LMFDB - Embedded newform 576.2.bb.e.49.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, 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:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			49.17
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.e.529.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.68781 + 0.388965i) q^{3} +(-0.846545 + 0.226831i) q^{5} +(0.567074 - 0.327400i) q^{7} +(2.69741 + 1.31300i) q^{9} +O(q^{10})$	\(q+(1.68781 + 0.388965i) q^{3} +(-0.846545 + 0.226831i) q^{5} +(0.567074 - 0.327400i) q^{7} +(2.69741 + 1.31300i) q^{9} +(1.54155 - 5.75313i) q^{11} +(1.19068 + 4.44367i) q^{13} +(-1.51704 + 0.0535712i) q^{15} +2.75816 q^{17} +(1.73499 - 1.73499i) q^{19} +(1.08446 - 0.332018i) q^{21} +(3.50762 + 2.02512i) q^{23} +(-3.66494 + 2.11595i) q^{25} +(4.04201 + 3.26530i) q^{27} +(2.47312 + 0.662669i) q^{29} +(-2.08801 + 3.61654i) q^{31} +(4.83961 - 9.11059i) q^{33} +(-0.405789 + 0.405789i) q^{35} +(-4.30563 - 4.30563i) q^{37} +(0.281205 + 7.96320i) q^{39} +(6.15806 + 3.55536i) q^{41} +(-0.225483 + 0.841515i) q^{43} +(-2.58131 - 0.499657i) q^{45} +(-4.65521 - 8.06305i) q^{47} +(-3.28562 + 5.69086i) q^{49} +(4.65526 + 1.07283i) q^{51} +(-7.64584 - 7.64584i) q^{53} +5.21996i q^{55} +(3.60318 - 2.25348i) q^{57} +(-6.83351 + 1.83103i) q^{59} +(-3.77755 - 1.01219i) q^{61} +(1.95951 - 0.138565i) q^{63} +(-2.01592 - 3.49168i) q^{65} +(-3.11705 - 11.6330i) q^{67} +(5.13249 + 4.78237i) q^{69} -4.34835i q^{71} -0.656583i q^{73} +(-7.00876 + 2.14580i) q^{75} +(-1.00941 - 3.76715i) q^{77} +(8.16172 + 14.1365i) q^{79} +(5.55206 + 7.08340i) q^{81} +(-5.36845 - 1.43847i) q^{83} +(-2.33491 + 0.625638i) q^{85} +(3.91640 + 2.08042i) q^{87} +5.11081i q^{89} +(2.13006 + 2.13006i) q^{91} +(-4.93087 + 5.29187i) q^{93} +(-1.07520 + 1.86230i) q^{95} +(3.05669 + 5.29434i) q^{97} +(11.7120 - 13.4945i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	1.68781	+	0.388965i	0.974458	+	0.224569i
$3$	1.68781	+	0.388965i	0.974458	+	0.224569i
$4$		0			0
$5$	−0.846545	+	0.226831i	−0.378587	+	0.101442i	−0.443094	−	0.896475i	$-0.646119\pi$
$5$	−0.846545	+	0.226831i	−0.378587	+	0.101442i	0.0645072	+	0.997917i	$0.479452\pi$
$6$		0			0
$7$	0.567074	−	0.327400i	0.214334	−	0.123746i	−0.388990	−	0.921242i	$-0.627176\pi$
$7$	0.567074	−	0.327400i	0.214334	−	0.123746i	0.603324	+	0.797496i	$0.293843\pi$
$8$		0			0
$9$	2.69741	+	1.31300i	0.899137	+	0.437667i
$10$		0			0
$11$	1.54155	−	5.75313i	0.464794	−	1.73463i	−0.192778	−	0.981242i	$-0.561750\pi$
$11$	1.54155	−	5.75313i	0.464794	−	1.73463i	0.657572	−	0.753392i	$-0.271584\pi$
$12$		0			0
$13$	1.19068	+	4.44367i	0.330234	+	1.23245i	0.908944	+	0.416918i	$0.136890\pi$
$13$	1.19068	+	4.44367i	0.330234	+	1.23245i	−0.578710	+	0.815534i	$0.696444\pi$
$14$		0			0
$15$	−1.51704	+	0.0535712i	−0.391698	+	0.0138320i
$16$		0			0
$17$	2.75816			0.668953			0.334477	−	0.942404i	$-0.391441\pi$
$17$	2.75816			0.668953			0.334477	+	0.942404i	$0.391441\pi$
$18$		0			0
$19$	1.73499	−	1.73499i	0.398034	−	0.398034i	−0.479505	−	0.877539i	$-0.659184\pi$
$19$	1.73499	−	1.73499i	0.398034	−	0.398034i	0.877539	+	0.479505i	$0.159184\pi$
$20$		0			0
$21$	1.08446	−	0.332018i	0.236649	−	0.0724522i
$22$		0			0
$23$	3.50762	+	2.02512i	0.731389	+	0.422268i	0.818930	−	0.573893i	$-0.194568\pi$
$23$	3.50762	+	2.02512i	0.731389	+	0.422268i	−0.0875410	+	0.996161i	$0.527901\pi$
$24$		0			0
$25$	−3.66494	+	2.11595i	−0.732988	+	0.423191i
$26$		0			0
$27$	4.04201	+	3.26530i	0.777885	+	0.628407i
$28$		0			0
$29$	2.47312	+	0.662669i	0.459246	+	0.123055i	0.481022	−	0.876708i	$-0.340266\pi$
$29$	2.47312	+	0.662669i	0.459246	+	0.123055i	−0.0217764	+	0.999763i	$0.506932\pi$
$30$		0			0
$31$	−2.08801	+	3.61654i	−0.375018	+	0.649550i	−0.990330	−	0.138734i	$-0.955697\pi$
$31$	−2.08801	+	3.61654i	−0.375018	+	0.649550i	0.615312	+	0.788284i	$0.289030\pi$
$32$		0			0
$33$	4.83961	−	9.11059i	0.842468	−	1.58595i
$34$		0			0
$35$	−0.405789	+	0.405789i	−0.0685909	+	0.0685909i
$36$		0			0
$37$	−4.30563	−	4.30563i	−0.707841	−	0.707841i	0.258240	−	0.966081i	$-0.416858\pi$
$37$	−4.30563	−	4.30563i	−0.707841	−	0.707841i	−0.966081	+	0.258240i	$0.916858\pi$
$38$		0			0
$39$	0.281205	+	7.96320i	0.0450288	+	1.27513i
$40$		0			0
$41$	6.15806	+	3.55536i	0.961728	+	0.555254i	0.896704	−	0.442630i	$-0.145954\pi$
$41$	6.15806	+	3.55536i	0.961728	+	0.555254i	0.0650233	+	0.997884i	$0.479288\pi$
$42$		0			0
$43$	−0.225483	+	0.841515i	−0.0343859	+	0.128330i	−0.980985	−	0.194082i	$-0.937827\pi$
$43$	−0.225483	+	0.841515i	−0.0343859	+	0.128330i	0.946599	+	0.322412i	$0.104494\pi$
$44$		0			0
$45$	−2.58131	−	0.499657i	−0.384799	−	0.0744845i
$46$		0			0
$47$	−4.65521	−	8.06305i	−0.679032	−	1.17612i	−0.975273	−	0.221004i	$-0.929067\pi$
