684i
$143$	−7.59821	−	13.1605i	−0.635394	−	1.10053i
$144$		0			0
$145$	−2.02037	+	3.49938i	−0.167782	+	0.290607i
$146$	5.18721	−	3.10253i	0.429297	−	0.256767i
$147$		0			0
$148$	−3.25283	−	1.74648i	−0.267381	−	0.143560i
$149$	8.15986	−	14.1333i	0.668481	−	1.15784i	−0.309847	−	0.950786i	$-0.600278\pi$
$149$	8.15986	−	14.1333i	0.668481	−	1.15784i	0.978329	−	0.207057i	$-0.0663887\pi$
$150$		0			0
$151$	7.81057	−	4.50943i	0.635615	−	0.366972i	−0.147309	−	0.989091i	$-0.547061\pi$
$151$	7.81057	−	4.50943i	0.635615	−	0.366972i	0.782923	+	0.622118i	$0.213728\pi$
$152$	−10.0109	−	5.17759i	−0.811994	−	0.419958i
$153$		0			0
$154$	−1.40524	+	13.6001i	−0.113238	+	1.09593i
$155$			3.81979i			0.306813i
$156$		0			0
$157$	−20.0104	+	11.5530i	−1.59700	+	0.922031i	−0.604944	+	0.796268i	$0.706804\pi$
$157$	−20.0104	+	11.5530i	−1.59700	+	0.922031i	−0.992060	+	0.125763i	$0.959862\pi$
$158$	−6.15719	+	11.0551i	−0.489839	+	0.879493i
$159$		0			0
$160$	3.24304	+	1.55238i	0.256384	+	0.122726i
$161$	7.14936	−	3.06669i	0.563449	−	0.241689i
$162$		0			0
$163$	6.10214	−	10.5692i	0.477956	−	0.827845i	−0.521724	−	0.853114i	$-0.674711\pi$
$163$	6.10214	−	10.5692i	0.477956	−	0.827845i	0.999681	+	0.0252693i	$0.00804434\pi$
$164$	0.647547	+	20.9762i	0.0505649	+	1.63796i
$165$		0			0
$166$	5.20000	−	0.0802445i	0.403599	−	0.00622818i
$167$	3.33534			0.258096			0.129048	−	0.991638i	$-0.458808\pi$
$167$	3.33534			0.258096			0.129048	+	0.991638i	$0.458808\pi$
$168$		0			0
$169$	−4.29472			−0.330363
$170$	−3.13316	+	0.0483498i	−0.240303	+	0.00370826i
$171$		0			0
$172$	5.67519	−	0.175196i	0.432729	−	0.0133586i
$173$	−4.79217	+	8.30028i	−0.364342	+	0.631058i	−0.988670	−	0.150104i	$-0.952039\pi$
$173$	−4.79217	+	8.30028i	−0.364342	+	0.631058i	0.624329	+	0.781162i	$0.285373\pi$
$174$		0			0
$175$	−1.43626	+	12.0748i	−0.108571	+	0.912771i
$176$	−12.1834	+	8.07514i	−0.918358	+	0.608687i
$177$		0			0
$178$	3.68273	−	6.61224i	0.276032	−	0.495609i
$179$	0.0283182	−	0.0163495i	0.00211660	−	0.00122202i	−0.498941	−	0.866636i	$-0.666278\pi$
$179$	0.0283182	−	0.0163495i	0.00211660	−	0.00122202i	0.501058	+	0.865414i	$0.332944\pi$
$180$		0			0
$181$		−	19.3654i		−	1.43942i	−0.694277	−	0.719708i	$-0.744276\pi$
$181$		−	19.3654i		−	1.43942i	0.694277	−	0.719708i	$-0.255724\pi$
$182$	12.6047	+	9.12401i	0.934323	+	0.676317i
$183$		0			0
$184$	7.38696	+	3.82049i	0.544574	+	0.281650i
$185$	−1.01611	+	0.586653i	−0.0747061	+	0.0431316i
$186$		0			0
$187$	6.36939	−	11.0321i	0.465776	−	0.806747i
$188$	8.73221	−	16.2638i	0.636862	−	1.18616i
$189$		0			0
$190$	−3.07387	+	1.83851i	−0.223002	+	0.133380i
$191$	−1.50826	+	2.61239i	−0.109134	+	0.189026i	−0.915420	−	0.402501i	$-0.868141\pi$
$191$	−1.50826	+	2.61239i	−0.109134	+	0.189026i	0.806286	+	0.591526i	$0.201474\pi$
$192$		0			0
$193$	−10.9565	−	18.9772i	−0.788666	−	1.36601i	−0.926785	−	0.375593i	$-0.877439\pi$
$193$	−10.9565	−	18.9772i	−0.788666	−	1.36601i	0.138119	−	0.990416i	$-0.455894\pi$
$194$	−0.385567	−	24.9855i	−0.0276821	−	1.79386i
$195$		0			0
$196$	−4.37306	−	13.2995i	−0.312362	−	0.949963i
$197$	15.2950			1.08972			0.544860	−	0.838527i	$-0.316583\pi$
$197$	15.2950			1.08972			0.544860	+	0.838527i	$0.316583\pi$
$198$		0			0
$199$	−2.77706	+	1.60334i	−0.196861	+	0.113658i	−0.595190	−	0.803585i	$-0.702923\pi$
$199$	−2.77706	+	1.60334i	−0.196861	+	0.113658i	0.398330	+	0.917242i	$0.369590\pi$
$200$	−10.9451	+	7.01376i	−0.773934	+	0.495947i
$201$		0			0
$202$	14.8691	−	8.89340i	1.04619	−	0.625737i
$203$	13.4715	+	10.0718i	0.945510	+	0.706902i
$204$		0			0
$205$	5.77577	+	3.33464i	0.403398	+	0.232902i
$206$	2.15355	−	3.86663i	0.150045	−	0.269401i
$207$		0			0
$208$	1.02607	+	16.6031i	0.0711453	+	1.15122i
$209$		−	14.5608i		−	1.00719i
$210$		0			0
$211$	−16.7059			−1.15008			−0.575040	−	0.818125i	$-0.695014\pi$
$211$	−16.7059			−1.15008			−0.575040	+	0.818125i	$0.695014\pi$
$212$	−6.31078	−	10.1909i	−0.433426	−	0.699912i
$213$		0			0
$214$	−4.48331	+	8.04967i	−0.306473	+	0.550264i
$215$	0.902202	−	1.56266i	0.0615297	−	0.106573i
$216$		0			0
$217$	15.7892	+	1.87808i	1.07184	+	0.127492i
$218$	1.03593	+	1.73200i	0.0701618	+	0.117306i
$219$		0			0
$220$	0.143327	+	4.64284i	0.00966312	+	0.313020i
$221$	−7.24887	−	12.5554i	−0.487611	−	0.844568i
$222$		0			0
$223$			19.1547i			1.28270i	0.767250	+	0.641348i	$0.221625\pi$
$223$			19.1547i			1.28270i	−0.767250	+	0.641348i	$0.778375\pi$
$224$	8.01132	−	12.6419i	0.535279	−	0.844676i
$225$		0			0
$226$	−4.63796	+	0.0715712i	−0.308512	+	0.00476084i
$227$	14.4962	−	8.36938i	0.962147	−	0.555496i	0.0653135	−	0.997865i	$-0.479195\pi$
$227$	14.4962	−	8.36938i	0.962147	−	0.555496i	0.896833	+	0.442369i	$0.145862\pi$
$228$		0			0
$229$	17.5029	+	10.1053i	1.15662	+	0.667777i	0.950492	−	0.310747i	$-0.100579\pi$
$229$	17.5029	+	10.1053i	1.15662	+	0.667777i	0.206131	+	0.978524i	$0.433913\pi$
$230$	2.26818	−	1.35662i	0.149559	−	0.0894529i
$231$		0			0
$232$	0.832093	+	17.9624i	0.0546296	+	1.17929i
$233$	17.3998	+	10.0458i	1.13990	+	0.658122i	0.946406	−	0.322979i	$-0.104684\pi$
$233$	17.3998	+	10.0458i	1.13990	+	0.658122i	0.193495	+	0.981101i	$0.438018\pi$
$234$		0			0
$235$	−2.93321	−	5.08047i	−0.191341	−	0.331413i
$236$	17.8685	−	11.0652i	1.16314	−	0.720283i
$237$		0			0
$238$	−1.34063	+	12.9748i	−0.0869003	+	0.841033i
$239$	13.2312			0.855855			0.427928	−	0.903813i	$-0.359244\pi$
$239$	13.2312			0.855855			0.427928	+	0.903813i	$0.359244\pi$
$240$		0			0
$241$	−5.90444	−	10.2268i	−0.380338	−	0.658765i	0.610772	−	0.791806i	$-0.290859\pi$
$241$	−5.90444	−	10.2268i	−0.380338	−	0.658765i	−0.991111	+	0.133041i	$0.957526\pi$
$242$	−2.90677	−	1.61895i	−0.186854	−	0.104070i
$243$		0			0
$244$	−3.50873	−	1.88388i	−0.224624	−	0.120603i
$245$	−4.32498	−	1.04365i	−0.276313	−	0.0666766i
$246$		0			0
$247$	−14.3512	−	8.28569i	−0.913147	−	0.527206i
$248$	9.17130	+	14.3120i	0.582378	+	0.908811i
$249$		0			0
$250$	0.133089	+	8.62444i	0.00841729	+	0.545458i
$251$		−	18.9939i		−	1.19888i	−0.800419	−	0.599441i	$-0.795390\pi$
$251$		−	18.9939i		−	1.19888i	0.800419	−	0.599441i	$-0.204610\pi$
$252$		0			0
$253$			10.7443i			0.675487i
