LMFDB - Embedded newform 567.2.s.f.458.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(26,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 5]))

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

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

chi := DirichletCharacter("567.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.s (of order $6$, degree $2$, not 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.13026266817859584.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 $ x^12 - 9x^10 + 59x^8 - 180x^6 + 403x^4 - 198*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			458.4
Root			$-1.65604 - 0.956115i$ of defining polynomial
Character	$\chi$	$=$	567.458
Dual form			567.2.s.f.26.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.568650 + 0.328310i) q^{2} +(-0.784425 - 1.35866i) q^{4} +3.31208 q^{5} +(0.799494 + 2.52206i) q^{7} -2.34338i q^{8} +O(q^{10})$	\(q+(0.568650 + 0.328310i) q^{2} +(-0.784425 - 1.35866i) q^{4} +3.31208 q^{5} +(0.799494 + 2.52206i) q^{7} -2.34338i q^{8} +(1.88341 + 1.08739i) q^{10} +2.34338i q^{11} +(1.36834 + 0.790014i) q^{13} +(-0.373387 + 1.69665i) q^{14} +(-0.799494 + 1.38476i) q^{16} +(-0.568650 + 0.984931i) q^{17} +(3.85327 - 2.22469i) q^{19} +(-2.59808 - 4.50000i) q^{20} +(-0.769355 + 1.33256i) q^{22} -9.39331i q^{23} +5.96986 q^{25} +(0.518739 + 0.898482i) q^{26} +(2.79949 - 3.06461i) q^{28} +(-3.16673 + 1.82831i) q^{29} +(6.33821 - 3.65936i) q^{31} +(-4.96812 + 2.86834i) q^{32} +(-0.646726 + 0.373387i) q^{34} +(2.64799 + 8.35327i) q^{35} +(2.58392 + 4.47548i) q^{37} +2.92155 q^{38} -7.76146i q^{40} +(-4.82277 + 8.35327i) q^{41} +(1.08392 + 1.87740i) q^{43} +(3.18386 - 1.83821i) q^{44} +(3.08392 - 5.34150i) q^{46} +(2.79334 - 4.83821i) q^{47} +(-5.72162 + 4.03275i) q^{49} +(3.39476 + 1.95997i) q^{50} -2.47883i q^{52} +(-8.70349 - 5.02496i) q^{53} +7.76146i q^{55} +(5.91015 - 1.87352i) q^{56} -2.40101 q^{58} +(-1.08739 - 1.88341i) q^{59} +(-3.46986 - 2.00333i) q^{61} +4.80563 q^{62} -0.568850 q^{64} +(4.53206 + 2.61659i) q^{65} +(5.38341 + 9.32435i) q^{67} +1.78425 q^{68} +(-1.23669 + 5.61945i) q^{70} -6.39331i q^{71} +(-9.25176 - 5.34150i) q^{73} +3.39331i q^{74} +(-6.04521 - 3.49020i) q^{76} +(-5.91015 + 1.87352i) q^{77} +(-0.616587 + 1.06796i) q^{79} +(-2.64799 + 4.58645i) q^{80} +(-5.48493 + 3.16673i) q^{82} +(0.518739 + 0.898482i) q^{83} +(-1.88341 + 3.26217i) q^{85} +1.42345i q^{86} +5.49143 q^{88} +(-3.73538 - 6.46986i) q^{89} +(-0.898482 + 4.08266i) q^{91} +(-12.7623 + 7.36834i) q^{92} +(3.17686 - 1.83416i) q^{94} +(12.7623 - 7.36834i) q^{95} +(-11.7367 + 6.77618i) q^{97} +(-4.57759 + 0.414758i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) $ 12 * q + 8 * q^4 + 4 * q^7	$ 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) $ 12 * q + 8 * q^4 + 4 * q^7 - 6 * q^10 - 24 * q^13 - 4 * q^16 - 6 * q^19 + 20 * q^22 + 48 * q^25 + 28 * q^28 + 12 * q^31 - 60 * q^34 + 8 * q^37 - 10 * q^43 + 14 * q^46 + 24 * q^49 - 40 * q^58 - 18 * q^61 + 28 * q^64 + 36 * q^67 + 66 * q^70 - 42 * q^73 - 108 * q^76 - 36 * q^79 - 54 * q^82 + 6 * q^85 + 148 * q^88 + 6 * q^91 + 114 * q^94 - 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.568650	+	0.328310i	0.402096	+	0.232150i	0.687388	−	0.726290i	$-0.258757\pi$
$2$	0.568650	+	0.328310i	0.402096	+	0.232150i	−0.285292	+	0.958441i	$0.592091\pi$
$3$		0			0
$3$		0			0
$4$	−0.784425	−	1.35866i	−0.392212	−	0.679332i
$5$	3.31208			1.48121			0.740603	−	0.671943i	$-0.234540\pi$
$5$	3.31208			1.48121			0.740603	+	0.671943i	$0.234540\pi$
$6$		0			0
$7$	0.799494	+	2.52206i	0.302180	+	0.953251i
$7$	0.799494	+	2.52206i	0.302180	+	0.953251i
$8$		−	2.34338i		−	0.828510i
$9$		0			0
$10$	1.88341	+	1.08739i	0.595588	+	0.343863i
$11$			2.34338i			0.706556i	0.935518	+	0.353278i	$0.114933\pi$
$11$			2.34338i			0.706556i	−0.935518	+	0.353278i	$0.885067\pi$
$12$		0			0
$13$	1.36834	+	0.790014i	0.379510	+	0.219110i	0.677605	−	0.735426i	$-0.263018\pi$
$13$	1.36834	+	0.790014i	0.379510	+	0.219110i	−0.298095	+	0.954536i	$0.596351\pi$
$14$	−0.373387	+	1.69665i	−0.0997919	+	0.453450i
$15$		0			0
$16$	−0.799494	+	1.38476i	−0.199874	+	0.346191i
$17$	−0.568650	+	0.984931i	−0.137918	+	0.238881i	−0.926708	−	0.375781i	$-0.877374\pi$
$17$	−0.568650	+	0.984931i	−0.137918	+	0.238881i	0.788790	+	0.614662i	$0.210708\pi$
$18$		0			0
$19$	3.85327	−	2.22469i	0.884002	−	0.510379i	0.0120260	−	0.999928i	$-0.496172\pi$
$19$	3.85327	−	2.22469i	0.884002	−	0.510379i	0.871976	+	0.489549i	$0.162839\pi$
$20$	−2.59808	−	4.50000i	−0.580948	−	1.00623i
$21$		0			0
$22$	−0.769355	+	1.33256i	−0.164027	+	0.284103i
$23$		−	9.39331i		−	1.95864i	−0.202317	−	0.979320i	$-0.564847\pi$
$23$		−	9.39331i		−	1.95864i	0.202317	−	0.979320i	$-0.435153\pi$
$24$		0			0
$25$	5.96986			1.19397
$26$	0.518739	+	0.898482i	0.101733	+	0.176207i
$27$		0			0
$28$	2.79949	−	3.06461i	0.529055	−	0.579158i
$29$	−3.16673	+	1.82831i	−0.588046	+	0.339509i	−0.764325	−	0.644832i	$-0.776927\pi$
$29$	−3.16673	+	1.82831i	−0.588046	+	0.339509i	0.176278	+	0.984340i	$0.443594\pi$
$30$		0			0
$31$	6.33821	−	3.65936i	1.13838	−	0.657241i	0.192347	−	0.981327i	$-0.438390\pi$
$31$	6.33821	−	3.65936i	1.13838	−	0.657241i	0.946028	+	0.324086i	$0.105057\pi$
$32$	−4.96812	+	2.86834i	−0.878247	+	0.507056i
$33$		0			0
$34$	−0.646726	+	0.373387i	−0.110913	+	0.0640354i
$35$	2.64799	+	8.35327i	0.447592	+	1.41196i
$36$		0			0
$37$	2.58392	+	4.47548i	0.424794	+	0.735764i	0.996401	−	0.0847630i	$-0.0270133\pi$
$37$	2.58392	+	4.47548i	0.424794	+	0.735764i	−0.571607	+	0.820527i	$0.693680\pi$
$38$	2.92155			0.473938
$39$		0			0
$40$		−	7.76146i		−	1.22719i
$41$	−4.82277	+	8.35327i	−0.753189	+	1.30456i	0.193080	+	0.981183i	$0.438152\pi$
$41$	−4.82277	+	8.35327i	−0.753189	+	1.30456i	−0.946269	+	0.323379i	$0.895181\pi$
$42$		0			0
$43$	1.08392	+	1.87740i	0.165296	+	0.286301i	0.936760	−	0.349971i	$-0.113809\pi$
$43$	1.08392	+	1.87740i	0.165296	+	0.286301i	−0.771464	+	0.636273i	$0.780475\pi$
$44$	3.18386	−	1.83821i	0.479986	−	0.277120i
$45$		0			0
$46$	3.08392	−	5.34150i	0.454699	−	0.787562i
$47$	2.79334	−	4.83821i	0.407450	−	0.705725i	−0.587153	−	0.809476i	$-0.699751\pi$
$47$	2.79334	−	4.83821i	0.407450	−	0.705725i	0.994603	+	0.103751i	$0.0330846\pi$
$48$		0			0
$49$	−5.72162	+	4.03275i	−0.817374	+	0.576107i
$50$	3.39476	+	1.95997i	0.480092	+	0.277181i
$51$		0			0
$52$		−	2.47883i		−	0.343751i
$53$	−8.70349	−	5.02496i	−1.19552	−	0.690232i	−0.235964	−	0.971762i	$-0.575825\pi$
$53$	−8.70349	−	5.02496i	−1.19552	−	0.690232i	−0.959552	+	0.281530i	$0.909158\pi$
$54$		0			0
$55$			7.76146i			1.04655i
$56$	5.91015	−	1.87352i	0.789778	−	0.250359i
$57$		0			0
$58$	−2.40101			−0.315268
$59$	−1.08739	−	1.88341i	−0.141566	−	0.245200i	0.786521	−	0.617564i	$-0.211880\pi$
$59$	−1.08739	−	1.88341i	−0.141566	−	0.245200i	−0.928087	+	0.372365i	$0.878547\pi$
$60$		0			0
$61$	−3.46986	−	2.00333i	−0.444270	−	0.256500i	0.261137	−	0.965302i	$-0.415903\pi$
$61$	−3.46986	−	2.00333i	−0.444270	−	0.256500i	−0.705407	+	0.708802i	$0.749236\pi$
$62$	4.80563			0.610315
$63$		0			0
$64$	−0.568850			−0.0711062
$65$	4.53206	+	2.61659i	0.562133	+	0.324548i
$66$		0			0
$67$	5.38341	+	9.32435i	0.657689	+	1.13915i	0.981213	+	0.192930i	$0.0617990\pi$
$67$	5.38341	+	9.32435i	0.657689	+	1.13915i	−0.323524	+	0.946220i	$0.604868\pi$
$68$	1.78425			0.216372
