LMFDB - Embedded newform 432.2.u.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 $ x^18 - 6x^17 + 24x^16 - 66x^15 + 153x^14 - 315x^13 + 651x^12 - 1350x^11 + 2700x^10 - 4941x^9 + 8100x^8 - 12150x^7 + 17577x^6 - 25515x^5 + 37179x^4 - 48114x^3 + 52488x^2 - 39366*x + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.1
Root			$-0.219955 + 1.71803i$ of defining polynomial
Character	$\chi$	$=$	432.49
Dual form			432.2.u.d.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.27282 + 1.17470i) q^{3} +(0.0952805 - 0.0346793i) q^{5} +(-0.165033 - 0.935950i) q^{7} +(0.240153 - 2.99037i) q^{9} +O(q^{10})$	\(q+(-1.27282 + 1.17470i) q^{3} +(0.0952805 - 0.0346793i) q^{5} +(-0.165033 - 0.935950i) q^{7} +(0.240153 - 2.99037i) q^{9} +(3.80173 + 1.38372i) q^{11} +(3.80098 + 3.18940i) q^{13} +(-0.0805374 + 0.156067i) q^{15} +(-3.11489 + 5.39515i) q^{17} +(0.514575 + 0.891271i) q^{19} +(1.30952 + 0.997433i) q^{21} +(-0.602747 + 3.41835i) q^{23} +(-3.82235 + 3.20733i) q^{25} +(3.20712 + 4.08832i) q^{27} +(-3.04952 + 2.55885i) q^{29} +(0.740609 - 4.20021i) q^{31} +(-6.46439 + 2.70467i) q^{33} +(-0.0481825 - 0.0834545i) q^{35} +(4.19601 - 7.26771i) q^{37} +(-8.58456 + 0.405477i) q^{39} +(2.15010 + 1.80415i) q^{41} +(6.32526 + 2.30221i) q^{43} +(-0.0808221 - 0.293253i) q^{45} +(1.35821 + 7.70280i) q^{47} +(5.72908 - 2.08522i) q^{49} +(-2.37299 - 10.5261i) q^{51} +12.9766 q^{53} +0.410217 q^{55} +(-1.70194 - 0.529957i) q^{57} +(-13.3926 + 4.87451i) q^{59} +(-0.469802 - 2.66438i) q^{61} +(-2.83847 + 0.268740i) q^{63} +(0.472765 + 0.172073i) q^{65} +(2.53622 + 2.12814i) q^{67} +(-3.24835 - 5.05900i) q^{69} +(7.26233 - 12.5787i) q^{71} +(-5.82171 - 10.0835i) q^{73} +(1.09751 - 8.57248i) q^{75} +(0.667678 - 3.78659i) q^{77} +(0.981804 - 0.823832i) q^{79} +(-8.88465 - 1.43629i) q^{81} +(-4.02663 + 3.37874i) q^{83} +(-0.109689 + 0.622075i) q^{85} +(0.875611 - 6.83924i) q^{87} +(-4.80559 - 8.32353i) q^{89} +(2.35783 - 4.08388i) q^{91} +(3.99132 + 6.21611i) q^{93} +(0.0799376 + 0.0670756i) q^{95} +(-3.70829 - 1.34971i) q^{97} +(5.05083 - 11.0363i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) $ 18 * q + 3 * q^5 + 6 * q^9	$ 18 q + 3 q^{5} + 6 q^{9} - 3 q^{11} + 9 q^{15} - 12 q^{17} - 30 q^{21} + 30 q^{23} + 9 q^{25} + 27 q^{27} - 24 q^{29} - 9 q^{31} - 18 q^{33} + 21 q^{35} - 3 q^{39} + 21 q^{41} + 9 q^{43} + 45 q^{45} - 45 q^{47} - 18 q^{49} - 63 q^{51} + 66 q^{53} + 54 q^{57} - 60 q^{59} - 18 q^{61} - 57 q^{63} + 33 q^{65} + 27 q^{67} - 9 q^{69} + 12 q^{71} + 9 q^{73} + 33 q^{75} - 75 q^{77} + 36 q^{79} - 54 q^{81} + 45 q^{83} - 36 q^{85} + 63 q^{87} - 48 q^{89} - 9 q^{91} - 33 q^{93} - 6 q^{95} - 27 q^{97} - 27 q^{99}+O(q^{100}) $ 18 * q + 3 * q^5 + 6 * q^9 - 3 * q^11 + 9 * q^15 - 12 * q^17 - 30 * q^21 + 30 * q^23 + 9 * q^25 + 27 * q^27 - 24 * q^29 - 9 * q^31 - 18 * q^33 + 21 * q^35 - 3 * q^39 + 21 * q^41 + 9 * q^43 + 45 * q^45 - 45 * q^47 - 18 * q^49 - 63 * q^51 + 66 * q^53 + 54 * q^57 - 60 * q^59 - 18 * q^61 - 57 * q^63 + 33 * q^65 + 27 * q^67 - 9 * q^69 + 12 * q^71 + 9 * q^73 + 33 * q^75 - 75 * q^77 + 36 * q^79 - 54 * q^81 + 45 * q^83 - 36 * q^85 + 63 * q^87 - 48 * q^89 - 9 * q^91 - 33 * q^93 - 6 * q^95 - 27 * q^97 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.27282	+	1.17470i	−0.734864	+	0.678214i
$3$	−1.27282	+	1.17470i	−0.734864	+	0.678214i
$4$		0			0
$5$	0.0952805	−	0.0346793i	0.0426107	−	0.0155090i	−0.320627	−	0.947206i	$-0.603894\pi$
$5$	0.0952805	−	0.0346793i	0.0426107	−	0.0155090i	0.363238	+	0.931697i	$0.381671\pi$
$6$		0			0
$7$	−0.165033	−	0.935950i	−0.0623767	−	0.353756i	−0.999982	−	0.00605342i	$-0.998073\pi$
$7$	−0.165033	−	0.935950i	−0.0623767	−	0.353756i	0.937605	−	0.347702i	$-0.113038\pi$
$8$		0			0
$9$	0.240153	−	2.99037i	0.0800509	−	0.996791i
$10$		0			0
$11$	3.80173	+	1.38372i	1.14627	+	0.417207i	0.844172	−	0.536072i	$-0.180092\pi$
$11$	3.80173	+	1.38372i	1.14627	+	0.417207i	0.302093	+	0.953278i	$0.402315\pi$
$12$		0			0
$13$	3.80098	+	3.18940i	1.05420	+	0.884581i	0.993529	−	0.113577i	$-0.0362309\pi$
$13$	3.80098	+	3.18940i	1.05420	+	0.884581i	0.0606729	+	0.998158i	$0.480675\pi$
$14$		0			0
$15$	−0.0805374	+	0.156067i	−0.0207947	+	0.0402963i
$16$		0			0
$17$	−3.11489	+	5.39515i	−0.755473	+	1.30852i	0.189667	+	0.981849i	$0.439259\pi$
$17$	−3.11489	+	5.39515i	−0.755473	+	1.30852i	−0.945139	+	0.326668i	$0.894074\pi$
$18$		0			0
$19$	0.514575	+	0.891271i	0.118052	+	0.204471i	0.918996	−	0.394268i	$-0.129002\pi$
$19$	0.514575	+	0.891271i	0.118052	+	0.204471i	−0.800944	+	0.598739i	$0.795668\pi$
$20$		0			0
$21$	1.30952	+	0.997433i	0.285761	+	0.217658i
$22$		0			0
$23$	−0.602747	+	3.41835i	−0.125681	+	0.712775i	0.855219	+	0.518266i	$0.173422\pi$
$23$	−0.602747	+	3.41835i	−0.125681	+	0.712775i	−0.980901	+	0.194509i	$0.937689\pi$
$24$		0			0
$25$	−3.82235	+	3.20733i	−0.764469	+	0.641466i
$26$		0			0
$27$	3.20712	+	4.08832i	0.617211	+	0.786798i
$28$		0			0
$29$	−3.04952	+	2.55885i	−0.566282	+	0.475167i	−0.880410	−	0.474214i	$-0.842732\pi$
$29$	−3.04952	+	2.55885i	−0.566282	+	0.475167i	0.314128	+	0.949381i	$0.398288\pi$
$30$		0			0
$31$	0.740609	−	4.20021i	0.133017	−	0.754379i	−0.843202	−	0.537596i	$-0.819333\pi$
$31$	0.740609	−	4.20021i	0.133017	−	0.754379i	0.976220	−	0.216783i	$-0.0695564\pi$
$32$		0			0
$33$	−6.46439	+	2.70467i	−1.12531	+	0.470823i
$34$		0			0
$35$	−0.0481825	−	0.0834545i	−0.00814433	−	0.0141064i
$36$		0			0
$37$	4.19601	−	7.26771i	0.689820	−	1.19480i	−0.282076	−	0.959392i	$-0.591023\pi$
$37$	4.19601	−	7.26771i	0.689820	−	1.19480i	0.971896	−	0.235411i	$-0.0756438\pi$
$38$		0			0
$39$	−8.58456	+	0.405477i	−1.37463	+	0.0649282i
$40$		0			0
$41$	2.15010	+	1.80415i	0.335790	+	0.281761i	0.795054	−	0.606539i	$-0.207443\pi$
$41$	2.15010	+	1.80415i	0.335790	+	0.281761i	−0.459264	+	0.888300i	$0.651887\pi$
$42$		0			0
$43$	6.32526	+	2.30221i	0.964593	+	0.351083i	0.775832	−	0.630940i	$-0.217330\pi$
$43$	6.32526	+	2.30221i	0.964593	+	0.351083i	0.188761	+	0.982023i	$0.439553\pi$
$44$		0			0
$45$	−0.0808221	−	0.293253i	−0.0120482	−	0.0437155i
$46$		0			0
$47$	1.35821	+	7.70280i	0.198115	+	1.12357i	0.907912	+	0.419161i	$0.137676\pi$
$47$	1.35821	+	7.70280i	0.198115	+	1.12357i	−0.709796	+	0.704407i	$0.751213\pi$
$48$		0			0
$49$	5.72908	−	2.08522i	0.818440	−	0.297888i
$50$		0			0
$51$	−2.37299	−	10.5261i	−0.332285	−	1.47395i
$52$		0			0
$53$	12.9766			1.78248			0.891238	−	0.453536i	$-0.149838\pi$
$53$	12.9766			1.78248			0.891238	+	0.453536i	$0.149838\pi$
$54$		0			0
$55$	0.410217			0.0553137
$56$		0			0
$57$	−1.70194	−	0.529957i	−0.225427	−	0.0701945i
$58$		0			0
$59$	−13.3926	+	4.87451i	−1.74357	+	0.634608i	−0.999441	−	0.0334278i	$-0.989358\pi$
$59$	−13.3926	+	4.87451i	−1.74357	+	0.634608i	−0.744129	+	0.668036i	$0.767135\pi$
$60$		0			0
$61$	−0.469802	−	2.66438i	−0.0601519	−	0.341139i	0.939848	−	0.341593i	$-0.110966\pi$
$61$	−0.469802	−	2.66438i	−0.0601519	−	0.341139i	−1.00000		0.000454456i	$0.999855\pi$
$62$		0			0
$63$	−2.83847	+	0.268740i	−0.357614	+	0.0338580i
$64$		0			0
$65$	0.472765	+	0.172073i	0.0586393	+	0.0213430i
$66$		0			0
$67$	2.53622	+	2.12814i	0.309849	+	0.259994i	0.784430	−	0.620218i	$-0.212956\pi$