$254$	−26.9558	+	0.415971i	−1.69135	+	0.0261003i
$255$		0			0
$256$	15.8782	−	1.97008i	0.992391	−	0.123130i
$257$	22.5458	+	13.0168i	1.40637	+	0.811966i	0.995036	−	0.0995204i	$-0.0317308\pi$
$257$	22.5458	+	13.0168i	1.40637	+	0.811966i	0.411331	+	0.911486i	$0.365064\pi$
$258$		0			0
$259$	1.92536	+	4.48858i	0.119636	+	0.278907i
$260$	4.65757	+	2.50070i	0.288850	+	0.155087i
$261$		0			0
$262$	8.94514	−	16.0607i	0.552632	−	0.992236i
$263$	13.3095	+	23.0527i	0.820698	+	1.42149i	0.905163	+	0.425064i	$0.139749\pi$
$263$	13.3095	+	23.0527i	0.820698	+	1.42149i	−0.0844650	+	0.996426i	$0.526918\pi$
$264$		0			0
$265$	−3.80929			−0.234003
$266$	6.08823	+	13.6099i	0.373294	+	0.834477i
$267$		0			0
$268$	16.8711	+	27.2441i	1.03057	+	1.66420i
$269$	−12.6453	−	21.9022i	−0.770995	−	1.33540i	−0.937018	−	0.349281i	$-0.886426\pi$
$269$	−12.6453	−	21.9022i	−0.770995	−	1.33540i	0.166022	−	0.986122i	$-0.446908\pi$
$270$		0			0
$271$	14.4561	+	8.34622i	0.878145	+	0.506997i	0.870046	−	0.492970i	$-0.164089\pi$
$271$	14.4561	+	8.34622i	0.878145	+	0.506997i	0.00809834	+	0.999967i	$0.497422\pi$
$272$	−11.6232	+	7.70387i	−0.704762	+	0.467116i
$273$		0			0
$274$	−0.986173	−	1.64881i	−0.0595769	−	0.0996085i
$275$	−14.5445	−	8.39725i	−0.877064	−	0.506373i
$276$		0			0
$277$	23.0279	−	13.2952i	1.38361	−	0.798830i	0.391029	−	0.920379i	$-0.372119\pi$
$277$	23.0279	−	13.2952i	1.38361	−	0.798830i	0.992585	+	0.121549i	$0.0387860\pi$
$278$	0.0667803	+	4.32750i	0.00400521	+	0.259546i
$279$		0			0
$280$	−2.07525	−	4.27970i	−0.124020	−	0.255761i
$281$		−	8.11615i		−	0.484169i	−0.970255	−	0.242085i	$-0.922169\pi$
$281$		−	8.11615i		−	0.484169i	0.970255	−	0.242085i	$-0.0778311\pi$
$282$		0			0
$283$	4.12929	+	7.15214i	0.245461	+	0.425150i	0.962261	−	0.272128i	$-0.0877274\pi$
$283$	4.12929	+	7.15214i	0.245461	+	0.425150i	−0.716800	+	0.697278i	$0.754394\pi$
$284$	−1.47520	+	0.0455403i	−0.0875371	+	0.00270232i
$285$		0			0
$286$	−18.4437	+	11.0314i	−1.09060	+	0.652299i
$287$	16.6237	−	22.2348i	0.981264	−	1.31248i
$288$		0			0
$289$	−2.42346	+	4.19755i	−0.142556	+	0.246915i
$290$	4.99236	+	2.78053i	0.293162	+	0.163278i
$291$		0			0
$292$	−4.50030	−	7.26725i	−0.263360	−	0.425284i
$293$	20.9952			1.22655			0.613277	−	0.789868i	$-0.289851\pi$
$293$	20.9952			1.22655			0.613277	+	0.789868i	$0.289851\pi$
$294$		0			0
$295$		−	6.67914i		−	0.388875i
$296$	−2.39862	+	4.63776i	−0.139417	+	0.269564i
$297$		0			0
$298$	−20.1632	−	11.2300i	−1.16802	−	0.650537i
$299$	10.5896	+	6.11392i	0.612414	+	0.353577i
$300$		0			0
$301$	−6.01572	−	4.49760i	−0.346741	−	0.259237i
$302$	−6.54698	−	10.9461i	−0.376736	−	0.629877i
$303$		0			0
$304$	−7.10290	+	14.2689i	−0.407379	+	0.818377i
$305$	−1.09605	+	0.632806i	−0.0627598	+	0.0362344i
$306$		0			0
$307$	18.1231			1.03434			0.517170	−	0.855882i	$-0.326985\pi$
$307$	18.1231			1.03434			0.517170	+	0.855882i	$0.326985\pi$
$308$	19.2618	+	1.69031i	1.09754	+	0.0963141i
$309$		0			0
$310$	5.40135	−	0.0833516i	0.306776	−	0.00473405i
$311$	−15.4208	−	26.7096i	−0.874433	−	1.51456i	−0.857366	−	0.514707i	$-0.827901\pi$
$311$	−15.4208	−	26.7096i	−0.874433	−	1.51456i	−0.0170667	−	0.999854i	$-0.505433\pi$
$312$		0			0
$313$	0.521916	−	0.903984i	0.0295004	−	0.0510962i	−0.850898	−	0.525330i	$-0.823942\pi$
$313$	0.521916	−	0.903984i	0.0295004	−	0.0510962i	0.880399	+	0.474234i	$0.157275\pi$
$314$	16.7731	+	28.0435i	0.946562	+	1.58259i
$315$		0			0
$316$	15.7667	+	8.46531i	0.886946	+	0.476211i
$317$	5.12901	−	8.88370i	0.288074	−	0.498958i	−0.685276	−	0.728283i	$-0.740319\pi$
$317$	5.12901	−	8.88370i	0.288074	−	0.498958i	0.973350	+	0.229325i	$0.0736518\pi$
$318$		0			0
$319$	−20.1186	+	11.6155i	−1.12643	+	0.650344i
$320$	2.12436	−	4.61967i	0.118756	−	0.258248i
$321$		0			0
$322$	−4.49244	−	10.0426i	−0.250354	−	0.559652i
$323$		−	13.8914i		−	0.772937i
$324$		0			0
$325$	−16.5527	+	9.55673i	−0.918181	+	0.530112i
$326$	−15.0785	−	8.39807i	−0.835121	−	0.465126i
$327$		0			0
$328$	29.6471	−	1.37338i	1.63699	−	0.0758323i
$329$	−22.4425	+	9.62660i	−1.23729	+	0.530732i
$330$		0			0
$331$	2.31756	−	4.01414i	0.127385	−	0.220637i	−0.795278	−	0.606245i	$-0.792675\pi$
$331$	2.31756	−	4.01414i	0.127385	−	0.220637i	0.922663	+	0.385608i	$0.126008\pi$
$332$	−0.226939	−	7.35129i	−0.0124549	−	0.403454i
$333$		0			0
$334$	−0.0727805	−	4.71632i	−0.00398237	−	0.258066i
$335$	10.1837			0.556394
$336$		0			0
$337$	−33.0263			−1.79906			−0.899528	−	0.436863i	$-0.856089\pi$
$337$	−33.0263			−1.79906			−0.899528	+	0.436863i	$0.856089\pi$
$338$	0.0937150	+	6.07292i	0.00509743	+	0.330324i
$339$		0			0
$340$	0.136738	+	4.42938i	0.00741563	+	0.240217i
$341$	−10.9804	+	19.0186i	−0.594621	+	1.02991i
$342$		0			0
$343$	−6.44045	+	17.3643i	−0.347752	+	0.937587i
$344$	−0.371574	−	8.02115i	−0.0200339	−	0.432472i
$345$		0			0
$346$	11.8415	+	6.59522i	0.636605	+	0.354561i
$347$	3.47551	−	2.00659i	0.186575	−	0.107719i	−0.403803	−	0.914846i	$-0.632312\pi$
$347$	3.47551	−	2.00659i	0.186575	−	0.107719i	0.590378	+	0.807127i	$0.298979\pi$
$348$		0			0
$349$		−	10.4671i		−	0.560291i	−0.959958	−	0.280145i	$-0.909617\pi$
$349$		−	10.4671i		−	0.560291i	0.959958	−	0.280145i	$-0.0903826\pi$
$350$	17.1057	+	1.76746i	0.914337	+	0.0944745i
$351$		0			0
$352$	11.6845	+	17.0517i	0.622785	+	0.908857i
$353$	−15.3486	+	8.86154i	−0.816925	+	0.471652i	−0.849355	−	0.527822i	$-0.823009\pi$
$353$	−15.3486	+	8.86154i	−0.816925	+	0.471652i	0.0324298	+	0.999474i	$0.489675\pi$
$354$		0			0
$355$	−0.234517	+	0.406196i	−0.0124469	+	0.0215586i
$356$	−9.43037	−	5.06326i	−0.499809	−	0.268352i
$357$		0			0
$358$	−0.0237369	−	0.0396865i	−0.00125453	−	0.00209750i
$359$	−6.52933	+	11.3091i	−0.344605	+	0.596873i	−0.985282	−	0.170937i	$-0.945320\pi$
$359$	−6.52933	+	11.3091i	−0.344605	+	0.596873i	0.640677	+	0.767811i	$0.278654\pi$
$360$		0			0
$361$	1.56085	+	2.70348i	0.0821503	+	0.142288i
$362$	−27.3835	+	0.422572i	−1.43924	+	0.0222099i
$363$		0			0
$364$	12.6267	−	18.0227i	0.661820	−	0.944647i
$365$	−2.71646			−0.142186
$366$		0			0
$367$	19.3899	−	11.1948i	1.01215	−	0.584363i	0.100327	−	0.994955i	$-0.468011\pi$
$367$	19.3899	−	11.1948i	1.01215	−	0.584363i	0.911819	+	0.410592i	$0.134678\pi$
