LMFDB - Embedded newform 504.2.bm.a.107.3

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.3
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.a.179.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.914214 + 1.58346i) q^{5} +(0.358719 + 2.62132i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.914214 + 1.58346i) q^{5} +(0.358719 + 2.62132i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-2.49768 - 0.669251i) q^{10} +(-1.37333 + 0.792893i) q^{11} -2.58579i q^{13} +(-3.44949 + 1.44949i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-5.40629 + 3.12132i) q^{17} +(1.29289 - 2.23936i) q^{19} -3.65685i q^{20} +(-1.58579 - 1.58579i) q^{22} +(-0.292893 + 0.507306i) q^{23} +(0.828427 + 1.43488i) q^{25} +(3.53225 - 0.946464i) q^{26} +(-3.24264 - 4.18154i) q^{28} -3.00000 q^{29} +(-3.82282 + 2.20711i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-6.24264 - 6.24264i) q^{34} +(-4.47871 - 1.82843i) q^{35} +(-7.85578 - 4.53553i) q^{37} +(3.53225 + 0.946464i) q^{38} +(4.99536 - 1.33850i) q^{40} +8.82843i q^{41} +11.4142 q^{43} +(1.58579 - 2.74666i) q^{44} +(-0.800199 - 0.214413i) q^{46} +(1.29289 - 2.23936i) q^{47} +(-6.74264 + 1.88064i) q^{49} +(-1.65685 + 1.65685i) q^{50} +(2.58579 + 4.47871i) q^{52} +(3.08579 + 5.34474i) q^{53} -2.89949i q^{55} +(4.52520 - 5.96008i) q^{56} +(-1.09808 - 4.09808i) q^{58} +(-6.98975 + 4.03553i) q^{59} +(5.40629 + 3.12132i) q^{61} +(-4.41421 - 4.41421i) q^{62} +8.00000i q^{64} +(4.09450 + 2.36396i) q^{65} +(3.82843 + 6.63103i) q^{67} +(6.24264 - 10.8126i) q^{68} +(0.858355 - 6.78729i) q^{70} +13.8995 q^{71} +(3.65685 + 6.33386i) q^{73} +(3.32024 - 12.3913i) q^{74} +5.17157i q^{76} +(-2.57107 - 3.31552i) q^{77} +(6.98975 + 4.03553i) q^{79} +(3.65685 + 6.33386i) q^{80} +(-12.0599 + 3.23143i) q^{82} -8.07107i q^{83} -11.4142i q^{85} +(4.17789 + 15.5921i) q^{86} +(4.33245 + 1.16088i) q^{88} +(6.77817 - 0.927572i) q^{91} -1.17157i q^{92} +(3.53225 + 0.946464i) q^{94} +(2.36396 + 4.09450i) q^{95} -15.8284 q^{97} +(-5.03698 - 8.52226i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8}+O(q^{10}) $ 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8	$ 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8} + 4 q^{10} - 8 q^{14} + 16 q^{16} + 16 q^{19} - 24 q^{22} - 8 q^{23} - 16 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} - 16 q^{34} + 16 q^{38} - 8 q^{40} + 80 q^{43} + 24 q^{44} - 8 q^{46} + 16 q^{47} - 20 q^{49} + 32 q^{50} + 32 q^{52} + 36 q^{53} + 8 q^{56} + 12 q^{58} - 24 q^{62} + 8 q^{67} + 16 q^{68} - 52 q^{70} + 32 q^{71} - 16 q^{73} - 8 q^{74} + 36 q^{77} - 16 q^{80} - 24 q^{82} - 40 q^{86} + 24 q^{88} - 8 q^{91} + 16 q^{94} - 32 q^{95} - 104 q^{97} - 20 q^{98}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8 + 4 * q^10 - 8 * q^14 + 16 * q^16 + 16 * q^19 - 24 * q^22 - 8 * q^23 - 16 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 - 16 * q^34 + 16 * q^38 - 8 * q^40 + 80 * q^43 + 24 * q^44 - 8 * q^46 + 16 * q^47 - 20 * q^49 + 32 * q^50 + 32 * q^52 + 36 * q^53 + 8 * q^56 + 12 * q^58 - 24 * q^62 + 8 * q^67 + 16 * q^68 - 52 * q^70 + 32 * q^71 - 16 * q^73 - 8 * q^74 + 36 * q^77 - 16 * q^80 - 24 * q^82 - 40 * q^86 + 24 * q^88 - 8 * q^91 + 16 * q^94 - 32 * q^95 - 104 * q^97 - 20 * q^98

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 $

$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$2$	0.366025	+	1.36603i	0.258819	+	0.965926i
$3$		0			0
$3$		0			0
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	−0.914214	+	1.58346i	−0.408849	+	0.708147i	−0.994761	−	0.102228i	$-0.967403\pi$
$5$	−0.914214	+	1.58346i	−0.408849	+	0.708147i	0.585912	+	0.810374i	$0.300736\pi$
$6$		0			0
$7$	0.358719	+	2.62132i	0.135583	+	0.990766i
$7$	0.358719	+	2.62132i	0.135583	+	0.990766i
$8$	−2.00000	−	2.00000i	−0.707107	−	0.707107i
$9$		0			0
$10$	−2.49768	−	0.669251i	−0.789835	−	0.211636i
$11$	−1.37333	+	0.792893i	−0.414075	+	0.239066i	−0.692539	−	0.721380i	$-0.743508\pi$
$11$	−1.37333	+	0.792893i	−0.414075	+	0.239066i	0.278464	+	0.960447i	$0.410175\pi$
$12$		0			0
$13$		−	2.58579i		−	0.717168i	−0.933497	−	0.358584i	$-0.883260\pi$
$13$		−	2.58579i		−	0.717168i	0.933497	−	0.358584i	$-0.116740\pi$
$14$	−3.44949	+	1.44949i	−0.921915	+	0.387392i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−5.40629	+	3.12132i	−1.31122	+	0.757031i	−0.982298	−	0.187327i	$-0.940018\pi$
$17$	−5.40629	+	3.12132i	−1.31122	+	0.757031i	−0.328919	+	0.944358i	$0.606684\pi$
$18$		0			0
$19$	1.29289	−	2.23936i	0.296610	−	0.513744i	−0.678748	−	0.734371i	$-0.737477\pi$
$19$	1.29289	−	2.23936i	0.296610	−	0.513744i	0.975358	+	0.220628i	$0.0708105\pi$
$20$		−	3.65685i		−	0.817697i
$21$		0			0
$22$	−1.58579	−	1.58579i	−0.338091	−	0.338091i
$23$	−0.292893	+	0.507306i	−0.0610725	+	0.105781i	−0.894945	−	0.446176i	$-0.852785\pi$
$23$	−0.292893	+	0.507306i	−0.0610725	+	0.105781i	0.833873	+	0.551957i	$0.186119\pi$
$24$		0			0
$25$	0.828427	+	1.43488i	0.165685	+	0.286976i
$26$	3.53225	−	0.946464i	0.692731	−	0.185617i
$27$		0			0
$28$	−3.24264	−	4.18154i	−0.612801	−	0.790237i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−3.82282	+	2.20711i	−0.686599	+	0.396408i	−0.802337	−	0.596872i	$-0.796410\pi$
$31$	−3.82282	+	2.20711i	−0.686599	+	0.396408i	0.115738	+	0.993280i	$0.463077\pi$
$32$	5.46410	+	1.46410i	0.965926	+	0.258819i
$33$		0			0
$34$	−6.24264	−	6.24264i	−1.07060	−	1.07060i
$35$	−4.47871	−	1.82843i	−0.757041	−	0.309061i
$36$		0			0
$37$	−7.85578	−	4.53553i	−1.29148	−	0.745637i	−0.312565	−	0.949896i	$-0.601188\pi$
$37$	−7.85578	−	4.53553i	−1.29148	−	0.745637i	−0.978917	+	0.204259i	$0.934521\pi$
$38$	3.53225	+	0.946464i	0.573007	+	0.153537i
$39$		0			0
$40$	4.99536	−	1.33850i	0.789835	−	0.211636i
$41$			8.82843i			1.37877i	0.724396	+	0.689384i	$0.242119\pi$
$41$			8.82843i			1.37877i	−0.724396	+	0.689384i	$0.757881\pi$
$42$		0			0
$43$	11.4142			1.74065			0.870326	−	0.492477i	$-0.163908\pi$
$43$	11.4142			1.74065			0.870326	+	0.492477i	$0.163908\pi$
$44$	1.58579	−	2.74666i	0.239066	−	0.414075i
$45$		0			0
$46$	−0.800199	−	0.214413i	−0.117983	−	0.0316134i
$47$	1.29289	−	2.23936i	0.188588	−	0.326644i	−0.756192	−	0.654350i	$-0.772942\pi$
$47$	1.29289	−	2.23936i	0.188588	−	0.326644i	0.944780	+	0.327706i	$0.106276\pi$
$48$		0			0
$49$	−6.74264	+	1.88064i	−0.963234	+	0.268662i
$50$	−1.65685	+	1.65685i	−0.234315	+	0.234315i
$51$		0			0
$52$	2.58579	+	4.47871i	0.358584	+	0.621086i
$53$	3.08579	+	5.34474i	0.423865	+	0.734156i	0.996314	−	0.0857844i	$-0.0273396\pi$
$53$	3.08579	+	5.34474i	0.423865	+	0.734156i	−0.572448	+	0.819941i	$0.694006\pi$
$54$		0			0
$55$		−	2.89949i		−	0.390968i
$56$	4.52520	−	5.96008i	0.604706	−	0.796449i
$57$		0			0
$58$	−1.09808	−	4.09808i	−0.144184	−	0.538104i
$59$	−6.98975	+	4.03553i	−0.909988	+	0.525382i	−0.880427	−	0.474181i	$-0.842744\pi$
$59$	−6.98975	+	4.03553i	−0.909988	+	0.525382i	−0.0295606	+	0.999563i	$0.509411\pi$
$60$		0			0
$61$	5.40629	+	3.12132i	0.692204	+	0.399644i	0.804437	−	0.594038i	$-0.202467\pi$
$61$	5.40629	+	3.12132i	0.692204	+	0.399644i	−0.112233	+	0.993682i	$0.535800\pi$
$62$	−4.41421	−	4.41421i	−0.560606	−	0.560606i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	4.09450	+	2.36396i	0.507860	+	0.293213i
$66$		0			0
$67$	3.82843	+	6.63103i	0.467717	+	0.810109i	0.999320	−	0.0368845i	$-0.0117434\pi$
$67$	3.82843	+	6.63103i	0.467717	+	0.810109i	−0.531603	+	0.846994i	$0.678410\pi$
$68$	6.24264	−	10.8126i	0.757031	−	1.31122i