$47$	−4.65521	−	8.06305i	−0.679032	−	1.17612i	0.296241	−	0.955113i	$-0.404267\pi$
$48$		0			0
$49$	−3.28562	+	5.69086i	−0.469374	+	0.812980i
$50$		0			0
$51$	4.65526	+	1.07283i	0.651867	+	0.150226i
$52$		0			0
$53$	−7.64584	−	7.64584i	−1.05024	−	1.05024i	−0.998669	−	0.0515677i	$-0.983578\pi$
$53$	−7.64584	−	7.64584i	−1.05024	−	1.05024i	−0.0515677	−	0.998669i	$-0.516422\pi$
$54$		0			0
$55$			5.21996i			0.703859i
$56$		0			0
$57$	3.60318	−	2.25348i	0.477253	−	0.298481i
$58$		0			0
$59$	−6.83351	+	1.83103i	−0.889647	+	0.238380i	−0.674565	−	0.738216i	$-0.735669\pi$
$59$	−6.83351	+	1.83103i	−0.889647	+	0.238380i	−0.215082	+	0.976596i	$0.569002\pi$
$60$		0			0
$61$	−3.77755	−	1.01219i	−0.483666	−	0.129598i	0.00874306	−	0.999962i	$-0.497217\pi$
$61$	−3.77755	−	1.01219i	−0.483666	−	0.129598i	−0.492409	+	0.870364i	$0.663884\pi$
$62$		0			0
$63$	1.95951	−	0.138565i	0.246875	−	0.0174576i
$64$		0			0
$65$	−2.01592	−	3.49168i	−0.250045	−	0.433090i
$66$		0			0
$67$	−3.11705	−	11.6330i	−0.380809	−	1.42120i	−0.844669	−	0.535289i	$-0.820203\pi$
$67$	−3.11705	−	11.6330i	−0.380809	−	1.42120i	0.463860	−	0.885908i	$-0.346464\pi$
$68$		0			0
$69$	5.13249	+	4.78237i	0.617880	+	0.575730i
$70$		0			0
$71$		−	4.34835i		−	0.516054i	−0.966138	−	0.258027i	$-0.916928\pi$
$71$		−	4.34835i		−	0.516054i	0.966138	−	0.258027i	$-0.0830723\pi$
$72$		0			0
$73$		−	0.656583i		−	0.0768472i	−0.999262	−	0.0384236i	$-0.987766\pi$
$73$		−	0.656583i		−	0.0768472i	0.999262	−	0.0384236i	$-0.0122336\pi$
$74$		0			0
$75$	−7.00876	+	2.14580i	−0.809302	+	0.247775i
$76$		0			0
$77$	−1.00941	−	3.76715i	−0.115032	−	0.429307i
$78$		0			0
$79$	8.16172	+	14.1365i	0.918266	+	1.59048i	0.802048	+	0.597259i	$0.203744\pi$
$79$	8.16172	+	14.1365i	0.918266	+	1.59048i	0.116217	+	0.993224i	$0.462923\pi$
$80$		0			0
$81$	5.55206	+	7.08340i	0.616896	+	0.787045i
$82$		0			0
$83$	−5.36845	−	1.43847i	−0.589264	−	0.157893i	−0.0481470	−	0.998840i	$-0.515332\pi$
$83$	−5.36845	−	1.43847i	−0.589264	−	0.157893i	−0.541117	+	0.840948i	$0.681998\pi$
$84$		0			0
$85$	−2.33491	+	0.625638i	−0.253257	+	0.0678599i
$86$		0			0
$87$	3.91640	+	2.08042i	0.419882	+	0.223044i
$88$		0			0
$89$			5.11081i			0.541744i	0.962615	+	0.270872i	$0.0873121\pi$
$89$			5.11081i			0.541744i	−0.962615	+	0.270872i	$0.912688\pi$
$90$		0			0
$91$	2.13006	+	2.13006i	0.223291	+	0.223291i
$92$		0			0
$93$	−4.93087	+	5.29187i	−0.511308	+	0.548741i
$94$		0			0
$95$	−1.07520	+	1.86230i	−0.110313	+	0.191068i
$96$		0			0
$97$	3.05669	+	5.29434i	0.310360	+	0.537559i	0.978440	−	0.206530i	$-0.0662171\pi$
$97$	3.05669	+	5.29434i	0.310360	+	0.537559i	−0.668080	+	0.744089i	$0.732884\pi$
$98$		0			0
$99$	11.7120	−	13.4945i	1.17711	−	1.35625i
$100$		0			0
$101$	3.30688	−	12.3415i	0.329047	−	1.22802i	−0.581133	−	0.813809i	$-0.697390\pi$
$101$	3.30688	−	12.3415i	0.329047	−	1.22802i	0.910180	−	0.414213i	$-0.135943\pi$
$102$		0			0
$103$	−1.82866	−	1.05577i	−0.180183	−	0.104029i	0.407196	−	0.913341i	$-0.366507\pi$
$103$	−1.82866	−	1.05577i	−0.180183	−	0.104029i	−0.587379	+	0.809312i	$0.699840\pi$
$104$		0			0
$105$	−0.842733	+	0.527057i	−0.0822423	+	0.0514355i
$106$		0			0
$107$	−7.26738	−	7.26738i	−0.702564	−	0.702564i	0.262396	−	0.964960i	$-0.415487\pi$
$107$	−7.26738	−	7.26738i	−0.702564	−	0.702564i	−0.964960	+	0.262396i	$0.915487\pi$
$108$		0			0
$109$	5.73169	−	5.73169i	0.548996	−	0.548996i	−0.377154	−	0.926150i	$-0.623097\pi$
$109$	5.73169	−	5.73169i	0.548996	−	0.548996i	0.926150	+	0.377154i	$0.123097\pi$
$110$		0			0
$111$	−5.59235	−	8.94183i	−0.530802	−	0.848721i
$112$		0			0
$113$	0.907975	−	1.57266i	0.0854151	−	0.147943i	−0.820153	−	0.572144i	$-0.806112\pi$
$113$	0.907975	−	1.57266i	0.0854151	−	0.147943i	0.905568	+	0.424201i	$0.139445\pi$
$114$		0			0
$115$	−3.42872	−	0.918723i	−0.319730	−	0.0856713i
$116$		0			0
$117$	−2.62279	+	13.5498i	−0.242477	+	1.25268i
$118$		0			0
$119$	1.56408	−	0.903023i	0.143379	−	0.0827800i
$120$		0			0
$121$	−21.1959	−	12.2374i	−1.92690	−	1.11249i
$122$		0			0
$123$	9.01073	+	8.39605i	0.812470	+	0.757046i
$124$		0			0
$125$	5.72115	−	5.72115i	0.511715	−	0.511715i
$126$		0			0
$127$	−19.2026			−1.70395			−0.851976	−	0.523581i	$-0.824596\pi$
$127$	−19.2026			−1.70395			−0.851976	+	0.523581i	$0.824596\pi$
$128$		0			0
$129$	−0.707893	+	1.33261i	−0.0623265	+	0.117330i
$130$		0			0
$131$	3.12885	+	11.6770i	0.273369	+	1.02023i	0.956927	+	0.290330i	$0.0937650\pi$
$131$	3.12885	+	11.6770i	0.273369	+	1.02023i	−0.683558	+	0.729896i	$0.739568\pi$
$132$		0			0
$133$	0.415831	−	1.55190i	0.0360571	−	0.134567i
$134$		0			0
$135$	−4.16242	−	1.84737i	−0.358244	−	0.158996i
$136$		0			0
$137$	−2.88080	+	1.66323i	−0.246123	+	0.142099i	−0.617988	−	0.786188i	$-0.712052\pi$
$137$	−2.88080	+	1.66323i	−0.246123	+	0.142099i	0.371865	+	0.928287i	$0.378719\pi$
$138$		0			0