$368$	5.24115	−	10.5289i	0.273214	−	0.548855i
$369$		0			0
$370$	0.851727	+	1.42403i	0.0442792	+	0.0740317i
$371$	−1.87292	+	15.7459i	−0.0972373	+	0.817484i
$372$		0			0
$373$	3.83798	+	2.21586i	0.198723	+	0.114733i	0.596060	−	0.802940i	$-0.296732\pi$
$373$	3.83798	+	2.21586i	0.198723	+	0.114733i	−0.397337	+	0.917673i	$0.630065\pi$
$374$	−15.7389	−	8.76587i	−0.813838	−	0.453272i
$375$		0			0
$376$	−23.1883	−	11.9928i	−1.19585	−	0.618484i
$377$			26.4387i			1.36166i
$378$		0			0
$379$	28.8901			1.48399			0.741993	−	0.670407i	$-0.233881\pi$
$379$	28.8901			1.48399			0.741993	+	0.670407i	$0.233881\pi$
$380$	2.66682	+	4.30647i	0.136805	+	0.220917i
$381$		0			0
$382$	3.72695	+	2.07575i	0.190687	+	0.106205i
$383$	−16.3811	+	28.3729i	−0.837037	+	1.44979i	0.0553247	+	0.998468i	$0.482381\pi$
$383$	−16.3811	+	28.3729i	−0.837037	+	1.44979i	−0.892361	+	0.451322i	$0.850953\pi$
$384$		0			0
$385$	3.67946	−	4.92143i	0.187523	−	0.250819i
$386$	−26.5955	+	15.9071i	−1.35368	+	0.809649i
$387$		0			0
$388$	−35.3223	+	1.09042i	−1.79322	+	0.0553576i
$389$	6.24881	+	10.8233i	0.316827	+	0.548761i	0.979824	−	0.199861i	$-0.0640490\pi$
$389$	6.24881	+	10.8233i	0.316827	+	0.548761i	−0.662997	+	0.748622i	$0.730716\pi$
$390$		0			0
$391$			10.2503i			0.518380i
$392$	−18.7106	+	6.47392i	−0.945030	+	0.326982i
$393$		0			0
$394$	−0.333751	−	21.6278i	−0.0168141	−	1.08959i
$395$	4.92518	−	2.84355i	0.247813	−	0.143075i
$396$		0			0
$397$	6.09678	+	3.51998i	0.305989	+	0.176663i	0.645130	−	0.764073i	$-0.276803\pi$
$397$	6.09678	+	3.51998i	0.305989	+	0.176663i	−0.339141	+	0.940735i	$0.610137\pi$
$398$	2.32779	+	3.89191i	0.116682	+	0.195084i
$399$		0			0
$400$	10.1566	+	15.3238i	0.507830	+	0.766190i
$401$	−25.7480	−	14.8656i	−1.28579	−	0.742353i	−0.307893	−	0.951421i	$-0.599624\pi$
$401$	−25.7480	−	14.8656i	−1.28579	−	0.742353i	−0.977901	+	0.209068i	$0.932957\pi$
$402$		0			0
$403$	12.4965	+	21.6446i	0.622497	+	1.07820i
$404$	−12.9001	−	20.8316i	−0.641805	−	1.03641i
$405$		0			0
$406$	13.9480	−	19.2690i	0.692229	−	0.956305i
$407$	−6.74558			−0.334366
$408$		0			0
$409$	−16.6222	−	28.7905i	−0.821914	−	1.42360i	−0.904255	−	0.426993i	$-0.859573\pi$
$409$	−16.6222	−	28.7905i	−0.821914	−	1.42360i	0.0823411	−	0.996604i	$-0.473760\pi$
$410$	4.58931	−	8.23997i	0.226650	−	0.406943i
$411$		0			0
$412$	−5.51459	−	2.96084i	−0.271684	−	0.145870i
$413$	−27.6085	−	3.28394i	−1.35852	−	0.161592i
$414$		0			0
$415$	−2.02417	−	1.16866i	−0.0993627	−	0.0573671i
$416$	23.4551	−	1.81321i	1.14998	−	0.0888998i
$417$		0			0
$418$	−20.5897	+	0.317732i	−1.00707	+	0.0155408i
$419$			8.95024i			0.437248i	0.975809	+	0.218624i	$0.0701568\pi$
$419$			8.95024i			0.437248i	−0.975809	+	0.218624i	$0.929843\pi$
$420$		0			0
$421$		−	26.3473i		−	1.28409i	−0.766667	−	0.642044i	$-0.778086\pi$
$421$		−	26.3473i		−	1.28409i	0.766667	−	0.642044i	$-0.221914\pi$
$422$	0.364539	+	23.6229i	0.0177455	+	1.14994i
$423$		0			0
$424$	−14.2727	+	9.14611i	−0.693141	+	0.444174i
$425$	−13.8758	−	8.01117i	−0.673073	−	0.388599i
$426$		0			0
$427$	2.07683	+	4.84171i	0.100505	+	0.234307i
$428$	11.4804	+	6.16396i	0.554927	+	0.297946i
$429$		0			0
$430$	−2.22936	−	1.24166i	−0.107509	−	0.0598780i
$431$	7.97354	+	13.8106i	0.384072	+	0.665232i	0.991640	−	0.129036i	$-0.0411882\pi$
$431$	7.97354	+	13.8106i	0.384072	+	0.665232i	−0.607568	+	0.794268i	$0.707855\pi$
$432$		0			0
$433$	12.5058			0.600991			0.300496	−	0.953783i	$-0.402848\pi$
$433$	12.5058			0.600991			0.300496	+	0.953783i	$0.402848\pi$
$434$	2.31115	−	22.3677i	0.110939	−	1.07368i
$435$		0			0
$436$	2.42652	−	1.50264i	0.116209	−	0.0719635i
$437$	5.85821	+	10.1467i	0.280236	+	0.485383i
$438$		0			0
$439$	−14.0552	−	8.11479i	−0.670820	−	0.387298i	0.125568	−	0.992085i	$-0.459925\pi$
$439$	−14.0552	−	8.11479i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$440$	6.56206	−	0.303983i	0.312834	−	0.0144918i
$441$		0			0
$442$	−17.5957	+	10.5242i	−0.836944	+	0.500585i
$443$	5.80303	+	3.35038i	0.275710	+	0.159181i	0.631480	−	0.775392i	$-0.282448\pi$
$443$	5.80303	+	3.35038i	0.275710	+	0.159181i	−0.355769	+	0.934574i	$0.615781\pi$
$444$		0			0
$445$	−2.94584	+	1.70078i	−0.139646	+	0.0806249i
$446$	27.0857	−	0.417976i	1.28254	−	0.0197917i
$447$		0			0
$448$	−18.0511	−	11.0525i	−0.852834	−	0.522182i
$449$			26.1155i			1.23246i	0.787565	+	0.616232i	$0.211342\pi$
$449$			26.1155i			1.23246i	−0.787565	+	0.616232i	$0.788658\pi$
$450$		0			0
$451$	19.1716	+	33.2061i	0.902754	+	1.56362i
$452$	0.202410	+	6.55672i	0.00952055	+	0.308402i
$453$		0			0
$454$	−12.1510	−	20.3157i	−0.570275	−	0.953461i
$455$	−2.75683	−	6.42699i	−0.129242	−	0.301302i
$456$		0			0
$457$	−16.0328	+	27.7697i	−0.749984	+	1.29901i	0.197846	+	0.980233i	$0.436606\pi$
$457$	−16.0328	+	27.7697i	−0.749984	+	1.29901i	−0.947830	+	0.318777i	$0.896728\pi$
$458$	13.9074	−	24.9704i	0.649851	−	1.16679i
$459$		0			0
$460$	−1.96782	−	3.17770i	−0.0917499	−	0.148161i
$461$	−39.2781			−1.82936			−0.914682	−	0.404175i	$-0.867559\pi$
$461$	−39.2781			−1.82936			−0.914682	+	0.404175i	$0.867559\pi$
$462$		0			0
$463$			2.26863i			0.105432i	0.998610	+	0.0527161i	$0.0167878\pi$
$463$			2.26863i			0.105432i	−0.998610	+	0.0527161i	$0.983212\pi$
$464$	25.3814	−	1.56857i	1.17830	−	0.0728192i
$465$		0			0
$466$	13.8255	−	24.8234i	0.640455	−	1.14992i
$467$	−20.8867	−	12.0590i	−0.966522	−	0.558022i	−0.0683480	−	0.997662i	$-0.521773\pi$
$467$	−20.8867	−	12.0590i	−0.966522	−	0.558022i	−0.898174	+	0.439640i	$0.855106\pi$
$468$		0			0
$469$	5.00703	−	42.0946i	0.231203	−	1.94375i
$470$	−7.12000	+	4.25855i	−0.328421	+	0.196432i
$471$		0			0
$472$	−16.0366	−	25.0254i	−0.738144	−	1.15189i
$473$	8.98406	−	5.18695i	0.413087	−	0.238496i
$474$		0			0
$475$	−18.3141			−0.840306
$476$	18.3762	+	1.61259i	0.842273	+	0.0739130i
$477$		0			0
$478$	−0.288718	−	18.7095i	−0.0132057	−	0.855753i
$479$	−6.19574	−	10.7313i	−0.283091	−	0.490328i	0.689054	−	0.724710i	$-0.258026\pi$
$479$	−6.19574	−	10.7313i	−0.283091	−	0.490328i	−0.972144	+	0.234383i	$0.924693\pi$
$480$		0			0
$481$	−3.83850	+	6.64848i	−0.175021	+	0.303145i
$482$	−14.3323	+	8.57230i	−0.652818	+	0.390458i