$67$	2.53622	+	2.12814i	0.309849	+	0.259994i	−0.474581	+	0.880212i	$0.657400\pi$
$68$		0			0
$69$	−3.24835	−	5.05900i	−0.391055	−	0.609032i
$70$		0			0
$71$	7.26233	−	12.5787i	0.861880	−	1.49282i	−0.00823275	−	0.999966i	$-0.502621\pi$
$71$	7.26233	−	12.5787i	0.861880	−	1.49282i	0.870112	−	0.492853i	$-0.164046\pi$
$72$		0			0
$73$	−5.82171	−	10.0835i	−0.681379	−	1.18018i	−0.974560	−	0.224127i	$-0.928047\pi$
$73$	−5.82171	−	10.0835i	−0.681379	−	1.18018i	0.293181	−	0.956057i	$-0.405286\pi$
$74$		0			0
$75$	1.09751	−	8.57248i	0.126730	−	0.989864i
$76$		0			0
$77$	0.667678	−	3.78659i	0.0760890	−	0.431522i
$78$		0			0
$79$	0.981804	−	0.823832i	0.110462	−	0.0926883i	−0.585884	−	0.810395i	$-0.699253\pi$
$79$	0.981804	−	0.823832i	0.110462	−	0.0926883i	0.696346	+	0.717707i	$0.254808\pi$
$80$		0			0
$81$	−8.88465	−	1.43629i	−0.987184	−	0.159588i
$82$		0			0
$83$	−4.02663	+	3.37874i	−0.441980	+	0.370865i	−0.836450	−	0.548044i	$-0.815373\pi$
$83$	−4.02663	+	3.37874i	−0.441980	+	0.370865i	0.394470	+	0.918909i	$0.370928\pi$
$84$		0			0
$85$	−0.109689	+	0.622075i	−0.0118974	+	0.0674735i
$86$		0			0
$87$	0.875611	−	6.83924i	0.0938754	−	0.733244i
$88$		0			0
$89$	−4.80559	−	8.32353i	−0.509392	−	0.882292i	−0.999941	−	0.0108788i	$-0.996537\pi$
$89$	−4.80559	−	8.32353i	−0.509392	−	0.882292i	0.490549	−	0.871414i	$-0.336796\pi$
$90$		0			0
$91$	2.35783	−	4.08388i	0.247168	−	0.428107i
$92$		0			0
$93$	3.99132	+	6.21611i	0.413881	+	0.644581i
$94$		0			0
$95$	0.0799376	+	0.0670756i	0.00820143	+	0.00688181i
$96$		0			0
$97$	−3.70829	−	1.34971i	−0.376520	−	0.137042i	0.146826	−	0.989162i	$-0.453094\pi$
$97$	−3.70829	−	1.34971i	−0.376520	−	0.137042i	−0.523346	+	0.852120i	$0.675317\pi$
$98$		0			0
$99$	5.05083	−	11.0363i	0.507627	−	1.10919i
$100$		0			0
$101$	1.61478	+	9.15788i	0.160677	+	0.911243i	0.953411	+	0.301675i	$0.0975459\pi$
$101$	1.61478	+	9.15788i	0.160677	+	0.911243i	−0.792734	+	0.609568i	$0.791343\pi$
$102$		0			0
$103$	8.22478	−	2.99358i	0.810412	−	0.294966i	0.0966179	−	0.995322i	$-0.469198\pi$
$103$	8.22478	−	2.99358i	0.810412	−	0.294966i	0.713794	+	0.700356i	$0.246975\pi$
$104$		0			0
$105$	0.159362	+	0.0496227i	0.0155521	+	0.00484268i
$106$		0			0
$107$	−10.0129			−0.967983			−0.483992	−	0.875073i	$-0.660813\pi$
$107$	−10.0129			−0.967983			−0.483992	+	0.875073i	$0.660813\pi$
$108$		0			0
$109$	1.78337			0.170816			0.0854081	−	0.996346i	$-0.472781\pi$
$109$	1.78337			0.170816			0.0854081	+	0.996346i	$0.472781\pi$
$110$		0			0
$111$	3.19661	+	14.1796i	0.303409	+	1.34586i
$112$		0			0
$113$	−12.0960	+	4.40258i	−1.13789	+	0.414159i	−0.841152	−	0.540798i	$-0.818122\pi$
$113$	−12.0960	+	4.40258i	−1.13789	+	0.414159i	−0.296742	+	0.954958i	$0.595900\pi$
$114$		0			0
$115$	0.0611158	+	0.346605i	0.00569907	+	0.0323211i
$116$		0			0
$117$	10.4503	−	10.6004i	0.966132	−	0.980007i
$118$		0			0
$119$	5.56365	+	2.02500i	0.510019	+	0.185632i
$120$		0			0
$121$	4.11201	+	3.45039i	0.373819	+	0.313671i
$122$		0			0
$123$	−4.85604	+	0.229366i	−0.437854	+	0.0206812i
$124$		0			0
$125$	−0.506456	+	0.877207i	−0.0452988	+	0.0784598i
$126$		0			0
$127$	−6.79053	−	11.7615i	−0.602562	−	1.04367i	−0.992432	−	0.122798i	$-0.960813\pi$
$127$	−6.79053	−	11.7615i	−0.602562	−	1.04367i	0.389869	−	0.920870i	$-0.372520\pi$
$128$		0			0
$129$	−10.7553	+	4.49999i	−0.946955	+	0.396202i
$130$		0			0
$131$	1.98908	−	11.2806i	0.173787	−	0.985593i	−0.765749	−	0.643140i	$-0.777631\pi$
$131$	1.98908	−	11.2806i	0.173787	−	0.985593i	0.939535	−	0.342453i	$-0.111258\pi$
$132$		0			0
$133$	0.749262	−	0.628706i	0.0649693	−	0.0545157i
$134$		0			0
$135$	0.447356	+	0.278317i	0.0385023	+	0.0239537i
$136$		0			0
$137$	0.126752	−	0.106358i	0.0108292	−	0.00908675i	−0.637357	−	0.770569i	$-0.719972\pi$
$137$	0.126752	−	0.106358i	0.0108292	−	0.00908675i	0.648186	+	0.761482i	$0.275528\pi$
$138$		0			0
$139$	−2.00785	+	11.3871i	−0.170303	+	0.965838i	0.773123	+	0.634256i	$0.218693\pi$
$139$	−2.00785	+	11.3871i	−0.170303	+	0.965838i	−0.943426	+	0.331582i	$0.892418\pi$
$140$		0			0
$141$	−10.7772	−	8.20880i	−0.907608	−	0.691306i
$142$		0			0
$143$	10.0371	+	17.3847i	0.839343	+	1.45378i
$144$		0			0
$145$	−0.201821	+	0.349564i	−0.0167603	+	0.0290297i
$146$		0			0
$147$	−4.84260	+	9.38407i	−0.399411	+	0.773985i
$148$		0			0
$149$	−5.39198	−	4.52441i	−0.441728	−	0.370654i	0.394627	−	0.918841i	$-0.370874\pi$
$149$	−5.39198	−	4.52441i	−0.441728	−	0.370654i	−0.836356	+	0.548187i	$0.815318\pi$
$150$		0			0
$151$	−20.2664	−	7.37636i	−1.64925	−	0.600280i	−0.660634	−	0.750708i	$-0.729712\pi$
$151$	−20.2664	−	7.37636i	−1.64925	−	0.600280i	−0.988621	+	0.150428i	$0.951935\pi$
$152$		0			0
$153$	15.3855	+	10.6104i	1.24384	+	0.857796i
$154$		0			0
$155$	−0.0750944	−	0.425882i	−0.00603173	−	0.0342076i
$156$		0			0
$157$	2.74695	−	0.999806i	0.219230	−	0.0797932i	−0.230070	−	0.973174i	$-0.573896\pi$
$157$	2.74695	−	0.999806i	0.219230	−	0.0797932i	0.449300	+	0.893381i	$0.351673\pi$
$158$		0			0
$159$	−16.5169	+	15.2437i	−1.30988	+	1.20890i
$160$		0			0
$161$	3.29887			0.259988
$162$		0			0
$163$	3.59864			0.281867			0.140933	−	0.990019i	$-0.454990\pi$
$163$	3.59864			0.281867			0.140933	+	0.990019i	$0.454990\pi$
$164$		0			0
$165$	−0.522134	+	0.481883i	−0.0406481	+	0.0375145i
$166$		0			0
$167$	4.31965	−	1.57223i	0.334265	−	0.121662i	−0.169435	−	0.985541i	$-0.554194\pi$
$167$	4.31965	−	1.57223i	0.334265	−	0.121662i	0.503699	+	0.863879i	$0.331972\pi$
$168$		0			0
$169$	2.01774	+	11.4432i	0.155211	+	0.880245i
$170$		0			0
$171$	2.78881	−	1.32473i	0.213265	−	0.101305i
$172$		0			0
$173$	14.9790	+	5.45191i	1.13883	+	0.414501i	0.841492	−	0.540270i	$-0.181678\pi$
$173$	14.9790	+	5.45191i	1.13883	+	0.414501i	0.297341	+	0.954771i	$0.403900\pi$
$174$		0			0
$175$	3.63271	+	3.04821i	0.274607	+	0.230423i
$176$		0			0
$177$	11.3203	−	21.9367i	0.850888	−	1.64886i
$178$		0			0
$179$	7.15473	−	12.3924i	0.534770	−	0.926248i	−0.464405	−	0.885623i	$-0.653732\pi$
$179$	7.15473	−	12.3924i	0.534770	−	0.926248i	0.999174	−	0.0406251i	$-0.0129349\pi$
$180$		0			0
$181$	8.02539	+	13.9004i	0.596523	+	1.03321i	0.993330	+	0.115306i	$0.0367848\pi$
$181$	8.02539	+	13.9004i	0.596523	+	1.03321i	−0.396807	+	0.917902i	$0.629882\pi$
$182$		0			0
$183$	3.72782	+	2.83940i	0.275569	+	0.209895i
$184$		0			0
$185$	0.147759	−	0.837986i	0.0108635	−	0.0616099i
$186$		0			0
$187$	−19.3074	+	16.2008i	−1.41189	+	1.18472i
$188$		0			0
$189$	3.29718	−	3.67641i	0.239835	−	0.267420i
$190$		0			0
$191$	3.74040	−	3.13857i	0.270646	−	0.227099i	−0.497356	−	0.867547i	$-0.665696\pi$
$191$	3.74040	−	3.13857i	0.270646	−	0.227099i	0.768002	+	0.640448i	$0.221251\pi$
$192$		0			0
$193$	−1.05629	+	5.99052i	−0.0760334	+	0.431207i	0.922900	+	0.385039i	$0.125812\pi$
$193$	−1.05629	+	5.99052i	−0.0760334	+	0.431207i	−0.998934	+	0.0461679i	$0.985299\pi$
$194$		0			0
$195$	−0.803880	+	0.336340i	−0.0575671	+	0.0240858i
$196$		0			0
$197$	−9.98715	−	17.2982i	−0.711555	−	1.23245i	−0.964273	−	0.264909i	$-0.914658\pi$
$197$	−9.98715	−	17.2982i	−0.711555	−	1.23245i	0.252718	−	0.967540i	$-0.418675\pi$
$198$		0			0
$199$	8.70822	−	15.0831i	0.617310	−	1.06921i	−0.372665	−	0.927966i	$-0.621556\pi$