$139$	−10.4536	+	2.80104i	−0.886666	+	0.237582i	−0.673281	−	0.739387i	$-0.735116\pi$
$139$	−10.4536	+	2.80104i	−0.886666	+	0.237582i	−0.213385	+	0.976968i	$0.568449\pi$
$140$		0			0
$141$	−4.72086	−	15.4196i	−0.397568	−	1.29857i
$142$		0			0
$143$	27.4005			2.29134
$144$		0			0
$145$	−2.24392			−0.186347
$146$		0			0
$147$	−7.75905	+	8.32710i	−0.639956	+	0.686808i
$148$		0			0
$149$	−19.1223	+	5.12380i	−1.56656	+	0.419758i	−0.934733	−	0.355351i	$-0.884361\pi$
$149$	−19.1223	+	5.12380i	−1.56656	+	0.419758i	−0.631827	+	0.775110i	$0.717695\pi$
$150$		0			0
$151$	−5.09441	+	2.94126i	−0.414577	+	0.239356i	−0.692754	−	0.721174i	$-0.743603\pi$
$151$	−5.09441	+	2.94126i	−0.414577	+	0.239356i	0.278177	+	0.960530i	$0.410270\pi$
$152$		0			0
$153$	7.43990	+	3.62147i	0.601481	+	0.292779i
$154$		0			0
$155$	0.947251	−	3.53519i	0.0760851	−	0.283953i
$156$		0			0
$157$	5.09096	+	18.9997i	0.406303	+	1.51634i	0.801640	+	0.597808i	$0.203961\pi$
$157$	5.09096	+	18.9997i	0.406303	+	1.51634i	−0.395336	+	0.918536i	$0.629372\pi$
$158$		0			0
$159$	−9.93077	−	15.8787i	−0.787561	−	1.25926i
$160$		0			0
$161$	2.65210			0.209015
$162$		0			0
$163$	−5.00716	+	5.00716i	−0.392191	+	0.392191i	−0.875468	−	0.483277i	$-0.839446\pi$
$163$	−5.00716	+	5.00716i	−0.392191	+	0.392191i	0.483277	+	0.875468i	$0.339446\pi$
$164$		0			0
$165$	−2.03038	+	8.81030i	−0.158065	+	0.685881i
$166$		0			0
$167$	−14.5023	−	8.37292i	−1.12222	−	0.647916i	−0.180255	−	0.983620i	$-0.557692\pi$
$167$	−14.5023	−	8.37292i	−1.12222	−	0.647916i	−0.941967	+	0.335704i	$0.891026\pi$
$168$		0			0
$169$	−7.07014	+	4.08195i	−0.543857	+	0.313996i
$170$		0			0
$171$	6.95802	−	2.40194i	0.532093	−	0.183681i
$172$		0			0
$173$	−16.2848	−	4.36351i	−1.23811	−	0.331751i	−0.420379	−	0.907349i	$-0.638103\pi$
$173$	−16.2848	−	4.36351i	−1.23811	−	0.331751i	−0.817733	+	0.575597i	$0.804770\pi$
$174$		0			0
$175$	−1.38553	+	2.39980i	−0.104736	+	0.181408i
$176$		0			0
$177$	−12.2459	+	0.432439i	−0.920456	+	0.0325041i
$178$		0			0
$179$	−6.56566	+	6.56566i	−0.490740	+	0.490740i	−0.908539	−	0.417799i	$-0.862802\pi$
$179$	−6.56566	+	6.56566i	−0.490740	+	0.490740i	0.417799	+	0.908539i	$0.362802\pi$
$180$		0			0
$181$	15.4877	+	15.4877i	1.15119	+	1.15119i	0.986315	+	0.164875i	$0.0527219\pi$
$181$	15.4877	+	15.4877i	1.15119	+	1.15119i	0.164875	+	0.986315i	$0.447278\pi$
$182$		0			0
$183$	−5.98209	−	3.17773i	−0.442209	−	0.234904i
$184$		0			0
$185$	4.62156	+	2.66826i	0.339784	+	0.196174i
$186$		0			0
$187$	4.25184	−	15.8681i	0.310925	−	1.16039i
$188$		0			0
$189$	3.36118	+	0.528309i	0.244490	+	0.0384288i
$190$		0			0
$191$	1.73038	+	2.99710i	0.125206	+	0.216863i	0.921813	−	0.387634i	$-0.126708\pi$
$191$	1.73038	+	2.99710i	0.125206	+	0.216863i	−0.796608	+	0.604497i	$0.793374\pi$
$192$		0			0
$193$	4.93395	−	8.54585i	0.355153	−	0.615144i	−0.631991	−	0.774976i	$-0.717762\pi$
$193$	4.93395	−	8.54585i	0.355153	−	0.615144i	0.987144	+	0.159832i	$0.0510953\pi$
$194$		0			0
$195$	−2.04436	−	6.67743i	−0.146399	−	0.478181i
$196$		0			0
$197$	4.95292	+	4.95292i	0.352881	+	0.352881i	0.861180	−	0.508299i	$-0.169726\pi$
$197$	4.95292	+	4.95292i	0.352881	+	0.352881i	−0.508299	+	0.861180i	$0.669726\pi$
$198$		0			0
$199$		−	19.3983i		−	1.37511i	−0.726132	−	0.687556i	$-0.758684\pi$
$199$		−	19.3983i		−	1.37511i	0.726132	−	0.687556i	$-0.241316\pi$
$200$		0			0
$201$	−0.736162	−	20.8467i	−0.0519248	−	1.47042i
$202$		0			0
$203$	1.61940	−	0.433916i	0.113659	−	0.0304549i
$204$		0			0
$205$	−6.01954	−	1.61293i	−0.420423	−	0.112652i
$206$		0			0
$207$	6.80250	+	10.0681i	0.472807	+	0.699781i
$208$		0			0
$209$	−7.30705	−	12.6562i	−0.505439	−	0.875446i
$210$		0			0
$211$	0.499784	+	1.86522i	0.0344066	+	0.128407i	0.980993	−	0.194043i	$-0.0621602\pi$
$211$	0.499784	+	1.86522i	0.0344066	+	0.128407i	−0.946586	+	0.322450i	$0.895494\pi$
$212$		0			0
$213$	1.69136	−	7.33919i	0.115890	−	0.502873i
$214$		0			0
$215$		−	0.763527i		−	0.0520721i
$216$		0			0
$217$			2.73446i			0.185627i
$218$		0			0
$219$	0.255388	−	1.10819i	0.0172575	−	0.0748844i
$220$		0			0
$221$	3.28408	+	12.2564i	0.220911	+	0.824452i
$222$		0			0
$223$	6.56173	+	11.3653i	0.439406	+	0.761074i	0.997644	−	0.0686072i	$-0.0218555\pi$
$223$	6.56173	+	11.3653i	0.439406	+	0.761074i	−0.558237	+	0.829681i	$0.688522\pi$
$224$		0			0
$225$	−12.6641	+	0.895533i	−0.844273	+	0.0597022i
$226$		0			0
$227$	−4.02317	−	1.07800i	−0.267027	−	0.0715497i	0.122821	−	0.992429i	$-0.460806\pi$
$227$	−4.02317	−	1.07800i	−0.267027	−	0.0715497i	−0.389848	+	0.920879i	$0.627473\pi$
$228$		0			0
$229$	26.9787	−	7.22892i	1.78280	−	0.477701i	0.791713	−	0.610894i	$-0.209190\pi$
$229$	26.9787	−	7.22892i	1.78280	−	0.477701i	0.991090	+	0.133193i	$0.0425231\pi$
$230$		0			0
$231$	−0.238393	−	6.75086i	−0.0156851	−	0.444174i