$483$		0			0
$484$	−2.22583	+	4.14564i	−0.101174	+	0.188438i
$485$	−5.61529	+	9.72596i	−0.254977	+	0.441633i
$486$		0			0
$487$	10.1179	−	5.84159i	0.458487	−	0.264708i	−0.252921	−	0.967487i	$-0.581391\pi$
$487$	10.1179	−	5.84159i	0.458487	−	0.264708i	0.711408	+	0.702779i	$0.248058\pi$
$488$	−2.58732	+	5.00262i	−0.117123	+	0.226458i
$489$		0			0
$490$	−1.38140	+	6.13850i	−0.0624052	+	0.277309i
$491$		−	42.8926i		−	1.93572i	−0.251498	−	0.967858i	$-0.580923\pi$
$491$		−	42.8926i		−	1.93572i	0.251498	−	0.967858i	$-0.419077\pi$
$492$		0			0
$493$	−19.1937	+	11.0815i	−0.864439	+	0.499084i
$494$	−11.4032	+	20.4741i	−0.513053	+	0.921173i
$495$		0			0
$496$	20.0376	−	13.2809i	0.899717	−	0.596332i
$497$	1.56372	+	1.16910i	0.0701424	+	0.0524413i
$498$		0			0
$499$	−4.49173	+	7.77991i	−0.201078	+	0.348277i	−0.948876	−	0.315649i	$-0.897778\pi$
$499$	−4.49173	+	7.77991i	−0.201078	+	0.348277i	0.747798	+	0.663926i	$0.231111\pi$
$500$	12.1925	−	0.376388i	0.545263	−	0.0168326i
$501$		0			0
$502$	−26.8582	+	0.414465i	−1.19874	+	0.0184985i
$503$	43.5055			1.93981			0.969907	−	0.243476i	$-0.0782878\pi$
$503$	43.5055			1.93981			0.969907	+	0.243476i	$0.0782878\pi$
$504$		0			0
$505$	−7.78673			−0.346505
$506$	15.1929	−	0.234451i	0.675407	−	0.0104226i
$507$		0			0
$508$	1.17640	+	38.1076i	0.0521945	+	1.69075i
$509$	−5.45911	+	9.45546i	−0.241971	+	0.419106i	−0.961276	−	0.275589i	$-0.911127\pi$
$509$	−5.45911	+	9.45546i	−0.241971	+	0.419106i	0.719305	+	0.694695i	$0.244460\pi$
$510$		0			0
$511$	−1.33561	+	11.2286i	−0.0590837	+	0.496723i
$512$	−3.13226	−	22.4096i	−0.138428	−	0.990373i
$513$		0			0
$514$	17.9144	−	32.1648i	0.790169	−	1.41873i
$515$	−1.72264	+	0.994565i	−0.0759085	+	0.0438258i
$516$		0			0
$517$		−	33.7272i		−	1.48332i
$518$	6.30504	−	2.82049i	0.277028	−	0.123925i
$519$		0			0
$520$	3.43446	−	6.64058i	0.150611	−	0.291209i
$521$	−19.4185	+	11.2113i	−0.850739	+	0.491174i	−0.860900	−	0.508774i	$-0.830099\pi$
$521$	−19.4185	+	11.2113i	−0.850739	+	0.491174i	0.0101612	+	0.999948i	$0.496766\pi$
$522$		0			0
$523$	−0.483187	+	0.836904i	−0.0211283	+	0.0365953i	−0.876396	−	0.481591i	$-0.840059\pi$
$523$	−0.483187	+	0.836904i	−0.0211283	+	0.0365953i	0.855268	+	0.518186i	$0.173393\pi$
$524$	−22.9058	−	12.2984i	−1.00065	−	0.537257i
$525$		0			0
$526$	32.3071	−	19.3232i	1.40866	−	0.842534i
$527$	−10.4755	+	18.1442i	−0.456321	+	0.790372i
$528$		0			0
$529$	7.17729	+	12.4314i	0.312056	+	0.540497i
$530$	0.0831226	+	5.38651i	0.00361062	+	0.233975i
$531$		0			0
$532$	19.1122	−	8.90602i	0.828618	−	0.386125i
$533$	43.6375			1.89015
$534$		0			0
$535$	3.58624	−	2.07051i	0.155046	−	0.0895161i
$536$	38.1562	−	24.4510i	1.64810	−	1.05612i
$537$		0			0
$538$	−30.6948	+	18.3589i	−1.32335	+	0.791509i
$539$	−18.5338	−	17.6289i	−0.798309	−	0.759332i
$540$		0			0
$541$	32.5318	+	18.7823i	1.39865	+	0.807512i	0.994251	−	0.107070i	$-0.0341469\pi$
$541$	32.5318	+	18.7823i	1.39865	+	0.807512i	0.404400	+	0.914582i	$0.367480\pi$
$542$	11.4865	−	20.6237i	0.493387	−	0.885863i
$543$		0			0
$544$	11.1473	+	16.2677i	0.477935	+	0.697471i
$545$		−	0.907020i		−	0.0388525i
$546$		0			0
$547$	13.8253			0.591126			0.295563	−	0.955323i	$-0.404493\pi$
$547$	13.8253			0.591126			0.295563	+	0.955323i	$0.404493\pi$
$548$	−2.30998	+	1.43047i	−0.0986773	+	0.0611067i
$549$		0			0
$550$	−11.5567	+	20.7498i	−0.492780	+	0.884773i
$551$	−12.6665	+	21.9390i	−0.539610	+	0.934632i
$552$		0			0
$553$	−9.33236	−	21.7565i	−0.396852	−	0.925180i
$554$	−19.3025	−	32.2724i	−0.820084	−	1.37112i
$555$		0			0
$556$	6.11782	−	0.188861i	0.259453	−	0.00800947i
$557$	−2.15732	−	3.73659i	−0.0914087	−	0.158325i	0.816695	−	0.577069i	$-0.195804\pi$
$557$	−2.15732	−	3.73659i	−0.0914087	−	0.158325i	−0.908104	+	0.418744i	$0.862470\pi$
$558$		0			0
$559$		−	11.8063i		−	0.499354i
$560$	−6.00641	+	3.02789i	−0.253817	+	0.127952i
$561$		0			0
$562$	−11.4766	+	0.177103i	−0.484111	+	0.00747062i
$563$	5.35371	−	3.09097i	0.225632	−	0.130269i	−0.382923	−	0.923780i	$-0.625083\pi$
$563$	5.35371	−	3.09097i	0.225632	−	0.130269i	0.608555	+	0.793511i	$0.291749\pi$
$564$		0			0
$565$	1.80539	+	1.04234i	0.0759532	+	0.0438516i
$566$	10.0233	−	5.99507i	0.421312	−	0.251991i
$567$		0			0
$568$	0.0965865	+	2.08501i	0.00405268	+	0.0874850i
$569$	−5.65848	−	3.26692i	−0.237216	−	0.136957i	0.376681	−	0.926343i	$-0.377065\pi$
$569$	−5.65848	−	3.26692i	−0.237216	−	0.136957i	−0.613896	+	0.789387i	$0.710399\pi$
$570$		0			0
$571$	−6.00146	−	10.3948i	−0.251153	−	0.435011i	0.712690	−	0.701479i	$-0.247477\pi$
$571$	−6.00146	−	10.3948i	−0.251153	−	0.435011i	−0.963844	+	0.266468i	$0.914143\pi$
$572$	16.0013	+	25.8395i	0.669049	+	1.08041i
$573$		0			0
$574$	−31.8038	−	23.0214i	−1.32746	−	0.960896i
$575$	13.5137			0.563562
$576$		0			0
$577$	1.42990	+	2.47666i	0.0595276	+	0.103105i	0.894253	−	0.447561i	$-0.147707\pi$
$577$	1.42990	+	2.47666i	0.0595276	+	0.103105i	−0.834726	+	0.550666i	$0.814374\pi$
$578$	5.98841	+	3.33528i	0.249085	+	0.138729i
$579$		0			0
$580$	3.82286	−	7.12010i	0.158735	−	0.295646i
$581$	−5.82591	+	7.79240i	−0.241700	+	0.323283i
$582$		0			0
$583$	−18.9663	−	10.9502i	−0.785505	−	0.453512i
$584$	−10.1780	+	6.52221i	−0.421169	+	0.269891i
$585$		0			0
$586$	−0.458137	−	29.6882i	−0.0189255	−	1.22641i
$587$			30.3998i			1.25473i	0.778723	+	0.627367i	$0.215868\pi$
$587$			30.3998i			1.25473i	−0.778723	+	0.627367i	$0.784132\pi$
$588$		0			0
$589$			23.9477i			0.986750i
$590$	−9.44460	+	0.145745i	−0.388828	+	0.00600025i
$591$		0			0
$592$	6.61034	+	3.29055i	0.271683	+	0.135241i
$593$	−1.46791	−	0.847496i	−0.0602797	−	0.0348025i	0.469557	−	0.882902i	$-0.344414\pi$
$593$	−1.46791	−	0.847496i	−0.0602797	−	0.0348025i	−0.529837	+	0.848100i	$0.677747\pi$
$594$		0			0
$595$	3.51029	−	4.69516i	0.143908	−	0.192483i
$596$	−15.4398	+	28.7567i	−0.632437	+	1.17792i
$597$		0			0
$598$	8.41428	−	15.1076i	0.344086	−	0.617796i
$599$	2.00010	+	3.46428i	0.0817219	+	0.141547i	0.903990	−	0.427554i	$-0.140625\pi$
$599$	2.00010	+	3.46428i	0.0817219	+	0.141547i	−0.822268	+	0.569101i	$0.807291\pi$
$600$		0			0
$601$	−33.9144			−1.38340			−0.691699	−	0.722186i	$-0.743138\pi$