$199$	8.70822	−	15.0831i	0.617310	−	1.06921i	0.989975	−	0.141246i	$-0.0451107\pi$
$200$		0			0
$201$	−5.72810	+	0.270556i	−0.404029	+	0.0190836i
$202$		0			0
$203$	2.89823	+	2.43190i	0.203416	+	0.170686i
$204$		0			0
$205$	0.267429	+	0.0973364i	0.0186781	+	0.00679827i
$206$		0			0
$207$	10.0774	+	2.62336i	0.700426	+	0.182336i
$208$		0			0
$209$	0.723011	+	4.10040i	0.0500117	+	0.283631i
$210$		0			0
$211$	6.96424	−	2.53478i	0.479438	−	0.174501i	−0.0909850	−	0.995852i	$-0.529002\pi$
$211$	6.96424	−	2.53478i	0.479438	−	0.174501i	0.570423	+	0.821351i	$0.306779\pi$
$212$		0			0
$213$	5.53259	+	24.5415i	0.379087	+	1.68156i
$214$		0			0
$215$	0.682513			0.0465470
$216$		0			0
$217$	−4.05341			−0.275163
$218$		0			0
$219$	19.2551	+	5.99573i	1.30114	+	0.405154i
$220$		0			0
$221$	−29.0469	+	10.5722i	−1.95391	+	0.711165i
$222$		0			0
$223$	2.23768	+	12.6905i	0.149846	+	0.849821i	0.963347	+	0.268257i	$0.0864477\pi$
$223$	2.23768	+	12.6905i	0.149846	+	0.849821i	−0.813501	+	0.581563i	$0.802441\pi$
$224$		0			0
$225$	8.67316	+	12.2005i	0.578211	+	0.813366i
$226$		0			0
$227$	−9.98946	−	3.63586i	−0.663023	−	0.241321i	−0.0114823	−	0.999934i	$-0.503655\pi$
$227$	−9.98946	−	3.63586i	−0.663023	−	0.241321i	−0.651541	+	0.758613i	$0.725877\pi$
$228$		0			0
$229$	−12.8689	−	10.7983i	−0.850403	−	0.713573i	0.109475	−	0.993990i	$-0.465083\pi$
$229$	−12.8689	−	10.7983i	−0.850403	−	0.713573i	−0.959878	+	0.280416i	$0.909527\pi$
$230$		0			0
$231$	3.59828	+	5.60398i	0.236749	+	0.368715i
$232$		0			0
$233$	9.06792	−	15.7061i	0.594059	−	1.02894i	−0.399619	−	0.916681i	$-0.630858\pi$
$233$	9.06792	−	15.7061i	0.594059	−	1.02894i	0.993679	−	0.112260i	$-0.0358090\pi$
$234$		0			0
$235$	0.396538	+	0.686825i	0.0258673	+	0.0448035i
$236$		0			0
$237$	−0.281906	+	2.20192i	−0.0183118	+	0.143030i
$238$		0			0
$239$	2.76646	−	15.6894i	0.178948	−	1.01486i	−0.754540	−	0.656254i	$-0.772140\pi$
$239$	2.76646	−	15.6894i	0.178948	−	1.01486i	0.933488	−	0.358609i	$-0.116749\pi$
$240$		0			0
$241$	−7.58708	+	6.36631i	−0.488727	+	0.410090i	−0.853570	−	0.520979i	$-0.825567\pi$
$241$	−7.58708	+	6.36631i	−0.488727	+	0.410090i	0.364843	+	0.931069i	$0.381123\pi$
$242$		0			0
$243$	12.9958	−	8.60867i	0.833681	−	0.552247i
$244$		0			0
$245$	0.473556	−	0.397361i	0.0302544	−	0.0253865i
$246$		0			0
$247$	−0.886729	+	5.02889i	−0.0564212	+	0.319980i
$248$		0			0
$249$	1.15617	−	9.03063i	0.0732692	−	0.572293i
$250$		0			0
$251$	1.14125	+	1.97671i	0.0720352	+	0.124769i	0.899793	−	0.436317i	$-0.143717\pi$
$251$	1.14125	+	1.97671i	0.0720352	+	0.124769i	−0.827758	+	0.561085i	$0.810384\pi$
$252$		0			0
$253$	−7.02151	+	12.1616i	−0.441439	+	0.764594i
$254$		0			0
$255$	−0.591138	−	0.920642i	−0.0370185	−	0.0576529i
$256$		0			0
$257$	8.93557	+	7.49783i	0.557385	+	0.467702i	0.877433	−	0.479700i	$-0.159254\pi$
$257$	8.93557	+	7.49783i	0.557385	+	0.467702i	−0.320047	+	0.947402i	$0.603699\pi$
$258$		0			0
$259$	−7.49469	−	2.72784i	−0.465697	−	0.169500i
$260$		0			0
$261$	6.91957	+	9.73372i	0.428311	+	0.602502i
$262$		0			0
$263$	0.305939	+	1.73507i	0.0188650	+	0.106989i	0.992786	−	0.119897i	$-0.0382566\pi$
$263$	0.305939	+	1.73507i	0.0188650	+	0.106989i	−0.973921	+	0.226886i	$0.927145\pi$
$264$		0			0
$265$	1.23642	−	0.450020i	0.0759526	−	0.0276445i
$266$		0			0
$267$	15.8943	+	4.94924i	0.972717	+	0.302888i
$268$		0			0
$269$	13.3454			0.813683			0.406842	−	0.913499i	$-0.366630\pi$
$269$	13.3454			0.813683			0.406842	+	0.913499i	$0.366630\pi$
$270$		0			0
$271$	−12.4524			−0.756430			−0.378215	−	0.925718i	$-0.623462\pi$
$271$	−12.4524			−0.756430			−0.378215	+	0.925718i	$0.623462\pi$
$272$		0			0
$273$	1.79624	+	7.96780i	0.108714	+	0.482233i
$274$		0			0
$275$	−18.9696	+	6.90436i	−1.14391	+	0.416349i
$276$		0			0
$277$	0.895322	+	5.07762i	0.0537947	+	0.305085i	0.999819	−	0.0190101i	$-0.00605145\pi$
$277$	0.895322	+	5.07762i	0.0537947	+	0.305085i	−0.946025	+	0.324095i	$0.894940\pi$
$278$		0			0
$279$	−12.3823	−	3.22339i	−0.741310	−	0.192979i
$280$		0			0
$281$	7.40344	+	2.69463i	0.441652	+	0.160748i	0.553268	−	0.833003i	$-0.313380\pi$
$281$	7.40344	+	2.69463i	0.441652	+	0.160748i	−0.111616	+	0.993751i	$0.535603\pi$
$282$		0			0
$283$	23.2505	+	19.5095i	1.38210	+	1.15972i	0.968428	+	0.249292i	$0.0801979\pi$
$283$	23.2505	+	19.5095i	1.38210	+	1.15972i	0.413670	+	0.910427i	$0.364247\pi$
$284$		0			0
$285$	−0.180540	+	0.00852749i	−0.0106943	+	0.000505125i
$286$		0			0
$287$	1.33375	−	2.31013i	0.0787291	−	0.136363i
$288$		0			0
$289$	−10.9051	−	18.8882i	−0.641477	−	1.11107i
$290$		0			0
$291$	6.30550	−	2.63820i	0.369635	−	0.154654i
$292$		0			0
$293$	3.58015	−	20.3041i	0.209155	−	1.18618i	−0.681612	−	0.731714i	$-0.738721\pi$
$293$	3.58015	−	20.3041i	0.209155	−	1.18618i	0.890766	−	0.454462i	$-0.150168\pi$
$294$		0			0
$295$	−1.10701	+	0.928893i	−0.0644527	+	0.0540822i
$296$		0			0
$297$	6.53555	+	19.9805i	0.379231	+	1.15938i
$298$		0			0
$299$	−13.1935	+	11.0707i	−0.763000	+	0.640233i
$300$		0			0
$301$	1.11087	−	6.30007i	0.0640296	−	0.363130i
$302$		0			0
$303$	−12.8131	−	9.75947i	−0.736094	−	0.560667i
$304$		0			0
$305$	−0.137162	−	0.237571i	−0.00785385	−	0.0136033i
$306$		0			0
$307$	−6.38621	+	11.0612i	−0.364480	+	0.631298i	−0.988693	−	0.149956i	$-0.952087\pi$
$307$	−6.38621	+	11.0612i	−0.364480	+	0.631298i	0.624212	+	0.781255i	$0.285420\pi$
$308$		0			0
$309$	−6.95213	+	13.4720i	−0.395493	+	0.766393i
$310$		0			0
$311$	3.15599	+	2.64819i	0.178960	+	0.150165i	0.727867	−	0.685718i	$-0.240512\pi$
$311$	3.15599	+	2.64819i	0.178960	+	0.150165i	−0.548908	+	0.835883i	$0.684956\pi$
$312$		0			0
$313$	−9.12637	−	3.32173i	−0.515853	−	0.187755i	0.0709578	−	0.997479i	$-0.477394\pi$
$313$	−9.12637	−	3.32173i	−0.515853	−	0.187755i	−0.586811	+	0.809724i	$0.699617\pi$
$314$		0			0
$315$	−0.261131	+	0.124042i	−0.0147131	+	0.00698896i
$316$		0			0
$317$	1.61909	+	9.18234i	0.0909374	+	0.515731i	0.995917	+	0.0902760i	$0.0287749\pi$
$317$	1.61909	+	9.18234i	0.0909374	+	0.515731i	−0.904979	+	0.425455i	$0.860114\pi$
$318$		0			0
$319$	−15.1342	+	5.50840i	−0.847353	+	0.308411i
$320$		0			0
$321$	12.7446	−	11.7622i	0.711336	−	0.656500i
$322$		0			0
$323$	−6.41139			−0.356739
$324$		0			0
$325$	−24.7581			−1.37333
$326$		0			0
$327$	−2.26992	+	2.09493i	−0.125527	+	0.115850i
$328$		0			0
$329$	6.98528	−	2.54243i	0.385111	−	0.140169i
$330$		0			0
$331$	2.93255	+	16.6313i	0.161187	+	0.914139i	0.952909	+	0.303257i	$0.0980739\pi$
$331$	2.93255	+	16.6313i	0.161187	+	0.914139i	−0.791722	+	0.610882i	$0.790815\pi$
$332$		0			0
$333$	−20.7255	−	14.2930i	−1.13575	−	0.783252i
$334$		0			0
$335$	0.315455	+	0.114816i	0.0172352	+	0.00627309i
$336$		0			0
$337$	21.4559	+	18.0036i	1.16878	+	0.980720i	0.999988	−	0.00493218i	$-0.00156997\pi$
$337$	21.4559	+	18.0036i	1.16878	+	0.980720i	0.168789	+	0.985652i	$0.446014\pi$
$338$		0			0
$339$	10.2243	−	19.8129i	0.555309	−	1.07609i
$340$		0			0
$341$	8.62750	−	14.9433i	0.467205	−	0.809223i
$342$		0			0
$343$	−6.22350	−	10.7794i	−0.336038	−	0.582034i
$344$		0			0
$345$	−0.484947	−	0.369373i	−0.0261086	−	0.0198864i
$346$		0			0
$347$	2.63336	−	14.9345i	0.141366	−	0.801728i	−0.828847	−	0.559476i	$-0.811003\pi$