$69$		0			0
$70$	−1.23669	+	5.61945i	−0.147812	+	0.671653i
$71$		−	6.39331i		−	0.758746i	−0.925244	−	0.379373i	$-0.876140\pi$
$71$		−	6.39331i		−	0.758746i	0.925244	−	0.379373i	$-0.123860\pi$
$72$		0			0
$73$	−9.25176	−	5.34150i	−1.08284	−	0.625176i	−0.151176	−	0.988507i	$-0.548306\pi$
$73$	−9.25176	−	5.34150i	−1.08284	−	0.625176i	−0.931660	+	0.363331i	$0.881639\pi$
$74$			3.39331i			0.394464i
$75$		0			0
$76$	−6.04521	−	3.49020i	−0.693433	−	0.400354i
$77$	−5.91015	+	1.87352i	−0.673525	+	0.213507i
$78$		0			0
$79$	−0.616587	+	1.06796i	−0.0693714	+	0.120155i	−0.898625	−	0.438718i	$-0.855433\pi$
$79$	−0.616587	+	1.06796i	−0.0693714	+	0.120155i	0.829253	+	0.558873i	$0.188766\pi$
$80$	−2.64799	+	4.58645i	−0.296054	+	0.512780i
$81$		0			0
$82$	−5.48493	+	3.16673i	−0.605709	+	0.349706i
$83$	0.518739	+	0.898482i	0.0569390	+	0.0986213i	0.893090	−	0.449878i	$-0.148533\pi$
$83$	0.518739	+	0.898482i	0.0569390	+	0.0986213i	−0.836151	+	0.548499i	$0.815199\pi$
$84$		0			0
$85$	−1.88341	+	3.26217i	−0.204285	+	0.353832i
$86$			1.42345i			0.153494i
$87$		0			0
$88$	5.49143			0.585388
$89$	−3.73538	−	6.46986i	−0.395949	−	0.685804i	0.597273	−	0.802038i	$-0.296251\pi$
$89$	−3.73538	−	6.46986i	−0.395949	−	0.685804i	−0.993222	+	0.116234i	$0.962918\pi$
$90$		0			0
$91$	−0.898482	+	4.08266i	−0.0941866	+	0.427979i
$92$	−12.7623	+	7.36834i	−1.33057	+	0.768203i
$93$		0			0
$94$	3.17686	−	1.83416i	0.327669	−	0.189180i
$95$	12.7623	−	7.36834i	1.30939	−	0.755976i
$96$		0			0
$97$	−11.7367	+	6.77618i	−1.19168	+	0.688017i	−0.958687	−	0.284462i	$-0.908185\pi$
$97$	−11.7367	+	6.77618i	−1.19168	+	0.688017i	−0.232993	+	0.972478i	$0.574852\pi$
$98$	−4.57759	+	0.414758i	−0.462407	+	0.0418969i
$99$		0			0
$100$	−4.68291	−	8.11103i	−0.468291	−	0.811103i
$101$	−13.7044			−1.36364			−0.681819	−	0.731521i	$-0.738811\pi$
$101$	−13.7044			−1.36364			−0.681819	+	0.731521i	$0.738811\pi$
$102$		0			0
$103$			4.89211i			0.482033i	0.970521	+	0.241017i	$0.0774809\pi$
$103$			4.89211i			0.482033i	−0.970521	+	0.241017i	$0.922519\pi$
$104$	1.85130	−	3.20655i	0.181535	−	0.314428i
$105$		0			0
$106$	−3.29949	−	5.71489i	−0.320475	−	0.555079i
$107$	−2.12487	+	1.22679i	−0.205419	+	0.118599i	−0.599180	−	0.800614i	$-0.704507\pi$
$107$	−2.12487	+	1.22679i	−0.205419	+	0.118599i	0.393762	+	0.919213i	$0.371173\pi$
$108$		0			0
$109$	−2.16784	+	3.75481i	−0.207641	+	0.359645i	−0.950971	−	0.309280i	$-0.899912\pi$
$109$	−2.16784	+	3.75481i	−0.207641	+	0.359645i	0.743330	+	0.668925i	$0.233245\pi$
$110$	−2.54817	+	4.41355i	−0.242958	+	0.420816i
$111$		0			0
$112$	−4.13166	−	0.909265i	−0.390405	−	0.0859174i
$113$	6.20086	+	3.58007i	0.583328	+	0.336784i	0.762455	−	0.647042i	$-0.223994\pi$
$113$	6.20086	+	3.58007i	0.583328	+	0.336784i	−0.179127	+	0.983826i	$0.557327\pi$
$114$		0			0
$115$		−	31.1114i		−	2.90115i
$116$	4.96812	+	2.86834i	0.461278	+	0.266319i
$117$		0			0
$118$		−	1.42800i		−	0.131458i
$119$	−2.93869	−	0.646726i	−0.269389	−	0.0592852i
$120$		0			0
$121$	5.50857			0.500779
$122$	−1.31542	−	2.27838i	−0.119093	−	0.206275i
$123$		0			0
$124$	−9.94369	−	5.74099i	−0.892970	−	0.515556i
$125$	3.21226			0.287313
$126$		0			0
$127$	−17.7065			−1.57120			−0.785601	−	0.618733i	$-0.787646\pi$
$127$	−17.7065			−1.57120			−0.785601	+	0.618733i	$0.787646\pi$
$128$	9.61276	+	5.54993i	0.849656	+	0.490549i
$129$		0			0
$130$	1.71810	+	2.97584i	0.150688	+	0.260999i
$131$	−13.6046			−1.18864			−0.594318	−	0.804230i	$-0.702578\pi$
$131$	−13.6046			−1.18864			−0.594318	+	0.804230i	$0.702578\pi$
$132$		0			0
$133$	8.69148	+	7.93958i	0.753647	+	0.688449i
$134$			7.06972i			0.610731i
$135$		0			0
$136$	2.30807	+	1.33256i	0.197915	+	0.114266i
$137$		−	10.1601i		−	0.868039i	−0.900904	−	0.434019i	$-0.857095\pi$
$137$		−	10.1601i		−	0.868039i	0.900904	−	0.434019i	$-0.142905\pi$
$138$		0			0
$139$	−3.33821	−	1.92731i	−0.283143	−	0.163473i	0.351703	−	0.936112i	$-0.385603\pi$
$139$	−3.33821	−	1.92731i	−0.283143	−	0.163473i	−0.634845	+	0.772639i	$0.718936\pi$
$140$	9.27214	−	10.1502i	0.783639	−	0.857852i
$141$		0			0
$142$	2.09899	−	3.63555i	0.176143	−	0.305089i
$143$	−1.85130	+	3.20655i	−0.154814	+	0.268145i
$144$		0			0
$145$	−10.4884	+	6.05551i	−0.871018	+	0.502882i
$146$	−3.50734	−	6.07489i	−0.290270	−	0.502762i
$147$		0			0
$148$	4.05378	−	7.02135i	0.333219	−	0.577152i
$149$			5.08007i			0.416175i	0.978110	+	0.208088i	$0.0667239\pi$
$149$			5.08007i			0.416175i	−0.978110	+	0.208088i	$0.933276\pi$
$150$		0			0
$151$	18.3055			1.48968			0.744842	−	0.667241i	$-0.232525\pi$
$151$	18.3055			1.48968			0.744842	+	0.667241i	$0.232525\pi$
$152$	−5.21329	−	9.02968i	−0.422854	−	0.732404i
$153$		0			0
$154$	−3.97590	−	0.874988i	−0.320387	−	0.0705085i
$155$	20.9926	−	12.1201i	1.68617	−	0.973510i
$156$		0			0
$157$	−2.86834	+	1.65604i	−0.228919	+	0.132166i	−0.610073	−	0.792345i	$-0.708860\pi$
$157$	−2.86834	+	1.65604i	−0.228919	+	0.132166i	0.381154	+	0.924511i	$0.375527\pi$
$158$	−0.701244	+	0.404864i	−0.0557880	+	0.0322092i
$159$		0			0
$160$	−16.4548	+	9.50018i	−1.30087	+	0.751055i
$161$	23.6905	−	7.50989i	1.86708	−	0.591863i
$162$		0			0
$163$	1.14673	+	1.98619i	0.0898185	+	0.155570i	0.907434	−	0.420194i	$-0.138038\pi$
$163$	1.14673	+	1.98619i	0.0898185	+	0.155570i	−0.817616	+	0.575764i	$0.804705\pi$
$164$	15.1324			1.18164
$165$		0			0
$166$			0.681229i			0.0528737i
$167$	−1.33256	+	2.30807i	−0.103117	+	0.178604i	−0.912967	−	0.408033i	$-0.866215\pi$
$167$	−1.33256	+	2.30807i	−0.103117	+	0.178604i	0.809850	+	0.586636i	$0.199548\pi$
$168$		0			0
$169$	−5.25176	−	9.09631i	−0.403981	−	0.699716i
$170$	−2.14201	+	1.23669i	−0.164284	+	0.0948496i
$171$		0			0
$172$	1.70051	−	2.94536i	0.129662	−	0.224582i
$173$	−1.28265	+	2.22162i	−0.0975182	+	0.168907i	−0.910657	−	0.413164i	$-0.864424\pi$
$173$	−1.28265	+	2.22162i	−0.0975182	+	0.168907i	0.813139	+	0.582070i	$0.197757\pi$
$174$		0			0
$175$	4.77287	+	15.0564i	0.360795	+	1.13815i
$176$	−3.24503	−	1.87352i	−0.244603	−	0.141222i
$177$		0			0
$178$		−	4.90545i		−	0.367679i
$179$	11.9828	+	6.91827i	0.895636	+	0.517096i	0.875782	−	0.482707i	$-0.160346\pi$
$179$	11.9828	+	6.91827i	0.895636	+	0.517096i	0.0198545	+	0.999803i	$0.493680\pi$
$180$		0			0
$181$		−	4.74008i		−	0.352328i	−0.984361	−	0.176164i	$-0.943631\pi$
$181$		−	4.74008i		−	0.352328i	0.984361	−	0.176164i	$-0.0563688\pi$
$182$	−1.85130	+	2.02662i	−0.137228	+	0.150223i
$183$		0			0
$184$	−22.0121			−1.62275
$185$	8.55814	+	14.8231i	0.629207	+	1.08982i
$186$		0			0
$187$	−2.30807	−	1.33256i	−0.168783	−	0.0974466i
$188$	−8.76466			−0.639228
$189$		0			0
$190$	9.67641			0.702001
$191$	−7.22558	−	4.17169i	−0.522825	−	0.301853i	0.215265	−	0.976556i	$-0.430938\pi$
$191$	−7.22558	−	4.17169i	−0.522825	−	0.301853i	−0.738090	+	0.674703i	$0.764272\pi$
$192$		0			0
$193$	8.92212	+	15.4536i	0.642229	+	1.11237i	0.984934	+	0.172930i	$0.0553233\pi$
$193$	8.92212	+	15.4536i	0.642229	+	1.11237i	−0.342706	+	0.939443i	$0.611343\pi$
$194$	−8.89876			−0.638893
$195$		0			0
$196$	9.96733	+	4.61036i	0.711952	+	0.329312i
$197$			15.1102i			1.07656i	0.842767	+	0.538279i	$0.180925\pi$
$197$			15.1102i			1.07656i	−0.842767	+	0.538279i	$0.819075\pi$
$198$		0			0
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	0.210032	−	0.977695i	$-0.432643\pi$
$199$	−7.50000	−	4.33013i	−0.531661	−	0.306955i	−0.741693	+	0.670740i	$0.765977\pi$
