LMFDB - Embedded newform 504.2.bm.a.107.1

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			107.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	504.107
Dual form			504.2.bm.a.179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$2$	−1.36603	+	0.366025i	−0.965926	+	0.258819i
$3$		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
$10$	0.669251	−	2.49768i	0.211636	−	0.789835i
$11$	1.37333	−	0.792893i	0.414075	−	0.239066i	−0.278464	−	0.960447i	$-0.589825\pi$
$11$	1.37333	−	0.792893i	0.414075	−	0.239066i	0.692539	+	0.721380i	$0.256492\pi$
$12$		0			0
$13$			2.58579i			0.717168i	0.933497	+	0.358584i	$0.116740\pi$
$13$			2.58579i			0.717168i	−0.933497	+	0.358584i	$0.883260\pi$
$14$	1.44949	+	3.44949i	0.387392	+	0.921915i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	5.40629	−	3.12132i	1.31122	−	0.757031i	0.328919	−	0.944358i	$-0.393316\pi$
$17$	5.40629	−	3.12132i	1.31122	−	0.757031i	0.982298	+	0.187327i	$0.0599823\pi$
$18$		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
$26$	−0.946464	−	3.53225i	−0.185617	−	0.692731i
$27$		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	−0.115738	−	0.993280i	$-0.536923\pi$
$31$	3.82282	−	2.20711i	0.686599	−	0.396408i	0.802337	+	0.596872i	$0.203590\pi$
$32$	−1.46410	+	5.46410i	−0.258819	+	0.965926i
$33$		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	0.978917	−	0.204259i	$-0.0654786\pi$
$37$	7.85578	+	4.53553i	1.29148	+	0.745637i	0.312565	+	0.949896i	$0.398812\pi$
$38$	−0.946464	+	3.53225i	−0.153537	+	0.573007i
$39$		0			0
$40$	−1.33850	−	4.99536i	−0.211636	−	0.789835i
$41$		−	8.82843i		−	1.37877i	−0.724396	−	0.689384i	$-0.757881\pi$
$41$		−	8.82843i		−	1.37877i	0.724396	−	0.689384i	$-0.242119\pi$
$42$		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
$46$	0.214413	−	0.800199i	0.0316134	−	0.117983i
$47$	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
$56$	5.96008	+	4.52520i	0.796449	+	0.604706i
$57$		0			0
$58$	4.09808	−	1.09808i	0.538104	−	0.144184i
$59$	6.98975	−	4.03553i	0.909988	−	0.525382i	0.0295606	−	0.999563i	$-0.490589\pi$
$59$	6.98975	−	4.03553i	0.909988	−	0.525382i	0.880427	+	0.474181i	$0.157256\pi$
$60$		0			0
$61$	−5.40629	−	3.12132i	−0.692204	−	0.399644i	0.112233	−	0.993682i	$-0.464200\pi$
$61$	−5.40629	−	3.12132i	−0.692204	−	0.399644i	−0.804437	+	0.594038i	$0.797533\pi$
$62$	−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
$70$	−6.78729	−	0.858355i	−0.811236	−	0.102593i
$71$	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	$0.692551\pi$
$74$	−12.3913	−	3.32024i	−1.44046	−	0.385970i
$75$		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	0.0522883	−	0.998632i	$-0.483349\pi$
$79$	−6.98975	−	4.03553i	−0.786408	−	0.454033i	−0.838697	+	0.544599i	$0.816682\pi$
$80$	3.65685	+	6.33386i	0.408849	+	0.708147i
$81$		0			0
$82$	3.23143	+	12.0599i	0.356852	+	1.33179i
$83$			8.07107i			0.885915i	0.896543	+	0.442957i	$0.146071\pi$
$83$			8.07107i			0.885915i	−0.896543	+	0.442957i	$0.853929\pi$
$84$		0			0
$85$			11.4142i			1.23805i
$86$	−15.5921	+	4.17789i	−1.68134	+	0.450514i
$87$		0			0
$88$	−1.16088	+	4.33245i	−0.123750	+	0.461841i
$89$		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
$94$	−0.946464	+	3.53225i	−0.0976203	+	0.364324i
$95$	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	$0.797067\pi$
$98$	8.52226	−	5.03698i	0.860878	−	0.508811i
$99$		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	$-0.997523\pi$
$103$	−15.2913	−	8.82843i	−1.50670	−	0.869891i	−0.506725	−	0.862108i	$-0.669144\pi$