$69$		0			0
$70$	0.858355	−	6.78729i	0.102593	−	0.811236i
$71$	13.8995			1.64957			0.824783	−	0.565449i	$-0.191297\pi$
$71$	13.8995			1.64957			0.824783	+	0.565449i	$0.191297\pi$
$72$		0			0
$73$	3.65685	+	6.33386i	0.428002	+	0.741322i	0.996696	−	0.0812278i	$-0.0258841\pi$
$73$	3.65685	+	6.33386i	0.428002	+	0.741322i	−0.568693	+	0.822550i	$0.692551\pi$
$74$	3.32024	−	12.3913i	0.385970	−	1.44046i
$75$		0			0
$76$			5.17157i			0.593220i
$77$	−2.57107	−	3.31552i	−0.293000	−	0.377838i
$78$		0			0
$79$	6.98975	+	4.03553i	0.786408	+	0.454033i	0.838697	−	0.544599i	$-0.183318\pi$
$79$	6.98975	+	4.03553i	0.786408	+	0.454033i	−0.0522883	+	0.998632i	$0.516651\pi$
$80$	3.65685	+	6.33386i	0.408849	+	0.708147i
$81$		0			0
$82$	−12.0599	+	3.23143i	−1.33179	+	0.356852i
$83$		−	8.07107i		−	0.885915i	−0.896543	−	0.442957i	$-0.853929\pi$
$83$		−	8.07107i		−	0.885915i	0.896543	−	0.442957i	$-0.146071\pi$
$84$		0			0
$85$		−	11.4142i		−	1.23805i
$86$	4.17789	+	15.5921i	0.450514	+	1.68134i
$87$		0			0
$88$	4.33245	+	1.16088i	0.461841	+	0.123750i
$89$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$89$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$90$		0			0
$91$	6.77817	−	0.927572i	0.710546	−	0.0972360i
$92$		−	1.17157i		−	0.122145i
$93$		0			0
$94$	3.53225	+	0.946464i	0.364324	+	0.0976203i
$95$	2.36396	+	4.09450i	0.242537	+	0.420087i
$96$		0			0
$97$	−15.8284			−1.60713			−0.803567	−	0.595215i	$-0.797067\pi$
$97$	−15.8284			−1.60713			−0.803567	+	0.595215i	$0.797067\pi$
$98$	−5.03698	−	8.52226i	−0.508811	−	0.860878i
$99$		0			0
$100$	−2.86976	−	1.65685i	−0.286976	−	0.165685i
$101$	−6.24264	−	10.8126i	−0.621166	−	1.07589i	−0.989269	−	0.146106i	$-0.953326\pi$
$101$	−6.24264	−	10.8126i	−0.621166	−	1.07589i	0.368103	−	0.929785i	$-0.380007\pi$
$102$		0			0
$103$	15.2913	+	8.82843i	1.50670	+	0.869891i	0.999970	+	0.00778320i	$0.00247749\pi$
$103$	15.2913	+	8.82843i	1.50670	+	0.869891i	0.506725	+	0.862108i	$0.330856\pi$
$104$	−5.17157	+	5.17157i	−0.507114	+	0.507114i
$105$		0			0
$106$	−6.17157	+	6.17157i	−0.599436	+	0.599436i
$107$	13.2005	+	7.62132i	1.27614	+	0.736781i	0.976137	−	0.217157i	$-0.0696783\pi$
$107$	13.2005	+	7.62132i	1.27614	+	0.736781i	0.300005	+	0.953938i	$0.403012\pi$
$108$		0			0
$109$	−2.15232	+	1.24264i	−0.206155	+	0.119023i	−0.599523	−	0.800358i	$-0.704643\pi$
$109$	−2.15232	+	1.24264i	−0.206155	+	0.119023i	0.393368	+	0.919381i	$0.371310\pi$
$110$	3.96078	−	1.06129i	0.377646	−	0.101190i
$111$		0			0
$112$	9.79796	+	4.00000i	0.925820	+	0.377964i
$113$			4.82843i			0.454220i	0.973869	+	0.227110i	$0.0729277\pi$
$113$			4.82843i			0.454220i	−0.973869	+	0.227110i	$0.927072\pi$
$114$		0			0
$115$	−0.535534	−	0.927572i	−0.0499388	−	0.0864965i
$116$	5.19615	−	3.00000i	0.482451	−	0.278543i
$117$		0			0
$118$	−8.07107	−	8.07107i	−0.743002	−	0.743002i
$119$	−10.1213	−	13.0519i	−0.927820	−	1.19647i
$120$		0			0
$121$	−4.24264	+	7.34847i	−0.385695	+	0.668043i
$122$	−2.28497	+	8.52761i	−0.206871	+	0.772053i
$123$		0			0
$124$	4.41421	−	7.64564i	0.396408	−	0.686599i
$125$	−12.1716			−1.08866
$126$		0			0
$127$			8.07107i			0.716191i	0.933685	+	0.358096i	$0.116574\pi$
$127$			8.07107i			0.716191i	−0.933685	+	0.358096i	$0.883426\pi$
$128$	−10.9282	+	2.92820i	−0.965926	+	0.258819i
$129$		0			0
$130$	−1.73054	+	6.45846i	−0.151778	+	0.566445i
$131$	−8.30153	−	4.79289i	−0.725308	−	0.418757i	0.0913949	−	0.995815i	$-0.470867\pi$
$131$	−8.30153	−	4.79289i	−0.725308	−	0.418757i	−0.816703	+	0.577058i	$0.804201\pi$
$132$		0			0
$133$	6.33386	+	2.58579i	0.549215	+	0.224216i
$134$	−7.65685	+	7.65685i	−0.661451	+	0.661451i
$135$		0			0
$136$	17.0552	+	4.56993i	1.46247	+	0.391868i
$137$	9.67487	−	5.58579i	0.826580	−	0.477226i	−0.0261005	−	0.999659i	$-0.508309\pi$
$137$	9.67487	−	5.58579i	0.826580	−	0.477226i	0.852680	+	0.522433i	$0.174976\pi$
$138$		0			0
$139$	−7.31371			−0.620341			−0.310170	−	0.950681i	$-0.600386\pi$
$139$	−7.31371			−0.620341			−0.310170	+	0.950681i	$0.600386\pi$
$140$	9.58579	−	1.31178i	0.810147	−	0.110866i
$141$		0			0
$142$	5.08757	+	18.9871i	0.426939	+	1.59336i
$143$	2.05025	+	3.55114i	0.171451	+	0.296961i
$144$		0			0
$145$	2.74264	−	4.75039i	0.227764	−	0.394499i
$146$	−7.31371	+	7.31371i	−0.605287	+	0.605287i
$147$		0			0
$148$	18.1421			1.49127
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$		0			0
$151$	−3.52565	+	2.03553i	−0.286913	+	0.165649i	−0.636549	−	0.771236i	$-0.719639\pi$
$151$	−3.52565	+	2.03553i	−0.286913	+	0.165649i	0.349636	+	0.936886i	$0.386305\pi$
$152$	−7.06450	+	1.89293i	−0.573007	+	0.153537i
$153$		0			0
$154$	3.58800	−	4.72571i	0.289129	−	0.380808i
$155$		−	8.07107i		−	0.648284i
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	−2.95422	+	11.0253i	−0.235025	+	0.877124i
$159$		0			0
$160$	−7.31371	+	7.31371i	−0.578199	+	0.578199i
$161$	−1.43488	−	0.585786i	−0.113084	−	0.0461664i
$162$		0			0
$163$	1.70711	−	2.95680i	0.133711	−	0.231594i	−0.791393	−	0.611307i	$-0.790644\pi$
$163$	1.70711	−	2.95680i	0.133711	−	0.231594i	0.925104	+	0.379713i	$0.123977\pi$
$164$	−8.82843	−	15.2913i	−0.689384	−	1.19405i
$165$		0			0
$166$	11.0253	−	2.95422i	0.855728	−	0.229292i
$167$	3.65685			0.282976			0.141488	−	0.989940i	$-0.454811\pi$
$167$	3.65685			0.282976			0.141488	+	0.989940i	$0.454811\pi$
$168$		0			0
$169$	6.31371			0.485670
$170$	15.5921	−	4.17789i	1.19586	−	0.320430i
$171$		0			0
$172$	−19.7700	+	11.4142i	−1.50745	+	0.870326i
$173$	−12.4853	+	21.6251i	−0.949238	+	1.64413i	−0.202204	+	0.979343i	$0.564810\pi$
$173$	−12.4853	+	21.6251i	−0.949238	+	1.64413i	−0.747034	+	0.664786i	$0.768523\pi$
$174$		0			0
$175$	−3.46410	+	2.68629i	−0.261861	+	0.203065i
$176$			6.34315i			0.478133i
$177$		0			0
$178$		0			0
$179$	12.8418	−	7.41421i	0.959841	−	0.554164i	0.0637168	−	0.997968i	$-0.479705\pi$
$179$	12.8418	−	7.41421i	0.959841	−	0.554164i	0.896124	+	0.443804i	$0.146371\pi$
$180$		0			0
$181$		−	8.82843i		−	0.656212i	−0.944641	−	0.328106i	$-0.893590\pi$
$181$		−	8.82843i		−	0.656212i	0.944641	−	0.328106i	$-0.106410\pi$
$182$	3.74807	+	8.91964i	0.277826	+	0.661168i
$183$		0			0
$184$	1.60040	−	0.428825i	0.117983	−	0.0316134i
$185$	14.3637	−	8.29289i	1.05604	−	0.609706i
$186$		0			0
$187$	4.94975	−	8.57321i	0.361961	−	0.626936i
$188$			5.17157i			0.377176i
$189$		0			0
$190$	−4.72792	+	4.72792i	−0.343000	+	0.343000i
$191$	6.48528	−	11.2328i	0.469258	−	0.812780i	−0.530124	−	0.847920i	$-0.677855\pi$
$191$	6.48528	−	11.2328i	0.469258	−	0.812780i	0.999382	+	0.0351407i	$0.0111879\pi$
$192$		0			0
$193$	−6.39949	−	11.0843i	−0.460646	−	0.797862i	0.538348	−	0.842723i	$-0.319049\pi$
$193$	−6.39949	−	11.0843i	−0.460646	−	0.797862i	−0.998993	+	0.0448611i	$0.985715\pi$
$194$	−5.79361	−	21.6220i	−0.415957	−	1.55237i
$195$		0			0
$196$	9.79796	−	10.0000i	0.699854	−	0.714286i
$197$	26.1421			1.86255			0.931275	−	0.364317i	$-0.118698\pi$
$197$	26.1421			1.86255			0.931275	+	0.364317i	$0.118698\pi$
$198$		0			0
$199$	−15.2913	+	8.82843i	−1.08397	+	0.625831i	−0.931965	−	0.362549i	$-0.881907\pi$
$199$	−15.2913	+	8.82843i	−1.08397	+	0.625831i	−0.152006	+	0.988380i	$0.548573\pi$
$200$	1.21290	−	4.52661i	0.0857651	−	0.320080i
$201$		0			0
$202$	12.4853	−	12.4853i	0.878461	−	0.878461i
$203$	−1.07616	−	7.86396i	−0.0755315	−	0.551942i
$204$		0			0
$205$	−13.9795	−	8.07107i	−0.976371	−	0.563708i
$206$	−6.46286	+	24.1197i	−0.450289	+	1.68050i
$207$		0			0
$208$	−8.95743	−	5.17157i	−0.621086	−	0.358584i