$200$		−	13.9897i		−	0.989218i
$201$		0			0
$202$	−7.79300	−	4.49929i	−0.548313	−	0.316569i
$203$	−7.14290	−	6.52496i	−0.501333	−	0.457963i
$204$		0			0
$205$	−15.9734	+	27.6667i	−1.11563	+	1.93233i
$206$	−1.60613	+	2.78190i	−0.111904	+	0.193824i
$207$		0			0
$208$	−2.18797	+	1.26322i	−0.151708	+	0.0875887i
$209$	5.21329	+	9.02968i	0.360611	+	0.624596i
$210$		0			0
$211$	7.29047	−	12.6275i	0.501897	−	0.869310i	−0.498101	−	0.867119i	$-0.665969\pi$
$211$	7.29047	−	12.6275i	0.501897	−	0.869310i	0.999998	−	0.00219128i	$-0.000697506\pi$
$212$			15.7668i			1.08287i
$213$		0			0
$214$	−1.61107			−0.110131
$215$	3.59002	+	6.21810i	0.244838	+	0.424071i
$216$		0			0
$217$	14.2965	+	13.0597i	0.970510	+	0.886552i
$218$	−2.46548	+	1.42345i	−0.166984	+	0.0964080i
$219$		0			0
$220$	10.5452	−	6.08828i	0.710958	−	0.410472i
$221$	−1.55622	+	0.898482i	−0.104683	+	0.0604385i
$222$		0			0
$223$	9.16531	−	5.29159i	0.613754	−	0.354351i	−0.160679	−	0.987007i	$-0.551368\pi$
$223$	9.16531	−	5.29159i	0.613754	−	0.354351i	0.774433	+	0.632655i	$0.218035\pi$
$224$	−11.2061	−	10.2367i	−0.748741	−	0.683967i
$225$		0			0
$226$	2.35075	+	4.07161i	0.156369	+	0.270839i
$227$	−6.72398			−0.446286			−0.223143	−	0.974786i	$-0.571632\pi$
$227$	−6.72398			−0.446286			−0.223143	+	0.974786i	$0.571632\pi$
$228$		0			0
$229$		−	12.2630i		−	0.810364i	−0.914236	−	0.405182i	$-0.867208\pi$
$229$		−	12.2630i		−	0.810364i	0.914236	−	0.405182i	$-0.132792\pi$
$230$	10.2142	−	17.6915i	0.673503	−	1.16654i
$231$		0			0
$232$	4.28442	+	7.42084i	0.281286	+	0.487202i
$233$	−4.87268	+	2.81324i	−0.319220	+	0.184302i	−0.651045	−	0.759039i	$-0.725669\pi$
$233$	−4.87268	+	2.81324i	−0.319220	+	0.184302i	0.331825	+	0.943341i	$0.392336\pi$
$234$		0			0
$235$	9.25176	−	16.0245i	0.603518	−	1.04532i
$236$	−1.70595	+	2.95479i	−0.111048	+	0.192341i
$237$		0			0
$238$	−1.45876	−	1.33256i	−0.0945574	−	0.0863772i
$239$	−13.8213	−	7.97976i	−0.894028	−	0.516168i	−0.0187704	−	0.999824i	$-0.505975\pi$
$239$	−13.8213	−	7.97976i	−0.894028	−	0.516168i	−0.875258	+	0.483656i	$0.839308\pi$
$240$		0			0
$241$			4.58806i			0.295543i	0.989022	+	0.147771i	$0.0472100\pi$
$241$			4.58806i			0.295543i	−0.989022	+	0.147771i	$0.952790\pi$
$242$	3.13245	+	1.80852i	0.201361	+	0.116256i
$243$		0			0
$244$			6.28583i			0.402409i
$245$	−18.9504	+	13.3568i	−1.21070	+	0.853334i
$246$		0			0
$247$	7.03014			0.447317
$248$	−8.57528	−	14.8528i	−0.544531	−	0.943155i
$249$		0			0
$250$	1.82665	+	1.05462i	0.115527	+	0.0666998i
$251$	−13.8042			−0.871314			−0.435657	−	0.900113i	$-0.643484\pi$
$251$	−13.8042			−0.871314			−0.435657	+	0.900113i	$0.643484\pi$
$252$		0			0
$253$	22.0121			1.38389
$254$	−10.0688	−	5.81324i	−0.631774	−	0.364755i
$255$		0			0
$256$	4.21305	+	7.29721i	0.263315	+	0.456076i
$257$	8.96430			0.559178			0.279589	−	0.960120i	$-0.409802\pi$
$257$	8.96430			0.559178			0.279589	+	0.960120i	$0.409802\pi$
$258$		0			0
$259$	−9.22162	+	10.0949i	−0.573003	+	0.627268i
$260$		−	8.21006i		−	0.509166i
$261$		0			0
$262$	−7.73623	−	4.46652i	−0.477946	−	0.275942i
$263$			28.5534i			1.76068i	0.474343	+	0.880340i	$0.342686\pi$
$263$			28.5534i			1.76068i	−0.474343	+	0.880340i	$0.657314\pi$
$264$		0			0
$265$	−28.8266	−	16.6431i	−1.77081	−	1.02238i
$266$	2.33576	+	7.36834i	0.143215	+	0.451782i
$267$		0			0
$268$	8.44577	−	14.6285i	0.515907	−	0.893578i
$269$	11.9657	−	20.7251i	0.729559	−	1.26363i	−0.227510	−	0.973776i	$-0.573059\pi$
$269$	11.9657	−	20.7251i	0.729559	−	1.26363i	0.957070	−	0.289858i	$-0.0936081\pi$
$270$		0			0
$271$	12.6467	−	7.30159i	0.768234	−	0.443540i	−0.0640103	−	0.997949i	$-0.520389\pi$
$271$	12.6467	−	7.30159i	0.768234	−	0.443540i	0.832244	+	0.554409i	$0.187056\pi$
$272$	−0.909265	−	1.57489i	−0.0551323	−	0.0954919i
$273$		0			0
$274$	3.33568	−	5.77756i	0.201516	−	0.349035i
$275$			13.9897i			0.843608i
$276$		0			0
$277$	22.3830			1.34486			0.672431	−	0.740160i	$-0.265250\pi$
$277$	22.3830			1.34486			0.672431	+	0.740160i	$0.265250\pi$
$278$	−1.26551	−	2.19193i	−0.0759005	−	0.131463i
$279$		0			0
$280$	19.5749	−	6.20524i	1.16982	−	0.370834i
$281$	10.0517	−	5.80335i	0.599634	−	0.346199i	−0.169264	−	0.985571i	$-0.554139\pi$
$281$	10.0517	−	5.80335i	0.599634	−	0.346199i	0.768897	+	0.639372i	$0.220806\pi$
$282$		0			0
$283$	12.9849	−	7.49685i	0.771874	−	0.445642i	−0.0616687	−	0.998097i	$-0.519642\pi$
$283$	12.9849	−	7.49685i	0.771874	−	0.445642i	0.833543	+	0.552455i	$0.186309\pi$
$284$	−8.68635	+	5.01507i	−0.515440	+	0.297590i
$285$		0			0
$286$	−2.10549	+	1.21560i	−0.124500	+	0.0718801i
$287$	−24.9233	−	5.48493i	−1.47117	−	0.323765i
$288$		0			0
$289$	7.85327	+	13.6023i	0.461957	+	0.800134i
$290$	−7.95234			−0.466977
$291$		0			0
$292$			16.7600i			0.980807i
$293$	8.16762	−	14.1467i	0.477157	−	0.826461i	−0.522500	−	0.852639i	$-0.675001\pi$
$293$	8.16762	−	14.1467i	0.477157	−	0.826461i	0.999657	+	0.0261787i	$0.00833389\pi$
$294$		0			0
$295$	−3.60152	−	6.23801i	−0.209688	−	0.363191i
$296$	10.4877	−	6.05510i	0.609588	−	0.351946i
$297$		0			0
$298$	−1.66784	+	2.88878i	−0.0966153	+	0.167343i
$299$	7.42084	−	12.8533i	0.429158	−	0.743324i
$300$		0			0
$301$	−3.86834	+	4.23469i	−0.222968	+	0.244083i
$302$	10.4094	+	6.00989i	0.598996	+	0.345831i
$303$		0			0
$304$			7.11450i			0.408045i
$305$	−11.4925	−	6.63517i	−0.658056	−	0.379929i
$306$		0			0
$307$		−	3.17340i		−	0.181115i	−0.995891	−	0.0905577i	$-0.971135\pi$
$307$		−	3.17340i		−	0.181115i	0.995891	−	0.0905577i	$-0.0288650\pi$
$308$	7.18155	+	6.56028i	0.409207	+	0.373806i
$309$		0			0
$310$	15.9166			0.904003
$311$	12.5671	+	21.7668i	0.712614	+	1.23428i	0.963873	+	0.266364i	$0.0858222\pi$
$311$	12.5671	+	21.7668i	0.712614	+	1.23428i	−0.251259	+	0.967920i	$0.580845\pi$
$312$		0			0
$313$	16.1463	+	9.32205i	0.912641	+	0.526914i	0.881280	−	0.472594i	$-0.156682\pi$
$313$	16.1463	+	9.32205i	0.912641	+	0.526914i	0.0313612	+	0.999508i	$0.490016\pi$
$314$	−2.17478			−0.122730
$315$		0			0
$316$	1.93466			0.108833
$317$	−6.91924	−	3.99483i	−0.388623	−	0.224372i	0.292940	−	0.956131i	$-0.405366\pi$
$317$	−6.91924	−	3.99483i	−0.388623	−	0.224372i	−0.681563	+	0.731759i	$0.738700\pi$
$318$		0			0
$319$	−4.28442	−	7.42084i	−0.239882	−	0.415487i
$320$	−1.88407			−0.105323
$321$		0			0
$322$	15.9372	+	3.50734i	0.888145	+	0.195456i
$323$			5.06028i			0.281561i
$324$		0			0
$325$	8.16882	+	4.71627i	0.453125	+	0.261612i
$326$			1.50593i			0.0834056i
$327$		0			0
$328$	19.5749	+	11.3016i	1.08084	+	0.624025i
$329$	14.4355	+	3.17686i	0.795856	+	0.175146i
$330$		0			0
$331$	4.46733	−	7.73765i	0.245547	−	0.425299i	−0.716738	−	0.697342i	$-0.754366\pi$
$331$	4.46733	−	7.73765i	0.245547	−	0.425299i	0.962285	+	0.272043i	$0.0876992\pi$
$332$	0.813824	−	1.40958i	0.0446644	−	0.0773610i
$333$		0			0
$334$	−1.51552	+	0.874988i	−0.0829258	+	0.0478772i
$335$	17.8303	+	30.8830i	0.974173	+	1.68732i
$336$		0			0
$337$	−2.12263	+	3.67650i	−0.115627	+	0.200272i	−0.918030	−	0.396510i	$-0.870221\pi$
$337$	−2.12263	+	3.67650i	−0.115627	+	0.200272i	0.802403	+	0.596782i	$0.203554\pi$
$338$		−	6.89682i		−	0.375138i
$339$		0			0
$340$	5.90958			0.320492
$341$	8.57528	+	14.8528i	0.464377	+	0.804325i
$342$		0			0
$343$	−14.7453	−	11.2061i	−0.796169	−	0.605074i
$344$	4.39947	−	2.54003i	0.237203	−	0.136949i
$345$		0			0
$346$	−1.45876	+	0.842215i	−0.0784234	+	0.0452778i