$104$	−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	−0.300005	−	0.953938i	$-0.596988\pi$
$107$	−13.2005	−	7.62132i	−1.27614	−	0.736781i	−0.976137	+	0.217157i	$0.930322\pi$
$108$		0			0
$109$	2.15232	−	1.24264i	0.206155	−	0.119023i	−0.393368	−	0.919381i	$-0.628690\pi$
$109$	2.15232	−	1.24264i	0.206155	−	0.119023i	0.599523	+	0.800358i	$0.295357\pi$
$110$	−1.06129	−	3.96078i	−0.101190	−	0.377646i
$111$		0			0
$112$	−9.79796	−	4.00000i	−0.925820	−	0.377964i
$113$		−	4.82843i		−	0.454220i	−0.973869	−	0.227110i	$-0.927072\pi$
$113$		−	4.82843i		−	0.454220i	0.973869	−	0.227110i	$-0.0729277\pi$
$114$		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
$122$	8.52761	+	2.28497i	0.772053	+	0.206871i
$123$		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	$-0.883426\pi$
$127$		−	8.07107i		−	0.716191i	0.933685	−	0.358096i	$-0.116574\pi$
$128$	2.92820	+	10.9282i	0.258819	+	0.965926i
$129$		0			0
$130$	6.45846	+	1.73054i	0.566445	+	0.151778i
$131$	8.30153	+	4.79289i	0.725308	+	0.418757i	0.816703	−	0.577058i	$-0.195799\pi$
$131$	8.30153	+	4.79289i	0.725308	+	0.418757i	−0.0913949	+	0.995815i	$0.529133\pi$
$132$		0			0
$133$	−6.33386	−	2.58579i	−0.549215	−	0.224216i
$134$	−7.65685	−	7.65685i	−0.661451	−	0.661451i
$135$		0			0
$136$	−4.56993	+	17.0552i	−0.391868	+	1.46247i
$137$	−9.67487	+	5.58579i	−0.826580	+	0.477226i	−0.852680	−	0.522433i	$-0.825024\pi$
$137$	−9.67487	+	5.58579i	−0.826580	+	0.477226i	0.0261005	+	0.999659i	$0.491691\pi$
$138$		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
$142$	−18.9871	+	5.08757i	−1.59336	+	0.426939i
$143$	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	−0.349636	−	0.936886i	$-0.613695\pi$
$151$	3.52565	−	2.03553i	0.286913	−	0.165649i	0.636549	+	0.771236i	$0.280361\pi$
$152$	1.89293	+	7.06450i	0.153537	+	0.573007i
$153$		0			0
$154$	4.72571	+	3.58800i	0.380808	+	0.289129i
$155$			8.07107i			0.648284i
$156$		0			0
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$	11.0253	+	2.95422i	0.877124	+	0.235025i
$159$		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
$166$	−2.95422	−	11.0253i	−0.229292	−	0.855728i
$167$	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
$170$	−4.17789	−	15.5921i	−0.320430	−	1.19586i
$171$		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	−0.896124	−	0.443804i	$-0.853629\pi$
$179$	−12.8418	+	7.41421i	−0.959841	+	0.554164i	−0.0637168	+	0.997968i	$0.520295\pi$
$180$		0			0
$181$			8.82843i			0.656212i	0.944641	+	0.328106i	$0.106410\pi$
$181$			8.82843i			0.656212i	−0.944641	+	0.328106i	$0.893590\pi$
$182$	−8.91964	+	3.74807i	−0.661168	+	0.277826i
$183$		0			0
$184$	−0.428825	−	1.60040i	−0.0316134	−	0.117983i
$185$	−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	$0.985715\pi$
$194$	21.6220	−	5.79361i	1.55237	−	0.415957i
$195$		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	0.152006	−	0.988380i	$-0.451427\pi$
$199$	15.2913	−	8.82843i	1.08397	−	0.625831i	0.931965	+	0.362549i	$0.118093\pi$
$200$	−4.52661	−	1.21290i	−0.320080	−	0.0857651i
$201$		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
$206$	24.1197	+	6.46286i	1.68050	+	0.450289i
$207$		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
$214$	20.8218	+	5.57919i	1.42335	+	0.381386i
$215$	−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	$0.330434\pi$
$223$			25.7279i			1.72287i	−0.507869	+	0.861435i	$0.669566\pi$
$224$	14.8484	+	1.87780i	0.992098	+	0.125466i
$225$		0			0
$226$	1.76733	+	6.59575i	0.117561	+	0.438743i
$227$	−10.1567	+	5.86396i	−0.674122	+	0.389205i	−0.797637	−	0.603138i	$-0.793917\pi$