$209$			4.10051i			0.283638i
$210$		0			0
$211$	−27.5563			−1.89706			−0.948529	−	0.316691i	$-0.897428\pi$
$211$	−27.5563			−1.89706			−0.948529	+	0.316691i	$0.897428\pi$
$212$	−10.6895	−	6.17157i	−0.734156	−	0.423865i
$213$		0			0
$214$	−5.57919	+	20.8218i	−0.381386	+	1.42335i
$215$	−10.4350	+	18.0740i	−0.711663	+	1.23264i
$216$		0			0
$217$	−7.15685	−	9.22911i	−0.485839	−	0.626513i
$218$	−2.48528	−	2.48528i	−0.168324	−	0.168324i
$219$		0			0
$220$	2.89949	+	5.02207i	0.195484	+	0.338588i
$221$	8.07107	+	13.9795i	0.542919	+	0.940363i
$222$		0			0
$223$		−	25.7279i		−	1.72287i	−0.507869	−	0.861435i	$-0.669566\pi$
$223$		−	25.7279i		−	1.72287i	0.507869	−	0.861435i	$-0.330434\pi$
$224$	−1.87780	+	14.8484i	−0.125466	+	0.992098i
$225$		0			0
$226$	−6.59575	+	1.76733i	−0.438743	+	0.117561i
$227$	10.1567	−	5.86396i	0.674122	−	0.389205i	−0.123514	−	0.992343i	$-0.539417\pi$
$227$	10.1567	−	5.86396i	0.674122	−	0.389205i	0.797637	+	0.603138i	$0.206083\pi$
$228$		0			0
$229$	1.31178	+	0.757359i	0.0866852	+	0.0500477i	0.542716	−	0.839916i	$-0.317396\pi$
$229$	1.31178	+	0.757359i	0.0866852	+	0.0500477i	−0.456031	+	0.889964i	$0.650729\pi$
$230$	1.07107	−	1.07107i	0.0706241	−	0.0706241i
$231$		0			0
$232$	6.00000	+	6.00000i	0.393919	+	0.393919i
$233$	−16.6391	−	9.60660i	−1.09007	−	0.629349i	−0.156471	−	0.987682i	$-0.550012\pi$
$233$	−16.6391	−	9.60660i	−1.09007	−	0.629349i	−0.933594	+	0.358333i	$0.883345\pi$
$234$		0			0
$235$	2.36396	+	4.09450i	0.154208	+	0.267096i
$236$	8.07107	−	13.9795i	0.525382	−	0.909988i
$237$		0			0
$238$	14.1246	−	18.6033i	0.915562	−	1.20587i
$239$	10.2426			0.662541			0.331271	−	0.943536i	$-0.392523\pi$
$239$	10.2426			0.662541			0.331271	+	0.943536i	$0.392523\pi$
$240$		0			0
$241$	5.32843	+	9.22911i	0.343234	+	0.594499i	0.985031	−	0.172375i	$-0.0551442\pi$
$241$	5.32843	+	9.22911i	0.343234	+	0.594499i	−0.641797	+	0.766874i	$0.721811\pi$
$242$	−11.5911	−	3.10583i	−0.745105	−	0.199650i
$243$		0			0
$244$	−12.4853			−0.799288
$245$	3.18629	−	12.3960i	0.203565	−	0.791954i
$246$		0			0
$247$	−5.79050	−	3.34315i	−0.368441	−	0.212719i
$248$	12.0599	+	3.23143i	0.765802	+	0.205196i
$249$		0			0
$250$	−4.45510	−	16.6267i	−0.281766	−	1.05156i
$251$		−	2.27208i		−	0.143412i	−0.997426	−	0.0717061i	$-0.977156\pi$
$251$		−	2.27208i		−	0.143412i	0.997426	−	0.0717061i	$-0.0228444\pi$
$252$		0			0
$253$		−	0.928932i		−	0.0584015i
$254$	−11.0253	+	2.95422i	−0.691788	+	0.185364i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$257$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$258$		0			0
$259$	9.07107	−	22.2195i	0.563649	−	1.38065i
$260$	−9.45584			−0.586427
$261$		0			0
$262$	3.50864	−	13.0944i	0.216765	−	0.808976i
$263$	0.636039	+	1.10165i	0.0392198	+	0.0679308i	0.884969	−	0.465650i	$-0.154179\pi$
$263$	0.636039	+	1.10165i	0.0392198	+	0.0679308i	−0.845749	+	0.533581i	$0.820846\pi$
$264$		0			0
$265$	−11.2843			−0.693187
$266$	−1.21390	+	9.59867i	−0.0744288	+	0.588532i
$267$		0			0
$268$	−13.2621	−	7.65685i	−0.810109	−	0.467717i
$269$	−12.3284	−	21.3535i	−0.751677	−	1.30194i	−0.947009	−	0.321206i	$-0.895912\pi$
$269$	−12.3284	−	21.3535i	−0.751677	−	1.30194i	0.195332	−	0.980737i	$-0.437422\pi$
$270$		0			0
$271$	6.98975	+	4.03553i	0.424597	+	0.245141i	0.697042	−	0.717030i	$-0.254499\pi$
$271$	6.98975	+	4.03553i	0.424597	+	0.245141i	−0.272445	+	0.962171i	$0.587832\pi$
$272$			24.9706i			1.51406i
$273$		0			0
$274$	11.1716	+	11.1716i	0.674899	+	0.674899i
$275$	−2.27541	−	1.31371i	−0.137212	−	0.0792196i
$276$		0			0
$277$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$277$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$278$	−2.67700	−	9.99071i	−0.160556	−	0.599203i
$279$		0			0
$280$	5.30057	+	12.6143i	0.316770	+	0.753847i
$281$		−	15.1716i		−	0.905060i	−0.891749	−	0.452530i	$-0.850522\pi$
$281$		−	15.1716i		−	0.905060i	0.891749	−	0.452530i	$-0.149478\pi$
$282$		0			0
$283$	−13.0208	−	22.5527i	−0.774007	−	1.34062i	−0.935351	−	0.353721i	$-0.884916\pi$
$283$	−13.0208	−	22.5527i	−0.774007	−	1.34062i	0.161344	−	0.986898i	$-0.448417\pi$
$284$	−24.0746	+	13.8995i	−1.42857	+	0.824783i
$285$		0			0
$286$	−4.10051	+	4.10051i	−0.242468	+	0.242468i
$287$	−23.1421	+	3.16693i	−1.36604	+	0.186938i
$288$		0			0
$289$	10.9853	−	19.0271i	0.646193	−	1.11924i
$290$	7.49303	+	2.00775i	0.440006	+	0.117899i
$291$		0			0
$292$	−12.6677	−	7.31371i	−0.741322	−	0.428002i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$		−	14.7574i		−	0.859207i
$296$	6.64048	+	24.7826i	0.385970	+	1.44046i
$297$		0			0
$298$	2.73205	+	0.732051i	0.158263	+	0.0424066i
$299$	1.31178	+	0.757359i	0.0758625	+	0.0437992i
$300$		0			0
$301$	4.09450	+	29.9203i	0.236003	+	1.72458i
$302$	−4.07107	−	4.07107i	−0.234264	−	0.234264i
$303$		0			0
$304$	−5.17157	−	8.95743i	−0.296610	−	0.513744i
$305$	−9.88500	+	5.70711i	−0.566013	+	0.326788i
$306$		0			0
$307$	18.7279			1.06886			0.534429	−	0.845213i	$-0.320527\pi$
$307$	18.7279			1.06886			0.534429	+	0.845213i	$0.320527\pi$
$308$	7.76874	+	3.17157i	0.442665	+	0.180717i
$309$		0			0
$310$	11.0253	−	2.95422i	0.626194	−	0.167788i
$311$	−1.82843	−	3.16693i	−0.103681	−	0.179580i	0.809518	−	0.587095i	$-0.199729\pi$
$311$	−1.82843	−	3.16693i	−0.103681	−	0.179580i	−0.913198	+	0.407515i	$0.866395\pi$
$312$		0			0
$313$	7.15685	−	12.3960i	0.404529	−	0.700665i	−0.589737	−	0.807595i	$-0.700769\pi$
$313$	7.15685	−	12.3960i	0.404529	−	0.700665i	0.994267	+	0.106930i	$0.0341020\pi$
$314$		0			0
$315$		0			0
$316$	−16.1421			−0.908066
$317$	−7.08579	+	12.2729i	−0.397977	+	0.689317i	−0.993476	−	0.114039i	$-0.963621\pi$
$317$	−7.08579	+	12.2729i	−0.397977	+	0.689317i	0.595499	+	0.803356i	$0.296954\pi$
$318$		0			0
$319$	4.11999	−	2.37868i	0.230675	−	0.133180i
$320$	−12.6677	−	7.31371i	−0.708147	−	0.408849i
$321$		0			0
$322$	0.274997	−	2.17449i	0.0153250	−	0.121180i
$323$			16.1421i			0.898172i
$324$		0			0
$325$	3.71029	−	2.14214i	0.205810	−	0.118824i
$326$	4.66390	+	1.24969i	0.258310	+	0.0692139i
$327$		0			0
$328$	17.6569	−	17.6569i	0.974937	−	0.974937i
$329$	6.33386	+	2.58579i	0.349197	+	0.142559i
$330$		0			0
$331$	−16.1421	+	27.9590i	−0.887252	+	1.53677i	−0.0441415	+	0.999025i	$0.514055\pi$
$331$	−16.1421	+	27.9590i	−0.887252	+	1.53677i	−0.843111	+	0.537740i	$0.819278\pi$
$332$	8.07107	+	13.9795i	0.442957	+	0.767225i
$333$		0			0
$334$	1.33850	+	4.99536i	0.0732395	+	0.273334i
$335$	−14.0000			−0.764902
$336$		0			0
$337$	−3.34315			−0.182113			−0.0910564	−	0.995846i	$-0.529024\pi$
$337$	−3.34315			−0.182113			−0.0910564	+	0.995846i	$0.529024\pi$
$338$	2.31098	+	8.62469i	0.125701	+	0.469121i
$339$		0			0
$340$	11.4142	+	19.7700i	0.619023	+	1.07218i
$341$	3.50000	−	6.06218i	0.189536	−	0.328285i
$342$		0			0
$343$	−7.34847	−	17.0000i	−0.396780	−	0.917914i
$344$	−22.8284	−	22.8284i	−1.23083	−	1.23083i
$345$		0			0
$346$	−34.1104	−	9.13986i	−1.83379	−	0.491362i
$347$	2.44949	−	1.41421i	0.131495	−	0.0759190i	−0.432809	−	0.901486i	$-0.642478\pi$
$347$	2.44949	−	1.41421i	0.131495	−	0.0759190i	0.564305	+	0.825567i	$0.309144\pi$
$348$		0			0
$349$			33.7990i			1.80922i	0.426242	+	0.904609i	$0.359837\pi$
$349$			33.7990i			1.80922i	−0.426242	+	0.904609i	$0.640163\pi$
$350$	−4.93749	−	3.74880i	−0.263920	−	0.200382i
$351$		0			0
$352$	−8.66490	+	2.32175i	−0.461841	+	0.123750i
$353$	27.9590	−	16.1421i	1.48811	−	0.859159i	0.488199	−	0.872732i	$-0.337654\pi$
$353$	27.9590	−	16.1421i	1.48811	−	0.859159i	0.999908	+	0.0135729i	$0.00432051\pi$