$232$		0			0
$233$			6.78106i			0.444242i	0.975019	+	0.222121i	$0.0712980\pi$
$233$			6.78106i			0.444242i	−0.975019	+	0.222121i	$0.928702\pi$
$234$		0			0
$235$	5.76980	+	5.76980i	0.376380	+	0.376380i
$236$		0			0
$237$	8.27683	+	27.0344i	0.537638	+	1.75607i
$238$		0			0
$239$	4.09048	−	7.08492i	0.264591	−	0.458286i	−0.702865	−	0.711323i	$-0.748096\pi$
$239$	4.09048	−	7.08492i	0.264591	−	0.458286i	0.967456	+	0.253038i	$0.0814296\pi$
$240$		0			0
$241$	−0.259428	−	0.449343i	−0.0167112	−	0.0289447i	0.857549	−	0.514403i	$-0.171986\pi$
$241$	−0.259428	−	0.449343i	−0.0167112	−	0.0289447i	−0.874260	+	0.485458i	$0.838653\pi$
$242$		0			0
$243$	6.61563	+	14.1150i	0.424393	+	0.905478i
$244$		0			0
$245$	1.49056	−	5.56285i	0.0952285	−	0.355397i
$246$		0			0
$247$	9.77552	+	5.64390i	0.622002	+	0.359113i
$248$		0			0
$249$	−8.50141	−	4.51601i	−0.538755	−	0.286190i
$250$		0			0
$251$	13.9609	+	13.9609i	0.881207	+	0.881207i	0.993657	−	0.112450i	$-0.0358699\pi$
$251$	13.9609	+	13.9609i	0.881207	+	0.881207i	−0.112450	+	0.993657i	$0.535870\pi$
$252$		0			0
$253$	17.0580	−	17.0580i	1.07243	−	1.07243i
$254$		0			0
$255$	−4.18424	+	0.147758i	−0.262027	+	0.00925298i
$256$		0			0
$257$	−8.72443	+	15.1112i	−0.544215	+	0.942609i	0.454441	+	0.890777i	$0.349839\pi$
$257$	−8.72443	+	15.1112i	−0.544215	+	0.942609i	−0.998656	+	0.0518315i	$0.983494\pi$
$258$		0			0
$259$	−3.85127	−	1.03195i	−0.239307	−	0.0641220i
$260$		0			0
$261$	5.80093	+	5.03469i	0.359068	+	0.311640i
$262$		0			0
$263$	9.06417	−	5.23320i	0.558921	−	0.322693i	−0.193791	−	0.981043i	$-0.562079\pi$
$263$	9.06417	−	5.23320i	0.558921	−	0.322693i	0.752712	+	0.658350i	$0.228745\pi$
$264$		0			0
$265$	8.20687	+	4.73824i	0.504144	+	0.291068i
$266$		0			0
$267$	−1.98793	+	8.62607i	−0.121659	+	0.527907i
$268$		0			0
$269$	14.8881	−	14.8881i	0.907746	−	0.907746i	−0.0883440	−	0.996090i	$-0.528157\pi$
$269$	14.8881	−	14.8881i	0.907746	−	0.907746i	0.996090	+	0.0883440i	$0.0281575\pi$
$270$		0			0
$271$	1.64797			0.100107			0.0500534	−	0.998747i	$-0.484061\pi$
$271$	1.64797			0.100107			0.0500534	+	0.998747i	$0.484061\pi$
$272$		0			0
$273$	2.76662	+	4.42366i	0.167443	+	0.267732i
$274$		0			0
$275$	6.52368	+	24.3467i	0.393393	+	1.46816i
$276$		0			0
$277$	3.13780	−	11.7104i	0.188532	−	0.703612i	−0.805315	−	0.592848i	$-0.798004\pi$
$277$	3.13780	−	11.7104i	0.188532	−	0.703612i	0.993847	−	0.110764i	$-0.0353298\pi$
$278$		0			0
$279$	−10.3807	+	7.01374i	−0.621479	+	0.419901i
$280$		0			0
$281$	2.28116	−	1.31703i	0.136083	−	0.0785674i	−0.430413	−	0.902632i	$-0.641632\pi$
$281$	2.28116	−	1.31703i	0.136083	−	0.0785674i	0.566496	+	0.824065i	$0.308299\pi$
$282$		0			0
$283$	10.3823	−	2.78192i	0.617162	−	0.165368i	0.0633245	−	0.997993i	$-0.479830\pi$
$283$	10.3823	−	2.78192i	0.617162	−	0.165368i	0.553837	+	0.832625i	$0.313163\pi$
$284$		0			0
$285$	−2.53910	+	2.72499i	−0.150403	+	0.161414i
$286$		0			0
$287$	4.65610			0.274841
$288$		0			0
$289$	−9.39253			−0.552502
$290$		0			0
$291$	3.09980	+	10.1248i	0.181713	+	0.593526i
$292$		0			0
$293$	3.95963	−	1.06098i	0.231324	−	0.0619831i	−0.141295	−	0.989968i	$-0.545127\pi$
$293$	3.95963	−	1.06098i	0.231324	−	0.0619831i	0.372619	+	0.927984i	$0.378460\pi$
$294$		0			0
$295$	5.36954	−	3.10010i	0.312627	−	0.180495i
$296$		0			0
$297$	25.0166	−	18.2206i	1.45161	−	1.05727i
$298$		0			0
$299$	−4.82254	+	17.9980i	−0.278895	+	1.04085i
$300$		0			0
$301$	0.147646	+	0.551024i	0.00851020	+	0.0317605i
$302$		0			0
$303$	10.3818	−	19.5438i	0.596419	−	1.12276i
$304$		0			0
$305$	3.42747			0.196256
$306$		0			0
$307$	−5.40346	+	5.40346i	−0.308392	+	0.308392i	−0.844286	−	0.535894i	$-0.819975\pi$
$307$	−5.40346	+	5.40346i	−0.308392	+	0.308392i	0.535894	+	0.844286i	$0.319975\pi$
$308$		0			0
$309$	−2.67576	−	2.49323i	−0.152219	−	0.141835i
$310$		0			0
$311$	13.4939	+	7.79068i	0.765167	+	0.441769i	0.831148	−	0.556052i	$-0.187684\pi$
$311$	13.4939	+	7.79068i	0.765167	+	0.441769i	−0.0659811	+	0.997821i	$0.521018\pi$
$312$		0			0
$313$	25.4594	−	14.6990i	1.43905	−	0.830835i	0.441265	−	0.897377i	$-0.354530\pi$
$313$	25.4594	−	14.6990i	1.43905	−	0.830835i	0.997784	+	0.0665417i	$0.0211965\pi$
$314$		0			0
$315$	−1.62738	+	0.561779i	−0.0916926	+	0.0316527i
$316$		0			0
$317$	5.27629	+	1.41378i	0.296346	+	0.0794057i	0.403929	−	0.914790i	$-0.367644\pi$
$317$	5.27629	+	1.41378i	0.296346	+	0.0794057i	−0.107583	+	0.994196i	$0.534311\pi$
$318$		0			0
$319$	7.62485	−	13.2066i	0.426909	−	0.739429i
$320$		0			0
$321$	−9.43920	−	15.0927i	−0.526845	−	0.842393i
$322$		0			0
$323$	4.78538	−	4.78538i	0.266266	−	0.266266i
$324$		0			0
$325$	−13.7664	−	13.7664i	−0.763620	−	0.763620i
$326$		0			0
$327$	11.9034	−	7.44458i	0.658261	−	0.411686i
$328$		0			0
$329$	−5.27969	−	3.04823i	−0.291079	−	0.168054i
$330$		0			0