$347$	−2.27460	+	1.31324i	−0.122107	+	0.0704985i	−0.559809	−	0.828621i	$-0.689126\pi$
$347$	−2.27460	+	1.31324i	−0.122107	+	0.0704985i	0.437702	+	0.899120i	$0.355792\pi$
$348$		0			0
$349$	−28.1387	+	16.2459i	−1.50623	+	0.869622i	−0.506255	+	0.862384i	$0.668971\pi$
$349$	−28.1387	+	16.2459i	−1.50623	+	0.869622i	−0.999974	+	0.00723825i	$0.997696\pi$
$350$	−2.22907	+	10.1288i	−0.119149	+	0.541407i
$351$		0			0
$352$	−6.72162	−	11.6422i	−0.358263	−	0.620531i
$353$	23.3842			1.24461			0.622307	−	0.782773i	$-0.286195\pi$
$353$	23.3842			1.24461			0.622307	+	0.782773i	$0.286195\pi$
$354$		0			0
$355$		−	21.1751i		−	1.12386i
$356$	−5.86024	+	10.1502i	−0.310592	+	0.537962i
$357$		0			0
$358$	4.54268	+	7.86815i	0.240088	+	0.415845i
$359$	18.4900	−	10.6752i	0.975865	−	0.563416i	0.0748455	−	0.997195i	$-0.476154\pi$
$359$	18.4900	−	10.6752i	0.975865	−	0.563416i	0.901019	+	0.433779i	$0.142820\pi$
$360$		0			0
$361$	0.398482	−	0.690192i	0.0209728	−	0.0363259i
$362$	1.55622	−	2.69545i	0.0817930	−	0.141670i
$363$		0			0
$364$	6.25176	−	1.98181i	0.327681	−	0.103875i
$365$	−30.6425	−	17.6915i	−1.60390	−	0.926014i
$366$		0			0
$367$		−	15.5229i		−	0.810289i	−0.914253	−	0.405145i	$-0.867221\pi$
$367$		−	15.5229i		−	0.810289i	0.914253	−	0.405145i	$-0.132779\pi$
$368$	13.0075	+	7.50989i	0.678064	+	0.391480i
$369$		0			0
$370$			11.2389i			0.584283i
$371$	5.71489	−	25.9682i	0.296702	−	1.34820i
$372$		0			0
$373$	−23.3528			−1.20916			−0.604582	−	0.796543i	$-0.706660\pi$
$373$	−23.3528			−1.20916			−0.604582	+	0.796543i	$0.706660\pi$
$374$	−0.874988	−	1.51552i	−0.0452445	−	0.0783659i
$375$		0			0
$376$	−11.3378	−	6.54585i	−0.584700	−	0.337577i
$377$	−5.77756			−0.297559
$378$		0			0
$379$	2.53871			0.130405			0.0652024	−	0.997872i	$-0.479231\pi$
$379$	2.53871			0.130405			0.0652024	+	0.997872i	$0.479231\pi$
$380$	−20.0222	−	11.5598i	−1.02712	−	0.593006i
$381$		0			0
$382$	−2.73922	−	4.74446i	−0.140151	−	0.242748i
$383$	16.2041			0.827993			0.413996	−	0.910278i	$-0.364133\pi$
$383$	16.2041			0.827993			0.413996	+	0.910278i	$0.364133\pi$
$384$		0			0
$385$	−19.5749	+	6.20524i	−0.997629	+	0.316248i
$386$			11.7169i			0.596374i
$387$		0			0
$388$	18.4131	+	10.6308i	0.934783	+	0.539697i
$389$		−	22.3330i		−	1.13233i	−0.824292	−	0.566165i	$-0.808427\pi$
$389$		−	22.3330i		−	1.13233i	0.824292	−	0.566165i	$-0.191573\pi$
$390$		0			0
$391$	9.25176	+	5.34150i	0.467881	+	0.270131i
$392$	9.45027	+	13.4079i	0.477311	+	0.677202i
$393$		0			0
$394$	−4.96083	+	8.59242i	−0.249923	+	0.432880i
$395$	−2.04218	+	3.53717i	−0.102753	+	0.177974i
$396$		0			0
$397$	28.3116	−	16.3457i	1.42092	−	0.820367i	0.424540	−	0.905409i	$-0.360436\pi$
$397$	28.3116	−	16.3457i	1.42092	−	0.820367i	0.996377	+	0.0850420i	$0.0271025\pi$
$398$	−2.84325	−	4.92465i	−0.142519	−	0.246851i
$399$		0			0
$400$	−4.77287	+	8.26685i	−0.238643	+	0.413343i
$401$		−	28.9270i		−	1.44454i	−0.691609	−	0.722272i	$-0.743098\pi$
$401$		−	28.9270i		−	1.44454i	0.691609	−	0.722272i	$-0.256902\pi$
$402$		0			0
$403$	11.5638			0.576033
$404$	10.7501	+	18.6196i	0.534835	+	0.926362i
$405$		0			0
$406$	−1.91959	−	6.05551i	−0.0952679	−	0.300530i
$407$	−10.4877	+	6.05510i	−0.519858	+	0.300140i
$408$		0			0
$409$	−0.910038	+	0.525411i	−0.0449985	+	0.0259799i	−0.522330	−	0.852743i	$-0.674937\pi$
$409$	−0.910038	+	0.525411i	−0.0449985	+	0.0259799i	0.477332	+	0.878723i	$0.341604\pi$
$410$	−18.1665	+	10.4884i	−0.897180	+	0.517987i
$411$		0			0
$412$	6.64673	−	3.83749i	0.327461	−	0.189060i
$413$	3.88073	−	4.24824i	0.190958	−	0.209042i
$414$		0			0
$415$	1.71810	+	2.97584i	0.0843384	+	0.146078i
$416$	−9.06412			−0.444405
$417$		0			0
$418$			6.84631i			0.334864i
$419$	−1.56060	+	2.70304i	−0.0762402	+	0.132052i	−0.901625	−	0.432519i	$-0.857625\pi$
$419$	−1.56060	+	2.70304i	−0.0762402	+	0.132052i	0.825385	+	0.564571i	$0.190958\pi$
$420$		0			0
$421$	4.35327	+	7.54009i	0.212166	+	0.367482i	0.952392	−	0.304876i	$-0.0986150\pi$
$421$	4.35327	+	7.54009i	0.212166	+	0.367482i	−0.740226	+	0.672358i	$0.765282\pi$
$422$	8.29145	−	4.78707i	0.403621	−	0.233031i
$423$		0			0
$424$	−11.7754	+	20.3956i	−0.571864	+	0.990497i
$425$	−3.39476	+	5.87990i	−0.164670	+	0.285217i
$426$		0			0
$427$	2.27838	−	10.3529i	0.110259	−	0.501010i
$428$	3.33360	+	1.92465i	0.161136	+	0.0930316i
$429$		0			0
$430$			4.71457i			0.227357i
$431$	−23.6279	−	13.6416i	−1.13811	−	0.657090i	−0.192151	−	0.981365i	$-0.561546\pi$
$431$	−23.6279	−	13.6416i	−1.13811	−	0.657090i	−0.945963	+	0.324275i	$0.894880\pi$
$432$		0			0
$433$		−	12.8711i		−	0.618547i	−0.950973	−	0.309274i	$-0.899914\pi$
$433$		−	12.8711i		−	0.618547i	0.950973	−	0.309274i	$-0.100086\pi$
$434$	3.84207	+	12.1201i	0.184425	+	0.581783i
$435$		0			0
$436$	6.80202			0.325758
$437$	−20.8972	−	36.1950i	−0.999648	−	1.73144i
$438$		0			0
$439$	−15.9734	−	9.22223i	−0.762368	−	0.440153i	0.0677776	−	0.997700i	$-0.478409\pi$
$439$	−15.9734	−	9.22223i	−0.762368	−	0.440153i	−0.830145	+	0.557547i	$0.811743\pi$
$440$	18.1880			0.867081
$441$		0			0
$442$	−1.17992			−0.0561233
$443$	−2.48550	−	1.43500i	−0.118090	−	0.0681790i	0.439792	−	0.898100i	$-0.355052\pi$
$443$	−2.48550	−	1.43500i	−0.118090	−	0.0681790i	−0.557881	+	0.829921i	$0.688386\pi$
$444$		0			0
$445$	−12.3719	−	21.4287i	−0.586482	−	1.01582i
$446$	6.94914			0.329051
$447$		0			0
$448$	−0.454792	−	1.43468i	−0.0214869	−	0.0677820i
$449$			1.81675i			0.0857380i	0.999081	+	0.0428690i	$0.0136498\pi$
$449$			1.81675i			0.0857380i	−0.999081	+	0.0428690i	$0.986350\pi$
$450$		0			0
$451$	−19.5749	−	11.3016i	−0.921746	−	0.532170i
$452$		−	11.2332i		−	0.528364i
$453$		0			0
$454$	−3.82359	−	2.20755i	−0.179450	−	0.103605i
$455$	−2.97584	+	13.5221i	−0.139510	+	0.633926i
$456$		0			0
$457$	−3.07788	+	5.33104i	−0.143977	+	0.249375i	−0.928991	−	0.370103i	$-0.879322\pi$
$457$	−3.07788	+	5.33104i	−0.143977	+	0.249375i	0.785014	+	0.619478i	$0.212656\pi$
$458$	4.02608	−	6.97338i	0.188126	−	0.325844i
$459$		0			0
$460$	−42.2699	+	24.4045i	−1.97084	+	1.13787i
$461$	−8.52537	−	14.7664i	−0.397066	−	0.687739i	0.596296	−	0.802764i	$-0.296638\pi$
$461$	−8.52537	−	14.7664i	−0.397066	−	0.687739i	−0.993363	+	0.115026i	$0.963305\pi$
$462$		0			0
$463$	−14.7065	+	25.4725i	−0.683471	+	1.18381i	0.290443	+	0.956892i	$0.406197\pi$
$463$	−14.7065	+	25.4725i	−0.683471	+	1.18381i	−0.973915	+	0.226915i	$0.927136\pi$
$464$		−	5.84689i		−	0.271435i
$465$		0			0
$466$	−3.69446			−0.171143
$467$	13.5590	+	23.4849i	0.627437	+	1.08675i	0.988064	+	0.154043i	$0.0492294\pi$
$467$	13.5590	+	23.4849i	0.627437	+	1.08675i	−0.360627	+	0.932710i	$0.617437\pi$
$468$		0			0
$469$	−19.2126	+	21.0321i	−0.887155	+	0.971171i
$470$	10.5220	−	6.07489i	0.485345	−	0.280214i
$471$		0			0
$472$	−4.41355	+	2.54817i	−0.203150	+	0.117289i
$473$	−4.39947	+	2.54003i	−0.202288	+	0.116791i
$474$		0			0
$475$	23.0035	−	13.2811i	1.05547	−	0.609378i
$476$	1.42650	+	4.50000i	0.0653835	+	0.206257i
$477$		0			0
$478$	−5.23967	−	9.07538i	−0.239657	−	0.415098i
$479$	−21.5569			−0.984960			−0.492480	−	0.870324i	$-0.663910\pi$
$479$	−21.5569			−0.984960			−0.492480	+	0.870324i	$0.663910\pi$
$480$		0			0
$481$			8.16532i			0.372307i
$482$	−1.50631	+	2.60900i	−0.0686104	+	0.118837i
$483$		0			0
$484$	−4.32106	−	7.48430i	−0.196412	−	0.340195i
$485$	−38.8728	+	22.4432i	−1.76512	+	1.01909i
$486$		0			0