$227$	−10.1567	+	5.86396i	−0.674122	+	0.389205i	0.123514	+	0.992343i	$0.460583\pi$
$228$		0			0
$229$	−1.31178	−	0.757359i	−0.0866852	−	0.0500477i	0.456031	−	0.889964i	$-0.349271\pi$
$229$	−1.31178	−	0.757359i	−0.0866852	−	0.0500477i	−0.542716	+	0.839916i	$0.682604\pi$
$230$	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	0.933594	−	0.358333i	$-0.116655\pi$
$233$	16.6391	+	9.60660i	1.09007	+	0.629349i	0.156471	+	0.987682i	$0.449988\pi$
$234$		0			0
$235$	2.36396	+	4.09450i	0.154208	+	0.267096i
$236$	8.07107	−	13.9795i	0.525382	−	0.909988i
$237$		0			0
$238$	18.6033	+	14.1246i	1.20587	+	0.915562i
$239$	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	$0.721811\pi$
$242$	3.10583	−	11.5911i	0.199650	−	0.745105i
$243$		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
$248$	−3.23143	+	12.0599i	−0.205196	+	0.765802i
$249$		0			0
$250$	16.6267	−	4.45510i	1.05156	−	0.281766i
$251$			2.27208i			0.143412i	0.997426	+	0.0717061i	$0.0228444\pi$
$251$			2.27208i			0.143412i	−0.997426	+	0.0717061i	$0.977156\pi$
$252$		0			0
$253$			0.928932i			0.0584015i
$254$	2.95422	+	11.0253i	0.185364	+	0.691788i
$255$		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
$262$	−13.0944	−	3.50864i	−0.808976	−	0.216765i
$263$	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
$266$	9.59867	+	1.21390i	0.588532	+	0.0744288i
$267$		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	0.272445	−	0.962171i	$-0.412168\pi$
$271$	−6.98975	−	4.03553i	−0.424597	−	0.245141i	−0.697042	+	0.717030i	$0.745501\pi$
$272$		−	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	$0.333333\pi$
$278$	9.99071	−	2.67700i	0.599203	−	0.160556i
$279$		0			0
$280$	−12.6143	+	5.30057i	−0.753847	+	0.316770i
$281$			15.1716i			0.905060i	0.891749	+	0.452530i	$0.149478\pi$
$281$			15.1716i			0.905060i	−0.891749	+	0.452530i	$0.850522\pi$
$282$		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
$290$	−2.00775	+	7.49303i	−0.117899	+	0.440006i
$291$		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
$296$	−24.7826	+	6.64048i	−1.44046	+	0.385970i
$297$		0			0
$298$	−0.732051	+	2.73205i	−0.0424066	+	0.158263i
$299$	−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
$310$	−2.95422	−	11.0253i	−0.167788	−	0.626194i
$311$	−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
$322$	−2.17449	−	0.274997i	−0.121180	−	0.0153250i
$323$		−	16.1421i		−	0.898172i
$324$		0			0
$325$	−3.71029	+	2.14214i	−0.205810	+	0.118824i
$326$	−1.24969	+	4.66390i	−0.0692139	+	0.258310i
$327$		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
$334$	−4.99536	+	1.33850i	−0.273334	+	0.0732395i
$335$	−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	$0.529024\pi$
$338$	−8.62469	+	2.31098i	−0.469121	+	0.125701i
$339$		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
$346$	9.13986	−	34.1104i	0.491362	−	1.83379i
$347$	−2.44949	+	1.41421i	−0.131495	+	0.0759190i	−0.564305	−	0.825567i	$-0.690856\pi$
$347$	−2.44949	+	1.41421i	−0.131495	+	0.0759190i	0.432809	+	0.901486i	$0.357522\pi$
$348$		0			0
$349$		−	33.7990i		−	1.80922i	−0.426242	−	0.904609i	$-0.640163\pi$
$349$		−	33.7990i		−	1.80922i	0.426242	−	0.904609i	$-0.359837\pi$
$350$	−3.74880	+	4.93749i	−0.200382	+	0.263920i
$351$		0			0
$352$	2.32175	+	8.66490i	0.123750	+	0.461841i
$353$	−27.9590	+	16.1421i	−1.48811	+	0.859159i	−0.999908	−	0.0135729i	$-0.995679\pi$
$353$	−27.9590	+	16.1421i	−1.48811	+	0.859159i	−0.488199	+	0.872732i	$0.662346\pi$
$354$		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
$362$	−3.23143	−	12.0599i	−0.169840	−	0.633852i
$363$		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	−0.00348080	−	0.999994i	$-0.501108\pi$