$331$	6.68483	−	24.9481i	0.367432	−	1.37127i	−0.496663	−	0.867944i	$-0.665441\pi$
$331$	6.68483	−	24.9481i	0.367432	−	1.37127i	0.864094	−	0.503330i	$-0.167892\pi$
$332$		0			0
$333$	−5.96076	−	17.2674i	−0.326648	−	0.946245i
$334$		0			0
$335$	5.27746	+	9.14082i	0.288338	+	0.499416i
$336$		0			0
$337$	−1.97680	+	3.42392i	−0.107683	+	0.186513i	−0.914831	−	0.403836i	$-0.867677\pi$
$337$	−1.97680	+	3.42392i	−0.107683	+	0.186513i	0.807148	+	0.590349i	$0.201010\pi$
$338$		0			0
$339$	2.14420	−	2.30118i	0.116457	−	0.124983i
$340$		0			0
$341$	17.5877	+	17.5877i	0.952425	+	0.952425i
$342$		0			0
$343$			8.88645i			0.479823i
$344$		0			0
$345$	−5.42968	−	2.88428i	−0.292324	−	0.155285i
$346$		0			0
$347$	−4.56059	+	1.22201i	−0.244825	+	0.0656008i	−0.379145	−	0.925337i	$-0.623782\pi$
$347$	−4.56059	+	1.22201i	−0.244825	+	0.0656008i	0.134320	+	0.990938i	$0.457115\pi$
$348$		0			0
$349$	−7.74559	−	2.07543i	−0.414612	−	0.111095i	0.0454819	−	0.998965i	$-0.485518\pi$
$349$	−7.74559	−	2.07543i	−0.414612	−	0.111095i	−0.460094	+	0.887870i	$0.652184\pi$
$350$		0			0
$351$	−9.69716	+	21.8493i	−0.517596	+	1.16623i
$352$		0			0
$353$	6.95793	+	12.0515i	0.370333	+	0.641436i	0.989617	−	0.143731i	$-0.0459101\pi$
$353$	6.95793	+	12.0515i	0.370333	+	0.641436i	−0.619283	+	0.785168i	$0.712577\pi$
$354$		0			0
$355$	0.986340	+	3.68107i	0.0523495	+	0.195371i
$356$		0			0
$357$	2.99112	−	0.915759i	0.158307	−	0.0484671i
$358$		0			0
$359$		−	0.491573i		−	0.0259443i	−0.999916	−	0.0129721i	$-0.995871\pi$
$359$		−	0.491573i		−	0.0259443i	0.999916	−	0.0129721i	$-0.00412927\pi$
$360$		0			0
$361$			12.9796i			0.683138i
$362$		0			0
$363$	−31.0147	−	28.8989i	−1.62785	−	1.51680i
$364$		0			0
$365$	0.148933	+	0.555827i	0.00779553	+	0.0290933i
$366$		0			0
$367$	−3.97080	−	6.87763i	−0.207274	−	0.359010i	0.743581	−	0.668646i	$-0.233126\pi$
$367$	−3.97080	−	6.87763i	−0.207274	−	0.359010i	−0.950855	+	0.309637i	$0.899793\pi$
$368$		0			0
$369$	11.9426	+	17.6758i	0.621709	+	0.920166i
$370$		0			0
$371$	−6.83901	−	1.83251i	−0.355064	−	0.0951390i
$372$		0			0
$373$	21.8895	−	5.86527i	1.13340	−	0.303692i	0.357103	−	0.934065i	$-0.383765\pi$
$373$	21.8895	−	5.86527i	1.13340	−	0.303692i	0.776293	+	0.630373i	$0.217098\pi$
$374$		0			0
$375$	11.8815	−	7.43088i	0.613560	−	0.383729i
$376$		0			0
$377$			11.7787i			0.606635i
$378$		0			0
$379$	24.5680	+	24.5680i	1.26197	+	1.26197i	0.950135	+	0.311839i	$0.100945\pi$
$379$	24.5680	+	24.5680i	1.26197	+	1.26197i	0.311839	+	0.950135i	$0.399055\pi$
$380$		0			0
$381$	−32.4103	−	7.46914i	−1.66043	−	0.382655i
$382$		0			0
$383$	−3.67713	+	6.36897i	−0.187892	+	0.325439i	−0.944547	−	0.328375i	$-0.893499\pi$
$383$	−3.67713	+	6.36897i	−0.187892	+	0.325439i	0.756655	+	0.653814i	$0.226832\pi$
$384$		0			0
$385$	1.70901	+	2.96010i	0.0870995	+	0.150861i
$386$		0			0
$387$	−1.71313	+	1.97385i	−0.0870833	+	0.100337i
$388$		0			0
$389$	−4.98406	+	18.6007i	−0.252702	+	0.943095i	0.716653	+	0.697430i	$0.245673\pi$
$389$	−4.98406	+	18.6007i	−0.252702	+	0.943095i	−0.969355	+	0.245665i	$0.920994\pi$
$390$		0			0
$391$	9.67459	+	5.58563i	0.489265	+	0.282477i
$392$		0			0
$393$	0.738947	+	20.9256i	0.0372750	+	1.05556i
$394$		0			0
$395$	−10.1159	−	10.1159i	−0.508985	−	0.508985i
$396$		0			0
$397$	−23.3235	+	23.3235i	−1.17057	+	1.17057i	−0.188500	+	0.982073i	$0.560362\pi$
$397$	−23.3235	+	23.3235i	−1.17057	+	1.17057i	−0.982073	+	0.188500i	$0.939638\pi$
$398$		0			0
$399$	1.30548	−	2.45757i	0.0653558	−	0.123033i
$400$		0			0
$401$	−4.61036	+	7.98538i	−0.230231	+	0.398771i	−0.957876	−	0.287183i	$-0.907281\pi$
$401$	−4.61036	+	7.98538i	−0.230231	+	0.398771i	0.727645	+	0.685954i	$0.240615\pi$
$402$		0			0
$403$	−18.5568	−	4.97229i	−0.924382	−	0.247687i
$404$		0			0
$405$	−6.30681	−	4.73704i	−0.313388	−	0.235386i
$406$		0			0
$407$	−31.4082	+	18.1335i	−1.55685	+	0.898845i
$408$		0			0
$409$	−17.2773	−	9.97503i	−0.854306	−	0.493234i	0.00779552	−	0.999970i	$-0.497519\pi$
$409$	−17.2773	−	9.97503i	−0.854306	−	0.493234i	−0.862101	+	0.506736i	$0.830852\pi$
$410$		0			0
$411$	−5.50919	+	1.68669i	−0.271748	+	0.0831982i
$412$		0			0
$413$	−3.27562	+	3.27562i	−0.161183	+	0.161183i
$414$		0			0
$415$	4.87092			0.239104
$416$		0			0
$417$	−18.7333	+	0.661529i	−0.917373	+	0.0323952i
$418$		0			0
$419$	−7.85913	−	29.3307i	−0.383943	−	1.43290i	−0.839826	−	0.542856i	$-0.817343\pi$
$419$	−7.85913	−	29.3307i	−0.383943	−	1.43290i	0.455882	−	0.890040i	$-0.349324\pi$
$420$		0			0
$421$	−2.70420	+	10.0922i	−0.131795	+	0.491864i	−0.999991	−	0.00435733i	$-0.998613\pi$
$421$	−2.70420	+	10.0922i	−0.131795	+	0.491864i	0.868196	+	0.496222i	$0.165280\pi$
$422$		0			0
$423$	−1.97022	−	27.8617i	−0.0957952	−	1.35468i
$424$		0			0
$425$	−10.1085	+	5.83615i	−0.490335	+	0.283095i
$426$		0			0