$601$	−33.9144			−1.38340			−0.691699	+	0.722186i	$0.743138\pi$
$602$	−6.22854	+	8.60465i	−0.253856	+	0.350699i
$603$		0			0
$604$	−15.3354	+	9.49657i	−0.623989	+	0.386410i
$605$	0.747673	+	1.29501i	0.0303972	+	0.0526495i
$606$		0			0
$607$	2.15442	+	1.24386i	0.0874452	+	0.0504865i	0.543085	−	0.839678i	$-0.317256\pi$
$607$	2.15442	+	1.24386i	0.0874452	+	0.0504865i	−0.455640	+	0.890164i	$0.650589\pi$
$608$	20.3319	+	9.73246i	0.824566	+	0.394703i
$609$		0			0
$610$	0.918734	+	1.53606i	0.0371984	+	0.0621932i
$611$	−33.2417	−	19.1921i	−1.34482	−	0.776431i
$612$		0			0
$613$	26.9572	−	15.5638i	1.08879	−	0.628614i	0.155537	−	0.987830i	$-0.450289\pi$
$613$	26.9572	−	15.5638i	1.08879	−	0.628614i	0.933255	+	0.359216i	$0.116956\pi$
$614$	−0.395465	−	25.6269i	−0.0159596	−	1.03422i
$615$		0			0
$616$	1.96986	−	27.2740i	0.0793678	−	1.09890i
$617$		−	8.23255i		−	0.331430i	−0.986174	−	0.165715i	$-0.947007\pi$
$617$		−	8.23255i		−	0.331430i	0.986174	−	0.165715i	$-0.0529932\pi$
$618$		0			0
$619$	18.6796	+	32.3540i	0.750796	+	1.30042i	0.947437	+	0.319941i	$0.103663\pi$
$619$	18.6796	+	32.3540i	0.750796	+	1.30042i	−0.196641	+	0.980475i	$0.563003\pi$
$620$	−0.235726	−	7.63594i	−0.00946698	−	0.306667i
$621$		0			0
$622$	−37.4321	+	22.3885i	−1.50089	+	0.897698i
$623$	5.58187	+	13.0130i	0.223633	+	0.521354i
$624$		0			0
$625$	−9.55180	+	16.5442i	−0.382072	+	0.661768i
$626$	−1.28966	−	0.718286i	−0.0515453	−	0.0287085i
$627$		0			0
$628$	39.2888	−	24.3299i	1.56779	−	0.970869i
$629$	−6.43544			−0.256598
$630$		0			0
$631$		−	1.68550i		−	0.0670986i	−0.999437	−	0.0335493i	$-0.989319\pi$
$631$		−	1.68550i		−	0.0670986i	0.999437	−	0.0335493i	$-0.0106811\pi$
$632$	11.6263	−	22.4796i	0.462469	−	0.894189i
$633$		0			0
$634$	−12.6739	−	7.05880i	−0.503344	−	0.280341i
$635$	10.4929	+	6.05808i	0.416398	+	0.240407i
$636$		0			0
$637$	−27.9216	+	8.23549i	−1.10630	+	0.326302i
$638$	16.8639	+	28.1952i	0.667647	+	1.11626i
$639$		0			0
$640$	−6.57878	−	2.90314i	−0.260049	−	0.114757i
$641$	−9.16827	+	5.29330i	−0.362125	+	0.209073i	−0.670012	−	0.742350i	$-0.733711\pi$
$641$	−9.16827	+	5.29330i	−0.362125	+	0.209073i	0.307888	+	0.951423i	$0.400378\pi$
$642$		0			0
$643$	−27.0154			−1.06538			−0.532692	−	0.846309i	$-0.678820\pi$
$643$	−27.0154			−1.06538			−0.532692	+	0.846309i	$0.678820\pi$
$644$	−14.1027	+	6.57166i	−0.555723	+	0.258960i
$645$		0			0
$646$	−19.6430	+	0.303124i	−0.772845	+	0.0119262i
$647$	−1.31353	−	2.27510i	−0.0516402	−	0.0894434i	0.839050	−	0.544055i	$-0.183112\pi$
$647$	−1.31353	−	2.27510i	−0.0516402	−	0.0894434i	−0.890690	+	0.454611i	$0.849778\pi$
$648$		0			0
$649$	19.1999	−	33.2552i	0.753661	−	1.30538i
$650$	13.8748	+	23.1978i	0.544216	+	0.909892i
$651$		0			0
$652$	−11.5462	+	21.5049i	−0.452185	+	0.842198i
$653$	16.6027	−	28.7567i	0.649712	−	1.12533i	−0.333479	−	0.942757i	$-0.608223\pi$
$653$	16.6027	−	28.7567i	0.649712	−	1.12533i	0.983191	−	0.182577i	$-0.0584440\pi$
$654$		0			0
$655$	−7.15528	+	4.13110i	−0.279580	+	0.161416i
$656$	−2.58895	−	41.8924i	−0.101082	−	1.63562i
$657$		0			0
$658$	14.1022	+	31.5246i	0.549760	+	1.22896i
$659$		−	0.108371i		−	0.00422154i	−0.999998	−	0.00211077i	$-0.999328\pi$
$659$		−	0.108371i		−	0.00422154i	0.999998	−	0.00211077i	$-0.000671879\pi$
$660$		0			0
$661$	−2.37028	+	1.36848i	−0.0921932	+	0.0532278i	−0.545388	−	0.838184i	$-0.683618\pi$
$661$	−2.37028	+	1.36848i	−0.0921932	+	0.0532278i	0.453195	+	0.891412i	$0.350284\pi$
$662$	−5.72674	−	3.18955i	−0.222576	−	0.123965i
$663$		0			0
$664$	−10.3901	+	0.481314i	−0.403214	+	0.0186786i
$665$	0.791462	−	6.65390i	0.0306916	−	0.258027i
$666$		0			0
$667$	9.34645	−	16.1885i	0.361896	−	0.626822i
$668$	−6.66750	+	0.205830i	−0.257974	+	0.00796379i
$669$		0			0
$670$	−0.222218	−	14.4002i	−0.00858503	−	0.556328i
$671$	−7.27627			−0.280897
$672$		0			0
$673$	15.7488			0.607071			0.303536	−	0.952820i	$-0.401833\pi$
$673$	15.7488			0.607071			0.303536	+	0.952820i	$0.401833\pi$
$674$	0.720666	+	46.7006i	0.0277590	+	1.79884i
$675$		0			0
$676$	8.58535	−	0.265035i	0.330206	−	0.0101936i
$677$	19.1246	−	33.1248i	0.735019	−	1.27309i	−0.219696	−	0.975568i	$-0.570507\pi$
$677$	19.1246	−	33.1248i	0.735019	−	1.27309i	0.954715	−	0.297522i	$-0.0961601\pi$
$678$		0			0
$679$	37.4418	+	27.9930i	1.43688	+	1.07427i
$680$	6.26036	−	0.290006i	0.240074	−	0.0111212i
$681$		0			0
$682$	27.1327	+	15.1117i	1.03897	+	0.578659i
$683$	3.06255	−	1.76816i	0.117185	−	0.0676569i	−0.440262	−	0.897869i	$-0.645114\pi$
$683$	3.06255	−	1.76816i	0.117185	−	0.0676569i	0.557447	+	0.830213i	$0.311781\pi$
$684$		0			0
$685$			0.863457i			0.0329910i
$686$	24.6945	+	8.72818i	0.942841	+	0.333244i
$687$		0			0
$688$	−11.3342	+	0.700452i	−0.432111	+	0.0267045i
$689$	−21.5852	+	12.4622i	−0.822330	+	0.474772i
$690$		0			0
$691$	7.99597	−	13.8494i	0.304181	−	0.526857i	−0.672898	−	0.739736i	$-0.734951\pi$
$691$	7.99597	−	13.8494i	0.304181	−	0.526857i	0.977079	+	0.212879i	$0.0682839\pi$
$692$	9.06754	−	16.8884i	0.344696	−	0.642000i
$693$		0			0
$694$	−2.91324	−	4.87074i	−0.110585	−	0.184891i
$695$	0.972568	−	1.68454i	0.0368916	−	0.0638981i
$696$		0			0
$697$	18.2901	+	31.6794i	0.692788	+	1.19994i
$698$	−14.8009	+	0.228402i	−0.560224	+	0.00864516i
$699$		0			0
$700$	2.12600	−	24.2268i	0.0803553	−	0.915686i
$701$	−42.7818			−1.61585			−0.807924	−	0.589287i	$-0.799409\pi$
$701$	−42.7818			−1.61585			−0.807924	+	0.589287i	$0.799409\pi$
$702$		0			0
$703$	−6.37041	+	3.67796i	−0.240265	+	0.138717i
$704$	23.8569	−	16.8945i	0.899139	−	0.636734i
$705$		0			0
$706$	12.8655	+	21.5103i	0.484201	+	0.809550i
$707$	−3.82852	+	32.1867i	−0.143986	+	1.21051i
$708$		0			0
$709$	17.0615	+	9.85048i	0.640759	+	0.369943i	0.784907	−	0.619614i	$-0.212711\pi$
$709$	17.0615	+	9.85048i	0.640759	+	0.369943i	−0.144148	+	0.989556i	$0.546044\pi$
$710$	0.579496	+	0.322754i	0.0217481	+	0.0121128i
$711$		0			0
$712$	−6.95390	+	13.4455i	−0.260609	+	0.503890i
$713$		−	17.6708i		−	0.661776i
$714$		0			0
$715$	9.65868			0.361214
$716$	−0.0556005	+	0.0344311i	−0.00207789	+	0.00128675i
$717$		0			0
$718$	16.1341	+	8.98599i	0.602119	+	0.335354i