$487$	7.29047	−	12.6275i	0.330363	−	0.572205i	−0.652220	−	0.758029i	$-0.726162\pi$
$487$	7.29047	−	12.6275i	0.330363	−	0.572205i	0.982583	+	0.185825i	$0.0594956\pi$
$488$	−4.69455	+	8.13120i	−0.212512	+	0.368082i
$489$		0			0
$490$	−15.1613	+	1.37371i	−0.684920	+	0.0620580i
$491$	−0.245174	−	0.141551i	−0.0110645	−	0.00638811i	0.494458	−	0.869202i	$-0.335367\pi$
$491$	−0.245174	−	0.141551i	−0.0110645	−	0.00638811i	−0.505522	+	0.862814i	$0.668700\pi$
$492$		0			0
$493$		−	4.15867i		−	0.187297i
$494$	3.99769	+	2.30807i	0.179864	+	0.103845i
$495$		0			0
$496$			11.7026i			0.525461i
$497$	16.1243	−	5.11141i	0.723275	−	0.229278i
$498$		0			0
$499$	12.3055			0.550871			0.275436	−	0.961319i	$-0.411178\pi$
$499$	12.3055			0.550871			0.275436	+	0.961319i	$0.411178\pi$
$500$	−2.51977	−	4.36438i	−0.112688	−	0.195181i
$501$		0			0
$502$	−7.84976	−	4.53206i	−0.350352	−	0.202276i
$503$	1.78425			0.0795559			0.0397779	−	0.999209i	$-0.487335\pi$
$503$	1.78425			0.0795559			0.0397779	+	0.999209i	$0.487335\pi$
$504$		0			0
$505$	−45.3900			−2.01983
$506$	12.5172	+	7.22679i	0.556456	+	0.321270i
$507$		0			0
$508$	13.8895	+	24.0572i	0.616245	+	1.06737i
$509$	39.0725			1.73186			0.865928	−	0.500168i	$-0.166728\pi$
$509$	39.0725			1.73186			0.865928	+	0.500168i	$0.166728\pi$
$510$		0			0
$511$	6.07489	−	27.6040i	0.268737	−	1.22113i
$512$		−	16.6670i		−	0.736583i
$513$		0			0
$514$	5.09755	+	2.94307i	0.224843	+	0.129813i
$515$			16.2030i			0.713991i
$516$		0			0
$517$	11.3378	+	6.54585i	0.498634	+	0.287886i
$518$	−8.55814	+	2.71293i	−0.376023	+	0.119199i
$519$		0			0
$520$	6.13166	−	10.6203i	0.268891	−	0.465733i
$521$	10.1814	−	17.6347i	0.446056	−	0.772591i	−0.552070	−	0.833798i	$-0.686162\pi$
$521$	10.1814	−	17.6347i	0.446056	−	0.772591i	0.998125	+	0.0612072i	$0.0194950\pi$
$522$		0			0
$523$	1.24066	−	0.716293i	0.0542501	−	0.0313213i	−0.472630	−	0.881261i	$-0.656695\pi$
$523$	1.24066	−	0.716293i	0.0542501	−	0.0313213i	0.526880	+	0.849940i	$0.323362\pi$
$524$	10.6718	+	18.4840i	0.466198	+	0.807478i
$525$		0			0
$526$	−9.37439	+	16.2369i	−0.408743	+	0.707963i
$527$			8.32359i			0.362581i
$528$		0			0
$529$	−65.2342			−2.83627
$530$	−10.9282	−	18.9282i	−0.474690	−	0.822187i
$531$		0			0
$532$	3.96941	−	18.0368i	0.172096	−	0.781994i
$533$	−13.1984	+	7.62010i	−0.571686	+	0.330063i
$534$		0			0
$535$	−7.03773	+	4.06323i	−0.304267	+	0.175669i
$536$	21.8505	−	12.6154i	0.943797	−	0.544901i
$537$		0			0
$538$	13.6085	−	7.85690i	0.586706	−	0.338735i
$539$	−9.45027	−	13.4079i	−0.407052	−	0.577520i
$540$		0			0
$541$	5.04521	+	8.73856i	0.216910	+	0.375700i	0.953862	−	0.300246i	$-0.0970687\pi$
$541$	5.04521	+	8.73856i	0.216910	+	0.375700i	−0.736951	+	0.675946i	$0.763735\pi$
$542$	9.58875			0.411872
$543$		0			0
$544$		−	6.52433i		−	0.279729i
$545$	−7.18005	+	12.4362i	−0.307559	+	0.532709i
$546$		0			0
$547$	−3.65024	−	6.32240i	−0.156073	−	0.270326i	0.777376	−	0.629036i	$-0.216550\pi$
$547$	−3.65024	−	6.32240i	−0.156073	−	0.270326i	−0.933449	+	0.358710i	$0.883217\pi$
$548$	−13.8042	+	7.96986i	−0.589686	+	0.340456i
$549$		0			0
$550$	−4.59295	+	7.95521i	−0.195844	+	0.339211i
$551$	−8.13484	+	14.0900i	−0.346556	+	0.600253i
$552$		0			0
$553$	−3.18642	−	0.701244i	−0.135500	−	0.0298199i
$554$	12.7281	+	7.34855i	0.540764	+	0.312210i
$555$		0			0
$556$			6.04733i			0.256464i
$557$	19.7970	+	11.4298i	0.838828	+	0.484297i	0.856866	−	0.515540i	$-0.172409\pi$
$557$	19.7970	+	11.4298i	0.838828	+	0.484297i	−0.0180379	+	0.999837i	$0.505742\pi$
$558$		0			0
$559$			3.42524i			0.144872i
$560$	−13.6844	−	3.01156i	−0.578270	−	0.127261i
$561$		0			0
$562$	7.62119			0.321481
$563$	10.5548	+	18.2814i	0.444832	+	0.770471i	0.998040	−	0.0625717i	$-0.0199302\pi$
$563$	10.5548	+	18.2814i	0.444832	+	0.770471i	−0.553209	+	0.833043i	$0.686597\pi$
$564$		0			0
$565$	20.5377	+	11.8575i	0.864029	+	0.498847i
$566$	9.84517			0.413824
$567$		0			0
$568$	−14.9819			−0.628629
$569$	22.9095	+	13.2268i	0.960415	+	0.554496i	0.896301	−	0.443447i	$-0.146244\pi$
$569$	22.9095	+	13.2268i	0.960415	+	0.554496i	0.0641144	+	0.997943i	$0.479578\pi$
$570$		0			0
$571$	−6.01507	−	10.4184i	−0.251723	−	0.435997i	0.712277	−	0.701898i	$-0.247664\pi$
$571$	−6.01507	−	10.4184i	−0.251723	−	0.435997i	−0.964000	+	0.265901i	$0.914330\pi$
$572$	5.80883			0.242879
$573$		0			0
$574$	−12.3719	−	11.3016i	−0.516391	−	0.471718i
$575$		−	56.0767i		−	2.33856i
$576$		0			0
$577$	−31.9055	−	18.4207i	−1.32824	−	0.766862i	−0.343216	−	0.939257i	$-0.611516\pi$
$577$	−31.9055	−	18.4207i	−1.32824	−	0.766862i	−0.985028	+	0.172395i	$0.944850\pi$
$578$			10.3132i			0.428974i
$579$		0			0
$580$	16.4548	+	9.50018i	0.683248	+	0.394473i
$581$	−1.85130	+	2.02662i	−0.0768049	+	0.0840786i
$582$		0			0
$583$	11.7754	−	20.3956i	0.487687	−	0.844699i
$584$	−12.5172	+	21.6804i	−0.517964	+	0.897140i
$585$		0			0
$586$	9.28903	−	5.36302i	0.383726	−	0.221544i
$587$	−14.3856	−	24.9166i	−0.593758	−	1.02842i	−0.993721	−	0.111887i	$-0.964310\pi$
$587$	−14.3856	−	24.9166i	−0.593758	−	1.02842i	0.399963	−	0.916531i	$-0.369023\pi$
$588$		0			0
$589$	16.2819	−	28.2011i	0.670884	−	1.16200i
$590$		−	4.72966i		−	0.194717i
$591$		0			0
$592$	−8.26331			−0.339620
$593$	−5.29159	−	9.16531i	−0.217300	−	0.376374i	0.736682	−	0.676240i	$-0.236392\pi$
$593$	−5.29159	−	9.16531i	−0.217300	−	0.376374i	−0.953982	+	0.299865i	$0.903058\pi$
$594$		0			0
$595$	−9.73317	−	2.14201i	−0.399021	−	0.0878137i
$596$	6.90210	−	3.98493i	0.282721	−	0.163229i
$597$		0			0
$598$	8.43972	−	4.87268i	0.345126	−	0.199259i
$599$	15.7553	−	9.09634i	0.643745	−	0.371666i	−0.142311	−	0.989822i	$-0.545453\pi$
$599$	15.7553	−	9.09634i	0.643745	−	0.371666i	0.786056	+	0.618156i	$0.212120\pi$
$600$		0			0
$601$	22.8719	−	13.2051i	0.932963	−	0.538646i	0.0452152	−	0.998977i	$-0.485603\pi$
$601$	22.8719	−	13.2051i	0.932963	−	0.538646i	0.887747	+	0.460331i	$0.152269\pi$
$602$	−3.59002	+	1.13804i	−0.146318	+	0.0463829i
$603$		0			0
$604$	−14.3593	−	24.8711i	−0.584272	−	1.01199i
$605$	18.2448			0.741757
$606$		0			0
$607$		−	24.9776i		−	1.01381i	−0.862003	−	0.506904i	$-0.830790\pi$
$607$		−	24.9776i		−	1.01381i	0.862003	−	0.506904i	$-0.169210\pi$
$608$	−12.7623	+	22.1050i	−0.517581	+	0.896477i
$609$		0			0
$610$	−4.35679	−	7.54618i	−0.176401	−	0.305536i
$611$	7.64450	−	4.41355i	0.309263	−	0.178553i
$612$		0			0
$613$	7.05631	−	12.2219i	0.285002	−	0.493637i	−0.687608	−	0.726082i	$-0.741339\pi$
$613$	7.05631	−	12.2219i	0.285002	−	0.493637i	0.972610	+	0.232445i	$0.0746725\pi$
$614$	1.04186	−	1.80455i	0.0420460	−	0.0728258i
$615$		0			0
$616$	4.39036	+	13.8497i	0.176893	+	0.558022i
$617$	12.6669	+	7.31324i	0.509950	+	0.294420i	0.732813	−	0.680430i	$-0.238207\pi$
$617$	12.6669	+	7.31324i	0.509950	+	0.294420i	−0.222863	+	0.974850i	$0.571540\pi$
$618$		0			0
$619$			26.5442i			1.06690i	0.845831	+	0.533452i	$0.179105\pi$
$619$			26.5442i			1.06690i	−0.845831	+	0.533452i	$0.820895\pi$
$620$	−32.9343	−	19.0146i	−1.32267	−	0.763645i
$621$		0			0
$622$			16.5036i			0.661734i
$623$	13.3310	−	14.5935i	0.534095	−	0.584675i
$624$		0			0
$625$	−19.2101			−0.768403
$626$	6.12105	+	10.6020i	0.244646	+	0.423740i
$627$		0			0
$628$	4.50000	+	2.59808i	0.179570	+	0.103675i
$629$	−5.87738			−0.234347
$630$		0			0
$631$	−8.20304			−0.326558			−0.163279	−	0.986580i	$-0.552207\pi$
$631$	−8.20304			−0.326558			−0.163279	+	0.986580i	$0.552207\pi$