$427$	−2.47354	+	0.662784i	−0.119703	+	0.0320744i
$428$		0			0
$429$	46.2468	+	10.6578i	2.23282	+	0.514565i
$430$		0			0
$431$	−11.3639			−0.547382			−0.273691	−	0.961818i	$-0.588244\pi$
$431$	−11.3639			−0.547382			−0.273691	+	0.961818i	$0.588244\pi$
$432$		0			0
$433$	−9.65126			−0.463810			−0.231905	−	0.972738i	$-0.574496\pi$
$433$	−9.65126			−0.463810			−0.231905	+	0.972738i	$0.574496\pi$
$434$		0			0
$435$	−3.78731	−	0.872807i	−0.181588	−	0.0418479i
$436$		0			0
$437$	9.59925	−	2.57211i	0.459194	−	0.123041i
$438$		0			0
$439$	13.6132	−	7.85957i	0.649722	−	0.375117i	−0.138628	−	0.990345i	$-0.544269\pi$
$439$	13.6132	−	7.85957i	0.649722	−	0.375117i	0.788350	+	0.615228i	$0.210936\pi$
$440$		0			0
$441$	−16.3348	+	11.0366i	−0.777846	+	0.525551i
$442$		0			0
$443$	4.97116	−	18.5526i	0.236187	−	0.881461i	−0.741424	−	0.671037i	$-0.765849\pi$
$443$	4.97116	−	18.5526i	0.236187	−	0.881461i	0.977610	−	0.210424i	$-0.0674843\pi$
$444$		0			0
$445$	−1.15929	−	4.32653i	−0.0549556	−	0.205097i
$446$		0			0
$447$	−34.2678	+	1.21010i	−1.62081	+	0.0572358i
$448$		0			0
$449$	35.3101			1.66639			0.833194	−	0.552982i	$-0.186510\pi$
$449$	35.3101			1.66639			0.833194	+	0.552982i	$0.186510\pi$
$450$		0			0
$451$	29.9474	−	29.9474i	1.41017	−	1.41017i
$452$		0			0
$453$	−9.74244	+	2.98274i	−0.457740	+	0.140141i
$454$		0			0
$455$	−2.28636	−	1.32003i	−0.107186	−	0.0618839i
$456$		0			0
$457$	0.565406	−	0.326437i	0.0264486	−	0.0152701i	−0.486717	−	0.873559i	$-0.661806\pi$
$457$	0.565406	−	0.326437i	0.0264486	−	0.0152701i	0.513166	+	0.858289i	$0.328473\pi$
$458$		0			0
$459$	11.1485	+	9.00622i	0.520369	+	0.420374i
$460$		0			0
$461$	−3.91317	−	1.04853i	−0.182255	−	0.0488350i	0.166537	−	0.986035i	$-0.446741\pi$
$461$	−3.91317	−	1.04853i	−0.182255	−	0.0488350i	−0.348792	+	0.937200i	$0.613408\pi$
$462$		0			0
$463$	21.0971	−	36.5413i	0.980466	−	1.69822i	0.319894	−	0.947453i	$-0.396353\pi$
$463$	21.0971	−	36.5413i	0.980466	−	1.69822i	0.660571	−	0.750763i	$-0.270314\pi$
$464$		0			0
$465$	2.97385	−	5.59828i	0.137909	−	0.259614i
$466$		0			0
$467$	0.180878	−	0.180878i	0.00837005	−	0.00837005i	−0.702909	−	0.711279i	$-0.748116\pi$
$467$	0.180878	−	0.180878i	0.00837005	−	0.00837005i	0.711279	+	0.702909i	$0.248116\pi$
$468$		0			0
$469$	−5.57625	−	5.57625i	−0.257487	−	0.257487i
$470$		0			0
$471$	1.20234	+	34.0482i	0.0554011	+	1.56886i
$472$		0			0
$473$	4.49375	+	2.59447i	0.206623	+	0.119294i
$474$		0			0
$475$	−2.68747	+	10.0298i	−0.123310	+	0.460198i
$476$		0			0
$477$	−10.5850	−	30.6630i	−0.484654	−	1.40396i
$478$		0			0
$479$	−6.98122	−	12.0918i	−0.318980	−	0.552490i	0.661295	−	0.750126i	$-0.270007\pi$
$479$	−6.98122	−	12.0918i	−0.318980	−	0.552490i	−0.980276	+	0.197636i	$0.936674\pi$
$480$		0			0
$481$	14.0062	−	24.2594i	0.638627	−	1.10613i
$482$		0			0
$483$	4.47625	+	1.03158i	0.203677	+	0.0469384i
$484$		0			0
$485$	−3.78855	−	3.78855i	−0.172029	−	0.172029i
$486$		0			0
$487$		−	2.93338i		−	0.132924i	−0.997789	−	0.0664621i	$-0.978829\pi$
$487$		−	2.93338i		−	0.132924i	0.997789	−	0.0664621i	$-0.0211712\pi$
$488$		0			0
$489$	−10.3987	+	6.50352i	−0.470247	+	0.294099i
$490$		0			0
$491$	−17.7814	+	4.76452i	−0.802465	+	0.215020i	−0.636666	−	0.771140i	$-0.719687\pi$
$491$	−17.7814	+	4.76452i	−0.802465	+	0.215020i	−0.165799	+	0.986160i	$0.553020\pi$
$492$		0			0
$493$	6.82126	+	1.82775i	0.307214	+	0.0823178i
$494$		0			0
$495$	−6.85380	+	14.0804i	−0.308056	+	0.632866i
$496$		0			0
$497$	−1.42365	−	2.46583i	−0.0638594	−	0.110608i
$498$		0			0
$499$	4.74054	+	17.6919i	0.212216	+	0.791999i	0.987128	+	0.159931i	$0.0511271\pi$
$499$	4.74054	+	17.6919i	0.212216	+	0.791999i	−0.774913	+	0.632068i	$0.782206\pi$
$500$		0			0
$501$	−21.2204	−	19.7728i	−0.948057	−	0.883383i
$502$		0			0
$503$			7.01136i			0.312621i	0.987708	+	0.156311i	$0.0499601\pi$
$503$			7.01136i			0.312621i	−0.987708	+	0.156311i	$0.950040\pi$
$504$		0			0
$505$			11.1977i			0.498292i
$506$		0			0
$507$	−13.5208	+	4.13952i	−0.600480	+	0.183842i
$508$		0			0
$509$	1.25064	+	4.66745i	0.0554336	+	0.206881i	0.988088	−	0.153890i	$-0.0491802\pi$
$509$	1.25064	+	4.66745i	0.0554336	+	0.206881i	−0.932654	+	0.360771i	$0.882514\pi$
$510$		0			0
$511$	−0.214965	−	0.372331i	−0.00950950	−	0.0164709i
$512$		0			0
$513$	12.6781	−	1.34759i	0.559751	−	0.0594975i
$514$		0			0
$515$	1.78752	+	0.478965i	0.0787676	+	0.0211057i
$516$		0			0
$517$	−53.5640	+	14.3524i	−2.35574	+	0.631219i
$518$		0			0
$519$	−25.7885	−	13.6990i	−1.13199	−	0.601320i
$520$		0			0
$521$		−	28.0687i		−	1.22971i	−0.788640	−	0.614855i	$-0.789215\pi$
$521$		−	28.0687i		−	1.22971i	0.788640	−	0.614855i	$-0.210785\pi$
$522$		0			0
$523$	−14.5264	−	14.5264i	−0.635193	−	0.635193i	0.314173	−	0.949366i	$-0.398273\pi$