$719$	5.14423	−	8.91007i	0.191847	−	0.332290i	−0.754015	−	0.656857i	$-0.771885\pi$
$719$	5.14423	−	8.91007i	0.191847	−	0.332290i	0.945863	+	0.324568i	$0.105219\pi$
$720$		0			0
$721$	3.26410	+	7.60958i	0.121561	+	0.283396i
$722$	3.78878	−	2.26611i	0.141004	−	0.0843360i
$723$		0			0
$724$	1.19507	+	38.7123i	0.0444144	+	1.43873i
$725$	14.6095	+	25.3045i	0.542584	+	0.939784i
$726$		0			0
$727$			40.0773i			1.48638i	0.669078	+	0.743192i	$0.266689\pi$
$727$			40.0773i			1.48638i	−0.669078	+	0.743192i	$0.733311\pi$
$728$	−25.7605	−	17.4615i	−0.954746	−	0.647165i
$729$		0			0
$730$	0.0592758	+	3.84119i	0.00219390	+	0.142169i
$731$	8.57100	−	4.94847i	0.317010	−	0.183026i
$732$		0			0
$733$	17.9716	+	10.3759i	0.663795	+	0.383242i	0.793721	−	0.608281i	$-0.208141\pi$
$733$	17.9716	+	10.3759i	0.663795	+	0.383242i	−0.129926	+	0.991524i	$0.541474\pi$
$734$	−16.2530	−	27.1740i	−0.599910	−	1.00301i
$735$		0			0
$736$	−15.0027	−	7.18148i	−0.553005	−	0.264713i
$737$	50.7041	+	29.2741i	1.86771	+	1.07832i
$738$		0			0
$739$	8.47770	+	14.6838i	0.311857	+	0.540152i	0.978764	−	0.204988i	$-0.0657157\pi$
$739$	8.47770	+	14.6838i	0.311857	+	0.540152i	−0.666907	+	0.745141i	$0.732382\pi$
$740$	1.99506	−	1.23545i	0.0733397	−	0.0454162i
$741$		0			0
$742$	22.3062	+	2.30481i	0.818887	+	0.0846121i
$743$	−5.45125			−0.199987			−0.0999935	−	0.994988i	$-0.531882\pi$
$743$	−5.45125			−0.199987			−0.0999935	+	0.994988i	$0.531882\pi$
$744$		0			0
$745$	5.18631	+	8.98296i	0.190012	+	0.329110i
$746$	3.04958	−	5.47543i	0.111653	−	0.200470i
$747$		0			0
$748$	−12.0519	+	22.4468i	−0.440661	+	0.820735i
$749$	−6.79530	−	15.8419i	−0.248295	−	0.578849i
$750$		0			0
$751$	−13.5551	−	7.82606i	−0.494634	−	0.285577i	0.231861	−	0.972749i	$-0.425519\pi$
$751$	−13.5551	−	7.82606i	−0.494634	−	0.285577i	−0.726495	+	0.687172i	$0.758852\pi$
$752$	−16.4524	+	33.0510i	−0.599959	+	1.20525i
$753$		0			0
$754$	37.3856	−	0.576919i	1.36150	−	0.0210102i
$755$			5.73229i			0.208619i
$756$		0			0
$757$			9.16577i			0.333136i	0.986030	+	0.166568i	$0.0532685\pi$
$757$			9.16577i			0.333136i	−0.986030	+	0.166568i	$0.946732\pi$
$758$	−0.630412	−	40.8520i	−0.0228976	−	1.48381i
$759$		0			0
$760$	6.03136	−	3.86497i	0.218780	−	0.140197i
$761$	1.73152	+	0.999696i	0.0627677	+	0.0362389i	0.531055	−	0.847337i	$-0.321796\pi$
$761$	1.73152	+	0.999696i	0.0627677	+	0.0362389i	−0.468288	+	0.883576i	$0.655129\pi$
$762$		0			0
$763$	−3.74920	−	0.445956i	−0.135730	−	0.0161447i
$764$	2.85388	−	5.31537i	0.103250	−	0.192303i
$765$		0			0
$766$	40.4781	+	22.5445i	1.46253	+	0.814567i
$767$	−21.8510	−	37.8470i	−0.788993	−	1.36658i
$768$		0			0
$769$	2.48446			0.0895920			0.0447960	−	0.998996i	$-0.485736\pi$
$769$	2.48446			0.0895920			0.0447960	+	0.998996i	$0.485736\pi$
$770$	−7.03942	−	5.09554i	−0.253683	−	0.183630i
$771$		0			0
$772$	23.0737	+	37.2602i	0.830440	+	1.34102i
$773$	26.3968	+	45.7206i	0.949427	+	1.64446i	0.746635	+	0.665234i	$0.231668\pi$
$773$	26.3968	+	45.7206i	0.949427	+	1.64446i	0.202792	+	0.979222i	$0.434998\pi$
$774$		0			0
$775$	23.9208	+	13.8107i	0.859261	+	0.496095i
$776$	2.31267	+	49.9235i	0.0830200	+	1.79215i
$777$		0			0
$778$	15.1682	−	9.07228i	0.543807	−	0.325257i
$779$	36.2106	+	20.9062i	1.29738	+	0.749042i
$780$		0			0
$781$	−2.33530	+	1.34829i	−0.0835637	+	0.0482455i
$782$	14.4944	−	0.223672i	0.518318	−	0.00799848i
$783$		0			0
$784$	9.56270	+	26.3164i	0.341525	+	0.939873i
$785$		−	14.6859i		−	0.524164i
$786$		0			0
$787$	−20.0243	−	34.6831i	−0.713789	−	1.23632i	−0.963425	−	0.267979i	$-0.913644\pi$
$787$	−20.0243	−	34.6831i	−0.713789	−	1.23632i	0.249635	−	0.968340i	$-0.419689\pi$
$788$	−30.5753	+	0.943879i	−1.08920	+	0.0336243i
$789$		0			0
$790$	−4.12838	−	6.90237i	−0.146881	−	0.245575i
$791$	5.19621	−	6.95015i	0.184756	−	0.247119i
$792$		0			0
$793$	−4.14048	+	7.17153i	−0.147033	+	0.254668i
$794$	4.84437	−	8.69793i	0.171920	−	0.308678i
$795$		0			0
$796$	5.45254	−	3.37653i	0.193260	−	0.119678i
$797$	−23.9157			−0.847139			−0.423570	−	0.905864i	$-0.639223\pi$
$797$	−23.9157			−0.847139			−0.423570	+	0.905864i	$0.639223\pi$
$798$		0			0
$799$		−	32.1766i		−	1.13833i
$800$	21.4469	−	14.6963i	0.758263	−	0.519592i
$801$		0			0
$802$	−20.4588	+	36.7332i	−0.722426	+	1.29710i
$803$	−13.5251	−	7.80874i	−0.477292	−	0.275564i
$804$		0			0
$805$	−0.584011	+	4.90984i	−0.0205837	+	0.173049i
$806$	30.3338	−	18.1430i	1.06846	−	0.639059i
$807$		0			0
$808$	−29.1753	+	18.6959i	−1.02638	+	0.657720i
$809$	23.2044	−	13.3971i	0.815824	−	0.471016i	−0.0331504	−	0.999450i	$-0.510554\pi$
$809$	23.2044	−	13.3971i	0.815824	−	0.471016i	0.848974	+	0.528434i	$0.177221\pi$
$810$		0			0
$811$	−43.7619			−1.53669			−0.768345	−	0.640036i	$-0.778919\pi$
$811$	−43.7619			−1.53669			−0.768345	+	0.640036i	$0.778919\pi$
$812$	−27.5516	−	19.3027i	−0.966872	−	0.677391i
$813$		0			0
$814$	0.147195	+	9.53856i	0.00515919	+	0.334326i
$815$	3.87845	+	6.71768i	0.135856	+	0.235310i
$816$		0			0
$817$	5.65626	−	9.79693i	0.197887	−	0.342751i
$818$	−40.3483	+	24.1328i	−1.41075	+	0.843782i
$819$		0			0
$820$	−11.7518	−	6.30968i	−0.410392	−	0.220344i
$821$	18.9005	−	32.7366i	0.659632	−	1.14252i	−0.321080	−	0.947052i	$-0.604046\pi$
$821$	18.9005	−	32.7366i	0.659632	−	1.14252i	0.980711	−	0.195463i	$-0.0626210\pi$
$822$		0			0
$823$	−19.9129	+	11.4967i	−0.694121	+	0.400751i	−0.805154	−	0.593066i	$-0.797917\pi$
$823$	−19.9129	+	11.4967i	−0.694121	+	0.400751i	0.111033	+	0.993817i	$0.464584\pi$
$824$	−4.06642	+	7.86248i	−0.141661	+	0.273903i
$825$		0			0
$826$	−4.04120	+	39.1113i	−0.140611	+	1.36086i
$827$			31.3424i			1.08988i	0.838474	+	0.544941i	$0.183448\pi$
$827$			31.3424i			1.08988i	−0.838474	+	0.544941i	$0.816552\pi$
$828$		0			0
$829$	−35.5914	+	20.5487i	−1.23614	+	0.713686i	−0.968303	−	0.249779i	$-0.919642\pi$
$829$	−35.5914	+	20.5487i	−1.23614	+	0.713686i	−0.267837	+	0.963464i	$0.586309\pi$
$830$	−1.60836	+	2.88777i	−0.0558271	+	0.100236i
$831$		0			0
$832$	−3.07577	−	33.1271i	−0.106633	−	1.14847i
$833$	−17.6817	−	16.8184i	−0.612635	−	0.582723i
$834$		0			0
$835$	−1.05995	+	1.83589i	−0.0366812	+	0.0635337i
$836$	0.898575	+	29.1078i	0.0310779	+	1.00671i
$837$		0			0