$354$		0			0
$355$	−12.7071	+	22.0094i	−0.674423	+	1.16814i
$356$		0			0
$357$		0			0
$358$	14.8284	+	14.8284i	0.783707	+	0.783707i
$359$	0.514719	−	0.891519i	0.0271658	−	0.0470526i	−0.852123	−	0.523342i	$-0.824685\pi$
$359$	0.514719	−	0.891519i	0.0271658	−	0.0470526i	0.879289	+	0.476289i	$0.158018\pi$
$360$		0			0
$361$	6.15685	+	10.6640i	0.324045	+	0.561262i
$362$	12.0599	−	3.23143i	0.633852	−	0.169840i
$363$		0			0
$364$	−10.8126	+	8.38478i	−0.566733	+	0.439482i
$365$	−13.3726			−0.699953
$366$		0			0
$367$	−16.4905	+	9.52082i	−0.860799	+	0.496983i	−0.864280	−	0.503011i	$-0.832225\pi$
$367$	−16.4905	+	9.52082i	−0.860799	+	0.496983i	0.00348080	+	0.999994i	$0.498892\pi$
$368$	1.17157	+	2.02922i	0.0610725	+	0.105781i
$369$		0			0
$370$	16.5858	+	16.5858i	0.862254	+	0.862254i
$371$	−12.9033	+	10.0061i	−0.669908	+	0.519491i
$372$		0			0
$373$	−13.9795	−	8.07107i	−0.723831	−	0.417904i	0.0923301	−	0.995728i	$-0.470569\pi$
$373$	−13.9795	−	8.07107i	−0.723831	−	0.417904i	−0.816161	+	0.577824i	$0.803902\pi$
$374$	13.5230	+	3.62347i	0.699256	+	0.187365i
$375$		0			0
$376$	−7.06450	+	1.89293i	−0.364324	+	0.0976203i
$377$			7.75736i			0.399524i
$378$		0			0
$379$	−6.68629			−0.343452			−0.171726	−	0.985145i	$-0.554934\pi$
$379$	−6.68629			−0.343452			−0.171726	+	0.985145i	$0.554934\pi$
$380$	−8.18900	−	4.72792i	−0.420087	−	0.242537i
$381$		0			0
$382$	17.7181	+	4.74756i	0.906538	+	0.242906i
$383$	−3.65685	+	6.33386i	−0.186857	+	0.323645i	−0.944201	−	0.329371i	$-0.893163\pi$
$383$	−3.65685	+	6.33386i	−0.186857	+	0.323645i	0.757344	+	0.653016i	$0.226497\pi$
$384$		0			0
$385$	7.60051	−	1.04011i	0.387358	−	0.0530087i
$386$	12.7990	−	12.7990i	0.651451	−	0.651451i
$387$		0			0
$388$	27.4156	−	15.8284i	1.39182	−	0.803567i
$389$	7.65685	+	13.2621i	0.388218	+	0.672413i	0.992210	−	0.124577i	$-0.0397575\pi$
$389$	7.65685	+	13.2621i	0.388218	+	0.672413i	−0.603992	+	0.796990i	$0.706424\pi$
$390$		0			0
$391$		−	3.65685i		−	0.184935i
$392$	17.2466	+	9.72401i	0.871083	+	0.491137i
$393$		0			0
$394$	9.56869	+	35.7108i	0.482063	+	1.79909i
$395$	−12.7802	+	7.37868i	−0.643044	+	0.371262i
$396$		0			0
$397$	30.5826	+	17.6569i	1.53490	+	0.886172i	0.999126	+	0.0418078i	$0.0133117\pi$
$397$	30.5826	+	17.6569i	1.53490	+	0.886172i	0.535769	+	0.844364i	$0.320022\pi$
$398$	−17.6569	−	17.6569i	−0.885058	−	0.885058i
$399$		0			0
$400$	6.62742			0.331371
$401$	−20.1903	−	11.6569i	−1.00825	−	0.582116i	−0.0975738	−	0.995228i	$-0.531108\pi$
$401$	−20.1903	−	11.6569i	−1.00825	−	0.582116i	−0.910680	+	0.413113i	$0.864442\pi$
$402$		0			0
$403$	5.70711	+	9.88500i	0.284291	+	0.492407i
$404$	21.6251	+	12.4853i	1.07589	+	0.621166i
$405$		0			0
$406$	10.3485	−	4.34847i	0.513586	−	0.215811i
$407$	14.3848			0.713027
$408$		0			0
$409$	9.74264	+	16.8747i	0.481743	+	0.834403i	0.999780	−	0.0209551i	$-0.00667070\pi$
$409$	9.74264	+	16.8747i	0.481743	+	0.834403i	−0.518038	+	0.855358i	$0.673337\pi$
$410$	5.90843	−	22.0506i	0.291797	−	1.08900i
$411$		0			0
$412$	−35.3137			−1.73978
$413$	−13.0858	−	16.8747i	−0.643909	−	0.830352i
$414$		0			0
$415$	12.7802	+	7.37868i	0.627358	+	0.362205i
$416$	3.78585	−	14.1290i	0.185617	−	0.692731i
$417$		0			0
$418$	−5.60139	+	1.50089i	−0.273973	+	0.0734109i
$419$			24.9706i			1.21989i	0.792443	+	0.609946i	$0.208809\pi$
$419$			24.9706i			1.21989i	−0.792443	+	0.609946i	$0.791191\pi$
$420$		0			0
$421$		−	20.8701i		−	1.01714i	−0.861019	−	0.508572i	$-0.830173\pi$
$421$		−	20.8701i		−	1.01714i	0.861019	−	0.508572i	$-0.169827\pi$
$422$	−10.0863	−	37.6427i	−0.490995	−	1.83242i
$423$		0			0
$424$	4.51790	−	16.8611i	0.219409	−	0.818845i
$425$	−8.95743	−	5.17157i	−0.434499	−	0.250858i
$426$		0			0
$427$	−6.24264	+	15.2913i	−0.302103	+	0.739997i
$428$	−30.4853			−1.47356
$429$		0			0
$430$	−28.5090	−	7.63897i	−1.37483	−	0.368384i
$431$	10.3137	+	17.8639i	0.496794	+	0.860472i	0.999993	−	0.00369819i	$-0.00117717\pi$
$431$	10.3137	+	17.8639i	0.496794	+	0.860472i	−0.503199	+	0.864170i	$0.667844\pi$
$432$		0			0
$433$	30.1421			1.44854			0.724269	−	0.689517i	$-0.242177\pi$
$433$	30.1421			1.44854			0.724269	+	0.689517i	$0.242177\pi$
$434$	9.98760	−	13.1545i	0.479420	−	0.631438i
$435$		0			0
$436$	2.48528	−	4.30463i	0.119023	−	0.206155i
$437$	0.757359	+	1.31178i	0.0362294	+	0.0627512i
$438$		0			0
$439$	6.44639	+	3.72183i	0.307669	+	0.177633i	0.645883	−	0.763436i	$-0.276489\pi$
$439$	6.44639	+	3.72183i	0.307669	+	0.177633i	−0.338214	+	0.941069i	$0.609823\pi$
$440$	−5.79899	+	5.79899i	−0.276456	+	0.276456i
$441$		0			0
$442$	−16.1421	+	16.1421i	−0.767803	+	0.767803i
$443$	2.93130	+	1.69239i	0.139270	+	0.0804078i	0.568016	−	0.823017i	$-0.307711\pi$
$443$	2.93130	+	1.69239i	0.139270	+	0.0804078i	−0.428746	+	0.903425i	$0.641044\pi$
$444$		0			0
$445$		0			0
$446$	35.1450	−	9.41707i	1.66416	−	0.445911i
$447$		0			0
$448$	−20.9706	+	2.86976i	−0.990766	+	0.135583i
$449$		−	23.5563i		−	1.11169i	−0.831285	−	0.555846i	$-0.812394\pi$
$449$		−	23.5563i		−	1.11169i	0.831285	−	0.555846i	$-0.187606\pi$
$450$		0			0
$451$	−7.00000	−	12.1244i	−0.329617	−	0.570914i
$452$	−4.82843	−	8.36308i	−0.227110	−	0.393366i
$453$		0			0
$454$	11.7279	+	11.7279i	0.550419	+	0.550419i
$455$	−4.72792	+	11.5810i	−0.221648	+	0.542925i
$456$		0			0
$457$	14.4706	−	25.0637i	0.676904	−	1.17243i	−0.299004	−	0.954252i	$-0.596654\pi$
$457$	14.4706	−	25.0637i	0.676904	−	1.17243i	0.975908	−	0.218181i	$-0.0700123\pi$
$458$	−0.554425	+	2.06914i	−0.0259066	+	0.0966848i
$459$		0			0
$460$	1.85514	+	1.07107i	0.0864965	+	0.0499388i
$461$	17.6569			0.822362			0.411181	−	0.911554i	$-0.365116\pi$
$461$	17.6569			0.822362			0.411181	+	0.911554i	$0.365116\pi$
$462$		0			0
$463$		−	22.8284i		−	1.06093i	−0.847708	−	0.530463i	$-0.822018\pi$
$463$		−	22.8284i		−	1.06093i	0.847708	−	0.530463i	$-0.177982\pi$
$464$	−6.00000	+	10.3923i	−0.278543	+	0.482451i
$465$		0			0
$466$	7.03252	−	26.2457i	0.325775	−	1.21581i
$467$	33.7495	+	19.4853i	1.56174	+	0.901671i	0.997081	+	0.0763471i	$0.0243257\pi$
$467$	33.7495	+	19.4853i	1.56174	+	0.901671i	0.564659	+	0.825324i	$0.309008\pi$
$468$		0			0
$469$	−16.0087	+	12.4142i	−0.739214	+	0.573235i
$470$	−4.72792	+	4.72792i	−0.218083	+	0.218083i
$471$		0			0
$472$	22.0506	+	5.90843i	1.01496	+	0.271958i
$473$	−15.6755	+	9.05025i	−0.720760	+	0.416131i
$474$		0			0
$475$	4.28427			0.196576
$476$	30.5826	+	12.4853i	1.40175	+	0.572262i
$477$		0			0
$478$	3.74907	+	13.9917i	0.171478	+	0.639966i
$479$	−10.4350	−	18.0740i	−0.476789	−	0.825822i	0.522858	−	0.852420i	$-0.324866\pi$
$479$	−10.4350	−	18.0740i	−0.476789	−	0.825822i	−0.999646	+	0.0265979i	$0.991533\pi$
$480$		0			0
$481$	−11.7279	+	20.3134i	−0.534747	+	0.926209i
$482$	−10.6569	+	10.6569i	−0.485406	+	0.485406i
$483$		0			0
$484$		−	16.9706i		−	0.771389i
$485$	14.4706	−	25.0637i	0.657074	−	1.13809i
$486$		0			0
$487$	35.9634	−	20.7635i	1.62966	−	0.940882i	0.645460	−	0.763794i	$-0.276666\pi$
$487$	35.9634	−	20.7635i	1.62966	−	0.940882i	0.984195	−	0.177088i	$-0.0566678\pi$
$488$	−4.56993	−	17.0552i	−0.206871	−	0.772053i
$489$		0			0
$490$	18.0996	−	0.184709i	0.817655	−	0.00834429i
$491$			20.8995i			0.943181i	0.881818	+	0.471591i	$0.156320\pi$
$491$			20.8995i			0.943181i	−0.881818	+	0.471591i	$0.843680\pi$
$492$		0			0
$493$	16.2189	−	9.36396i	0.730461	−	0.421732i
$494$	2.44735	−	9.13364i	0.110112	−	0.410942i
$495$		0			0
$496$			17.6569i			0.792816i
$497$	4.98602	+	36.4350i	0.223654	+	1.63433i