$632$	2.50264	+	1.44490i	0.0995495	+	0.0574749i
$633$		0			0
$634$	−2.62308	−	4.54331i	−0.104176	−	0.180438i
$635$	−58.6455			−2.32727
$636$		0			0
$637$	−11.0151	+	0.998034i	−0.436433	+	0.0395436i
$638$		−	5.62648i		−	0.222755i
$639$		0			0
$640$	31.8382	+	18.3818i	1.25852	+	0.726604i
$641$			16.0499i			0.633934i	0.948437	+	0.316967i	$0.102664\pi$
$641$			16.0499i			0.633934i	−0.948437	+	0.316967i	$0.897336\pi$
$642$		0			0
$643$	22.8719	+	13.2051i	0.901978	+	0.520757i	0.877841	−	0.478951i	$-0.158983\pi$
$643$	22.8719	+	13.2051i	0.901978	+	0.520757i	0.0241366	+	0.999709i	$0.492316\pi$
$644$	−28.7869	−	26.2965i	−1.13436	−	1.03623i
$645$		0			0
$646$	−1.66134	+	2.87753i	−0.0653646	+	0.113215i
$647$	−15.8508	+	27.4543i	−0.623158	+	1.07934i	0.365736	+	0.930719i	$0.380817\pi$
$647$	−15.8508	+	27.4543i	−0.623158	+	1.07934i	−0.988894	+	0.148623i	$0.952516\pi$
$648$		0			0
$649$	4.41355	−	2.54817i	0.173247	−	0.100024i
$650$	3.09680	+	5.36382i	0.121467	+	0.210386i
$651$		0			0
$652$	1.79904	−	3.11603i	0.0704558	−	0.122033i
$653$			13.2901i			0.520083i	0.965597	+	0.260041i	$0.0837362\pi$
$653$			13.2901i			0.520083i	−0.965597	+	0.260041i	$0.916264\pi$
$654$		0			0
$655$	−45.0594			−1.76062
$656$	−7.71155	−	13.3568i	−0.301085	−	0.521495i
$657$		0			0
$658$	7.16576	+	6.54585i	0.279351	+	0.255184i
$659$	−31.3609	+	18.1062i	−1.22165	+	0.705319i	−0.965269	−	0.261257i	$-0.915863\pi$
$659$	−31.3609	+	18.1062i	−1.22165	+	0.705319i	−0.256379	+	0.966576i	$0.582530\pi$
$660$		0			0
$661$	−43.9880	+	25.3965i	−1.71093	+	0.987809i	−0.777630	+	0.628722i	$0.783578\pi$
$661$	−43.9880	+	25.3965i	−1.71093	+	0.987809i	−0.933304	+	0.359087i	$0.883088\pi$
$662$	5.08070	−	2.93334i	0.197467	−	0.114008i
$663$		0			0
$664$	2.10549	−	1.21560i	0.0817087	−	0.0471745i
$665$	28.7869	+	26.2965i	1.11631	+	1.01973i
$666$		0			0
$667$	17.1739	+	29.7460i	0.664975	+	1.15177i
$668$	4.18118			0.161775
$669$		0			0
$670$			23.4155i			0.904618i
$671$	4.69455	−	8.13120i	0.181231	−	0.313902i
$672$		0			0
$673$	−1.66432	−	2.88269i	−0.0641550	−	0.111120i	0.832164	−	0.554530i	$-0.187102\pi$
$673$	−1.66432	−	2.88269i	−0.0641550	−	0.111120i	−0.896319	+	0.443410i	$0.853769\pi$
$674$	−2.41407	+	1.39376i	−0.0929864	+	0.0536857i
$675$		0			0
$676$	−8.23922	+	14.2707i	−0.316893	+	0.548875i
$677$	−9.96901	+	17.2668i	−0.383140	+	0.663618i	−0.991509	−	0.130036i	$-0.958491\pi$
$677$	−9.96901	+	17.2668i	−0.383140	+	0.663618i	0.608369	+	0.793654i	$0.291824\pi$
$678$		0			0
$679$	−26.4734	−	24.1832i	−1.01595	−	0.928065i
$680$	7.64450	+	4.41355i	0.293153	+	0.169252i
$681$		0			0
$682$			11.2614i			0.431222i
$683$	24.8234	+	14.3318i	0.949843	+	0.548392i	0.893032	−	0.449993i	$-0.148574\pi$
$683$	24.8234	+	14.3318i	0.949843	+	0.548392i	0.0568107	+	0.998385i	$0.481907\pi$
$684$		0			0
$685$		−	33.6512i		−	1.28574i
$686$	−4.70581	−	11.2134i	−0.179668	−	0.428129i
$687$		0			0
$688$	−3.46635			−0.132153
$689$	−7.93958	−	13.7518i	−0.302474	−	0.523900i
$690$		0			0
$691$	17.6387	+	10.1837i	0.671007	+	0.387406i	0.796458	−	0.604694i	$-0.206704\pi$
$691$	17.6387	+	10.1837i	0.671007	+	0.387406i	−0.125451	+	0.992100i	$0.540038\pi$
$692$	4.02458			0.152991
$693$		0			0
$694$	−1.72460			−0.0654650
$695$	−11.0564	−	6.38341i	−0.419393	−	0.242137i
$696$		0			0
$697$	−5.48493	−	9.50018i	−0.207757	−	0.359845i
$698$	−21.3347			−0.807532
$699$		0			0
$700$	16.7126	−	18.2953i	0.631677	−	0.691498i
$701$			49.1172i			1.85513i	0.373659	+	0.927566i	$0.378103\pi$
$701$			49.1172i			1.85513i	−0.373659	+	0.927566i	$0.621897\pi$
$702$		0			0
$703$	19.9131	+	11.4968i	0.751037	+	0.433611i
$704$		−	1.33303i		−	0.0502405i
$705$		0			0
$706$	13.2974	+	7.67727i	0.500455	+	0.288938i
$707$	−10.9566	−	34.5633i	−0.412064	−	1.29989i
$708$		0			0
$709$	−11.6829	+	20.2354i	−0.438761	+	0.759956i	−0.997594	−	0.0693240i	$-0.977916\pi$
$709$	−11.6829	+	20.2354i	−0.438761	+	0.759956i	0.558833	+	0.829280i	$0.311249\pi$
$710$	6.95201	−	12.0412i	0.260904	−	0.451900i
$711$		0			0
$712$	−15.1613	+	8.75340i	−0.568195	+	0.328048i
$713$	−34.3735	−	59.5367i	−1.28730	−	2.22967i
$714$		0			0
$715$	−6.13166	+	10.6203i	−0.229311	+	0.397178i
$716$		−	21.7075i		−	0.811246i
$717$		0			0
$718$	14.0191			0.523189
$719$	−6.33345	−	10.9699i	−0.236198	−	0.409107i	0.723422	−	0.690406i	$-0.242568\pi$
$719$	−6.33345	−	10.9699i	−0.236198	−	0.409107i	−0.959620	+	0.281299i	$0.909235\pi$
$720$		0			0
$721$	−12.3382	+	3.91121i	−0.459499	+	0.145661i
$722$	0.453194	−	0.261652i	0.0168661	−	0.00973767i
$723$		0			0
$724$	−6.44018	+	3.71824i	−0.239347	+	0.138187i
$725$	−18.9049	+	10.9148i	−0.702111	+	0.405364i
$726$		0			0
$727$	−2.34172	+	1.35199i	−0.0868495	+	0.0501426i	−0.542796	−	0.839865i	$-0.682634\pi$
$727$	−2.34172	+	1.35199i	−0.0868495	+	0.0501426i	0.455946	+	0.890007i	$0.349301\pi$
$728$	9.56723	+	2.10549i	0.354585	+	0.0780345i
$729$		0			0
$730$	−11.6166	−	20.1205i	−0.429949	−	0.744694i
$731$	−2.46548			−0.0911891
$732$		0			0
$733$			21.8087i			0.805524i	0.915305	+	0.402762i	$0.131950\pi$
$733$			21.8087i			0.805524i	−0.915305	+	0.402762i	$0.868050\pi$
$734$	5.09633	−	8.82710i	0.188109	−	0.325814i
$735$		0			0
$736$	26.9432	+	46.6671i	0.993141	+	1.72017i
$737$	−21.8505	+	12.6154i	−0.804873	+	0.464694i
$738$		0			0
$739$	−16.0633	+	27.8225i	−0.590899	+	1.02347i	0.403212	+	0.915107i	$0.367894\pi$
$739$	−16.0633	+	27.8225i	−0.590899	+	1.02347i	−0.994112	+	0.108361i	$0.965440\pi$
$740$	13.4264	−	23.2553i	0.493566	−	0.854881i
$741$		0			0
$742$	11.7754	−	12.8906i	0.432288	−	0.473227i
$743$	35.7433	+	20.6364i	1.31129	+	0.757075i	0.982310	−	0.187261i	$-0.0599609\pi$
$743$	35.7433	+	20.6364i	1.31129	+	0.757075i	0.328983	+	0.944336i	$0.393294\pi$
$744$		0			0
$745$			16.8256i			0.616442i
$746$	−13.2796	−	7.66697i	−0.486200	−	0.280708i
$747$		0			0
$748$			4.18118i			0.152879i
$749$	−4.79287	−	4.37824i	−0.175128	−	0.159977i
$750$		0			0
$751$	45.8091			1.67160			0.835798	−	0.549037i	$-0.185005\pi$
$751$	45.8091			1.67160			0.835798	+	0.549037i	$0.185005\pi$
$752$	4.46652	+	7.73623i	0.162877	+	0.282111i
$753$		0			0
$754$	−3.28541	−	1.89683i	−0.119648	−	0.0690785i
$755$	60.6294			2.20653
$756$		0			0
$757$	50.3427			1.82974			0.914868	−	0.403752i	$-0.132294\pi$
$757$	50.3427			1.82974			0.914868	+	0.403752i	$0.132294\pi$
$758$	1.44364	+	0.833485i	0.0524353	+	0.0302735i
$759$		0			0
$760$	−17.2668	−	29.9070i	−0.626334	−	1.08484i
$761$	−30.3646			−1.10072			−0.550358	−	0.834929i	$-0.685509\pi$
$761$	−30.3646			−1.10072			−0.550358	+	0.834929i	$0.685509\pi$
$762$		0			0
$763$	−11.2030	−	2.46548i	−0.405577	−	0.0892564i
$764$			13.0895i			0.473562i
$765$		0			0
$766$	9.21448	+	5.31999i	0.332933	+	0.192219i
$767$		−	3.43621i		−	0.124074i
$768$		0			0
$769$	−35.8000	−	20.6692i	−1.29098	−	0.745349i	−0.312154	−	0.950032i	$-0.601050\pi$
$769$	−35.8000	−	20.6692i	−1.29098	−	0.745349i	−0.978828	+	0.204683i	$0.934384\pi$
$770$	−13.1685	−	2.89803i	−0.474560	−	0.104438i
$771$		0			0
$772$	13.9975	−	24.2443i	0.503780	−	0.872573i
$773$	6.99754	−	12.1201i	0.251684	−	0.435930i	−0.712305	−	0.701870i	$-0.752349\pi$
$773$	6.99754	−	12.1201i	0.251684	−	0.435930i	0.963990	+	0.265940i	$0.0856823\pi$
$774$		0			0
$775$	37.8382	−	21.8459i	1.35919	−	0.784728i
$776$	15.8792	+	27.5035i	0.570029	+	0.987319i
$777$		0			0
$778$	7.33216	−	12.6997i	0.262871	−	0.455305i
$779$			42.9166i			1.53765i