$523$	−14.5264	−	14.5264i	−0.635193	−	0.635193i	−0.949366	+	0.314173i	$0.898273\pi$
$524$		0			0
$525$	−3.27195	+	3.51149i	−0.142800	+	0.153254i
$526$		0			0
$527$	−5.75907	+	9.97501i	−0.250869	+	0.434518i
$528$		0			0
$529$	−3.29774	−	5.71185i	−0.143380	−	0.248341i
$530$		0			0
$531$	−20.8369	−	4.03335i	−0.904246	−	0.175032i
$532$		0			0
$533$	−8.46657	+	31.5977i	−0.366728	+	1.36865i
$534$		0			0
$535$	7.80063	+	4.50370i	0.337251	+	0.194712i
$536$		0			0
$537$	−13.6354	+	8.52777i	−0.588411	+	0.368001i
$538$		0			0
$539$	27.6753	+	27.6753i	1.19206	+	1.19206i
$540$		0			0
$541$	18.4081	−	18.4081i	0.791427	−	0.791427i	−0.190299	−	0.981726i	$-0.560946\pi$
$541$	18.4081	−	18.4081i	0.791427	−	0.791427i	0.981726	+	0.190299i	$0.0609458\pi$
$542$		0			0
$543$	20.1161	+	32.1644i	0.863264	+	1.38031i
$544$		0			0
$545$	−3.55201	+	6.15226i	−0.152151	+	0.263534i
$546$		0			0
$547$	15.9583	+	4.27602i	0.682328	+	0.182829i	0.583302	−	0.812256i	$-0.301761\pi$
$547$	15.9583	+	4.27602i	0.682328	+	0.182829i	0.0990263	+	0.995085i	$0.468427\pi$
$548$		0			0
$549$	−8.86061	−	7.69023i	−0.378162	−	0.328211i
$550$		0			0
$551$	5.44055	−	3.14110i	0.231775	−	0.133816i
$552$		0			0
$553$	9.25660	+	5.34430i	0.393631	+	0.227263i
$554$		0			0
$555$	6.76246	+	6.30115i	0.287051	+	0.267469i
$556$		0			0
$557$	−15.4219	+	15.4219i	−0.653447	+	0.653447i	−0.953821	−	0.300375i	$-0.902888\pi$
$557$	−15.4219	+	15.4219i	−0.653447	+	0.653447i	0.300375	+	0.953821i	$0.402888\pi$
$558$		0			0
$559$	−4.00789			−0.169516
$560$		0			0
$561$	13.3484	−	25.1285i	0.563571	−	1.06093i
$562$		0			0
$563$	−1.67165	−	6.23868i	−0.0704516	−	0.262929i	0.921712	−	0.387875i	$-0.126791\pi$
$563$	−1.67165	−	6.23868i	−0.0704516	−	0.262929i	−0.992164	+	0.124946i	$0.960124\pi$
$564$		0			0
$565$	−0.411914	+	1.53728i	−0.0173293	+	0.0646740i
$566$		0			0
$567$	5.46754	+	2.19907i	0.229615	+	0.0923521i
$568$		0			0
$569$	7.90864	−	4.56605i	0.331547	−	0.191419i	−0.324981	−	0.945721i	$-0.605358\pi$
$569$	7.90864	−	4.56605i	0.331547	−	0.191419i	0.656528	+	0.754302i	$0.272024\pi$
$570$		0			0
$571$	−27.5804	+	7.39016i	−1.15421	+	0.309268i	−0.784649	−	0.619940i	$-0.787157\pi$
$571$	−27.5804	+	7.39016i	−1.15421	+	0.309268i	−0.369556	+	0.929208i	$0.620490\pi$
$572$		0			0
$573$	1.75478	+	5.73160i	0.0733071	+	0.239441i
$574$		0			0
$575$	−17.1403			−0.714799
$576$		0			0
$577$	0.350515			0.0145921			0.00729607	−	0.999973i	$-0.497678\pi$
$577$	0.350515			0.0145921			0.00729607	+	0.999973i	$0.497678\pi$
$578$		0			0
$579$	11.6516	−	12.5046i	0.484224	−	0.519675i
$580$		0			0
$581$	−3.51526	+	0.941911i	−0.145838	+	0.0390771i
$582$		0			0
$583$	−55.7739	+	32.2011i	−2.30992	+	1.33363i
$584$		0			0
$585$	−0.853197	−	12.0654i	−0.0352754	−	0.498844i
$586$		0			0
$587$	−0.259943	+	0.970122i	−0.0107290	+	0.0400412i	−0.971083	−	0.238743i	$-0.923265\pi$
$587$	−0.259943	+	0.970122i	−0.0107290	+	0.0400412i	0.960354	+	0.278784i	$0.0899314\pi$
$588$		0			0
$589$	2.65198	+	9.89733i	0.109273	+	0.407812i
$590$		0			0
$591$	6.43308	+	10.2861i	0.264621	+	0.423114i
$592$		0			0
$593$	7.12791			0.292708			0.146354	−	0.989232i	$-0.453246\pi$
$593$	7.12791			0.292708			0.146354	+	0.989232i	$0.453246\pi$
$594$		0			0
$595$	−1.11923	+	1.11923i	−0.0458841	+	0.0458841i
$596$		0			0
$597$	7.54528	−	32.7407i	0.308808	−	1.33999i
$598$		0			0
$599$	1.83973	+	1.06217i	0.0751695	+	0.0433991i	0.537114	−	0.843510i	$-0.319515\pi$
$599$	1.83973	+	1.06217i	0.0751695	+	0.0433991i	−0.461944	+	0.886909i	$0.652848\pi$
$600$		0			0
$601$	32.6223	−	18.8345i	1.33069	−	0.768275i	0.345286	−	0.938497i	$-0.387782\pi$
$601$	32.6223	−	18.8345i	1.33069	−	0.768275i	0.985406	+	0.170222i	$0.0544485\pi$
$602$		0			0
$603$	6.86616	−	35.4717i	0.279612	−	1.44452i
$604$		0			0
$605$	20.7191	+	5.55166i	0.842351	+	0.225707i
$606$		0			0
$607$	−10.2096	+	17.6835i	−0.414393	+	0.717750i	−0.995365	−	0.0961740i	$-0.969339\pi$
$607$	−10.2096	+	17.6835i	−0.414393	+	0.717750i	0.580971	+	0.813924i	$0.302673\pi$
$608$		0			0
$609$	2.90201	−	0.102479i	0.117596	−	0.00415266i
$610$		0			0
$611$	30.2867	−	30.2867i	1.22527	−	1.22527i
$612$		0			0
$613$	−10.2801	−	10.2801i	−0.415208	−	0.415208i	0.468340	−	0.883548i	$-0.344852\pi$
$613$	−10.2801	−	10.2801i	−0.415208	−	0.415208i	−0.883548	+	0.468340i	$0.844852\pi$
$614$		0			0
$615$	−9.53248	−	5.06372i	−0.384387	−	0.204189i
$616$		0			0
$617$	−41.2817	−	23.8340i	−1.66194	−	0.959521i	−0.971788	−	0.235856i	$-0.924210\pi$
$617$	−41.2817	−	23.8340i	−1.66194	−	0.959521i	−0.690152	−	0.723665i	$-0.742456\pi$
$618$		0			0
$619$	1.41291	−	5.27305i	0.0567896	−	0.211942i	−0.931700	−	0.363228i	$-0.881675\pi$
$619$	1.41291	−	5.27305i	0.0567896	−	0.211942i	0.988490	+	0.151286i	$0.0483414\pi$
$620$		0			0
$621$	7.56520	+	19.6390i	0.303581	+	0.788085i
$622$		0			0
$623$	1.67328	+	2.89820i	0.0670385	+	0.116114i