$347$	2.63336	−	14.9345i	0.141366	−	0.801728i	0.970213	−	0.242253i	$-0.0778863\pi$
$348$		0			0
$349$	9.23615	−	7.75005i	0.494400	−	0.414851i	−0.361200	−	0.932488i	$-0.617633\pi$
$349$	9.23615	−	7.75005i	0.494400	−	0.414851i	0.855600	+	0.517638i	$0.173188\pi$
$350$		0			0
$351$	−0.849081	+	25.7684i	−0.0453206	+	1.37542i
$352$		0			0
$353$	17.0061	−	14.2698i	0.905142	−	0.759504i	−0.0660466	−	0.997817i	$-0.521039\pi$
$353$	17.0061	−	14.2698i	0.905142	−	0.759504i	0.971189	+	0.238312i	$0.0765942\pi$
$354$		0			0
$355$	0.255737	−	1.45036i	0.0135731	−	0.0769771i
$356$		0			0
$357$	−9.46031	+	3.95816i	−0.500693	+	0.209488i
$358$		0			0
$359$	−12.3272	−	21.3513i	−0.650604	−	1.12688i	−0.982977	−	0.183731i	$-0.941182\pi$
$359$	−12.3272	−	21.3513i	−0.650604	−	1.12688i	0.332372	−	0.943148i	$-0.392151\pi$
$360$		0			0
$361$	8.97042	−	15.5372i	0.472128	−	0.817749i
$362$		0			0
$363$	−9.28703	+	0.438656i	−0.487443	+	0.0230235i
$364$		0			0
$365$	−0.904384	−	0.758868i	−0.0473376	−	0.0397210i
$366$		0			0
$367$	8.89085	+	3.23601i	0.464099	+	0.168918i	0.563477	−	0.826132i	$-0.309463\pi$
$367$	8.89085	+	3.23601i	0.464099	+	0.168918i	−0.0993785	+	0.995050i	$0.531685\pi$
$368$		0			0
$369$	5.91143	−	5.99633i	0.307737	−	0.312157i
$370$		0			0
$371$	−2.14157	−	12.1455i	−0.111185	−	0.630561i
$372$		0			0
$373$	−31.6826	+	11.5315i	−1.64046	+	0.597080i	−0.987120	−	0.159981i	$-0.948857\pi$
$373$	−31.6826	+	11.5315i	−1.64046	+	0.597080i	−0.653344	+	0.757061i	$0.726634\pi$
$374$		0			0
$375$	−0.385828	−	1.71146i	−0.0199241	−	0.0883796i
$376$		0			0
$377$	−19.7524			−1.01730
$378$		0			0
$379$	−0.919811			−0.0472475			−0.0236238	−	0.999721i	$-0.507520\pi$
$379$	−0.919811			−0.0472475			−0.0236238	+	0.999721i	$0.507520\pi$
$380$		0			0
$381$	22.4595	+	6.99351i	1.15063	+	0.358288i
$382$		0			0
$383$	−13.3294	+	4.85151i	−0.681101	+	0.247900i	−0.659320	−	0.751862i	$-0.729156\pi$
$383$	−13.3294	+	4.85151i	−0.681101	+	0.247900i	−0.0217808	+	0.999763i	$0.506934\pi$
$384$		0			0
$385$	−0.0676995	−	0.383943i	−0.00345028	−	0.0195675i
$386$		0			0
$387$	8.40348	−	18.3620i	0.427173	−	0.933393i
$388$		0			0
$389$	−26.3120	−	9.57678i	−1.33407	−	0.485562i	−0.426131	−	0.904662i	$-0.640124\pi$
$389$	−26.3120	−	9.57678i	−1.33407	−	0.485562i	−0.907940	+	0.419099i	$0.862346\pi$
$390$		0			0
$391$	−16.5650	−	13.8997i	−0.837729	−	0.702938i
$392$		0			0
$393$	10.7196	+	16.6948i	0.540733	+	0.842141i
$394$		0			0
$395$	0.0649769	−	0.112543i	0.00326934	−	0.00566267i
$396$		0			0
$397$	0.616169	+	1.06724i	0.0309246	+	0.0535631i	0.881074	−	0.472979i	$-0.156821\pi$
$397$	0.616169	+	1.06724i	0.0309246	+	0.0535631i	−0.850149	+	0.526542i	$0.823488\pi$
$398$		0			0
$399$	−0.215136	+	1.68039i	−0.0107703	+	0.0841247i
$400$		0			0
$401$	1.92747	−	10.9312i	0.0962533	−	0.545880i	−0.898103	−	0.439786i	$-0.855054\pi$
$401$	1.92747	−	10.9312i	0.0962533	−	0.545880i	0.994356	−	0.106094i	$-0.0338345\pi$
$402$		0			0
$403$	16.2112	−	13.6028i	0.807536	−	0.677603i
$404$		0			0
$405$	−0.896344	+	0.171263i	−0.0445397	+	0.00851011i
$406$		0			0
$407$	26.0086	−	21.8238i	1.28920	−	1.08176i
$408$		0			0
$409$	0.953015	−	5.40482i	0.0471236	−	0.267251i	−0.952138	−	0.305668i	$-0.901120\pi$
$409$	0.953015	−	5.40482i	0.0471236	−	0.267251i	0.999262	+	0.0384167i	$0.0122314\pi$
$410$		0			0
$411$	−0.0363944	+	0.284270i	−0.00179520	+	0.0140220i
$412$		0			0
$413$	6.77253	+	11.7304i	0.333254	+	0.577213i
$414$		0			0
$415$	−0.266487	+	0.461569i	−0.0130813	+	0.0226575i
$416$		0			0
$417$	−10.8208	−	16.8523i	−0.529895	−	0.825262i
$418$		0			0
$419$	6.93845	+	5.82205i	0.338966	+	0.284426i	0.796341	−	0.604848i	$-0.206766\pi$
$419$	6.93845	+	5.82205i	0.338966	+	0.284426i	−0.457376	+	0.889274i	$0.651210\pi$
$420$		0			0
$421$	−8.40248	−	3.05825i	−0.409512	−	0.149050i	0.129046	−	0.991639i	$-0.458808\pi$
$421$	−8.40248	−	3.05825i	−0.409512	−	0.149050i	−0.538558	+	0.842589i	$0.681031\pi$
$422$		0			0
$423$	23.3604	−	2.21171i	1.13582	−	0.107537i
$424$		0			0
$425$	−5.39783	−	30.6126i	−0.261833	−	1.48493i
$426$		0			0
$427$	−2.41619	+	0.879421i	−0.116928	+	0.0425582i
$428$		0			0
$429$	−33.1973	−	10.3371i	−1.60278	−	0.499080i
$430$		0			0
$431$	29.7499			1.43300			0.716502	−	0.697585i	$-0.245742\pi$
$431$	29.7499			1.43300			0.716502	+	0.697585i	$0.245742\pi$
$432$		0			0
$433$	25.3444			1.21798			0.608988	−	0.793179i	$-0.291576\pi$
$433$	25.3444			1.21798			0.608988	+	0.793179i	$0.291576\pi$
$434$		0			0
$435$	−0.153751	−	0.682012i	−0.00737181	−	0.0327000i
$436$		0			0
$437$	−3.35683	+	1.22179i	−0.160579	+	0.0584460i
$438$		0			0
$439$	−7.11268	−	40.3380i	−0.339470	−	1.92523i	−0.377628	−	0.925957i	$-0.623260\pi$
$439$	−7.11268	−	40.3380i	−0.339470	−	1.92523i	0.0381586	−	0.999272i	$-0.487851\pi$
$440$		0			0
$441$	−4.85972	−	17.6329i	−0.231415	−	0.839660i
$442$		0			0
$443$	8.66629	+	3.15427i	0.411748	+	0.149864i	0.539585	−	0.841931i	$-0.318581\pi$
$443$	8.66629	+	3.15427i	0.411748	+	0.149864i	−0.127837	+	0.991795i	$0.540803\pi$
$444$		0			0
$445$	−0.746533	−	0.626416i	−0.0353891	−	0.0296950i
$446$		0			0
$447$	12.1779	−	0.575200i	0.575993	−	0.0272060i
$448$		0			0
$449$	−15.7331	+	27.2505i	−0.742491	+	1.28603i	0.208867	+	0.977944i	$0.433022\pi$
$449$	−15.7331	+	27.2505i	−0.742491	+	1.28603i	−0.951358	+	0.308088i	$0.900311\pi$
$450$		0			0
$451$	5.67768	+	9.83403i	0.267351	+	0.463066i
$452$		0			0
$453$	34.4605	−	14.4182i	1.61910	−	0.677424i
$454$		0			0
$455$	0.0830292	−	0.470882i	0.00389247	−	0.0220753i
$456$		0			0
$457$	−22.2841	+	18.6986i	−1.04241	+	0.874682i	−0.992275	−	0.124060i	$-0.960408\pi$
$457$	−22.2841	+	18.6986i	−1.04241	+	0.874682i	−0.0501311	+	0.998743i	$0.515964\pi$
$458$		0			0
$459$	−32.0470	+	4.56824i	−1.49582	+	0.213227i
$460$		0			0
$461$	−24.7453	+	20.7638i	−1.15251	+	0.967067i	−0.999775	−	0.0212014i	$-0.993251\pi$
$461$	−24.7453	+	20.7638i	−1.15251	+	0.967067i	−0.152730	+	0.988268i	$0.548806\pi$
$462$		0			0
$463$	2.62449	−	14.8842i	0.121970	−	0.691728i	−0.861091	−	0.508451i	$-0.830218\pi$
$463$	2.62449	−	14.8842i	0.121970	−	0.691728i	0.983061	−	0.183277i	$-0.0586706\pi$
$464$		0			0
$465$	0.595865	+	0.453858i	0.0276326	+	0.0210472i
$466$		0			0
$467$	−14.2309	−	24.6486i	−0.658527	−	1.14060i	−0.980997	−	0.194022i	$-0.937847\pi$
$467$	−14.2309	−	24.6486i	−0.658527	−	1.14060i	0.322471	−	0.946579i	$-0.395487\pi$
$468$		0			0
$469$	1.57327	−	2.72499i	0.0726471	−	0.125828i
$470$		0			0
$471$	−2.32190	+	4.49942i	−0.106987	+	0.207322i
$472$		0			0
$473$	20.8614	+	17.5048i	0.959206	+	0.804869i
$474$		0			0
$475$	−4.82548	−	1.75633i	−0.221408	−	0.0805861i
$476$		0			0
$477$	3.11637	−	38.8049i	0.142689	−	1.77676i
$478$		0			0
$479$	4.91403	+	27.8688i	0.224528	+	1.27336i	0.863586	+	0.504202i	$0.168213\pi$
$479$	4.91403	+	27.8688i	0.224528	+	1.27336i	−0.639058	+	0.769158i	$0.720676\pi$
$480$		0			0
$481$	39.1286	−	14.2416i	1.78411	−	0.649363i
$482$		0			0
$483$	−4.19888	+	3.87519i	−0.191056	+	0.176327i
$484$		0			0
$485$	−0.400135			−0.0181692
$486$		0			0
$487$	9.59334			0.434716			0.217358	−	0.976092i	$-0.430256\pi$
$487$	9.59334			0.434716			0.217358	+	0.976092i	$0.430256\pi$
$488$		0			0
$489$	−4.58042	+	4.22732i	−0.207134	+	0.191166i