$780$		0			0
$781$	14.9819			0.536096
$782$	3.50734	+	6.07489i	0.125422	+	0.217238i
$783$		0			0
$784$	−1.01001	−	11.1473i	−0.0360718	−	0.398116i
$785$	−9.50018	+	5.48493i	−0.339076	+	0.195766i
$786$		0			0
$787$	−11.6799	+	6.74341i	−0.416344	+	0.240377i	−0.693512	−	0.720445i	$-0.743938\pi$
$787$	−11.6799	+	6.74341i	−0.416344	+	0.240377i	0.277168	+	0.960822i	$0.410604\pi$
$788$	20.5297	−	11.8528i	0.731340	−	0.422239i
$789$		0			0
$790$	−2.32258	+	1.34094i	−0.0826335	+	0.0477085i
$791$	−4.07161	+	18.5012i	−0.144770	+	0.657827i
$792$		0			0
$793$	−3.16531	−	5.48248i	−0.112403	−	0.194688i
$794$	21.4658			0.761794
$795$		0			0
$796$			13.5866i			0.481566i
$797$	−4.15867	+	7.20304i	−0.147308	+	0.255145i	−0.930232	−	0.366973i	$-0.880394\pi$
$797$	−4.15867	+	7.20304i	−0.147308	+	0.255145i	0.782924	+	0.622118i	$0.213727\pi$
$798$		0			0
$799$	3.17686	+	5.50249i	0.112389	+	0.194664i
$800$	−29.6590	+	17.1236i	−1.04860	+	0.605411i
$801$		0			0
$802$	9.49702	−	16.4493i	0.335351	−	0.580846i
$803$	12.5172	−	21.6804i	0.441721	−	0.765084i
$804$		0			0
$805$	78.4649	−	24.8734i	2.76552	−	0.876671i
$806$	6.57575	+	3.79651i	0.231621	+	0.133726i
$807$		0			0
$808$			32.1146i			1.12979i
$809$	12.5955	+	7.27200i	0.442833	+	0.255670i	0.704799	−	0.709407i	$-0.251037\pi$
$809$	12.5955	+	7.27200i	0.442833	+	0.255670i	−0.261965	+	0.965077i	$0.584371\pi$
$810$		0			0
$811$		−	41.8287i		−	1.46880i	−0.678715	−	0.734401i	$-0.737463\pi$
$811$		−	41.8287i		−	1.46880i	0.678715	−	0.734401i	$-0.262537\pi$
$812$	−3.26217	+	14.8231i	−0.114480	+	0.520190i
$813$		0			0
$814$	−7.95181			−0.278711
$815$	3.79804	+	6.57841i	0.133040	+	0.230432i
$816$		0			0
$817$	8.35327	+	4.82277i	0.292244	+	0.168727i
$818$	−0.689991			−0.0241250
$819$		0			0
$820$	50.1196			1.75025
$821$	40.2553	+	23.2414i	1.40492	+	0.811131i	0.994892	−	0.100942i	$-0.0321858\pi$
$821$	40.2553	+	23.2414i	1.40492	+	0.811131i	0.410027	+	0.912073i	$0.365519\pi$
$822$		0			0
$823$	−3.86834	−	6.70017i	−0.134842	−	0.233553i	0.790695	−	0.612210i	$-0.209719\pi$
$823$	−3.86834	−	6.70017i	−0.134842	−	0.233553i	−0.925537	+	0.378657i	$0.876386\pi$
$824$	11.4641			0.399369
$825$		0			0
$826$	3.60152	−	1.14168i	0.125313	−	0.0397242i
$827$		−	20.8898i		−	0.726409i	−0.931709	−	0.363205i	$-0.881683\pi$
$827$		−	20.8898i		−	0.726409i	0.931709	−	0.363205i	$-0.118317\pi$
$828$		0			0
$829$	41.2282	+	23.8031i	1.43191	+	0.826716i	0.997267	−	0.0738846i	$-0.0235396\pi$
$829$	41.2282	+	23.8031i	1.43191	+	0.826716i	0.434647	+	0.900601i	$0.356873\pi$
$830$			2.25628i			0.0783168i
$831$		0			0
$832$	−0.778382	−	0.449399i	−0.0269855	−	0.0155801i
$833$	−0.718383	−	7.92862i	−0.0248905	−	0.274710i
$834$		0			0
$835$	−4.41355	+	7.64450i	−0.152737	+	0.264549i
$836$	8.17887	−	14.1662i	0.282872	−	0.489949i
$837$		0			0
$838$	−1.77487	+	1.02472i	−0.0613118	+	0.0353984i
$839$	−11.2017	−	19.4020i	−0.386727	−	0.669831i	0.605280	−	0.796013i	$-0.293061\pi$
$839$	−11.2017	−	19.4020i	−0.386727	−	0.669831i	−0.992007	+	0.126181i	$0.959728\pi$
$840$		0			0
$841$	−7.81456	+	13.5352i	−0.269468	+	0.466732i
$842$			5.71690i			0.197017i
$843$		0			0
$844$	−22.8753			−0.787400
$845$	−17.3942	−	30.1277i	−0.598380	−	1.03642i
$846$		0			0
$847$	4.40407	+	13.8930i	0.151326	+	0.477368i
$848$	13.9168	−	8.03486i	0.477904	−	0.275918i
$849$		0			0
$850$	−3.86086	+	2.22907i	−0.132426	+	0.0764565i
$851$	42.0396	−	24.2715i	1.44110	−	0.832018i
$852$		0			0
$853$	41.9393	−	24.2136i	1.43597	−	0.829060i	0.438406	−	0.898777i	$-0.355543\pi$
$853$	41.9393	−	24.2136i	1.43597	−	0.829060i	0.997567	+	0.0697173i	$0.0222097\pi$
$854$	4.69455	−	5.13914i	0.160644	−	0.175858i
$855$		0			0
$856$	2.87484	+	4.97937i	0.0982600	+	0.170191i
$857$	49.0655			1.67605			0.838023	−	0.545636i	$-0.183712\pi$
$857$	49.0655			1.67605			0.838023	+	0.545636i	$0.183712\pi$
$858$		0			0
$859$		−	12.0245i		−	0.410272i	−0.978733	−	0.205136i	$-0.934236\pi$
$859$		−	12.0245i		−	0.410272i	0.978733	−	0.205136i	$-0.0657636\pi$
$860$	5.63221	−	9.75527i	0.192057	−	0.332652i
$861$		0			0
$862$	−8.95732	−	15.5145i	−0.305088	−	0.528427i
$863$	39.8804	−	23.0250i	1.35754	−	0.783779i	0.368252	−	0.929726i	$-0.379956\pi$
$863$	39.8804	−	23.0250i	1.35754	−	0.783779i	0.989292	+	0.145947i	$0.0466229\pi$
$864$		0			0
$865$	−4.24824	+	7.35817i	−0.144445	+	0.250185i
$866$	4.22572	−	7.31917i	0.143596	−	0.248715i
$867$		0			0
$868$	6.52923	−	29.6685i	0.221617	−	1.00702i
$869$	−2.50264	−	1.44490i	−0.0848961	−	0.0490148i
$870$		0			0
$871$			17.0119i			0.576426i
$872$	8.79893	+	5.08007i	0.297970	+	0.172033i
$873$		0			0
$874$		−	27.4430i		−	0.928275i
$875$	2.56818	+	8.10152i	0.0868203	+	0.273881i
$876$		0			0
$877$	13.4734			0.454964			0.227482	−	0.973782i	$-0.426951\pi$
$877$	13.4734			0.454964			0.227482	+	0.973782i	$0.426951\pi$
$878$	−6.05551	−	10.4884i	−0.204363	−	0.353968i
$879$		0			0
$880$	−10.7478	−	6.20524i	−0.362308	−	0.209179i
$881$	−25.5247			−0.859949			−0.429974	−	0.902841i	$-0.641477\pi$
$881$	−25.5247			−0.859949			−0.429974	+	0.902841i	$0.641477\pi$
$882$		0			0
$883$	6.45532			0.217239			0.108619	−	0.994083i	$-0.465357\pi$
$883$	6.45532			0.217239			0.108619	+	0.994083i	$0.465357\pi$
$884$	2.44147	+	1.40958i	0.0821156	+	0.0474094i
$885$		0			0
$886$	−0.942252	−	1.63203i	−0.0316556	−	0.0548291i
$887$	33.1208			1.11209			0.556043	−	0.831153i	$-0.312319\pi$
$887$	33.1208			1.11209			0.556043	+	0.831153i	$0.312319\pi$
$888$		0			0
$889$	−14.1563	−	44.6571i	−0.474786	−	1.49775i
$890$		−	16.2472i		−	0.544608i
$891$		0			0
$892$	−14.3790	−	8.30171i	−0.481444	−	0.277962i
$893$		−	24.8572i		−	0.831816i
$894$		0			0
$895$	39.6880	+	22.9139i	1.32662	+	0.765926i
$896$	−6.31193	+	28.6811i	−0.210867	+	0.958169i
$897$		0			0
$898$	−0.596459	+	1.03310i	−0.0199041	+	0.0344749i
$899$	−13.3809	+	23.1764i	−0.446278	+	0.772977i
$900$		0			0
$901$	9.89848	−	5.71489i	0.329766	−	0.190391i
$902$	−7.42084	−	12.8533i	−0.247087	−	0.427967i
$903$		0			0
$904$	8.38946	−	14.5310i	0.279029	−	0.483293i
$905$		−	15.6995i		−	0.521870i
$906$		0			0
$907$	6.21512			0.206370			0.103185	−	0.994662i	$-0.467097\pi$
$907$	6.21512			0.206370			0.103185	+	0.994662i	$0.467097\pi$
$908$	5.27446	+	9.13562i	0.175039	+	0.303176i
$909$		0			0
$910$	−6.13166	+	6.71234i	−0.203262	+	0.222512i
$911$	−15.6296	+	9.02376i	−0.517832	+	0.298970i	−0.736047	−	0.676930i	$-0.763310\pi$
$911$	−15.6296	+	9.02376i	−0.517832	+	0.298970i	0.218215	+	0.975901i	$0.429977\pi$
$912$		0			0
$913$	−2.10549	+	1.21560i	−0.0696814	+	0.0402306i
$914$	−3.50047	+	2.02100i	−0.115785	+	0.0668486i
$915$		0			0
$916$	−16.6613	+	9.61943i	−0.550506	+	0.317835i
$917$	−10.8768	−	34.3116i	−0.359182	−	1.13307i
$918$		0			0
$919$	4.12913	+	7.15186i	0.136207	+	0.235918i	0.926058	−	0.377381i	$-0.123175\pi$
$919$	4.12913	+	7.15186i	0.136207	+	0.235918i	−0.789851	+	0.613299i	$0.789842\pi$
$920$	−72.9057			−2.40363
$921$		0			0
$922$		−	11.1959i		−	0.368716i
$923$	5.05080	−	8.74824i	0.166249	−	0.287952i
$924$		0			0
$925$	15.4256	+	26.7180i	0.507192	+	0.878482i
$926$	−16.7258	+	9.65662i	−0.549642	+	0.317336i
$927$		0			0
$928$	10.4884	−	18.1665i	0.344300	−	0.596345i
$929$	−17.3855	+	30.1125i	−0.570399	+	0.987960i	0.426126	+	0.904664i	$0.359878\pi$
$929$	−17.3855	+	30.1125i	−0.570399	+	0.987960i	−0.996525	+	0.0832958i	$0.973455\pi$
$930$		0			0