$498$		0			0
$499$	−16.1421	+	27.9590i	−0.722621	+	1.25162i	0.237324	+	0.971430i	$0.423730\pi$
$499$	−16.1421	+	27.9590i	−0.722621	+	1.25162i	−0.959946	+	0.280186i	$0.909604\pi$
$500$	21.0818	−	12.1716i	0.942806	−	0.544329i
$501$		0			0
$502$	3.10372	−	0.831638i	0.138526	−	0.0371178i
$503$	−20.2426			−0.902575			−0.451287	−	0.892379i	$-0.649035\pi$
$503$	−20.2426			−0.902575			−0.451287	+	0.892379i	$0.649035\pi$
$504$		0			0
$505$	22.8284			1.01585
$506$	1.26894	−	0.340013i	0.0564115	−	0.0151154i
$507$		0			0
$508$	−8.07107	−	13.9795i	−0.358096	−	0.620240i
$509$	−8.22792	+	14.2512i	−0.364696	+	0.631672i	−0.988727	−	0.149727i	$-0.952160\pi$
$509$	−8.22792	+	14.2512i	−0.364696	+	0.631672i	0.624031	+	0.781399i	$0.285494\pi$
$510$		0			0
$511$	−15.2913	+	11.8579i	−0.676447	+	0.524561i
$512$	16.0000	−	16.0000i	0.707107	−	0.707107i
$513$		0			0
$514$		0			0
$515$	−27.9590	+	16.1421i	−1.23202	+	0.711307i
$516$		0			0
$517$			4.10051i			0.180340i
$518$	33.6726	+	4.25841i	1.47949	+	0.187104i
$519$		0			0
$520$	−3.46108	−	12.9169i	−0.151778	−	0.566445i
$521$	−17.5306	+	10.1213i	−0.768031	+	0.443423i	−0.832172	−	0.554518i	$-0.812903\pi$
$521$	−17.5306	+	10.1213i	−0.768031	+	0.443423i	0.0641405	+	0.997941i	$0.479569\pi$
$522$		0			0
$523$	−7.84924	+	13.5953i	−0.343223	+	0.594480i	−0.985029	−	0.172387i	$-0.944852\pi$
$523$	−7.84924	+	13.5953i	−0.343223	+	0.594480i	0.641806	+	0.766867i	$0.278185\pi$
$524$	19.1716			0.837514
$525$		0			0
$526$	−1.27208	+	1.27208i	−0.0554652	+	0.0554652i
$527$	13.7782	−	23.8645i	0.600187	−	1.03955i
$528$		0			0
$529$	11.3284	+	19.6214i	0.492540	+	0.853105i
$530$	−4.13033	−	15.4146i	−0.179410	−	0.669567i
$531$		0			0
$532$	−13.5563	+	1.85514i	−0.587742	+	0.0804307i
$533$	22.8284			0.988809
$534$		0			0
$535$	−24.1362	+	13.9350i	−1.04350	+	0.602464i
$536$	5.60521	−	20.9189i	0.242108	−	0.903560i
$537$		0			0
$538$	24.6569	−	24.6569i	1.06303	−	1.06303i
$539$	7.76874	−	7.92893i	0.334623	−	0.341523i
$540$		0			0
$541$	23.8645	+	13.7782i	1.02601	+	0.592370i	0.915840	−	0.401542i	$-0.131526\pi$
$541$	23.8645	+	13.7782i	1.02601	+	0.592370i	0.110174	+	0.993912i	$0.464859\pi$
$542$	−2.95422	+	11.0253i	−0.126894	+	0.473576i
$543$		0			0
$544$	−34.1104	+	9.13986i	−1.46247	+	0.391868i
$545$		−	4.54416i		−	0.194650i
$546$		0			0
$547$	−0.928932			−0.0397183			−0.0198591	−	0.999803i	$-0.506322\pi$
$547$	−0.928932			−0.0397183			−0.0198591	+	0.999803i	$0.506322\pi$
$548$	−11.1716	+	19.3497i	−0.477226	+	0.826580i
$549$		0			0
$550$	0.961701	−	3.58912i	0.0410071	−	0.153041i
$551$	−3.87868	+	6.71807i	−0.165237	+	0.286199i
$552$		0			0
$553$	−8.07107	+	19.7700i	−0.343217	+	0.840706i
$554$		0			0
$555$		0			0
$556$	12.6677	−	7.31371i	0.537231	−	0.310170i
$557$	−10.0858	−	17.4691i	−0.427348	−	0.740189i	0.569288	−	0.822138i	$-0.307219\pi$
$557$	−10.0858	−	17.4691i	−0.427348	−	0.740189i	−0.996637	+	0.0819488i	$0.973886\pi$
$558$		0			0
$559$		−	29.5147i		−	1.24834i
$560$	−15.2913	+	11.8579i	−0.646175	+	0.501086i
$561$		0			0
$562$	20.7248	−	5.55318i	0.874221	−	0.234247i
$563$	−9.61332	+	5.55025i	−0.405153	+	0.233915i	−0.688705	−	0.725042i	$-0.741820\pi$
$563$	−9.61332	+	5.55025i	−0.405153	+	0.233915i	0.283552	+	0.958957i	$0.408487\pi$
$564$		0			0
$565$	−7.64564	−	4.41421i	−0.321655	−	0.185707i
$566$	26.0416	−	26.0416i	1.09461	−	1.09461i
$567$		0			0
$568$	−27.7990	−	27.7990i	−1.16642	−	1.16642i
$569$	12.1604	+	7.02082i	0.509791	+	0.294328i	0.732748	−	0.680500i	$-0.238238\pi$
$569$	12.1604	+	7.02082i	0.509791	+	0.294328i	−0.222957	+	0.974828i	$0.571571\pi$
$570$		0			0
$571$	−3.29289	−	5.70346i	−0.137803	−	0.238682i	0.788862	−	0.614571i	$-0.210671\pi$
$571$	−3.29289	−	5.70346i	−0.137803	−	0.238682i	−0.926665	+	0.375889i	$0.877338\pi$
$572$	−7.10228	−	4.10051i	−0.296961	−	0.171451i
$573$		0			0
$574$	−12.7967	−	30.4536i	−0.534125	−	1.27111i
$575$	−0.970563			−0.0404753
$576$		0			0
$577$	3.81371	+	6.60554i	0.158767	+	0.274992i	0.934424	−	0.356162i	$-0.115915\pi$
$577$	3.81371	+	6.60554i	0.158767	+	0.274992i	−0.775657	+	0.631154i	$0.782582\pi$
$578$	30.0123	+	8.04178i	1.24835	+	0.334494i
$579$		0			0
$580$			10.9706i			0.455528i
$581$	21.1569	−	2.89525i	0.877734	−	0.120115i
$582$		0			0
$583$	−8.47561	−	4.89340i	−0.351024	−	0.202664i
$584$	5.35401	−	19.9814i	0.221550	−	0.826837i
$585$		0			0
$586$	7.68653	+	28.6865i	0.317528	+	1.18503i
$587$		−	22.6985i		−	0.936867i	−0.883499	−	0.468433i	$-0.844819\pi$
$587$		−	22.6985i		−	0.936867i	0.883499	−	0.468433i	$-0.155181\pi$
$588$		0			0
$589$			11.4142i			0.470314i
$590$	20.1589	−	5.40157i	0.829930	−	0.222379i
$591$		0			0
$592$	−31.4231	+	18.1421i	−1.29148	+	0.745637i
$593$	−14.9071	−	8.60660i	−0.612160	−	0.353431i	0.161650	−	0.986848i	$-0.448318\pi$
$593$	−14.9071	−	8.60660i	−0.612160	−	0.353431i	−0.773810	+	0.633417i	$0.781652\pi$
$594$		0			0
$595$	29.9203	−	4.09450i	1.22661	−	0.167858i
$596$			4.00000i			0.163846i
$597$		0			0
$598$	−0.554425	+	2.06914i	−0.0226721	+	0.0846136i
$599$	−24.3137	−	42.1126i	−0.993431	−	1.72067i	−0.595816	−	0.803121i	$-0.703171\pi$
$599$	−24.3137	−	42.1126i	−0.993431	−	1.72067i	−0.397615	−	0.917552i	$-0.630162\pi$
$600$		0			0
$601$	−14.3137			−0.583868			−0.291934	−	0.956438i	$-0.594299\pi$
$601$	−14.3137			−0.583868			−0.291934	+	0.956438i	$0.594299\pi$
$602$	−39.3732	+	16.5448i	−1.60473	+	0.674315i
$603$		0			0
$604$	4.07107	−	7.05130i	0.165649	−	0.286913i
$605$	−7.75736	−	13.4361i	−0.315382	−	0.546257i
$606$		0			0
$607$	−6.44639	−	3.72183i	−0.261651	−	0.151064i	0.363437	−	0.931619i	$-0.381603\pi$
$607$	−6.44639	−	3.72183i	−0.261651	−	0.151064i	−0.625087	+	0.780555i	$0.714937\pi$
$608$	10.3431	−	10.3431i	0.419470	−	0.419470i
$609$		0			0
$610$	−11.4142	−	11.4142i	−0.462148	−	0.462148i
$611$	−5.79050	−	3.34315i	−0.234258	−	0.135249i
$612$		0			0
$613$	−4.09450	+	2.36396i	−0.165375	+	0.0954795i	−0.580403	−	0.814329i	$-0.697105\pi$
$613$	−4.09450	+	2.36396i	−0.165375	+	0.0954795i	0.415028	+	0.909809i	$0.363772\pi$
$614$	6.85490	+	25.5828i	0.276641	+	1.03244i
$615$		0			0
$616$	−1.48889	+	11.7732i	−0.0599893	+	0.474354i
$617$			17.7574i			0.714884i	0.933935	+	0.357442i	$0.116351\pi$
$617$			17.7574i			0.714884i	−0.933935	+	0.357442i	$0.883649\pi$
$618$		0			0
$619$	−3.87868	−	6.71807i	−0.155897	−	0.270022i	0.777488	−	0.628898i	$-0.216494\pi$
$619$	−3.87868	−	6.71807i	−0.155897	−	0.270022i	−0.933385	+	0.358876i	$0.883160\pi$
$620$	8.07107	+	13.9795i	0.324142	+	0.561430i
$621$		0			0
$622$	3.65685	−	3.65685i	0.146626	−	0.146626i
$623$		0			0
$624$		0			0
$625$	6.98528	−	12.0989i	0.279411	−	0.483954i
$626$	19.5529	+	5.23918i	0.781491	+	0.209400i
$627$		0			0
$628$		0			0
$629$	56.6274			2.25788
$630$		0			0
$631$			24.2132i			0.963912i	0.876195	+	0.481956i	$0.160074\pi$
$631$			24.2132i			0.963912i	−0.876195	+	0.481956i	$0.839926\pi$
$632$	−5.90843	−	22.0506i	−0.235025	−	0.877124i
$633$		0			0
$634$	−19.3587	−	5.18716i	−0.768833	−	0.206008i
$635$	−12.7802	−	7.37868i	−0.507169	−	0.292814i
$636$		0			0
$637$	4.86293	+	17.4350i	0.192676	+	0.690801i
$638$	4.75736	+	4.75736i	0.188346	+	0.188346i
$639$		0			0
$640$	5.35401	−	19.9814i	0.211636	−	0.789835i
$641$	−12.3345	+	7.12132i	−0.487183	+	0.281275i	−0.723405	−	0.690424i	$-0.757424\pi$
$641$	−12.3345	+	7.12132i	−0.487183	+	0.281275i	0.236222	+	0.971699i	$0.424091\pi$
$642$		0			0
$643$	28.6274			1.12896			0.564478	−	0.825448i	$-0.309078\pi$