$490$		0			0
$491$	−6.81662	+	2.48105i	−0.307630	+	0.111968i	−0.491222	−	0.871034i	$-0.663450\pi$
$491$	−6.81662	+	2.48105i	−0.307630	+	0.111968i	0.183592	+	0.983002i	$0.441227\pi$
$492$		0			0
$493$	−4.30647	−	24.4232i	−0.193954	−	1.09997i
$494$		0			0
$495$	0.0985148	−	1.22670i	0.00442791	−	0.0551362i
$496$		0			0
$497$	−12.9716	−	4.72127i	−0.581854	−	0.211778i
$498$		0			0
$499$	−33.4291	−	28.0503i	−1.49649	−	1.25571i	−0.886001	−	0.463683i	$-0.846528\pi$
$499$	−33.4291	−	28.0503i	−1.49649	−	1.25571i	−0.610491	−	0.792023i	$-0.709028\pi$
$500$		0			0
$501$	−3.65126	+	7.07547i	−0.163126	+	0.316109i
$502$		0			0
$503$	−14.7562	+	25.5585i	−0.657946	+	1.13960i	0.323201	+	0.946330i	$0.395241\pi$
$503$	−14.7562	+	25.5585i	−0.657946	+	1.13960i	−0.981147	+	0.193265i	$0.938092\pi$
$504$		0			0
$505$	0.471446	+	0.816568i	0.0209791	+	0.0363368i
$506$		0			0
$507$	−16.0106	−	12.1949i	−0.711054	−	0.541595i
$508$		0			0
$509$	3.48382	−	19.7577i	0.154417	−	0.875745i	−0.804899	−	0.593412i	$-0.797781\pi$
$509$	3.48382	−	19.7577i	0.154417	−	0.875745i	0.959316	−	0.282333i	$-0.0911083\pi$
$510$		0			0
$511$	−8.47687	+	7.11294i	−0.374995	+	0.314658i
$512$		0			0
$513$	−1.99349	+	4.96216i	−0.0880149	+	0.219085i
$514$		0			0
$515$	0.679846	−	0.570459i	0.0299576	−	0.0251374i
$516$		0			0
$517$	−5.49494	+	31.1634i	−0.241667	+	1.37056i
$518$		0			0
$519$	−25.4700	+	10.6566i	−1.11801	+	0.467771i
$520$		0			0
$521$	10.4778	+	18.1480i	0.459039	+	0.795079i	0.998910	−	0.0466683i	$-0.0148604\pi$
$521$	10.4778	+	18.1480i	0.459039	+	0.795079i	−0.539871	+	0.841748i	$0.681527\pi$
$522$		0			0
$523$	−7.39257	+	12.8043i	−0.323254	+	0.559893i	−0.981158	−	0.193209i	$-0.938110\pi$
$523$	−7.39257	+	12.8043i	−0.323254	+	0.559893i	0.657903	+	0.753103i	$0.271444\pi$
$524$		0			0
$525$	−8.20453	+	0.387526i	−0.358075	+	0.0169130i
$526$		0			0
$527$	20.3538	+	17.0789i	0.886627	+	0.743968i
$528$		0			0
$529$	10.2911	+	3.74567i	0.447441	+	0.162855i
$530$		0			0
$531$	11.3603	+	41.2195i	0.492997	+	1.78878i
$532$		0			0
$533$	2.41834	+	13.7151i	0.104750	+	0.594066i
$534$		0			0
$535$	−0.954034	+	0.347240i	−0.0412465	+	0.0150125i
$536$		0			0
$537$	5.45062	+	24.1779i	0.235212	+	1.04335i
$538$		0			0
$539$	24.6658			1.06243
$540$		0			0
$541$	39.7536			1.70914			0.854571	−	0.519335i	$-0.173820\pi$
$541$	39.7536			1.70914			0.854571	+	0.519335i	$0.173820\pi$
$542$		0			0
$543$	−26.5437	−	8.26528i	−1.13910	−	0.354697i
$544$		0			0
$545$	0.169921	−	0.0618461i	0.00727860	−	0.00264919i
$546$		0			0
$547$	0.305425	+	1.73215i	0.0130590	+	0.0740614i	0.990641	−	0.136495i	$-0.0435837\pi$
$547$	0.305425	+	1.73215i	0.0130590	+	0.0740614i	−0.977582	+	0.210556i	$0.932473\pi$
$548$		0			0
$549$	−8.08031	+	0.765024i	−0.344859	+	0.0326504i
$550$		0			0
$551$	−3.84984	−	1.40123i	−0.164009	−	0.0596943i
$552$		0			0
$553$	−0.933095	−	0.782960i	−0.0396792	−	0.0332948i
$554$		0			0
$555$	0.796311	+	1.24018i	0.0338015	+	0.0526427i
$556$		0			0
$557$	−1.51071	+	2.61662i	−0.0640107	+	0.110870i	−0.896255	−	0.443540i	$-0.853723\pi$
$557$	−1.51071	+	2.61662i	−0.0640107	+	0.110870i	0.832244	+	0.554410i	$0.187056\pi$
$558$		0			0
$559$	16.6995	+	28.9244i	0.706315	+	1.22337i
$560$		0			0
$561$	5.54373	−	43.3011i	0.234057	−	1.82817i
$562$		0			0
$563$	−0.992932	+	5.63120i	−0.0418471	+	0.237327i	−0.998556	−	0.0537196i	$-0.982892\pi$
$563$	−0.992932	+	5.63120i	−0.0418471	+	0.237327i	0.956709	+	0.291046i	$0.0940034\pi$
$564$		0			0
$565$	−0.999833	+	0.838959i	−0.0420633	+	0.0352953i
$566$		0			0
$567$	0.121965	+	8.55262i	0.00512207	+	0.359176i
$568$		0			0
$569$	8.15160	−	6.84000i	0.341733	−	0.286748i	−0.455727	−	0.890119i	$-0.650621\pi$
$569$	8.15160	−	6.84000i	0.341733	−	0.286748i	0.797460	+	0.603372i	$0.206176\pi$
$570$		0			0
$571$	2.83788	−	16.0944i	0.118761	−	0.673530i	−0.866057	−	0.499944i	$-0.833354\pi$
$571$	2.83788	−	16.0944i	0.118761	−	0.673530i	0.984819	−	0.173585i	$-0.0555352\pi$
$572$		0			0
$573$	−1.07398	+	8.38870i	−0.0448663	+	0.350443i
$574$		0			0
$575$	−8.65986	−	14.9993i	−0.361141	−	0.625515i
$576$		0			0
$577$	−3.07063	+	5.31849i	−0.127832	+	0.221412i	−0.922836	−	0.385192i	$-0.874135\pi$
$577$	−3.07063	+	5.31849i	−0.127832	+	0.221412i	0.795004	+	0.606604i	$0.207469\pi$
$578$		0			0
$579$	−5.69260	−	8.86569i	−0.236576	−	0.368445i
$580$		0			0
$581$	3.82686	+	3.21112i	0.158765	+	0.133220i
$582$		0			0
$583$	49.3337	+	17.9560i	2.04319	+	0.743661i
$584$		0			0
$585$	0.628097	−	1.37242i	0.0259686	−	0.0567426i
$586$		0			0
$587$	−1.04696	−	5.93760i	−0.0432126	−	0.245071i	0.955548	−	0.294834i	$-0.0952644\pi$
$587$	−1.04696	−	5.93760i	−0.0432126	−	0.245071i	−0.998761	+	0.0497632i	$0.984153\pi$
$588$		0			0
$589$	4.12462	−	1.50124i	0.169952	−	0.0618574i
$590$		0			0
$591$	33.0321	+	10.2857i	1.35876	+	0.423096i
$592$		0			0
$593$	−31.3099			−1.28574			−0.642871	−	0.765974i	$-0.722257\pi$
$593$	−31.3099			−1.28574			−0.642871	+	0.765974i	$0.722257\pi$
$594$		0			0
$595$	0.600333			0.0246113
$596$		0			0
$597$	6.63410	+	29.4277i	0.271516	+	1.20439i
$598$		0			0
$599$	−24.6626	+	8.97645i	−1.00769	+	0.366768i	−0.792544	−	0.609815i	$-0.791244\pi$
$599$	−24.6626	+	8.97645i	−1.00769	+	0.366768i	−0.215142	+	0.976583i	$0.569022\pi$
$600$		0			0
$601$	3.39074	+	19.2298i	0.138311	+	0.784401i	0.972497	+	0.232917i	$0.0748271\pi$
$601$	3.39074	+	19.2298i	0.138311	+	0.784401i	−0.834185	+	0.551484i	$0.814062\pi$
$602$		0			0
$603$	6.97303	−	7.07317i	0.283964	−	0.288042i
$604$		0			0
$605$	0.511451	+	0.186153i	0.0207935	+	0.00756820i
$606$		0			0
$607$	14.0120	+	11.7574i	0.568729	+	0.477220i	0.881224	−	0.472699i	$-0.156720\pi$
$607$	14.0120	+	11.7574i	0.568729	+	0.477220i	−0.312495	+	0.949919i	$0.601165\pi$
$608$		0			0
$609$	−6.54569	+	0.309174i	−0.265245	+	0.0125284i
$610$		0			0
$611$	−19.4048	+	33.6101i	−0.785033	+	1.35972i
$612$		0			0
$613$	7.86513	+	13.6228i	0.317669	+	0.550220i	0.980001	−	0.198991i	$-0.0637664\pi$
$613$	7.86513	+	13.6228i	0.317669	+	0.550220i	−0.662332	+	0.749211i	$0.730433\pi$
$614$		0			0
$615$	−0.454731	+	0.190258i	−0.0183365	+	0.00767194i
$616$		0			0
$617$	0.326210	−	1.85003i	0.0131327	−	0.0744795i	−0.977537	−	0.210764i	$-0.932405\pi$
$617$	0.326210	−	1.85003i	0.0131327	−	0.0744795i	0.990670	+	0.136284i	$0.0435160\pi$
$618$		0			0
$619$	20.1764	−	16.9300i	0.810956	−	0.680473i	−0.139880	−	0.990169i	$-0.544672\pi$
$619$	20.1764	−	16.9300i	0.810956	−	0.680473i	0.950836	+	0.309695i	$0.100227\pi$
$620$		0			0
$621$	−15.9084	+	8.49884i	−0.638381	+	0.341047i
$622$		0			0
$623$	−6.99732	+	5.87145i	−0.280342	+	0.235235i
$624$		0			0
$625$	4.31444	−	24.4684i	0.172578	−	0.978737i
$626$		0			0
$627$	−5.73701	−	4.36976i	−0.229114	−	0.174511i
$628$		0			0
$629$	26.1403	+	45.2763i	1.04228	+	1.80528i
$630$		0			0
$631$	−16.2892	+	28.2137i	−0.648463	+	1.12317i	0.335027	+	0.942208i	$0.391254\pi$
$631$	−16.2892	+	28.2137i	−0.648463	+	1.12317i	−0.983490	+	0.180962i	$0.942079\pi$
$632$		0			0
$633$	−5.88663	+	11.4072i	−0.233973	+	0.453396i
$634$		0			0
$635$	−1.05489	−	0.885156i	−0.0418619	−	0.0351263i
$636$		0			0
$637$	28.4267	+	10.3465i	1.12631	+	0.409942i
$638$		0			0
$639$	−35.8710	−	24.7379i	−1.41903	−	0.978615i