$367$	16.4905	−	9.52082i	0.860799	−	0.496983i	0.864280	+	0.503011i	$0.167775\pi$
$368$	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	0.816161	−	0.577824i	$-0.196098\pi$
$373$	13.9795	+	8.07107i	0.723831	+	0.417904i	−0.0923301	+	0.995728i	$0.529431\pi$
$374$	−3.62347	+	13.5230i	−0.187365	+	0.699256i
$375$		0			0
$376$	1.89293	+	7.06450i	0.0976203	+	0.364324i
$377$		−	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
$382$	−4.74756	+	17.7181i	−0.242906	+	0.906538i
$383$	−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
$392$	9.72401	−	17.2466i	0.491137	−	0.871083i
$393$		0			0
$394$	−35.7108	+	9.56869i	−1.79909	+	0.482063i
$395$	12.7802	−	7.37868i	0.643044	−	0.371262i
$396$		0			0
$397$	−30.5826	−	17.6569i	−1.53490	−	0.886172i	−0.999126	−	0.0418078i	$-0.986688\pi$
$397$	−30.5826	−	17.6569i	−1.53490	−	0.886172i	−0.535769	−	0.844364i	$-0.679978\pi$
$398$	−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	0.910680	−	0.413113i	$-0.135558\pi$
$401$	20.1903	+	11.6569i	1.00825	+	0.582116i	0.0975738	+	0.995228i	$0.468892\pi$
$402$		0			0
$403$	5.70711	+	9.88500i	0.284291	+	0.492407i
$404$	−21.6251	−	12.4853i	−1.07589	−	0.621166i
$405$		0			0
$406$	−4.34847	−	10.3485i	−0.215811	−	0.513586i
$407$	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	$0.673337\pi$
$410$	−22.0506	−	5.90843i	−1.08900	−	0.291797i
$411$		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
$416$	−14.1290	−	3.78585i	−0.692731	−	0.185617i
$417$		0			0
$418$	1.50089	+	5.60139i	0.0734109	+	0.273973i
$419$		−	24.9706i		−	1.21989i	−0.792443	−	0.609946i	$-0.791191\pi$
$419$		−	24.9706i		−	1.21989i	0.792443	−	0.609946i	$-0.208809\pi$
$420$		0			0
$421$			20.8701i			1.01714i	0.861019	+	0.508572i	$0.169827\pi$
$421$			20.8701i			1.01714i	−0.861019	+	0.508572i	$0.830173\pi$
$422$	37.6427	−	10.0863i	1.83242	−	0.490995i
$423$		0			0
$424$	−16.8611	−	4.51790i	−0.818845	−	0.219409i
$425$	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
$430$	7.63897	−	28.5090i	0.368384	−	1.37483i
$431$	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	$0.242177\pi$
$434$	13.1545	+	9.98760i	0.631438	+	0.479420i
$435$		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	0.338214	−	0.941069i	$-0.390177\pi$
$439$	−6.44639	−	3.72183i	−0.307669	−	0.177633i	−0.645883	+	0.763436i	$0.723511\pi$
$440$	−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	0.428746	−	0.903425i	$-0.358956\pi$
$443$	−2.93130	−	1.69239i	−0.139270	−	0.0804078i	−0.568016	+	0.823017i	$0.692289\pi$
$444$		0			0
$445$		0			0
$446$	−9.41707	−	35.1450i	−0.445911	−	1.66416i
$447$		0			0
$448$	−20.9706	+	2.86976i	−0.990766	+	0.135583i
$449$			23.5563i			1.11169i	0.831285	+	0.555846i	$0.187606\pi$
$449$			23.5563i			1.11169i	−0.831285	+	0.555846i	$0.812394\pi$
$450$		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	$-0.0700123\pi$
$458$	2.06914	+	0.554425i	0.0966848	+	0.0259066i
$459$		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	$0.177982\pi$
$463$			22.8284i			1.06093i	−0.847708	+	0.530463i	$0.822018\pi$
$464$	−6.00000	+	10.3923i	−0.278543	+	0.482451i
$465$		0			0
$466$	−26.2457	−	7.03252i	−1.21581	−	0.325775i
$467$	−33.7495	−	19.4853i	−1.56174	−	0.901671i	−0.997081	−	0.0763471i	$-0.975674\pi$
$467$	−33.7495	−	19.4853i	−1.56174	−	0.901671i	−0.564659	−	0.825324i	$-0.690992\pi$
$468$		0			0
$469$	16.0087	−	12.4142i	0.739214	−	0.573235i
$470$	−4.72792	−	4.72792i	−0.218083	−	0.218083i
$471$		0			0
$472$	−5.90843	+	22.0506i	−0.271958	+	1.01496i