$643$	28.6274			1.12896			0.564478	+	0.825448i	$0.309078\pi$
$644$	3.07107	−	0.420266i	0.121017	−	0.0165608i
$645$		0			0
$646$	−22.0506	+	5.90843i	−0.867568	+	0.232464i
$647$	22.6066	+	39.1558i	0.888757	+	1.53937i	0.841346	+	0.540497i	$0.181764\pi$
$647$	22.6066	+	39.1558i	0.888757	+	1.53937i	0.0474114	+	0.998875i	$0.484903\pi$
$648$		0			0
$649$	6.39949	−	11.0843i	0.251202	−	0.435095i
$650$	4.28427	+	4.28427i	0.168043	+	0.168043i
$651$		0			0
$652$			6.82843i			0.267422i
$653$	−23.9853	+	41.5437i	−0.938617	+	1.62573i	−0.170562	+	0.985347i	$0.554558\pi$
$653$	−23.9853	+	41.5437i	−0.938617	+	1.62573i	−0.768054	+	0.640385i	$0.778775\pi$
$654$		0			0
$655$	15.1788	−	8.76346i	0.593083	−	0.342417i
$656$	30.5826	+	17.6569i	1.19405	+	0.689384i
$657$		0			0
$658$	−1.21390	+	9.59867i	−0.0473226	+	0.374195i
$659$			4.20101i			0.163648i	0.996647	+	0.0818241i	$0.0260746\pi$
$659$			4.20101i			0.163648i	−0.996647	+	0.0818241i	$0.973925\pi$
$660$		0			0
$661$	25.7196	−	14.8492i	1.00038	−	0.577569i	0.0920180	−	0.995757i	$-0.470668\pi$
$661$	25.7196	−	14.8492i	1.00038	−	0.577569i	0.908360	+	0.418189i	$0.137335\pi$
$662$	−44.1011	−	11.8169i	−1.71404	−	0.459275i
$663$		0			0
$664$	−16.1421	+	16.1421i	−0.626436	+	0.626436i
$665$	−9.88500	+	7.66548i	−0.383324	+	0.297254i
$666$		0			0
$667$	0.878680	−	1.52192i	0.0340226	−	0.0589289i
$668$	−6.33386	+	3.65685i	−0.245064	+	0.141488i
$669$		0			0
$670$	−5.12436	−	19.1244i	−0.197971	−	0.738838i
$671$	−9.89949			−0.382166
$672$		0			0
$673$	26.1716			1.00884			0.504420	−	0.863458i	$-0.331706\pi$
$673$	26.1716			1.00884			0.504420	+	0.863458i	$0.331706\pi$
$674$	−1.22368	−	4.56682i	−0.0471342	−	0.175907i
$675$		0			0
$676$	−10.9357	+	6.31371i	−0.420602	+	0.242835i
$677$	−5.32843	+	9.22911i	−0.204788	+	0.354703i	−0.950065	−	0.312051i	$-0.898984\pi$
$677$	−5.32843	+	9.22911i	−0.204788	+	0.354703i	0.745277	+	0.666755i	$0.232317\pi$
$678$		0			0
$679$	−5.67796	−	41.4914i	−0.217900	−	1.59229i
$680$	−22.8284	+	22.8284i	−0.875430	+	0.875430i
$681$		0			0
$682$	9.56218	+	2.56218i	0.366155	+	0.0981109i
$683$	26.0423	−	15.0355i	0.996481	−	0.575319i	0.0892760	−	0.996007i	$-0.471545\pi$
$683$	26.0423	−	15.0355i	0.996481	−	0.575319i	0.907205	+	0.420688i	$0.138211\pi$
$684$		0			0
$685$			20.4264i			0.780453i
$686$	20.5327	−	16.2606i	0.783942	−	0.620834i
$687$		0			0
$688$	22.8284	−	39.5400i	0.870326	−	1.50745i
$689$	13.8204	−	7.97918i	0.526514	−	0.303983i
$690$		0			0
$691$	−0.313708	+	0.543359i	−0.0119340	+	0.0206704i	−0.871931	−	0.489629i	$-0.837132\pi$
$691$	−0.313708	+	0.543359i	−0.0119340	+	0.0206704i	0.859997	+	0.510300i	$0.170465\pi$
$692$		−	49.9411i		−	1.89848i
$693$		0			0
$694$	2.82843	+	2.82843i	0.107366	+	0.107366i
$695$	6.68629	−	11.5810i	0.253625	−	0.439292i
$696$		0			0
$697$	−27.5563	−	47.7290i	−1.04377	−	1.80786i
$698$	−46.1703	+	12.3713i	−1.74757	+	0.468260i
$699$		0			0
$700$	3.31371	−	8.11689i	0.125246	−	0.306790i
$701$	−14.6569			−0.553582			−0.276791	−	0.960930i	$-0.589271\pi$
$701$	−14.6569			−0.553582			−0.276791	+	0.960930i	$0.589271\pi$
$702$		0			0
$703$	−20.3134	+	11.7279i	−0.766133	+	0.442327i
$704$	−6.34315	−	10.9867i	−0.239066	−	0.414075i
$705$		0			0
$706$	32.2843	+	32.2843i	1.21503	+	1.21503i
$707$	26.1039	−	20.2426i	0.981737	−	0.761303i
$708$		0			0
$709$	−26.2779	−	15.1716i	−0.986889	−	0.569780i	−0.0825458	−	0.996587i	$-0.526305\pi$
$709$	−26.2779	−	15.1716i	−0.986889	−	0.569780i	−0.904343	+	0.426807i	$0.859638\pi$
$710$	−34.7165	−	9.30225i	−1.30289	−	0.349107i
$711$		0			0
$712$		0			0
$713$		−	2.58579i		−	0.0968385i
$714$		0			0
$715$	−7.49747			−0.280390
$716$	−14.8284	+	25.6836i	−0.554164	+	0.959841i
$717$		0			0
$718$	1.40624	+	0.376800i	0.0524803	+	0.0140621i
$719$	−22.8284	+	39.5400i	−0.851357	+	1.47459i	0.0286276	+	0.999590i	$0.490886\pi$
$719$	−22.8284	+	39.5400i	−0.851357	+	1.47459i	−0.879984	+	0.475003i	$0.842447\pi$
$720$		0			0
$721$	−17.6569	+	43.2503i	−0.657576	+	1.61072i
$722$	−12.3137	+	12.3137i	−0.458269	+	0.458269i
$723$		0			0
$724$	8.82843	+	15.2913i	0.328106	+	0.568296i
$725$	−2.48528	−	4.30463i	−0.0923010	−	0.159870i
$726$		0			0
$727$			42.7574i			1.58578i	0.609363	+	0.792891i	$0.291425\pi$
$727$			42.7574i			1.58578i	−0.609363	+	0.792891i	$0.708575\pi$
$728$	−15.4115	−	11.7012i	−0.571188	−	0.433676i
$729$		0			0
$730$	−4.89471	−	18.2673i	−0.181161	−	0.676103i
$731$	−61.7085	+	35.6274i	−2.28237	+	1.31773i
$732$		0			0
$733$	−25.7196	−	14.8492i	−0.949977	−	0.548469i	−0.0569030	−	0.998380i	$-0.518123\pi$
$733$	−25.7196	−	14.8492i	−0.949977	−	0.548469i	−0.893074	+	0.449910i	$0.851456\pi$
$734$	−19.0416	−	19.0416i	−0.702839	−	0.702839i
$735$		0			0
$736$	−2.34315	+	2.34315i	−0.0863695	+	0.0863695i
$737$	−10.5154	−	6.07107i	−0.387340	−	0.223631i
$738$		0			0
$739$	−14.1421	−	24.4949i	−0.520227	−	0.901059i	−0.999723	−	0.0235156i	$-0.992514\pi$
$739$	−14.1421	−	24.4949i	−0.520227	−	0.901059i	0.479497	−	0.877544i	$-0.340819\pi$
$740$	−16.5858	+	28.7274i	−0.609706	+	1.05604i
$741$		0			0
$742$	−18.3915	−	13.9638i	−0.675174	−	0.512627i
$743$	−2.68629			−0.0985505			−0.0492752	−	0.998785i	$-0.515691\pi$
$743$	−2.68629			−0.0985505			−0.0492752	+	0.998785i	$0.515691\pi$
$744$		0			0
$745$	1.82843	+	3.16693i	0.0669884	+	0.116027i
$746$	5.90843	−	22.0506i	0.216323	−	0.807329i
$747$		0			0
$748$			19.7990i			0.723923i
$749$	−15.2426	+	37.3367i	−0.556954	+	1.36425i
$750$		0			0
$751$	19.7085	+	11.3787i	0.719172	+	0.415214i	0.814448	−	0.580237i	$-0.197040\pi$
$751$	19.7085	+	11.3787i	0.719172	+	0.415214i	−0.0952761	+	0.995451i	$0.530373\pi$
$752$	−5.17157	−	8.95743i	−0.188588	−	0.326644i
$753$		0			0
$754$	−10.5967	+	2.83939i	−0.385911	+	0.103405i
$755$		−	7.44365i		−	0.270902i
$756$		0			0
$757$		−	40.1838i		−	1.46050i	−0.683178	−	0.730252i	$-0.739403\pi$
$757$		−	40.1838i		−	1.46050i	0.683178	−	0.730252i	$-0.260597\pi$
$758$	−2.44735	−	9.13364i	−0.0888918	−	0.331749i
$759$		0			0
$760$	3.46108	−	12.9169i	0.125547	−	0.468546i
$761$	−0.384213	−	0.221825i	−0.0139277	−	0.00804116i	0.493020	−	0.870018i	$-0.335893\pi$
$761$	−0.384213	−	0.221825i	−0.0139277	−	0.00804116i	−0.506948	+	0.861977i	$0.669226\pi$
$762$		0			0
$763$	−4.02944	−	5.19615i	−0.145875	−	0.188113i
$764$			25.9411i			0.938517i
$765$		0			0
$766$	−9.99071	−	2.67700i	−0.360979	−	0.0967241i
$767$	10.4350	+	18.0740i	0.376787	+	0.652614i
$768$		0			0
$769$	−14.3137			−0.516166			−0.258083	−	0.966123i	$-0.583091\pi$
$769$	−14.3137			−0.516166			−0.258083	+	0.966123i	$0.583091\pi$
$770$	4.20279	+	10.0018i	0.151458	+	0.360439i
$771$		0			0
$772$	22.1685	+	12.7990i	0.797862	+	0.460646i
$773$	−14.3137	−	24.7921i	−0.514828	−	0.891709i	−0.999852	−	0.0172077i	$-0.994522\pi$
$773$	−14.3137	−	24.7921i	−0.514828	−	0.891709i	0.485024	−	0.874501i	$-0.338811\pi$
$774$		0			0
$775$	−6.33386	−	3.65685i	−0.227519	−	0.131358i
$776$	31.6569	+	31.6569i	1.13641	+	1.13641i
$777$		0			0
$778$	−15.3137	+	15.3137i	−0.549023	+	0.549023i
$779$	19.7700	+	11.4142i	0.708334	+	0.408957i
$780$		0			0
$781$	−19.0886	+	11.0208i	−0.683044	+	0.394356i
$782$	4.99536	−	1.33850i	0.178634	−	0.0478647i
$783$		0			0
$784$	−6.97056	+	27.1185i	−0.248949	+	0.968517i
$785$		0			0
$786$		0			0
$787$	−14.8492	−	25.7196i	−0.529318	−	0.916806i	−0.999415	−	0.0341915i	$-0.989114\pi$
$787$	−14.8492	−	25.7196i	−0.529318	−	0.916806i	0.470097	−	0.882615i	$-0.344219\pi$
$788$	−45.2795	+	26.1421i	−1.61302	+	0.931275i
$789$		0			0
$790$	−14.7574	−	14.7574i	−0.525043	−	0.525043i