$640$		0			0
$641$	−0.412014	−	2.33665i	−0.0162736	−	0.0922920i	0.975589	−	0.219603i	$-0.0704763\pi$
$641$	−0.412014	−	2.33665i	−0.0162736	−	0.0922920i	−0.991863	+	0.127311i	$0.959365\pi$
$642$		0			0
$643$	−1.69677	+	0.617575i	−0.0669143	+	0.0243548i	−0.375260	−	0.926919i	$-0.622447\pi$
$643$	−1.69677	+	0.617575i	−0.0669143	+	0.0243548i	0.308346	+	0.951274i	$0.400224\pi$
$644$		0			0
$645$	−0.868718	+	0.801749i	−0.0342057	+	0.0315688i
$646$		0			0
$647$	−8.00144			−0.314569			−0.157284	−	0.987553i	$-0.550274\pi$
$647$	−8.00144			−0.314569			−0.157284	+	0.987553i	$0.550274\pi$
$648$		0			0
$649$	−57.6601			−2.26336
$650$		0			0
$651$	5.15926	−	4.76154i	0.202207	−	0.186620i
$652$		0			0
$653$	−7.33713	+	2.67050i	−0.287124	+	0.104505i	−0.481567	−	0.876409i	$-0.659932\pi$
$653$	−7.33713	+	2.67050i	−0.287124	+	0.104505i	0.194443	+	0.980914i	$0.437710\pi$
$654$		0			0
$655$	−0.201683	−	1.14380i	−0.00788042	−	0.0446921i
$656$		0			0
$657$	−31.5515	+	14.9875i	−1.23094	+	0.584718i
$658$		0			0
$659$	40.1695	+	14.6205i	1.56478	+	0.569533i	0.971825	−	0.235702i	$-0.0757389\pi$
$659$	40.1695	+	14.6205i	1.56478	+	0.569533i	0.592955	+	0.805236i	$0.297961\pi$
$660$		0			0
$661$	−16.9298	−	14.2058i	−0.658493	−	0.552541i	0.251142	−	0.967950i	$-0.419194\pi$
$661$	−16.9298	−	14.2058i	−0.658493	−	0.552541i	−0.909635	+	0.415409i	$0.863638\pi$
$662$		0			0
$663$	24.5524	−	47.5781i	0.953536	−	1.84778i
$664$		0			0
$665$	0.0495870	−	0.0858873i	0.00192290	−	0.00333057i
$666$		0			0
$667$	−6.90896	−	11.9667i	−0.267516	−	0.463351i
$668$		0			0
$669$	−17.7558	−	13.5242i	−0.686477	−	0.522875i
$670$		0			0
$671$	1.90069	−	10.7793i	0.0733752	−	0.416131i
$672$		0			0
$673$	18.1009	−	15.1885i	0.697738	−	0.585472i	−0.223391	−	0.974729i	$-0.571713\pi$
$673$	18.1009	−	15.1885i	0.697738	−	0.585472i	0.921129	+	0.389257i	$0.127268\pi$
$674$		0			0
$675$	−25.3713	−	5.34068i	−0.976543	−	0.205563i
$676$		0			0
$677$	−2.58528	+	2.16931i	−0.0993604	+	0.0833733i	−0.691115	−	0.722745i	$-0.742880\pi$
$677$	−2.58528	+	2.16931i	−0.0993604	+	0.0833733i	0.591754	+	0.806118i	$0.298436\pi$
$678$		0			0
$679$	−0.651268	+	3.69352i	−0.0249934	+	0.141744i
$680$		0			0
$681$	16.9859	−	7.10682i	0.650899	−	0.272334i
$682$		0			0
$683$	9.78934	+	16.9556i	0.374579	+	0.648790i	0.990264	−	0.139203i	$-0.0444540\pi$
$683$	9.78934	+	16.9556i	0.374579	+	0.648790i	−0.615685	+	0.787992i	$0.711121\pi$
$684$		0			0
$685$	0.00838860	−	0.0145295i	0.000320512	−	0.000555143i
$686$		0			0
$687$	29.0647	−	1.37282i	1.10889	−	0.0523763i
$688$		0			0
$689$	49.3239	+	41.3876i	1.87909	+	1.57674i
$690$		0			0
$691$	25.2617	+	9.19449i	0.960998	+	0.349775i	0.774425	−	0.632666i	$-0.218039\pi$
$691$	25.2617	+	9.19449i	0.960998	+	0.349775i	0.186574	+	0.982441i	$0.440262\pi$
$692$		0			0
$693$	−11.1630	−	2.90597i	−0.424046	−	0.110388i
$694$		0			0
$695$	0.203586	+	1.15460i	0.00772247	+	0.0437963i
$696$		0			0
$697$	−16.4310	+	5.98040i	−0.622369	+	0.226524i
$698$		0			0
$699$	6.90813	+	30.6432i	0.261289	+	1.15903i
$700$		0			0
$701$	1.75124			0.0661433			0.0330717	−	0.999453i	$-0.489471\pi$
$701$	1.75124			0.0661433			0.0330717	+	0.999453i	$0.489471\pi$
$702$		0			0
$703$	8.63666			0.325738
$704$		0			0
$705$	−1.31154	−	0.408391i	−0.0493953	−	0.0153809i
$706$		0			0
$707$	8.30482	−	3.02271i	0.312335	−	0.113681i
$708$		0			0
$709$	−7.04557	−	39.9574i	−0.264602	−	1.50063i	−0.770167	−	0.637843i	$-0.779827\pi$
$709$	−7.04557	−	39.9574i	−0.264602	−	1.50063i	0.505565	−	0.862789i	$-0.331284\pi$
$710$		0			0
$711$	−2.22778	−	3.13381i	−0.0835483	−	0.117527i
$712$		0			0
$713$	13.9114	+	5.06332i	0.520985	+	0.189623i
$714$		0			0
$715$	1.55923	+	1.30835i	0.0583118	+	0.0489294i
$716$		0			0
$717$	14.9091	+	23.2196i	0.556792	+	0.867151i
$718$		0			0
$719$	−7.70782	+	13.3503i	−0.287453	+	0.497884i	−0.973201	−	0.229956i	$-0.926142\pi$
$719$	−7.70782	+	13.3503i	−0.287453	+	0.497884i	0.685748	+	0.727839i	$0.259475\pi$
$720$		0			0
$721$	−4.15920	−	7.20394i	−0.154897	−	0.268289i
$722$		0			0
$723$	2.17848	−	17.0157i	0.0810186	−	0.632822i
$724$		0			0
$725$	3.44925	−	19.5616i	0.128102	−	0.726501i
$726$		0			0
$727$	16.0258	−	13.4473i	0.594366	−	0.498732i	−0.295263	−	0.955416i	$-0.595407\pi$
$727$	16.0258	−	13.4473i	0.594366	−	0.498732i	0.889629	+	0.456684i	$0.150963\pi$
$728$		0			0
$729$	−6.42872	+	26.2235i	−0.238101	+	0.971240i
$730$		0			0
$731$	−32.1233	+	26.9546i	−1.18812	+	0.996953i
$732$		0			0
$733$	1.39463	−	7.90937i	0.0515120	−	0.292139i	−0.948159	−	0.317797i	$-0.897057\pi$
$733$	1.39463	−	7.90937i	0.0515120	−	0.292139i	0.999671	+	0.0256579i	$0.00816806\pi$
$734$		0			0
$735$	−0.135972	+	1.06206i	−0.00501542	+	0.0391746i
$736$		0			0
$737$	6.69729	+	11.6001i	0.246698	+	0.427294i
$738$		0			0
$739$	21.1683	−	36.6645i	0.778688	−	1.34873i	−0.154010	−	0.988069i	$-0.549219\pi$
$739$	21.1683	−	36.6645i	0.778688	−	1.34873i	0.932698	−	0.360658i	$-0.117448\pi$
$740$		0			0
$741$	−4.77879	−	7.44252i	−0.175553	−	0.273408i
$742$		0			0
$743$	36.0606	+	30.2584i	1.32293	+	1.11007i	0.985674	+	0.168663i	$0.0539450\pi$
$743$	36.0606	+	30.2584i	1.32293	+	1.11007i	0.337261	+	0.941411i	$0.390499\pi$
$744$		0			0
$745$	−0.670654	−	0.244098i	−0.0245709	−	0.00894306i
$746$		0			0
$747$	9.13669	+	12.8525i	0.334294	+	0.470250i
$748$		0			0
$749$	1.65246	+	9.37156i	0.0603796	+	0.342429i
$750$		0			0
$751$	25.2663	−	9.19620i	0.921982	−	0.335574i	0.162955	−	0.986633i	$-0.447897\pi$
$751$	25.2663	−	9.19620i	0.921982	−	0.335574i	0.759027	+	0.651059i	$0.225675\pi$
$752$		0			0
$753$	−3.77465	−	1.17537i	−0.137556	−	0.0428327i
$754$		0			0
$755$	−2.18680			−0.0795857
$756$		0			0
$757$	26.9419			0.979220			0.489610	−	0.871942i	$-0.337139\pi$
$757$	26.9419			0.979220			0.489610	+	0.871942i	$0.337139\pi$
$758$		0			0
$759$	−5.34913	−	23.7277i	−0.194161	−	0.861263i
$760$		0			0
$761$	−4.38287	+	1.59523i	−0.158879	+	0.0578272i	−0.420235	−	0.907415i	$-0.638052\pi$
$761$	−4.38287	+	1.59523i	−0.158879	+	0.0578272i	0.261356	+	0.965242i	$0.415830\pi$
$762$		0			0
$763$	−0.294316	−	1.66915i	−0.0106549	−	0.0604272i
$764$		0			0
$765$	1.83389	+	0.477403i	0.0663046	+	0.0172605i
$766$		0			0
$767$	−66.4518	−	24.1865i	−2.39944	−	0.873324i
$768$		0			0
$769$	−5.97601	−	5.01447i	−0.215501	−	0.180826i	0.528647	−	0.848842i	$-0.322700\pi$
$769$	−5.97601	−	5.01447i	−0.215501	−	0.180826i	−0.744147	+	0.668015i	$0.767144\pi$
$770$		0			0
$771$	−20.1811	+	0.953218i	−0.726805	+	0.0343293i
$772$		0			0
$773$	23.3076	−	40.3699i	0.838315	−	1.45200i	−0.0529872	−	0.998595i	$-0.516874\pi$
$773$	23.3076	−	40.3699i	0.838315	−	1.45200i	0.891302	−	0.453409i	$-0.149792\pi$
$774$		0			0
$775$	10.6406	+	18.4300i	0.382221	+	0.662026i
$776$		0			0
$777$	12.7438	−	5.33196i	0.457182	−	0.191283i
$778$		0			0
$779$	−0.501596	+	2.84469i	−0.0179715	+	0.101922i
$780$		0			0
$781$	45.0148	−	37.7719i	1.61076	−	1.35159i
$782$		0			0
$783$	−20.2416	−	4.26087i	−0.723376	−	0.152271i
$784$		0			0
$785$	0.227058	−	0.190524i	0.00810404	−	0.00680010i
$786$		0			0
$787$	−7.17649	+	40.6999i	−0.255814	+	1.45080i	0.538159	+	0.842843i	$0.319120\pi$
$787$	−7.17649	+	40.6999i	−0.255814	+	1.45080i	−0.793974	+	0.607952i	$0.791991\pi$