$473$	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
$478$	−13.9917	+	3.74907i	−0.639966	+	0.171478i
$479$	−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	$0.723334\pi$
$487$	−35.9634	+	20.7635i	−1.62966	+	0.940882i	−0.984195	+	0.177088i	$0.943332\pi$
$488$	17.0552	−	4.56993i	0.772053	−	0.206871i
$489$		0			0
$490$	0.184709	+	18.0996i	0.00834429	+	0.817655i
$491$		−	20.8995i		−	0.943181i	−0.881818	−	0.471591i	$-0.843680\pi$
$491$		−	20.8995i		−	0.943181i	0.881818	−	0.471591i	$-0.156320\pi$
$492$		0			0
$493$	−16.2189	+	9.36396i	−0.730461	+	0.421732i
$494$	−9.13364	−	2.44735i	−0.410942	−	0.110112i
$495$		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
$502$	−0.831638	−	3.10372i	−0.0371178	−	0.138526i
$503$	−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
$506$	−0.340013	−	1.26894i	−0.0151154	−	0.0564115i
$507$		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
$518$	−4.25841	+	33.6726i	−0.187104	+	1.47949i
$519$		0			0
$520$	12.9169	−	3.46108i	0.566445	−	0.151778i
$521$	17.5306	−	10.1213i	0.768031	−	0.443423i	−0.0641405	−	0.997941i	$-0.520431\pi$
$521$	17.5306	−	10.1213i	0.768031	−	0.443423i	0.832172	+	0.554518i	$0.187097\pi$
$522$		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
$530$	15.4146	−	4.13033i	0.669567	−	0.179410i
$531$		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
$536$	−20.9189	−	5.60521i	−0.903560	−	0.242108i
$537$		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	−0.110174	−	0.993912i	$-0.535141\pi$
$541$	−23.8645	−	13.7782i	−1.02601	−	0.592370i	−0.915840	+	0.401542i	$0.868474\pi$
$542$	11.0253	+	2.95422i	0.473576	+	0.126894i
$543$		0			0
$544$	9.13986	+	34.1104i	0.391868	+	1.46247i
$545$			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
$550$	−3.58912	−	0.961701i	−0.153041	−	0.0410071i
$551$	−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
$562$	−5.55318	−	20.7248i	−0.234247	−	0.874221i
$563$	9.61332	−	5.55025i	0.405153	−	0.233915i	−0.283552	−	0.958957i	$-0.591513\pi$
$563$	9.61332	−	5.55025i	0.405153	−	0.233915i	0.688705	+	0.725042i	$0.258180\pi$
$564$		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	0.222957	−	0.974828i	$-0.428429\pi$
$569$	−12.1604	−	7.02082i	−0.509791	−	0.294328i	−0.732748	+	0.680500i	$0.761762\pi$
$570$		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
$574$	30.4536	−	12.7967i	1.27111	−	0.534125i
$575$	−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	$0.782582\pi$
$578$	−8.04178	+	30.0123i	−0.334494	+	1.24835i
$579$		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
$584$	−19.9814	−	5.35401i	−0.826837	−	0.221550i
$585$		0			0
$586$	−28.6865	+	7.68653i	−1.18503	+	0.317528i
$587$			22.6985i			0.936867i	0.883499	+	0.468433i	$0.155181\pi$
$587$			22.6985i			0.936867i	−0.883499	+	0.468433i	$0.844819\pi$
$588$		0			0
$589$		−	11.4142i		−	0.470314i
$590$	−5.40157	−	20.1589i	−0.222379	−	0.829930i
$591$		0			0
$592$	31.4231	−	18.1421i	1.29148	−	0.745637i
$593$	14.9071	+	8.60660i	0.612160	+	0.353431i	0.773810	−	0.633417i	$-0.218348\pi$
$593$	14.9071	+	8.60660i	0.612160	+	0.353431i	−0.161650	+	0.986848i	$0.551682\pi$
$594$		0			0
$595$	29.9203	−	4.09450i	1.22661	−	0.167858i
$596$		−	4.00000i		−	0.163846i
$597$		0			0
$598$	2.06914	+	0.554425i	0.0846136	+	0.0226721i
$599$	−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	$0.594299\pi$
$602$	16.5448	+	39.3732i	0.674315	+	1.60473i
$603$		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	0.625087	−	0.780555i	$-0.285063\pi$
$607$	6.44639	+	3.72183i	0.261651	+	0.151064i	−0.363437	+	0.931619i	$0.618397\pi$