$791$	−12.6569	+	1.73205i	−0.450026	+	0.0615846i
$792$		0			0
$793$	8.07107	−	13.9795i	0.286612	−	0.496427i
$794$	−12.9257	+	48.2394i	−0.458716	+	1.71195i
$795$		0			0
$796$	17.6569	−	30.5826i	0.625831	−	1.08397i
$797$	−40.7990			−1.44517			−0.722587	−	0.691280i	$-0.757047\pi$
$797$	−40.7990			−1.44517			−0.722587	+	0.691280i	$0.757047\pi$
$798$		0			0
$799$			16.1421i			0.571068i
$800$	2.42580	+	9.05322i	0.0857651	+	0.320080i
$801$		0			0
$802$	8.53341	−	31.8471i	0.301325	−	1.12456i
$803$	−10.0441	−	5.79899i	−0.354450	−	0.204642i
$804$		0			0
$805$	2.23936	−	1.73654i	0.0789270	−	0.0612051i
$806$	−11.4142	+	11.4142i	−0.402049	+	0.402049i
$807$		0			0
$808$	−9.13986	+	34.1104i	−0.321539	+	1.20000i
$809$	−2.02922	+	1.17157i	−0.0713437	+	0.0411903i	−0.535248	−	0.844695i	$-0.679782\pi$
$809$	−2.02922	+	1.17157i	−0.0713437	+	0.0411903i	0.463904	+	0.885886i	$0.346448\pi$
$810$		0			0
$811$	18.2843			0.642048			0.321024	−	0.947071i	$-0.395973\pi$
$811$	18.2843			0.642048			0.321024	+	0.947071i	$0.395973\pi$
$812$	9.72792	+	12.5446i	0.341383	+	0.440230i
$813$		0			0
$814$	5.26519	+	19.6500i	0.184545	+	0.688731i
$815$	3.12132	+	5.40629i	0.109335	+	0.189374i
$816$		0			0
$817$	14.7574	−	25.5605i	0.516295	−	0.894249i
$818$	−19.4853	+	19.4853i	−0.681287	+	0.681287i
$819$		0			0
$820$	32.2843			1.12742
$821$	−5.57107	+	9.64937i	−0.194432	+	0.336765i	−0.946714	−	0.322075i	$-0.895620\pi$
$821$	−5.57107	+	9.64937i	−0.194432	+	0.336765i	0.752282	+	0.658841i	$0.228953\pi$
$822$		0			0
$823$	−8.18900	+	4.72792i	−0.285451	+	0.164805i	−0.635888	−	0.771781i	$-0.719366\pi$
$823$	−8.18900	+	4.72792i	−0.285451	+	0.164805i	0.350438	+	0.936586i	$0.386033\pi$
$824$	−12.9257	−	48.2394i	−0.450289	−	1.68050i
$825$		0			0
$826$	18.2616	−	24.0521i	0.635403	−	0.836880i
$827$		−	9.24264i		−	0.321398i	−0.987003	−	0.160699i	$-0.948625\pi$
$827$		−	9.24264i		−	0.321398i	0.987003	−	0.160699i	$-0.0513749\pi$
$828$		0			0
$829$	−12.5086	+	7.22183i	−0.434441	+	0.250824i	−0.701237	−	0.712929i	$-0.747368\pi$
$829$	−12.5086	+	7.22183i	−0.434441	+	0.250824i	0.266796	+	0.963753i	$0.414035\pi$
$830$	−5.40157	+	20.1589i	−0.187491	+	0.699727i
$831$		0			0
$832$	20.6863			0.717168
$833$	30.5826	−	31.2132i	1.05962	−	1.08147i
$834$		0			0
$835$	−3.34315	+	5.79050i	−0.115694	+	0.200388i
$836$	−4.10051	−	7.10228i	−0.141819	−	0.245638i
$837$		0			0
$838$	−34.1104	+	9.13986i	−1.17833	+	0.315731i
$839$	24.5269			0.846763			0.423382	−	0.905951i	$-0.360843\pi$
$839$	24.5269			0.846763			0.423382	+	0.905951i	$0.360843\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	28.5090	−	7.63897i	0.982486	−	0.263256i
$843$		0			0
$844$	47.7290	−	27.5563i	1.64290	−	0.948529i
$845$	−5.77208	+	9.99753i	−0.198566	+	0.343926i
$846$		0			0
$847$	−20.7846	−	8.48528i	−0.714168	−	0.291558i
$848$	24.6863			0.847731
$849$		0			0
$850$	3.78585	−	14.1290i	0.129854	−	0.484621i
$851$	4.60181	−	2.65685i	0.157748	−	0.0910758i
$852$		0			0
$853$		−	1.51472i		−	0.0518630i	−0.999664	−	0.0259315i	$-0.991745\pi$
$853$		−	1.51472i		−	0.0518630i	0.999664	−	0.0259315i	$-0.00825517\pi$
$854$	−23.1732	−	2.93061i	−0.792972	−	0.100283i
$855$		0			0
$856$	−11.1584	−	41.6437i	−0.381386	−	1.42335i
$857$	16.9873	−	9.80761i	0.580274	−	0.335022i	−0.180968	−	0.983489i	$-0.557923\pi$
$857$	16.9873	−	9.80761i	0.580274	−	0.335022i	0.761242	+	0.648467i	$0.224590\pi$
$858$		0			0
$859$	10.4350	−	18.0740i	0.356039	−	0.616677i	−0.631257	−	0.775574i	$-0.717460\pi$
$859$	10.4350	−	18.0740i	0.356039	−	0.616677i	0.987295	+	0.158897i	$0.0507938\pi$
$860$		−	41.7401i		−	1.42333i
$861$		0			0
$862$	−20.6274	+	20.6274i	−0.702573	+	0.702573i
$863$	14.8284	−	25.6836i	0.504766	−	0.874280i	−0.495219	−	0.868768i	$-0.664912\pi$
$863$	14.8284	−	25.6836i	0.504766	−	0.874280i	0.999985	−	0.00551153i	$-0.00175438\pi$
$864$		0			0
$865$	−22.8284	−	39.5400i	−0.776190	−	1.34440i
$866$	11.0328	+	41.1749i	0.374909	+	1.39918i
$867$		0			0
$868$	21.6251	+	8.82843i	0.734005	+	0.299656i
$869$	−12.7990			−0.434176
$870$		0			0
$871$	17.1464	−	9.89949i	0.580985	−	0.335432i
$872$	6.78991	+	1.81935i	0.229936	+	0.0616110i
$873$		0			0
$874$	−1.51472	+	1.51472i	−0.0512361	+	0.0512361i
$875$	−4.36618	−	31.9056i	−0.147604	−	1.07861i
$876$		0			0
$877$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$877$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$878$	−2.72457	+	10.1682i	−0.0919496	+	0.343161i
$879$		0			0
$880$	−10.0441	−	5.79899i	−0.338588	−	0.195484i
$881$		−	26.4853i		−	0.892312i	−0.894955	−	0.446156i	$-0.852793\pi$
$881$		−	26.4853i		−	0.892312i	0.894955	−	0.446156i	$-0.147207\pi$
$882$		0			0
$883$	6.68629			0.225012			0.112506	−	0.993651i	$-0.464112\pi$
$883$	6.68629			0.225012			0.112506	+	0.993651i	$0.464112\pi$
$884$	−27.9590	−	16.1421i	−0.940363	−	0.542919i
$885$		0			0
$886$	−1.23891	+	4.62369i	−0.0416221	+	0.155336i
$887$	27.0208	−	46.8014i	0.907270	−	1.57144i	0.0894296	−	0.995993i	$-0.471496\pi$
$887$	27.0208	−	46.8014i	0.907270	−	1.57144i	0.817841	−	0.575445i	$-0.195171\pi$
$888$		0			0
$889$	−21.1569	+	2.89525i	−0.709578	+	0.0971035i
$890$		0			0
$891$		0			0
$892$	25.7279	+	44.5621i	0.861435	+	1.49205i
$893$	−3.34315	−	5.79050i	−0.111874	−	0.193772i
$894$		0			0
$895$			27.1127i			0.906278i
$896$	−11.5959	−	27.5959i	−0.387392	−	0.921915i
$897$		0			0
$898$	32.1786	−	8.62222i	1.07381	−	0.287727i
$899$	11.4685	−	6.62132i	0.382495	−	0.220833i
$900$		0			0
$901$	−33.3653	−	19.2635i	−1.11156	−	0.641759i
$902$	14.0000	−	14.0000i	0.466149	−	0.466149i
$903$		0			0
$904$	9.65685	−	9.65685i	0.321182	−	0.321182i
$905$	13.9795	+	8.07107i	0.464694	+	0.268291i
$906$		0			0
$907$	0.979185	+	1.69600i	0.0325133	+	0.0563147i	0.881824	−	0.471578i	$-0.156316\pi$
$907$	0.979185	+	1.69600i	0.0325133	+	0.0563147i	−0.849311	+	0.527893i	$0.822982\pi$
$908$	−11.7279	+	20.3134i	−0.389205	+	0.674122i
$909$		0			0
$910$	−17.5505	−	2.21952i	−0.581793	−	0.0735765i
$911$	11.0711			0.366801			0.183400	−	0.983038i	$-0.441290\pi$
$911$	11.0711			0.366801			0.183400	+	0.983038i	$0.441290\pi$
$912$		0			0
$913$	6.39949	+	11.0843i	0.211792	+	0.366835i
$914$	39.5343	+	10.5932i	1.30768	+	0.350391i
$915$		0			0
$916$	−3.02944			−0.100095
$917$	9.58579	−	23.4803i	0.316551	−	0.775387i
$918$		0			0
$919$	29.9882	+	17.3137i	0.989220	+	0.571127i	0.905041	−	0.425324i	$-0.139840\pi$
$919$	29.9882	+	17.3137i	0.989220	+	0.571127i	0.0841791	+	0.996451i	$0.473173\pi$
$920$	−0.784076	+	2.92621i	−0.0258502	+	0.0964743i
$921$		0			0
$922$	6.46286	+	24.1197i	0.212843	+	0.794340i
$923$		−	35.9411i		−	1.18302i
$924$		0			0
$925$		−	15.0294i		−	0.494165i
$926$	31.1842	−	8.35578i	1.02478	−	0.274588i
$927$		0			0
$928$	−16.3923	−	4.39230i	−0.538104	−	0.144184i
$929$	32.8219	+	18.9497i	1.07685	+	0.621721i	0.930046	−	0.367444i	$-0.119767\pi$
$929$	32.8219	+	18.9497i	1.07685	+	0.621721i	0.146807	+	0.989165i	$0.453100\pi$
$930$		0			0
$931$	−4.50610	+	17.5306i	−0.147681	+	0.574544i
$932$	38.4264			1.25870
$933$		0			0
$934$	−14.2642	+	53.2348i	−0.466739	+	1.74190i
$935$	9.05025	+	15.6755i	0.295975	+	0.512644i
$936$		0			0
$937$	−33.4853			−1.09392			−0.546958	−	0.837160i	$-0.684214\pi$
$937$	−33.4853			−1.09392			−0.546958	+	0.837160i	$0.684214\pi$
$938$	−22.8177	−	17.3244i	−0.745025	−	0.565662i
$939$		0			0
$940$	−8.18900	−	4.72792i	−0.267096	−	0.154208i
$941$	−1.67157	−	2.89525i	−0.0544917	−	0.0943824i	0.837493	−	0.546448i	$-0.184021\pi$