$788$		0			0
$789$	−2.42759	−	1.84904i	−0.0864245	−	0.0658277i
$790$		0			0
$791$	6.11683	+	10.5947i	0.217489	+	0.376703i
$792$		0			0
$793$	6.71206	−	11.6256i	0.238352	−	0.412838i
$794$		0			0
$795$	−1.04510	+	2.02522i	−0.0370660	+	0.0718271i
$796$		0			0
$797$	−1.22417	−	1.02720i	−0.0433623	−	0.0363853i	0.620849	−	0.783930i	$-0.286788\pi$
$797$	−1.22417	−	1.02720i	−0.0433623	−	0.0363853i	−0.664211	+	0.747545i	$0.731232\pi$
$798$		0			0
$799$	−45.7884	−	16.6656i	−1.61988	−	0.589588i
$800$		0			0
$801$	−26.0445	+	12.3716i	−0.920238	+	0.437129i
$802$		0			0
$803$	−8.17987	−	46.3904i	−0.288661	−	1.63708i
$804$		0			0
$805$	0.314318	−	0.114403i	0.0110783	−	0.00403216i
$806$		0			0
$807$	−16.9863	+	15.6769i	−0.597947	+	0.551852i
$808$		0			0
$809$	−51.3152			−1.80415			−0.902074	−	0.431582i	$-0.857956\pi$
$809$	−51.3152			−1.80415			−0.902074	+	0.431582i	$0.857956\pi$
$810$		0			0
$811$	−2.89450			−0.101640			−0.0508198	−	0.998708i	$-0.516183\pi$
$811$	−2.89450			−0.101640			−0.0508198	+	0.998708i	$0.516183\pi$
$812$		0			0
$813$	15.8497	−	14.6279i	0.555873	−	0.513021i
$814$		0			0
$815$	0.342880	−	0.124798i	0.0120106	−	0.00437149i
$816$		0			0
$817$	1.20293	+	6.82218i	0.0420853	+	0.238678i
$818$		0			0
$819$	−11.6461	−	8.03155i	−0.406947	−	0.280645i
$820$		0			0
$821$	18.6181	+	6.77643i	0.649776	+	0.236499i	0.645816	−	0.763493i	$-0.276517\pi$
$821$	18.6181	+	6.77643i	0.649776	+	0.236499i	0.00395982	+	0.999992i	$0.498740\pi$
$822$		0			0
$823$	−18.1424	−	15.2232i	−0.632403	−	0.530649i	0.269272	−	0.963064i	$-0.413217\pi$
$823$	−18.1424	−	15.2232i	−0.632403	−	0.530649i	−0.901675	+	0.432415i	$0.857661\pi$
$824$		0			0
$825$	16.0343	−	31.0716i	0.558244	−	1.08177i
$826$		0			0
$827$	−12.1938	+	21.1203i	−0.424020	+	0.734424i	−0.996328	−	0.0856145i	$-0.972715\pi$
$827$	−12.1938	+	21.1203i	−0.424020	+	0.734424i	0.572308	+	0.820038i	$0.306048\pi$
$828$		0			0
$829$	16.2138	+	28.0832i	0.563130	+	0.975369i	0.997221	+	0.0745003i	$0.0237362\pi$
$829$	16.2138	+	28.0832i	0.563130	+	0.975369i	−0.434091	+	0.900869i	$0.642930\pi$
$830$		0			0
$831$	−7.10427	−	5.41117i	−0.246445	−	0.187712i
$832$		0			0
$833$	−6.59542	+	37.4045i	−0.228518	+	1.29599i
$834$		0			0
$835$	0.357055	−	0.299605i	0.0123564	−	0.0103683i
$836$		0			0
$837$	19.5470	−	10.4427i	0.675643	−	0.360953i
$838$		0			0
$839$	14.1004	−	11.8316i	0.486800	−	0.408474i	−0.366078	−	0.930584i	$-0.619300\pi$
$839$	14.1004	−	11.8316i	0.486800	−	0.408474i	0.852878	+	0.522111i	$0.174855\pi$
$840$		0			0
$841$	−2.28394	+	12.9529i	−0.0787565	+	0.446650i
$842$		0			0
$843$	−12.5887	+	5.26704i	−0.433576	+	0.181407i
$844$		0			0
$845$	0.589093	+	1.02034i	0.0202654	+	0.0351007i
$846$		0			0
$847$	2.55077	−	4.41806i	0.0876455	−	0.151806i
$848$		0			0
$849$	−52.5116	+	2.48029i	−1.80219	+	0.0851234i
$850$		0			0
$851$	22.3144	+	18.7240i	0.764928	+	0.641851i
$852$		0			0
$853$	2.57001	+	0.935406i	0.0879954	+	0.0320277i	0.385643	−	0.922648i	$-0.373980\pi$
$853$	2.57001	+	0.935406i	0.0879954	+	0.0320277i	−0.297647	+	0.954676i	$0.596202\pi$
$854$		0			0
$855$	0.219778	−	0.222935i	0.00751626	−	0.00762421i
$856$		0			0
$857$	−9.64418	−	54.6948i	−0.329439	−	1.86834i	−0.476445	−	0.879204i	$-0.658075\pi$
$857$	−9.64418	−	54.6948i	−0.329439	−	1.86834i	0.147006	−	0.989136i	$-0.453036\pi$
$858$		0			0
$859$	−5.25846	+	1.91392i	−0.179416	+	0.0653023i	−0.430166	−	0.902750i	$-0.641545\pi$
$859$	−5.25846	+	1.91392i	−0.179416	+	0.0653023i	0.250750	+	0.968052i	$0.419323\pi$
$860$		0			0
$861$	1.01608	+	4.50715i	0.0346280	+	0.153603i
$862$		0			0
$863$	−27.4069			−0.932941			−0.466470	−	0.884537i	$-0.654475\pi$
$863$	−27.4069			−0.932941			−0.466470	+	0.884537i	$0.654475\pi$
$864$		0			0
$865$	1.61628			0.0549550
$866$		0			0
$867$	36.0683	+	11.2311i	1.22494	+	0.381428i
$868$		0			0
$869$	4.87251	−	1.77345i	0.165289	−	0.0601601i
$870$		0			0
$871$	2.85263	+	16.1781i	0.0966577	+	0.548173i
$872$		0			0
$873$	−4.92669	+	10.7650i	−0.166743	+	0.364341i
$874$		0			0
$875$	0.904604	+	0.329249i	0.0305812	+	0.0111306i
$876$		0			0
$877$	−26.0184	−	21.8320i	−0.878578	−	0.737214i	0.0873083	−	0.996181i	$-0.472173\pi$
$877$	−26.0184	−	21.8320i	−0.878578	−	0.737214i	−0.965886	+	0.258967i	$0.916618\pi$
$878$		0			0
$879$	19.2943	+	30.0491i	0.650781	+	1.01353i
$880$		0			0
$881$	−1.25859	+	2.17994i	−0.0424030	+	0.0734442i	−0.886448	−	0.462828i	$-0.846835\pi$
$881$	−1.25859	+	2.17994i	−0.0424030	+	0.0734442i	0.844045	+	0.536272i	$0.180168\pi$
$882$		0			0
$883$	2.38728	+	4.13489i	0.0803384	+	0.139150i	0.903395	−	0.428809i	$-0.141067\pi$
$883$	2.38728	+	4.13489i	0.0803384	+	0.139150i	−0.823057	+	0.567959i	$0.807733\pi$
$884$		0			0
$885$	0.317857	−	2.48272i	0.0106846	−	0.0834558i
$886$		0			0
$887$	5.85391	−	33.1992i	0.196555	−	1.11472i	−0.713631	−	0.700521i	$-0.752951\pi$
$887$	5.85391	−	33.1992i	0.196555	−	1.11472i	0.910187	−	0.414198i	$-0.135938\pi$
$888$		0			0
$889$	−9.88755	+	8.29664i	−0.331618	+	0.278260i
$890$		0			0
$891$	−31.7897	−	17.7543i	−1.06499	−	0.594790i
$892$		0			0
$893$	−6.16637	+	5.17420i	−0.206350	+	0.173148i
$894$		0			0
$895$	0.251948	−	1.42887i	0.00842171	−	0.0477619i
$896$		0			0
$897$	3.78826	−	29.5894i	0.126486	−	0.987962i
$898$		0			0
$899$	8.48920	+	14.7037i	0.283131	+	0.490397i
$900$		0			0
$901$	−40.4208	+	70.0109i	−1.34661	+	2.33240i
$902$		0			0
$903$	5.98676	+	9.32381i	0.199227	+	0.310277i
$904$		0			0
$905$	1.24672	+	1.04612i	0.0414423	+	0.0347743i
$906$		0			0
$907$	−20.0746	−	7.30656i	−0.666566	−	0.242610i	−0.0134974	−	0.999909i	$-0.504297\pi$
$907$	−20.0746	−	7.30656i	−0.666566	−	0.242610i	−0.653069	+	0.757299i	$0.726519\pi$
$908$		0			0
$909$	27.7733	−	2.62951i	0.921181	−	0.0872153i
$910$		0			0
$911$	−2.33787	−	13.2587i	−0.0774570	−	0.439281i	−0.998731	−	0.0503660i	$-0.983961\pi$
$911$	−2.33787	−	13.2587i	−0.0774570	−	0.439281i	0.921274	−	0.388915i	$-0.127150\pi$
$912$		0			0
$913$	−19.9834	+	7.27336i	−0.661354	+	0.240713i
$914$		0			0
$915$	0.453657	+	0.141262i	0.0149974	+	0.00466996i
$916$		0			0
$917$	−10.8864			−0.359499
$918$		0			0
$919$	6.18401			0.203992			0.101996	−	0.994785i	$-0.467477\pi$
$919$	6.18401			0.203992			0.101996	+	0.994785i	$0.467477\pi$
$920$		0			0
$921$	−4.86515	−	21.5809i	−0.160312	−	0.711114i
$922$		0			0
$923$	67.7225	−	24.6490i	2.22911	−	0.811331i
$924$		0			0
$925$	7.27132	+	41.2377i	0.239079	+	1.35589i
$926$		0			0
$927$	−6.97670	−	25.3141i	−0.229145	−	0.831423i
$928$		0			0
$929$	−36.2225	−	13.1839i	−1.18842	−	0.432551i	−0.329253	−	0.944242i	$-0.606797\pi$
$929$	−36.2225	−	13.1839i	−1.18842	−	0.432551i	−0.859169	+	0.511691i	$0.829019\pi$
$930$		0			0
$931$	4.80654	+	4.03316i	0.157528	+	0.132182i
$932$		0			0
$933$	−7.12784	+	0.336671i	−0.233355	+	0.0110221i
$934$		0			0
$935$	−1.27778	+	2.21319i	−0.0417880	+	0.0723789i
$936$		0			0
$937$	12.2768	+	21.2641i	0.401066	+	0.694667i	0.993855	−	0.110691i	$-0.0353064\pi$
$937$	12.2768	+	21.2641i	0.401066	+	0.694667i	−0.592789	+	0.805358i	$0.701973\pi$
$938$		0			0
$939$	15.5183	−	6.49279i	0.506420	−	0.211884i
$940$		0			0
$941$	−3.10858	+	17.6296i	−0.101337	+	0.574709i	0.891284	+	0.453446i	$0.149806\pi$