$608$	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	−0.415028	−	0.909809i	$-0.636228\pi$
$613$	4.09450	−	2.36396i	0.165375	−	0.0954795i	0.580403	+	0.814329i	$0.302895\pi$
$614$	−25.5828	+	6.85490i	−1.03244	+	0.276641i
$615$		0			0
$616$	11.7732	+	1.48889i	0.474354	+	0.0599893i
$617$		−	17.7574i		−	0.714884i	−0.933935	−	0.357442i	$-0.883649\pi$
$617$		−	17.7574i		−	0.714884i	0.933935	−	0.357442i	$-0.116351\pi$
$618$		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
$626$	−5.23918	+	19.5529i	−0.209400	+	0.781491i
$627$		0			0
$628$		0			0
$629$	56.6274			2.25788
$630$		0			0
$631$		−	24.2132i		−	0.963912i	−0.876195	−	0.481956i	$-0.839926\pi$
$631$		−	24.2132i		−	0.963912i	0.876195	−	0.481956i	$-0.160074\pi$
$632$	22.0506	−	5.90843i	0.877124	−	0.235025i
$633$		0			0
$634$	5.18716	−	19.3587i	0.206008	−	0.768833i
$635$	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
$640$	−19.9814	−	5.35401i	−0.789835	−	0.211636i
$641$	12.3345	−	7.12132i	0.487183	−	0.281275i	−0.236222	−	0.971699i	$-0.575909\pi$
$641$	12.3345	−	7.12132i	0.487183	−	0.281275i	0.723405	+	0.690424i	$0.242576\pi$
$642$		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
$646$	5.90843	+	22.0506i	0.232464	+	0.867568i
$647$	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
$658$	9.59867	+	1.21390i	0.374195	+	0.0473226i
$659$		−	4.20101i		−	0.163648i	−0.996647	−	0.0818241i	$-0.973925\pi$
$659$		−	4.20101i		−	0.163648i	0.996647	−	0.0818241i	$-0.0260746\pi$
$660$		0			0
$661$	−25.7196	+	14.8492i	−1.00038	+	0.577569i	−0.908360	−	0.418189i	$-0.862665\pi$
$661$	−25.7196	+	14.8492i	−1.00038	+	0.577569i	−0.0920180	+	0.995757i	$0.529332\pi$
$662$	11.8169	−	44.1011i	0.459275	−	1.71404i
$663$		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
$670$	19.1244	−	5.12436i	0.738838	−	0.197971i
$671$	−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	$0.331706\pi$
$674$	4.56682	−	1.22368i	0.175907	−	0.0471342i
$675$		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
$682$	−2.56218	+	9.56218i	−0.0981109	+	0.366155i
$683$	−26.0423	+	15.0355i	−0.996481	+	0.575319i	−0.907205	−	0.420688i	$-0.861789\pi$
$683$	−26.0423	+	15.0355i	−0.996481	+	0.575319i	−0.0892760	+	0.996007i	$0.528455\pi$
$684$		0			0
$685$		−	20.4264i		−	0.780453i
$686$	−16.2606	−	20.5327i	−0.620834	−	0.783942i
$687$		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
$698$	12.3713	+	46.1703i	0.468260	+	1.74757i
$699$		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	0.904343	−	0.426807i	$-0.140362\pi$
$709$	26.2779	+	15.1716i	0.986889	+	0.569780i	0.0825458	+	0.996587i	$0.473695\pi$
$710$	9.30225	−	34.7165i	0.349107	−	1.30289i
$711$		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
$718$	−0.376800	+	1.40624i	−0.0140621	+	0.0524803i
$719$	−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	$-0.708575\pi$
$727$		−	42.7574i		−	1.58578i	0.609363	−	0.792891i	$-0.291425\pi$
$728$	−11.7012	+	15.4115i	−0.433676	+	0.571188i
$729$		0			0
$730$	18.2673	−	4.89471i	0.676103	−	0.181161i
$731$	61.7085	−	35.6274i	2.28237	−	1.31773i
$732$		0			0
$733$	25.7196	+	14.8492i	0.949977	+	0.548469i	0.893074	−	0.449910i	$-0.148544\pi$
$733$	25.7196	+	14.8492i	0.949977	+	0.548469i	0.0569030	+	0.998380i	$0.481877\pi$
$734$	−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
$742$	−13.9638	+	18.3915i	−0.512627	+	0.675174i
$743$	−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
$746$	−22.0506	−	5.90843i	−0.807329	−	0.216323i
$747$		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	0.0952761	−	0.995451i	$-0.469627\pi$