$941$	−1.67157	−	2.89525i	−0.0544917	−	0.0943824i	−0.891985	+	0.452066i	$0.850687\pi$
$942$		0			0
$943$	−4.47871	−	2.58579i	−0.145847	−	0.0842048i
$944$			32.2843i			1.05076i
$945$		0			0
$946$	−18.1005	−	18.1005i	−0.588498	−	0.588498i
$947$	−4.89898	−	2.82843i	−0.159195	−	0.0919115i	0.418286	−	0.908315i	$-0.362631\pi$
$947$	−4.89898	−	2.82843i	−0.159195	−	0.0919115i	−0.577481	+	0.816404i	$0.695964\pi$
$948$		0			0
$949$	16.3780	−	9.45584i	0.531652	−	0.306950i
$950$	1.56815	+	5.85242i	0.0508776	+	0.189878i
$951$		0			0
$952$	−5.86121	+	46.3465i	−0.189963	+	1.50210i
$953$		−	4.44365i		−	0.143944i	−0.997407	−	0.0719720i	$-0.977071\pi$
$953$		−	4.44365i		−	0.143944i	0.997407	−	0.0719720i	$-0.0229292\pi$
$954$		0			0
$955$	11.8579	+	20.5384i	0.383711	+	0.664608i
$956$	−17.7408	+	10.2426i	−0.573778	+	0.331271i
$957$		0			0
$958$	20.8701	−	20.8701i	0.674281	−	0.674281i
$959$	18.1127	+	23.3572i	0.584890	+	0.754243i
$960$		0			0
$961$	−5.75736	+	9.97204i	−0.185721	+	0.321679i
$962$	−32.0413	−	8.58543i	−1.03305	−	0.276806i
$963$		0			0
$964$	−18.4582	−	10.6569i	−0.594499	−	0.343234i
$965$	23.4020			0.753338
$966$		0			0
$967$			21.4437i			0.689581i	0.938680	+	0.344791i	$0.112050\pi$
$967$			21.4437i			0.689581i	−0.938680	+	0.344791i	$0.887950\pi$
$968$	23.1822	−	6.21166i	0.745105	−	0.199650i
$969$		0			0
$970$	39.5343	+	10.5932i	1.26937	+	0.340127i
$971$	31.7818	+	18.3492i	1.01993	+	0.588855i	0.914083	−	0.405528i	$-0.132912\pi$
$971$	31.7818	+	18.3492i	1.01993	+	0.588855i	0.105844	+	0.994383i	$0.466245\pi$
$972$		0			0
$973$	−2.62357	−	19.1716i	−0.0841078	−	0.614612i
$974$	41.5269	+	41.5269i	1.33061	+	1.33061i
$975$		0			0
$976$	21.6251	−	12.4853i	0.692204	−	0.399644i
$977$	17.3566	−	10.0208i	0.555286	−	0.320594i	−0.195966	−	0.980611i	$-0.562784\pi$
$977$	17.3566	−	10.0208i	0.555286	−	0.320594i	0.751251	+	0.660017i	$0.229451\pi$
$978$		0			0
$979$		0			0
$980$	6.87722	+	24.6569i	0.219685	+	0.787634i
$981$		0			0
$982$	−28.5492	+	7.64975i	−0.911043	+	0.244113i
$983$	0.313708	+	0.543359i	0.0100057	+	0.0173305i	0.870985	−	0.491310i	$-0.163482\pi$
$983$	0.313708	+	0.543359i	0.0100057	+	0.0173305i	−0.860979	+	0.508640i	$0.830148\pi$
$984$		0			0
$985$	−23.8995	+	41.3951i	−0.761501	+	1.31896i
$986$	18.7279	+	18.7279i	0.596419	+	0.596419i
$987$		0			0
$988$	13.3726			0.425439
$989$	−3.34315	+	5.79050i	−0.106306	+	0.184127i
$990$		0			0
$991$	−6.74356	+	3.89340i	−0.214216	+	0.123678i	−0.603269	−	0.797537i	$-0.706136\pi$
$991$	−6.74356	+	3.89340i	−0.214216	+	0.123678i	0.389053	+	0.921215i	$0.372802\pi$
$992$	−24.1197	+	6.46286i	−0.765802	+	0.205196i
$993$		0			0
$994$	−47.9462	+	20.1472i	−1.52076	+	0.639030i
$995$		−	32.2843i		−	1.02348i
$996$		0			0
$997$	47.1856	−	27.2426i	1.49438	−	0.862783i	0.494405	−	0.869232i	$-0.335386\pi$
$997$	47.1856	−	27.2426i	1.49438	−	0.862783i	0.999979	+	0.00644862i	$0.00205267\pi$
$998$	−44.1011	−	11.8169i	−1.39600	−	0.374056i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.bm.a.107.3	yes	8
3.2	odd	2		504.2.bm.b.107.2	yes	8
4.3	odd	2		2016.2.bu.b.1871.1		8
7.4	even	3	inner	504.2.bm.a.179.1	yes	8
8.3	odd	2		504.2.bm.b.107.4	yes	8
8.5	even	2		2016.2.bu.a.1871.4		8
12.11	even	2		2016.2.bu.a.1871.3		8
21.11	odd	6		504.2.bm.b.179.4	yes	8
24.5	odd	2		2016.2.bu.b.1871.2		8
24.11	even	2	inner	504.2.bm.a.107.1	✓	8
28.11	odd	6		2016.2.bu.b.431.2		8
56.11	odd	6		504.2.bm.b.179.2	yes	8
56.53	even	6		2016.2.bu.a.431.3		8
84.11	even	6		2016.2.bu.a.431.4		8
168.11	even	6	inner	504.2.bm.a.179.3	yes	8
168.53	odd	6		2016.2.bu.b.431.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bm.a.107.1	✓	8	24.11	even	2	inner
504.2.bm.a.107.3	yes	8	1.1	even	1	trivial
504.2.bm.a.179.1	yes	8	7.4	even	3	inner
504.2.bm.a.179.3	yes	8	168.11	even	6	inner
504.2.bm.b.107.2	yes	8	3.2	odd	2
504.2.bm.b.107.4	yes	8	8.3	odd	2
504.2.bm.b.179.2	yes	8	56.11	odd	6
504.2.bm.b.179.4	yes	8	21.11	odd	6
2016.2.bu.a.431.3		8	56.53	even	6
2016.2.bu.a.431.4		8	84.11	even	6
2016.2.bu.a.1871.3		8	12.11	even	2
2016.2.bu.a.1871.4		8	8.5	even	2
2016.2.bu.b.431.1		8	168.53	odd	6
2016.2.bu.b.431.2		8	28.11	odd	6
2016.2.bu.b.1871.1		8	4.3	odd	2
2016.2.bu.b.1871.2		8	24.5	odd	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)

\(f(q)\)	\(=\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.914214 + 1.58346i) q^{5} +(0.358719 + 2.62132i) q^{7} +(-2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(0.366025 + 1.36603i) q^{2} +(-1.73205 + 1.00000i) q^{4} +(-0.914214 + 1.58346i) q^{5} +(0.358719 + 2.62132i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-2.49768 - 0.669251i) q^{10} +(-1.37333 + 0.792893i) q^{11} -2.58579i q^{13} +(-3.44949 + 1.44949i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-5.40629 + 3.12132i) q^{17} +(1.29289 - 2.23936i) q^{19} -3.65685i q^{20} +(-1.58579 - 1.58579i) q^{22} +(-0.292893 + 0.507306i) q^{23} +(0.828427 + 1.43488i) q^{25} +(3.53225 - 0.946464i) q^{26} +(-3.24264 - 4.18154i) q^{28} -3.00000 q^{29} +(-3.82282 + 2.20711i) q^{31} +(5.46410 + 1.46410i) q^{32} +(-6.24264 - 6.24264i) q^{34} +(-4.47871 - 1.82843i) q^{35} +(-7.85578 - 4.53553i) q^{37} +(3.53225 + 0.946464i) q^{38} +(4.99536 - 1.33850i) q^{40} +8.82843i q^{41} +11.4142 q^{43} +(1.58579 - 2.74666i) q^{44} +(-0.800199 - 0.214413i) q^{46} +(1.29289 - 2.23936i) q^{47} +(-6.74264 + 1.88064i) q^{49} +(-1.65685 + 1.65685i) q^{50} +(2.58579 + 4.47871i) q^{52} +(3.08579 + 5.34474i) q^{53} -2.89949i q^{55} +(4.52520 - 5.96008i) q^{56} +(-1.09808 - 4.09808i) q^{58} +(-6.98975 + 4.03553i) q^{59} +(5.40629 + 3.12132i) q^{61} +(-4.41421 - 4.41421i) q^{62} +8.00000i q^{64} +(4.09450 + 2.36396i) q^{65} +(3.82843 + 6.63103i) q^{67} +(6.24264 - 10.8126i) q^{68} +(0.858355 - 6.78729i) q^{70} +13.8995 q^{71} +(3.65685 + 6.33386i) q^{73} +(3.32024 - 12.3913i) q^{74} +5.17157i q^{76} +(-2.57107 - 3.31552i) q^{77} +(6.98975 + 4.03553i) q^{79} +(3.65685 + 6.33386i) q^{80} +(-12.0599 + 3.23143i) q^{82} -8.07107i q^{83} -11.4142i q^{85} +(4.17789 + 15.5921i) q^{86} +(4.33245 + 1.16088i) q^{88} +(6.77817 - 0.927572i) q^{91} -1.17157i q^{92} +(3.53225 + 0.946464i) q^{94} +(2.36396 + 4.09450i) q^{95} -15.8284 q^{97} +(-5.03698 - 8.52226i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8}+O(q^{10}) \) 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8	\( 8 q - 4 q^{2} + 4 q^{5} - 16 q^{8} + 4 q^{10} - 8 q^{14} + 16 q^{16} + 16 q^{19} - 24 q^{22} - 8 q^{23} - 16 q^{25} + 16 q^{26} + 8 q^{28} - 24 q^{29} + 16 q^{32} - 16 q^{34} + 16 q^{38} - 8 q^{40} + 80 q^{43} + 24 q^{44} - 8 q^{46} + 16 q^{47} - 20 q^{49} + 32 q^{50} + 32 q^{52} + 36 q^{53} + 8 q^{56} + 12 q^{58} - 24 q^{62} + 8 q^{67} + 16 q^{68} - 52 q^{70} + 32 q^{71} - 16 q^{73} - 8 q^{74} + 36 q^{77} - 16 q^{80} - 24 q^{82} - 40 q^{86} + 24 q^{88} - 8 q^{91} + 16 q^{94} - 32 q^{95} - 104 q^{97} - 20 q^{98}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^5 - 16 * q^8 + 4 * q^10 - 8 * q^14 + 16 * q^16 + 16 * q^19 - 24 * q^22 - 8 * q^23 - 16 * q^25 + 16 * q^26 + 8 * q^28 - 24 * q^29 + 16 * q^32 - 16 * q^34 + 16 * q^38 - 8 * q^40 + 80 * q^43 + 24 * q^44 - 8 * q^46 + 16 * q^47 - 20 * q^49 + 32 * q^50 + 32 * q^52 + 36 * q^53 + 8 * q^56 + 12 * q^58 - 24 * q^62 + 8 * q^67 + 16 * q^68 - 52 * q^70 + 32 * q^71 - 16 * q^73 - 8 * q^74 + 36 * q^77 - 16 * q^80 - 24 * q^82 - 40 * q^86 + 24 * q^88 - 8 * q^91 + 16 * q^94 - 32 * q^95 - 104 * q^97 - 20 * q^98

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