$838$	12.6560	−	0.195303i	0.437196	−	0.00674664i
$839$	5.17046			0.178504			0.0892520	−	0.996009i	$-0.471552\pi$
$839$	5.17046			0.178504			0.0892520	+	0.996009i	$0.471552\pi$
$840$		0			0
$841$	11.4173			0.393701
$842$	−37.2563	+	0.574924i	−1.28394	+	0.0198132i
$843$		0			0
$844$	33.3958	−	1.03095i	1.14953	−	0.0354867i
$845$	1.36484	−	2.36397i	0.0469518	−	0.0813230i
$846$		0			0
$847$	5.72057	−	2.45381i	0.196561	−	0.0843141i
$848$	13.2445	+	19.9826i	0.454816	+	0.686205i
$849$		0			0
$850$	−11.0254	+	19.7957i	−0.378167	+	0.678989i
$851$	4.70066	−	2.71393i	0.161136	−	0.0930322i
$852$		0			0
$853$			23.8844i			0.817786i	0.912582	+	0.408893i	$0.134085\pi$
$853$			23.8844i			0.817786i	−0.912582	+	0.408893i	$0.865915\pi$
$854$	6.80108	−	3.04238i	0.232728	−	0.104108i
$855$		0			0
$856$	8.46560	−	16.3683i	0.289348	−	0.559458i
$857$	16.7053	−	9.64484i	0.570644	−	0.329461i	−0.186763	−	0.982405i	$-0.559800\pi$
$857$	16.7053	−	9.64484i	0.570644	−	0.329461i	0.757406	+	0.652944i	$0.226466\pi$
$858$		0			0
$859$	4.54550	−	7.87303i	0.155090	−	0.268624i	−0.778002	−	0.628262i	$-0.783766\pi$
$859$	4.54550	−	7.87303i	0.155090	−	0.268624i	0.933092	+	0.359638i	$0.117100\pi$
$860$	−1.70711	+	3.17951i	−0.0582120	+	0.108420i
$861$		0			0
$862$	19.3548	−	11.5763i	0.659226	−	0.394290i
$863$	11.0104	−	19.0706i	0.374799	−	0.649170i	−0.615498	−	0.788138i	$-0.711045\pi$
$863$	11.0104	−	19.0706i	0.374799	−	0.649170i	0.990297	+	0.138968i	$0.0443785\pi$
$864$		0			0
$865$	−3.04585	−	5.27556i	−0.103562	−	0.179375i
$866$	−0.272889	−	17.6838i	−0.00927316	−	0.600920i
$867$		0			0
$868$	−31.6793	−	2.77999i	−1.07527	−	0.0943591i
$869$	32.6964			1.10915
$870$		0			0
$871$	57.7053	−	33.3162i	1.95527	−	1.12888i
$872$	−2.17775	−	3.39842i	−0.0737480	−	0.115085i
$873$		0			0
$874$	14.2201	−	8.50518i	0.481002	−	0.287692i
$875$	−12.9240	−	9.66254i	−0.436912	−	0.326654i
$876$		0			0
$877$	−23.0512	−	13.3086i	−0.778385	−	0.449401i	0.0574726	−	0.998347i	$-0.481696\pi$
$877$	−23.0512	−	13.3086i	−0.778385	−	0.449401i	−0.835858	+	0.548946i	$0.815029\pi$
$878$	−11.1680	+	20.0518i	−0.376901	+	0.676716i
$879$		0			0
$880$	−0.573036	−	9.27242i	−0.0193170	−	0.312573i
$881$			5.95975i			0.200789i	0.994948	+	0.100395i	$0.0320105\pi$
$881$			5.95975i			0.200789i	−0.994948	+	0.100395i	$0.967990\pi$
$882$		0			0
$883$	−8.91564			−0.300035			−0.150018	−	0.988683i	$-0.547933\pi$
$883$	−8.91564			−0.300035			−0.150018	+	0.988683i	$0.547933\pi$
$884$	15.2656	+	24.6515i	0.513439	+	0.829120i
$885$		0			0
$886$	4.61096	−	8.27886i	0.154908	−	0.278134i
$887$	26.1142	−	45.2311i	0.876829	−	1.51871i	0.0220275	−	0.999757i	$-0.492988\pi$
$887$	26.1142	−	45.2311i	0.876829	−	1.51871i	0.854802	−	0.518955i	$-0.173679\pi$
$888$		0			0
$889$	30.2003	−	40.3942i	1.01289	−	1.35478i
$890$	2.46927	+	4.12844i	0.0827700	+	0.138386i
$891$		0			0
$892$	−1.18207	−	38.2913i	−0.0395787	−	1.28209i
$893$	−18.3894	−	31.8514i	−0.615379	−	1.06587i
$894$		0			0
$895$			0.0207832i			0.000694704i
$896$	−15.2348	+	25.7662i	−0.508961	+	0.860790i
$897$		0			0
$898$	36.9284	−	0.569865i	1.23232	−	0.0190166i
$899$	33.0885	−	19.1037i	1.10356	−	0.637143i
$900$		0			0
$901$	−18.0943	−	10.4468i	−0.602809	−	0.348032i
$902$	46.5366	−	27.8341i	1.54950	−	0.926773i
$903$		0			0
$904$	9.26708	−	0.429291i	0.308219	−	0.0142780i
$905$	10.6594	+	6.15421i	0.354330	+	0.204573i
$906$		0			0
$907$	−8.71744	−	15.0990i	−0.289458	−	0.501355i	0.684223	−	0.729273i	$-0.260142\pi$
$907$	−8.71744	−	15.0990i	−0.289458	−	0.501355i	−0.973680	+	0.227918i	$0.926808\pi$
$908$	−28.4621	+	17.6254i	−0.944548	+	0.584919i
$909$		0			0
$910$	−9.02789	+	4.03852i	−0.299272	+	0.133876i
$911$	−39.1655			−1.29761			−0.648805	−	0.760954i	$-0.724731\pi$
$911$	−39.1655			−1.29761			−0.648805	+	0.760954i	$0.724731\pi$
$912$		0			0
$913$	−6.71885	−	11.6374i	−0.222361	−	0.385141i
$914$	39.6174	+	22.0652i	1.31043	+	0.729851i
$915$		0			0
$916$	−35.6127	−	19.1208i	−1.17668	−	0.631770i
$917$	13.5580	+	31.6078i	0.447725	+	1.04378i
$918$		0			0
$919$	−35.0892	−	20.2588i	−1.15749	−	0.668276i	−0.206787	−	0.978386i	$-0.566301\pi$
$919$	−35.0892	−	20.2588i	−1.15749	−	0.668276i	−0.950701	+	0.310110i	$0.899634\pi$
$920$	−4.45047	+	2.85192i	−0.146728	+	0.0940251i
$921$		0			0
$922$	0.857087	+	55.5410i	0.0282267	+	1.82915i
$923$			3.06892i			0.101015i
$924$		0			0
$925$			8.48433i			0.278963i
$926$	3.20795	−	0.0495038i	0.105420	−	0.00162680i
$927$		0			0
$928$	−2.77188	−	35.8563i	−0.0909915	−	1.17704i
$929$	−14.0117	−	8.08966i	−0.459709	−	0.265413i	0.252213	−	0.967672i	$-0.418842\pi$
$929$	−14.0117	−	8.08966i	−0.459709	−	0.265413i	−0.711922	+	0.702259i	$0.752175\pi$
$930$		0			0
$931$	−27.1150	−	6.54307i	−0.888659	−	0.214441i
$932$	−35.4030	−	19.0083i	−1.15966	−	0.622636i
$933$		0			0
$934$	−16.5961	+	29.7979i	−0.543042	+	0.975017i
$935$	4.04831	+	7.01188i	0.132394	+	0.229313i
$936$		0			0
$937$	7.65486			0.250073			0.125037	−	0.992152i	$-0.460095\pi$
$937$	7.65486			0.250073			0.125037	+	0.992152i	$0.460095\pi$
$938$	−59.6330	−	6.16162i	−1.94709	−	0.201184i
$939$		0			0
$940$	6.17715	+	9.97508i	0.201476	+	0.325351i
$941$	11.8841	+	20.5839i	0.387411	+	0.671016i	0.992101	−	0.125445i	$-0.0400360\pi$
$941$	11.8841	+	20.5839i	0.387411	+	0.671016i	−0.604689	+	0.796462i	$0.706703\pi$
$942$		0			0
$943$	−26.7194	−	15.4265i	−0.870104	−	0.502355i
$944$	−35.0371	+	23.2226i	−1.14036	+	0.755830i
$945$		0			0
$946$	−7.53062	−	12.5907i	−0.244842	−	0.409358i
$947$	35.2481	+	20.3505i	1.14541	+	0.661302i	0.947764	−	0.318972i	$-0.103338\pi$
$947$	35.2481	+	20.3505i	1.14541	+	0.661302i	0.197644	+	0.980274i	$0.436671\pi$
$948$		0			0
$949$	−15.3927	+	8.88696i	−0.499667	+	0.288483i
$950$	0.399631	+	25.8969i	0.0129657	+	0.840206i
$951$		0			0
$952$	1.87929	−	26.0200i	0.0609081	−	0.843314i
$953$			19.5679i			0.633867i	0.948448	+	0.316934i	$0.102653\pi$
$953$			19.5679i			0.633867i	−0.948448	+	0.316934i	$0.897347\pi$
$954$		0			0
$955$	−0.958636	−	1.66041i	−0.0310207	−	0.0537295i
$956$	−26.4498	+	0.816521i	−0.855448	+	0.0264082i
$957$		0			0
$958$	−15.0394	+	8.99523i	−0.485901	+	0.290623i
$959$	3.56913	+	0.424537i	0.115253	+	0.0137090i