$751$	−19.7085	−	11.3787i	−0.719172	−	0.415214i	−0.814448	+	0.580237i	$0.802960\pi$
$752$	−5.17157	−	8.95743i	−0.188588	−	0.326644i
$753$		0			0
$754$	2.83939	+	10.5967i	0.103405	+	0.385911i
$755$			7.44365i			0.270902i
$756$		0			0
$757$			40.1838i			1.46050i	0.683178	+	0.730252i	$0.260597\pi$
$757$			40.1838i			1.46050i	−0.683178	+	0.730252i	$0.739403\pi$
$758$	9.13364	−	2.44735i	0.331749	−	0.0888918i
$759$		0			0
$760$	−12.9169	−	3.46108i	−0.468546	−	0.125547i
$761$	0.384213	+	0.221825i	0.0139277	+	0.00804116i	0.506948	−	0.861977i	$-0.330774\pi$
$761$	0.384213	+	0.221825i	0.0139277	+	0.00804116i	−0.493020	+	0.870018i	$0.664107\pi$
$762$		0			0
$763$	−4.02944	−	5.19615i	−0.145875	−	0.188113i
$764$		−	25.9411i		−	0.938517i
$765$		0			0
$766$	2.67700	−	9.99071i	0.0967241	−	0.360979i
$767$	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	$0.583091\pi$
$770$	−10.0018	+	4.20279i	−0.360439	+	0.151458i
$771$		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
$782$	−1.33850	−	4.99536i	−0.0478647	−	0.178634i
$783$		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
$794$	48.2394	+	12.9257i	1.71195	+	0.458716i
$795$		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
$800$	−9.05322	+	2.42580i	−0.320080	+	0.0857651i
$801$		0			0
$802$	−31.8471	−	8.53341i	−1.12456	−	0.301325i
$803$	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
$808$	34.1104	+	9.13986i	1.20000	+	0.321539i
$809$	2.02922	−	1.17157i	0.0713437	−	0.0411903i	−0.463904	−	0.885886i	$-0.653552\pi$
$809$	2.02922	−	1.17157i	0.0713437	−	0.0411903i	0.535248	+	0.844695i	$0.320218\pi$
$810$		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
$814$	−19.6500	+	5.26519i	−0.688731	+	0.184545i
$815$	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	−0.350438	−	0.936586i	$-0.613967\pi$
$823$	8.18900	−	4.72792i	0.285451	−	0.164805i	0.635888	+	0.771781i	$0.280634\pi$
$824$	48.2394	−	12.9257i	1.68050	−	0.450289i
$825$		0			0
$826$	24.0521	+	18.2616i	0.836880	+	0.635403i
$827$			9.24264i			0.321398i	0.987003	+	0.160699i	$0.0513749\pi$
$827$			9.24264i			0.321398i	−0.987003	+	0.160699i	$0.948625\pi$
$828$		0			0
$829$	12.5086	−	7.22183i	0.434441	−	0.250824i	−0.266796	−	0.963753i	$-0.585965\pi$
$829$	12.5086	−	7.22183i	0.434441	−	0.250824i	0.701237	+	0.712929i	$0.252632\pi$
$830$	20.1589	+	5.40157i	0.699727	+	0.187491i
$831$		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
$838$	9.13986	+	34.1104i	0.315731	+	1.17833i
$839$	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
$842$	−7.63897	−	28.5090i	−0.263256	−	0.982486i
$843$		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
$850$	−14.1290	−	3.78585i	−0.484621	−	0.129854i
$851$	−4.60181	+	2.65685i	−0.157748	+	0.0910758i
$852$		0			0
$853$			1.51472i			0.0518630i	0.999664	+	0.0259315i	$0.00825517\pi$
$853$			1.51472i			0.0518630i	−0.999664	+	0.0259315i	$0.991745\pi$
$854$	2.93061	−	23.1732i	0.100283	−	0.792972i
$855$		0			0
$856$	41.6437	−	11.1584i	1.42335	−	0.381386i
$857$	−16.9873	+	9.80761i	−0.580274	+	0.335022i	−0.761242	−	0.648467i	$-0.775410\pi$
$857$	−16.9873	+	9.80761i	−0.580274	+	0.335022i	0.180968	+	0.983489i	$0.442077\pi$
$858$		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
$866$	−41.1749	+	11.0328i	−1.39918	+	0.374909i
$867$		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
$872$	−1.81935	+	6.78991i	−0.0616110	+	0.229936i
$873$		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	$0.666667\pi$
$878$	10.1682	+	2.72457i	0.343161	+	0.0919496i
$879$		0			0
$880$	10.0441	+	5.79899i	0.338588	+	0.195484i
$881$			26.4853i			0.892312i	0.894955	+	0.446156i	$0.147207\pi$