$941$	−3.10858	+	17.6296i	−0.101337	+	0.574709i	−0.992620	+	0.121263i	$0.961306\pi$
$942$		0			0
$943$	−7.46318	+	6.26235i	−0.243035	+	0.203930i
$944$		0			0
$945$	0.186662	−	0.464634i	0.00607210	−	0.0151146i
$946$		0			0
$947$	24.8014	−	20.8109i	0.805939	−	0.676263i	−0.143696	−	0.989622i	$-0.545899\pi$
$947$	24.8014	−	20.8109i	0.805939	−	0.676263i	0.949635	+	0.313359i	$0.101454\pi$
$948$		0			0
$949$	10.0321	−	56.8949i	0.325656	−	1.84689i
$950$		0			0
$951$	−12.8473	−	9.78553i	−0.416603	−	0.317318i
$952$		0			0
$953$	−14.9798	−	25.9458i	−0.485243	−	0.840466i	0.514613	−	0.857423i	$-0.327936\pi$
$953$	−14.9798	−	25.9458i	−0.485243	−	0.840466i	−0.999856	+	0.0169566i	$0.994602\pi$
$954$		0			0
$955$	0.247544	−	0.428759i	0.00801034	−	0.0138743i
$956$		0			0
$957$	12.7924	−	24.7894i	0.413520	−	0.801327i
$958$		0			0
$959$	−0.120464	−	0.101081i	−0.00388997	−	0.00326408i
$960$		0			0
$961$	12.0373	+	4.38120i	0.388298	+	0.141329i
$962$		0			0
$963$	−2.40462	+	29.9423i	−0.0774879	+	0.964877i
$964$		0			0
$965$	0.107103	+	0.607411i	0.00344777	+	0.0195533i
$966$		0			0
$967$	−34.3990	+	12.5202i	−1.10620	+	0.402623i	−0.829598	−	0.558362i	$-0.811430\pi$
$967$	−34.3990	+	12.5202i	−1.10620	+	0.402623i	−0.276600	+	0.960985i	$0.589208\pi$
$968$		0			0
$969$	8.16056	−	7.53147i	0.262155	−	0.241946i
$970$		0			0
$971$	25.0872			0.805086			0.402543	−	0.915401i	$-0.368126\pi$
$971$	25.0872			0.805086			0.402543	+	0.915401i	$0.368126\pi$
$972$		0			0
$973$	10.9891			0.352293
$974$		0			0
$975$	31.5127	−	29.0834i	1.00921	−	0.931414i
$976$		0			0
$977$	−18.1277	+	6.59796i	−0.579958	+	0.211087i	−0.615307	−	0.788288i	$-0.710968\pi$
$977$	−18.1277	+	6.59796i	−0.579958	+	0.211087i	0.0353492	+	0.999375i	$0.488746\pi$
$978$		0			0
$979$	−6.75216	−	38.2934i	−0.215800	−	1.22386i
$980$		0			0
$981$	0.428282	−	5.33295i	0.0136740	−	0.170268i
$982$		0			0
$983$	−43.1667	−	15.7114i	−1.37680	−	0.501116i	−0.455597	−	0.890186i	$-0.650574\pi$
$983$	−43.1667	−	15.7114i	−1.37680	−	0.501116i	−0.921208	+	0.389070i	$0.872796\pi$
$984$		0			0
$985$	−1.55147	−	1.30184i	−0.0494340	−	0.0414800i
$986$		0			0
$987$	−5.90442	+	11.4417i	−0.187940	+	0.364193i
$988$		0			0
$989$	−11.6823	+	20.2343i	−0.371475	+	0.643413i
$990$		0			0
$991$	−25.5649	−	44.2797i	−0.812096	−	1.40659i	−0.911394	−	0.411534i	$-0.864993\pi$
$991$	−25.5649	−	44.2797i	−0.812096	−	1.40659i	0.0992981	−	0.995058i	$-0.468340\pi$
$992$		0			0
$993$	−23.2694	−	17.7238i	−0.738433	−	0.562448i
$994$		0			0
$995$	0.306654	−	1.73912i	0.00972157	−	0.0551338i
$996$		0			0
$997$	31.9866	−	26.8399i	1.01302	−	0.850029i	0.0242895	−	0.999705i	$-0.492268\pi$
$997$	31.9866	−	26.8399i	1.01302	−	0.850029i	0.988735	+	0.149676i	$0.0478232\pi$
$998$		0			0
$999$	43.1698	−	6.15379i	1.36583	−	0.194697i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.d.49.1		18
4.3	odd	2		108.2.i.a.49.3	✓	18
12.11	even	2		324.2.i.a.37.2		18
27.16	even	9	inner	432.2.u.d.97.1		18
36.7	odd	6		972.2.i.a.433.2		18
36.11	even	6		972.2.i.d.433.2		18
36.23	even	6		972.2.i.b.757.2		18
36.31	odd	6		972.2.i.c.757.2		18
108.7	odd	18		972.2.i.c.217.2		18
108.11	even	18		324.2.i.a.289.2		18
108.23	even	18		2916.2.a.c.1.5		9
108.31	odd	18		2916.2.a.d.1.5		9
108.43	odd	18		108.2.i.a.97.3	yes	18
108.47	even	18		972.2.i.b.217.2		18
108.59	even	18		2916.2.e.d.973.5		18
108.67	odd	18		2916.2.e.c.1945.5		18
108.79	odd	18		972.2.i.a.541.2		18
108.83	even	18		972.2.i.d.541.2		18
108.95	even	18		2916.2.e.d.1945.5		18
108.103	odd	18		2916.2.e.c.973.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.i.a.49.3	✓	18	4.3	odd	2
108.2.i.a.97.3	yes	18	108.43	odd	18
324.2.i.a.37.2		18	12.11	even	2
324.2.i.a.289.2		18	108.11	even	18
432.2.u.d.49.1		18	1.1	even	1	trivial
432.2.u.d.97.1		18	27.16	even	9	inner
972.2.i.a.433.2		18	36.7	odd	6
972.2.i.a.541.2		18	108.79	odd	18
972.2.i.b.217.2		18	108.47	even	18
972.2.i.b.757.2		18	36.23	even	6
972.2.i.c.217.2		18	108.7	odd	18
972.2.i.c.757.2		18	36.31	odd	6
972.2.i.d.433.2		18	36.11	even	6
972.2.i.d.541.2		18	108.83	even	18
2916.2.a.c.1.5		9	108.23	even	18
2916.2.a.d.1.5		9	108.31	odd	18
2916.2.e.c.973.5		18	108.103	odd	18
2916.2.e.c.1945.5		18	108.67	odd	18
2916.2.e.d.973.5		18	108.59	even	18
2916.2.e.d.1945.5		18	108.95	even	18

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:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.27282 + 1.17470i) q^{3} +(0.0952805 - 0.0346793i) q^{5} +(-0.165033 - 0.935950i) q^{7} +(0.240153 - 2.99037i) q^{9} +O(q^{10})\)	\(q+(-1.27282 + 1.17470i) q^{3} +(0.0952805 - 0.0346793i) q^{5} +(-0.165033 - 0.935950i) q^{7} +(0.240153 - 2.99037i) q^{9} +(3.80173 + 1.38372i) q^{11} +(3.80098 + 3.18940i) q^{13} +(-0.0805374 + 0.156067i) q^{15} +(-3.11489 + 5.39515i) q^{17} +(0.514575 + 0.891271i) q^{19} +(1.30952 + 0.997433i) q^{21} +(-0.602747 + 3.41835i) q^{23} +(-3.82235 + 3.20733i) q^{25} +(3.20712 + 4.08832i) q^{27} +(-3.04952 + 2.55885i) q^{29} +(0.740609 - 4.20021i) q^{31} +(-6.46439 + 2.70467i) q^{33} +(-0.0481825 - 0.0834545i) q^{35} +(4.19601 - 7.26771i) q^{37} +(-8.58456 + 0.405477i) q^{39} +(2.15010 + 1.80415i) q^{41} +(6.32526 + 2.30221i) q^{43} +(-0.0808221 - 0.293253i) q^{45} +(1.35821 + 7.70280i) q^{47} +(5.72908 - 2.08522i) q^{49} +(-2.37299 - 10.5261i) q^{51} +12.9766 q^{53} +0.410217 q^{55} +(-1.70194 - 0.529957i) q^{57} +(-13.3926 + 4.87451i) q^{59} +(-0.469802 - 2.66438i) q^{61} +(-2.83847 + 0.268740i) q^{63} +(0.472765 + 0.172073i) q^{65} +(2.53622 + 2.12814i) q^{67} +(-3.24835 - 5.05900i) q^{69} +(7.26233 - 12.5787i) q^{71} +(-5.82171 - 10.0835i) q^{73} +(1.09751 - 8.57248i) q^{75} +(0.667678 - 3.78659i) q^{77} +(0.981804 - 0.823832i) q^{79} +(-8.88465 - 1.43629i) q^{81} +(-4.02663 + 3.37874i) q^{83} +(-0.109689 + 0.622075i) q^{85} +(0.875611 - 6.83924i) q^{87} +(-4.80559 - 8.32353i) q^{89} +(2.35783 - 4.08388i) q^{91} +(3.99132 + 6.21611i) q^{93} +(0.0799376 + 0.0670756i) q^{95} +(-3.70829 - 1.34971i) q^{97} +(5.05083 - 11.0363i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{5} + 6 q^{9}+O(q^{10}) \) 18 * q + 3 * q^5 + 6 * q^9	\( 18 q + 3 q^{5} + 6 q^{9} - 3 q^{11} + 9 q^{15} - 12 q^{17} - 30 q^{21} + 30 q^{23} + 9 q^{25} + 27 q^{27} - 24 q^{29} - 9 q^{31} - 18 q^{33} + 21 q^{35} - 3 q^{39} + 21 q^{41} + 9 q^{43} + 45 q^{45} - 45 q^{47} - 18 q^{49} - 63 q^{51} + 66 q^{53} + 54 q^{57} - 60 q^{59} - 18 q^{61} - 57 q^{63} + 33 q^{65} + 27 q^{67} - 9 q^{69} + 12 q^{71} + 9 q^{73} + 33 q^{75} - 75 q^{77} + 36 q^{79} - 54 q^{81} + 45 q^{83} - 36 q^{85} + 63 q^{87} - 48 q^{89} - 9 q^{91} - 33 q^{93} - 6 q^{95} - 27 q^{97} - 27 q^{99}+O(q^{100}) \) 18 * q + 3 * q^5 + 6 * q^9 - 3 * q^11 + 9 * q^15 - 12 * q^17 - 30 * q^21 + 30 * q^23 + 9 * q^25 + 27 * q^27 - 24 * q^29 - 9 * q^31 - 18 * q^33 + 21 * q^35 - 3 * q^39 + 21 * q^41 + 9 * q^43 + 45 * q^45 - 45 * q^47 - 18 * q^49 - 63 * q^51 + 66 * q^53 + 54 * q^57 - 60 * q^59 - 18 * q^61 - 57 * q^63 + 33 * q^65 + 27 * q^67 - 9 * q^69 + 12 * q^71 + 9 * q^73 + 33 * q^75 - 75 * q^77 + 36 * q^79 - 54 * q^81 + 45 * q^83 - 36 * q^85 + 63 * q^87 - 48 * q^89 - 9 * q^91 - 33 * q^93 - 6 * q^95 - 27 * q^97 - 27 * q^99

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