$960$		0			0
$961$	2.55908	−	4.43245i	0.0825509	−	0.142982i
$962$	9.48501	+	5.28274i	0.305809	+	0.170322i
$963$		0			0
$964$	12.4344	+	20.0795i	0.400484	+	0.646716i
$965$	13.9277			0.448347
$966$		0			0
$967$		−	24.6339i		−	0.792174i	−0.918213	−	0.396087i	$-0.870368\pi$
$967$		−	24.6339i		−	0.792174i	0.918213	−	0.396087i	$-0.129632\pi$
$968$	5.91069	+	3.05697i	0.189977	+	0.0982547i
$969$		0			0
$970$	13.8755	+	7.72804i	0.445515	+	0.248132i
$971$	−41.0803	−	23.7177i	−1.31833	−	0.761137i	−0.334869	−	0.942265i	$-0.608692\pi$
$971$	−41.0803	−	23.7177i	−1.31833	−	0.761137i	−0.983460	+	0.181128i	$0.942025\pi$
$972$		0			0
$973$	−6.48491	−	4.84838i	−0.207897	−	0.155432i
$974$	−8.48106	−	14.1797i	−0.271751	−	0.454348i
$975$		0			0
$976$	7.13039	+	3.54943i	0.228238	+	0.113614i
$977$	48.9364	−	28.2534i	1.56561	−	0.903908i	0.568943	−	0.822377i	$-0.307352\pi$
$977$	48.9364	−	28.2534i	1.56561	−	0.903908i	0.996671	−	0.0815309i	$-0.0259809\pi$
$978$		0			0
$979$	−19.5563			−0.625023
$980$	8.71025	+	1.81941i	0.278239	+	0.0581189i
$981$		0			0
$982$	−60.6521	+	0.935959i	−1.93549	+	0.0298677i
$983$	−18.0801	−	31.3156i	−0.576665	−	0.998814i	−0.995859	−	0.0909167i	$-0.971020\pi$
$983$	−18.0801	−	31.3156i	−0.576665	−	0.998814i	0.419193	−	0.907897i	$-0.362313\pi$
$984$		0			0
$985$	−4.86065	+	8.41890i	−0.154873	+	0.268248i
$986$	16.0885	+	26.8989i	0.512363	+	0.856635i
$987$		0			0
$988$	29.2001	+	15.6778i	0.928980	+	0.498779i
$989$	−4.17369	+	7.22905i	−0.132716	+	0.229870i
$990$		0			0
$991$	−8.72687	+	5.03846i	−0.277218	+	0.160052i	−0.632163	−	0.774835i	$-0.717833\pi$
$991$	−8.72687	+	5.03846i	−0.277218	+	0.160052i	0.354945	+	0.934887i	$0.384500\pi$
$992$	−19.2171	−	28.0443i	−0.610143	−	0.890408i
$993$		0			0
$994$	1.61904	−	2.23668i	0.0513528	−	0.0709432i
$995$		−	2.03813i		−	0.0646130i
$996$		0			0
$997$	14.5584	−	8.40532i	0.461070	−	0.266199i	−0.251424	−	0.967877i	$-0.580899\pi$
$997$	14.5584	−	8.40532i	0.461070	−	0.266199i	0.712494	+	0.701678i	$0.247565\pi$
$998$	11.0992	+	6.18175i	0.351338	+	0.195680i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.c.107.12	yes	48
3.2	odd	2	inner	504.2.bm.c.107.13	yes	48
4.3	odd	2		2016.2.bu.c.1871.10		48
7.4	even	3	inner	504.2.bm.c.179.21	yes	48
8.3	odd	2	inner	504.2.bm.c.107.4	✓	48
8.5	even	2		2016.2.bu.c.1871.16		48
12.11	even	2		2016.2.bu.c.1871.15		48
21.11	odd	6	inner	504.2.bm.c.179.4	yes	48
24.5	odd	2		2016.2.bu.c.1871.9		48
24.11	even	2	inner	504.2.bm.c.107.21	yes	48
28.11	odd	6		2016.2.bu.c.431.9		48
56.11	odd	6	inner	504.2.bm.c.179.13	yes	48
56.53	even	6		2016.2.bu.c.431.15		48
84.11	even	6		2016.2.bu.c.431.16		48
168.11	even	6	inner	504.2.bm.c.179.12	yes	48
168.53	odd	6		2016.2.bu.c.431.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.c.107.4	✓	48	8.3	odd	2	inner
504.2.bm.c.107.12	yes	48	1.1	even	1	trivial
504.2.bm.c.107.13	yes	48	3.2	odd	2	inner
504.2.bm.c.107.21	yes	48	24.11	even	2	inner
504.2.bm.c.179.4	yes	48	21.11	odd	6	inner
504.2.bm.c.179.12	yes	48	168.11	even	6	inner
504.2.bm.c.179.13	yes	48	56.11	odd	6	inner
504.2.bm.c.179.21	yes	48	7.4	even	3	inner
2016.2.bu.c.431.9		48	28.11	odd	6
2016.2.bu.c.431.10		48	168.53	odd	6
2016.2.bu.c.431.15		48	56.53	even	6
2016.2.bu.c.431.16		48	84.11	even	6
2016.2.bu.c.1871.9		48	24.5	odd	2
2016.2.bu.c.1871.10		48	4.3	odd	2
2016.2.bu.c.1871.15		48	12.11	even	2
2016.2.bu.c.1871.16		48	8.5	even	2

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.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0218210 - 1.41405i) q^{2} +(-1.99905 + 0.0617118i) q^{4} +(-0.317795 + 0.550436i) q^{5} +(2.11900 + 1.58425i) q^{7} +(0.130884 + 2.82540i) q^{8} +O(q^{10})\)	\(q+(-0.0218210 - 1.41405i) q^{2} +(-1.99905 + 0.0617118i) q^{4} +(-0.317795 + 0.550436i) q^{5} +(2.11900 + 1.58425i) q^{7} +(0.130884 + 2.82540i) q^{8} +(0.785276 + 0.437365i) q^{10} +(-3.16457 + 1.82707i) q^{11} +4.15869i q^{13} +(2.19396 - 3.03093i) q^{14} +(3.99238 - 0.246730i) q^{16} +(-3.01908 + 1.74306i) q^{17} +(-1.99238 + 3.45090i) q^{19} +(0.601318 - 1.11996i) q^{20} +(2.65261 + 4.43498i) q^{22} +(1.47015 - 2.54638i) q^{23} +(2.29801 + 3.98028i) q^{25} +(5.88058 - 0.0907468i) q^{26} +(-4.33375 - 3.03622i) q^{28} +6.35746 q^{29} +(5.20467 - 3.00492i) q^{31} +(-0.436004 - 5.64003i) q^{32} +(2.53065 + 4.23107i) q^{34} +(-1.54543 + 0.662908i) q^{35} +(1.59870 + 0.923007i) q^{37} +(4.92321 + 2.74201i) q^{38} +(-1.59680 - 0.825852i) q^{40} -10.4931i q^{41} -2.83895 q^{43} +(6.21338 - 3.84768i) q^{44} +(-3.63278 - 2.02330i) q^{46} +(-4.61494 + 7.99332i) q^{47} +(1.98031 + 6.71404i) q^{49} +(5.57814 - 3.33635i) q^{50} +(-0.256640 - 8.31342i) q^{52} +(2.99666 + 5.19038i) q^{53} -2.32253i q^{55} +(-4.19879 + 6.19437i) q^{56} +(-0.138726 - 8.98974i) q^{58} +(-9.10070 + 5.25429i) q^{59} +(1.72447 + 0.995622i) q^{61} +(-4.36266 - 7.29407i) q^{62} +(-7.96574 + 0.739601i) q^{64} +(-2.28909 - 1.32161i) q^{65} +(-8.01122 - 13.8758i) q^{67} +(5.92771 - 3.67078i) q^{68} +(0.971104 + 2.17085i) q^{70} +0.737952 q^{71} +(2.13696 + 3.70132i) q^{73} +(1.27029 - 2.28077i) q^{74} +(3.76990 - 7.02147i) q^{76} +(-9.60025 - 1.14192i) q^{77} +(-7.74900 - 4.47389i) q^{79} +(-1.13295 + 2.27596i) q^{80} +(-14.8377 + 0.228970i) q^{82} +3.67740i q^{83} -2.21574i q^{85} +(0.0619487 + 4.01440i) q^{86} +(-5.57638 - 8.70204i) q^{88} +(4.63483 + 2.67592i) q^{89} +(-6.58841 + 8.81226i) q^{91} +(-2.78177 + 5.18107i) q^{92} +(11.4036 + 6.35132i) q^{94} +(-1.26633 - 2.19335i) q^{95} +17.6696 q^{97} +(9.45075 - 2.94675i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q - 8 q^{10} - 28 q^{16} - 32 q^{19} + 32 q^{22} + 4 q^{28} + 112 q^{34} - 36 q^{40} - 160 q^{43} + 40 q^{46} + 56 q^{49} - 36 q^{52} + 12 q^{58} - 24 q^{64} + 92 q^{70} + 16 q^{73} - 120 q^{76} + 20 q^{82} - 100 q^{88} - 32 q^{91} - 20 q^{94} + 240 q^{97}+O(q^{100}) \) 48 * q - 8 * q^10 - 28 * q^16 - 32 * q^19 + 32 * q^22 + 4 * q^28 + 112 * q^34 - 36 * q^40 - 160 * q^43 + 40 * q^46 + 56 * q^49 - 36 * q^52 + 12 * q^58 - 24 * q^64 + 92 * q^70 + 16 * q^73 - 120 * q^76 + 20 * q^82 - 100 * q^88 - 32 * q^91 - 20 * q^94 + 240 * q^97

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