$881$			26.4853i			0.892312i	−0.894955	+	0.446156i	$0.852793\pi$
$882$		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
$886$	4.62369	+	1.23891i	0.155336	+	0.0416221i
$887$	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
$896$	27.5959	−	11.5959i	0.921915	−	0.387392i
$897$		0			0
$898$	−8.62222	−	32.1786i	−0.287727	−	1.07381i
$899$	−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
$910$	2.21952	−	17.5505i	0.0735765	−	0.581793i
$911$	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
$914$	−10.5932	+	39.5343i	−0.350391	+	1.30768i
$915$		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	−0.0841791	−	0.996451i	$-0.526827\pi$
$919$	−29.9882	−	17.3137i	−0.989220	−	0.571127i	−0.905041	+	0.425324i	$0.860160\pi$
$920$	2.92621	+	0.784076i	0.0964743	+	0.0258502i
$921$		0			0
$922$	−24.1197	+	6.46286i	−0.794340	+	0.212843i
$923$			35.9411i			1.18302i
$924$		0			0
$925$			15.0294i			0.494165i
$926$	−8.35578	−	31.1842i	−0.274588	−	1.02478i
$927$		0			0
$928$	4.39230	−	16.3923i	0.144184	−	0.538104i
$929$	−32.8219	−	18.9497i	−1.07685	−	0.621721i	−0.146807	−	0.989165i	$-0.546900\pi$
$929$	−32.8219	−	18.9497i	−1.07685	−	0.621721i	−0.930046	+	0.367444i	$0.880233\pi$
$930$		0			0
$931$	−4.50610	+	17.5306i	−0.147681	+	0.574544i
$932$	38.4264			1.25870
$933$		0			0
$934$	53.2348	+	14.2642i	1.74190	+	0.466739i
$935$	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	$0.684214\pi$
$938$	−17.3244	+	22.8177i	−0.565662	+	0.745025i
$939$		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	0.577481	−	0.816404i	$-0.304036\pi$
$947$	4.89898	+	2.82843i	0.159195	+	0.0919115i	−0.418286	+	0.908315i	$0.637369\pi$
$948$		0			0
$949$	−16.3780	+	9.45584i	−0.531652	+	0.306950i
$950$	−5.85242	+	1.56815i	−0.189878	+	0.0508776i
$951$		0			0
$952$	46.3465	+	5.86121i	1.50210	+	0.189963i
$953$			4.44365i			0.143944i	0.997407	+	0.0719720i	$0.0229292\pi$
$953$			4.44365i			0.143944i	−0.997407	+	0.0719720i	$0.977071\pi$
$954$		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
$962$	8.58543	−	32.0413i	0.276806	−	1.03305i
$963$		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	$-0.887950\pi$
$967$		−	21.4437i		−	0.689581i	0.938680	−	0.344791i	$-0.112050\pi$
$968$	−6.21166	−	23.1822i	−0.199650	−	0.745105i
$969$		0			0
$970$	−10.5932	+	39.5343i	−0.340127	+	1.26937i
$971$	−31.7818	−	18.3492i	−1.01993	−	0.588855i	−0.105844	−	0.994383i	$-0.533755\pi$
$971$	−31.7818	−	18.3492i	−1.01993	−	0.588855i	−0.914083	+	0.405528i	$0.867088\pi$
$972$		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	−0.751251	−	0.660017i	$-0.770549\pi$
$977$	−17.3566	+	10.0208i	−0.555286	+	0.320594i	0.195966	+	0.980611i	$0.437216\pi$
$978$		0			0
$979$		0			0
$980$	−6.87722	−	24.6569i	−0.219685	−	0.787634i
$981$		0			0
$982$	7.64975	+	28.5492i	0.244113	+	0.911043i
$983$	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	−0.389053	−	0.921215i	$-0.627198\pi$
$991$	6.74356	−	3.89340i	0.214216	−	0.123678i	0.603269	+	0.797537i	$0.293864\pi$
$992$	6.46286	+	24.1197i	0.205196	+	0.765802i
$993$		0			0
$994$	20.1472	+	47.9462i	0.639030	+	1.52076i
$995$			32.2843i			1.02348i
$996$		0			0
$997$	−47.1856	+	27.2426i	−1.49438	+	0.862783i	−0.999979	−	0.00644862i	$-0.997947\pi$
$997$	−47.1856	+	27.2426i	−1.49438	+	0.862783i	−0.494405	+	0.869232i	$0.664614\pi$
$998$	11.8169	−	44.1011i	0.374056	−	1.39600i
$999$		0			0

Twists

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

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

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