$931$	−13.0753	+	28.2681i	−0.428527	+	0.926450i
$932$	7.64450	+	4.41355i	0.250404	+	0.144571i
$933$		0			0
$934$			17.8063i			0.582639i
$935$	−7.64450	−	4.41355i	−0.250002	−	0.144339i
$936$		0			0
$937$			51.0703i			1.66839i	0.551466	+	0.834197i	$0.314069\pi$
$937$			51.0703i			1.66839i	−0.551466	+	0.834197i	$0.685931\pi$
$938$	−17.8303	+	5.65220i	−0.582179	+	0.184551i
$939$		0			0
$940$	−29.0292			−0.946829
$941$	1.73872	+	3.01156i	0.0566807	+	0.0981739i	0.892974	−	0.450109i	$-0.148615\pi$
$941$	1.73872	+	3.01156i	0.0566807	+	0.0981739i	−0.836293	+	0.548283i	$0.815282\pi$
$942$		0			0
$943$	78.4649	+	45.3017i	2.55517	+	1.47523i
$944$	3.47744			0.113181
$945$		0			0
$946$	−3.33568			−0.108452
$947$	12.4189	+	7.17003i	0.403559	+	0.232995i	0.688018	−	0.725693i	$-0.258481\pi$
$947$	12.4189	+	7.17003i	0.403559	+	0.232995i	−0.284460	+	0.958688i	$0.591814\pi$
$948$		0			0
$949$	−8.43972	−	14.6180i	−0.273965	−	0.474521i
$950$	17.4413			0.565869
$951$		0			0
$952$	−1.51552	+	6.88647i	−0.0491184	+	0.223192i
$953$		−	7.53697i		−	0.244147i	−0.992521	−	0.122073i	$-0.961046\pi$
$953$		−	7.53697i		−	0.244147i	0.992521	−	0.122073i	$-0.0389543\pi$
$954$		0			0
$955$	−23.9317	−	13.8170i	−0.774411	−	0.447106i
$956$			25.0381i			0.809789i
$957$		0			0
$958$	−12.2583	−	7.07735i	−0.396049	−	0.228659i
$959$	25.6245	−	8.12297i	0.827459	−	0.262304i
$960$		0			0
$961$	11.2819	−	19.5408i	0.363932	−	0.630349i
$962$	−2.68076	+	4.64321i	−0.0864312	+	0.149703i
$963$		0			0
$964$	6.23363	−	3.59899i	0.200772	−	0.115916i
$965$	29.5508	+	51.1834i	0.951273	+	1.64765i
$966$		0			0
$967$	5.80807	−	10.0599i	0.186775	−	0.323503i	−0.757398	−	0.652953i	$-0.773530\pi$
$967$	5.80807	−	10.0599i	0.186775	−	0.323503i	0.944173	+	0.329450i	$0.106863\pi$
$968$		−	12.9087i		−	0.414901i
$969$		0			0
$970$	−29.4734			−0.946333
$971$	−17.7476	−	30.7397i	−0.569548	−	0.986485i	−0.996611	−	0.0822636i	$-0.973785\pi$
$971$	−17.7476	−	30.7397i	−0.569548	−	0.986485i	0.427063	−	0.904222i	$-0.359548\pi$
$972$		0			0
$973$	2.19193	−	9.96004i	0.0702702	−	0.319304i
$974$	8.29145	−	4.78707i	0.265675	−	0.153388i
$975$		0			0
$976$	5.54827	−	3.20329i	0.177596	−	0.102535i
$977$	−27.7210	+	16.0047i	−0.886873	+	0.512036i	−0.872918	−	0.487866i	$-0.837775\pi$
$977$	−27.7210	+	16.0047i	−0.886873	+	0.512036i	−0.0139546	+	0.999903i	$0.504442\pi$
$978$		0			0
$979$	15.1613	−	8.75340i	0.484559	−	0.279760i
$980$	33.0126	+	15.2699i	1.05455	+	0.487779i
$981$		0			0
$982$	−0.0929453	−	0.160986i	−0.00296600	−	0.00513727i
$983$	−49.4648			−1.57768			−0.788841	−	0.614598i	$-0.789318\pi$
$983$	−49.4648			−1.57768			−0.788841	+	0.614598i	$0.789318\pi$
$984$		0			0
$985$			50.0462i			1.59460i
$986$	1.36534	−	2.36483i	0.0434811	−	0.0753115i
$987$		0			0
$988$	−5.51462	−	9.55159i	−0.175443	−	0.303877i
$989$	17.6350	−	10.1816i	0.560761	−	0.323756i
$990$		0			0
$991$	−8.97590	+	15.5467i	−0.285129	+	0.493858i	−0.972640	−	0.232316i	$-0.925370\pi$
$991$	−8.97590	+	15.5467i	−0.285129	+	0.493858i	0.687511	+	0.726174i	$0.258703\pi$
$992$	−20.9926	+	36.3603i	−0.666517	+	1.15444i
$993$		0			0
$994$	10.8472	+	2.38718i	0.344053	+	0.0757167i
$995$	−24.8406	−	14.3417i	−0.787500	−	0.454663i
$996$		0			0
$997$			33.5037i			1.06107i	0.847662	+	0.530537i	$0.178010\pi$
$997$			33.5037i			1.06107i	−0.847662	+	0.530537i	$0.821990\pi$
$998$	6.99754	+	4.04003i	0.221503	+	0.127885i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.s.f.458.4		12
3.2	odd	2	inner	567.2.s.f.458.3		12
7.5	odd	6		567.2.i.f.215.3		12
9.2	odd	6		567.2.i.f.269.4		12
9.4	even	3		189.2.p.d.80.3	yes	12
9.5	odd	6		189.2.p.d.80.4	yes	12
9.7	even	3		567.2.i.f.269.3		12
21.5	even	6		567.2.i.f.215.4		12
63.4	even	3		1323.2.c.d.1322.6		12
63.5	even	6		189.2.p.d.26.3	✓	12
63.31	odd	6		1323.2.c.d.1322.5		12
63.32	odd	6		1323.2.c.d.1322.7		12
63.40	odd	6		189.2.p.d.26.4	yes	12
63.47	even	6	inner	567.2.s.f.26.4		12
63.59	even	6		1323.2.c.d.1322.8		12
63.61	odd	6	inner	567.2.s.f.26.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.p.d.26.3	✓	12	63.5	even	6
189.2.p.d.26.4	yes	12	63.40	odd	6
189.2.p.d.80.3	yes	12	9.4	even	3
189.2.p.d.80.4	yes	12	9.5	odd	6
567.2.i.f.215.3		12	7.5	odd	6
567.2.i.f.215.4		12	21.5	even	6
567.2.i.f.269.3		12	9.7	even	3
567.2.i.f.269.4		12	9.2	odd	6
567.2.s.f.26.3		12	63.61	odd	6	inner
567.2.s.f.26.4		12	63.47	even	6	inner
567.2.s.f.458.3		12	3.2	odd	2	inner
567.2.s.f.458.4		12	1.1	even	1	trivial
1323.2.c.d.1322.5		12	63.31	odd	6
1323.2.c.d.1322.6		12	63.4	even	3
1323.2.c.d.1322.7		12	63.32	odd	6
1323.2.c.d.1322.8		12	63.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.568650 + 0.328310i) q^{2} +(-0.784425 - 1.35866i) q^{4} +3.31208 q^{5} +(0.799494 + 2.52206i) q^{7} -2.34338i q^{8} +O(q^{10})\)	\(q+(0.568650 + 0.328310i) q^{2} +(-0.784425 - 1.35866i) q^{4} +3.31208 q^{5} +(0.799494 + 2.52206i) q^{7} -2.34338i q^{8} +(1.88341 + 1.08739i) q^{10} +2.34338i q^{11} +(1.36834 + 0.790014i) q^{13} +(-0.373387 + 1.69665i) q^{14} +(-0.799494 + 1.38476i) q^{16} +(-0.568650 + 0.984931i) q^{17} +(3.85327 - 2.22469i) q^{19} +(-2.59808 - 4.50000i) q^{20} +(-0.769355 + 1.33256i) q^{22} -9.39331i q^{23} +5.96986 q^{25} +(0.518739 + 0.898482i) q^{26} +(2.79949 - 3.06461i) q^{28} +(-3.16673 + 1.82831i) q^{29} +(6.33821 - 3.65936i) q^{31} +(-4.96812 + 2.86834i) q^{32} +(-0.646726 + 0.373387i) q^{34} +(2.64799 + 8.35327i) q^{35} +(2.58392 + 4.47548i) q^{37} +2.92155 q^{38} -7.76146i q^{40} +(-4.82277 + 8.35327i) q^{41} +(1.08392 + 1.87740i) q^{43} +(3.18386 - 1.83821i) q^{44} +(3.08392 - 5.34150i) q^{46} +(2.79334 - 4.83821i) q^{47} +(-5.72162 + 4.03275i) q^{49} +(3.39476 + 1.95997i) q^{50} -2.47883i q^{52} +(-8.70349 - 5.02496i) q^{53} +7.76146i q^{55} +(5.91015 - 1.87352i) q^{56} -2.40101 q^{58} +(-1.08739 - 1.88341i) q^{59} +(-3.46986 - 2.00333i) q^{61} +4.80563 q^{62} -0.568850 q^{64} +(4.53206 + 2.61659i) q^{65} +(5.38341 + 9.32435i) q^{67} +1.78425 q^{68} +(-1.23669 + 5.61945i) q^{70} -6.39331i q^{71} +(-9.25176 - 5.34150i) q^{73} +3.39331i q^{74} +(-6.04521 - 3.49020i) q^{76} +(-5.91015 + 1.87352i) q^{77} +(-0.616587 + 1.06796i) q^{79} +(-2.64799 + 4.58645i) q^{80} +(-5.48493 + 3.16673i) q^{82} +(0.518739 + 0.898482i) q^{83} +(-1.88341 + 3.26217i) q^{85} +1.42345i q^{86} +5.49143 q^{88} +(-3.73538 - 6.46986i) q^{89} +(-0.898482 + 4.08266i) q^{91} +(-12.7623 + 7.36834i) q^{92} +(3.17686 - 1.83416i) q^{94} +(12.7623 - 7.36834i) q^{95} +(-11.7367 + 6.77618i) q^{97} +(-4.57759 + 0.414758i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 8 q^{4} + 4 q^{7}+O(q^{10}) \) 12 * q + 8 * q^4 + 4 * q^7	\( 12 q + 8 q^{4} + 4 q^{7} - 6 q^{10} - 24 q^{13} - 4 q^{16} - 6 q^{19} + 20 q^{22} + 48 q^{25} + 28 q^{28} + 12 q^{31} - 60 q^{34} + 8 q^{37} - 10 q^{43} + 14 q^{46} + 24 q^{49} - 40 q^{58} - 18 q^{61} + 28 q^{64} + 36 q^{67} + 66 q^{70} - 42 q^{73} - 108 q^{76} - 36 q^{79} - 54 q^{82} + 6 q^{85} + 148 q^{88} + 6 q^{91} + 114 q^{94} - 60 q^{97}+O(q^{100}) \) 12 * q + 8 * q^4 + 4 * q^7 - 6 * q^10 - 24 * q^13 - 4 * q^16 - 6 * q^19 + 20 * q^22 + 48 * q^25 + 28 * q^28 + 12 * q^31 - 60 * q^34 + 8 * q^37 - 10 * q^43 + 14 * q^46 + 24 * q^49 - 40 * q^58 - 18 * q^61 + 28 * q^64 + 36 * q^67 + 66 * q^70 - 42 * q^73 - 108 * q^76 - 36 * q^79 - 54 * q^82 + 6 * q^85 + 148 * q^88 + 6 * q^91 + 114 * q^94 - 60 * q^97

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