$624$		0			0
$625$	7.03430	−	12.1838i	0.281372	−	0.487350i
$626$		0			0
$627$	−7.41010	−	24.2034i	−0.295931	−	0.966592i
$628$		0			0
$629$	−11.8756	−	11.8756i	−0.473513	−	0.473513i
$630$		0			0
$631$		−	20.7362i		−	0.825496i	−0.910845	−	0.412748i	$-0.864569\pi$
$631$		−	20.7362i		−	0.825496i	0.910845	−	0.412748i	$-0.135431\pi$
$632$		0			0
$633$	0.118035	+	3.34254i	0.00469148	+	0.132854i
$634$		0			0
$635$	16.2558	−	4.35574i	0.645094	−	0.172852i
$636$		0			0
$637$	−29.2004	−	7.82422i	−1.15696	−	0.310007i
$638$		0			0
$639$	5.70938	−	11.7293i	0.225860	−	0.464003i
$640$		0			0
$641$	3.67059	+	6.35766i	0.144980	+	0.251112i	0.929365	−	0.369161i	$-0.120355\pi$
$641$	3.67059	+	6.35766i	0.144980	+	0.251112i	−0.784386	+	0.620273i	$0.787022\pi$
$642$		0			0
$643$	2.23207	+	8.33019i	0.0880241	+	0.328511i	0.995870	−	0.0907942i	$-0.0289405\pi$
$643$	2.23207	+	8.33019i	0.0880241	+	0.328511i	−0.907846	+	0.419305i	$0.862274\pi$
$644$		0			0
$645$	0.296986	−	1.28869i	0.0116938	−	0.0507421i
$646$		0			0
$647$			11.6387i			0.457566i	0.973477	+	0.228783i	$0.0734746\pi$
$647$			11.6387i			0.457566i	−0.973477	+	0.228783i	$0.926525\pi$
$648$		0			0
$649$			42.1367i			1.65401i
$650$		0			0
$651$	−1.06361	+	4.61525i	−0.0416862	+	0.180886i
$652$		0			0
$653$	−5.20569	−	19.4279i	−0.203715	−	0.760273i	−0.989838	−	0.142203i	$-0.954581\pi$
$653$	−5.20569	−	19.4279i	−0.203715	−	0.760273i	0.786123	−	0.618070i	$-0.212085\pi$
$654$		0			0
$655$	−5.29742	−	9.17541i	−0.206988	−	0.358513i
$656$		0			0
$657$	0.862093	−	1.77107i	0.0336335	−	0.0690962i
$658$		0			0
$659$	14.5489	+	3.89836i	0.566744	+	0.151859i	0.530803	−	0.847495i	$-0.321890\pi$
$659$	14.5489	+	3.89836i	0.566744	+	0.151859i	0.0359413	+	0.999354i	$0.488557\pi$
$660$		0			0
$661$	−9.83468	+	2.63519i	−0.382525	+	0.102497i	−0.444957	−	0.895552i	$-0.646781\pi$
$661$	−9.83468	+	2.63519i	−0.382525	+	0.102497i	0.0624321	+	0.998049i	$0.480114\pi$
$662$		0			0
$663$	0.775609	+	21.9638i	0.0301222	+	0.853004i
$664$		0			0
$665$			1.40808i			0.0546030i
$666$		0			0
$667$	7.33276	+	7.33276i	0.283926	+	0.283926i
$668$		0			0
$669$	6.65428	+	21.7347i	0.257269	+	0.840312i
$670$		0			0
$671$	−11.6465	+	20.1724i	−0.449610	+	0.778747i
$672$		0			0
$673$	16.1240	+	27.9276i	0.621534	+	1.07653i	0.989200	+	0.146571i	$0.0468236\pi$
$673$	16.1240	+	27.9276i	0.621534	+	1.07653i	−0.367666	+	0.929958i	$0.619843\pi$
$674$		0			0
$675$	−21.7229	−	3.41441i	−0.836116	−	0.131421i
$676$		0			0
$677$	9.43821	−	35.2239i	0.362740	−	1.35376i	−0.507719	−	0.861523i	$-0.669511\pi$
$677$	9.43821	−	35.2239i	0.362740	−	1.35376i	0.870459	−	0.492241i	$-0.163822\pi$
$678$		0			0
$679$	3.46674	+	2.00152i	0.133041	+	0.0768113i
$680$		0			0
$681$	−6.37104	−	3.38434i	−0.244139	−	0.129688i
$682$		0			0
$683$	1.95185	+	1.95185i	0.0746855	+	0.0746855i	0.743463	−	0.668777i	$-0.233182\pi$
$683$	1.95185	+	1.95185i	0.0746855	+	0.0746855i	−0.668777	+	0.743463i	$0.733182\pi$
$684$		0			0
$685$	2.06146	−	2.06146i	0.0787642	−	0.0787642i
$686$		0			0
$687$	48.3467	−	1.70727i	1.84454	−	0.0651364i
$688$		0			0
$689$	24.8719	−	43.0793i	0.947542	−	1.64119i
$690$		0			0
$691$	−1.50428	−	0.403069i	−0.0572253	−	0.0153335i	0.230093	−	0.973169i	$-0.426097\pi$
$691$	−1.50428	−	0.403069i	−0.0572253	−	0.0153335i	−0.287318	+	0.957835i	$0.592764\pi$
$692$		0			0
$693$	2.22349	−	11.4869i	0.0844634	−	0.436352i
$694$		0			0
$695$	8.21412	−	4.74242i	0.311579	−	0.179890i
$696$		0			0
$697$	16.9849	+	9.80626i	0.643351	+	0.371439i
$698$		0			0
$699$	−2.63760	+	11.4451i	−0.0997631	+	0.432895i
$700$		0			0
$701$	−21.5819	+	21.5819i	−0.815136	+	0.815136i	−0.985399	−	0.170263i	$-0.945538\pi$
$701$	−21.5819	+	21.5819i	−0.815136	+	0.815136i	0.170263	+	0.985399i	$0.445538\pi$
$702$		0			0
$703$	−14.9404			−0.563489
$704$		0			0
$705$	7.49407	+	11.9826i	0.282243	+	0.451290i
$706$		0			0
$707$	−2.16535	−	8.08119i	−0.0814363	−	0.303925i
$708$		0			0
$709$	−5.51773	+	20.5925i	−0.207223	+	0.773366i	0.781538	+	0.623858i	$0.214436\pi$
$709$	−5.51773	+	20.5925i	−0.207223	+	0.773366i	−0.988760	+	0.149508i	$0.952231\pi$
$710$		0			0
$711$	3.45428	+	48.8484i	0.129545	+	1.83196i
$712$		0			0
$713$	−14.6479	+	8.45696i	−0.548568	+	0.316716i
$714$		0			0
$715$	−23.1958	+	6.21528i	−0.867472	+	0.232438i
$716$		0			0
$717$	9.65975	−	10.3670i	0.360750	−	0.387161i
$718$		0			0
$719$	−28.4354			−1.06046			−0.530230	−	0.847854i	$-0.677894\pi$
$719$	−28.4354			−1.06046			−0.530230	+	0.847854i	$0.677894\pi$
$720$		0			0
$721$	−1.38264			−0.0514923
$722$		0			0
$723$	−0.263087	−	0.859315i	−0.00978431	−	0.0319583i
$724$		0			0
$725$	−10.4660	+	2.80436i	−0.388697	+	0.104151i
$726$		0			0
$727$	−23.2100	+	13.4003i	−0.860812	+	0.496990i	−0.864284	−	0.503004i	$-0.832228\pi$
$727$	−23.2100	+	13.4003i	−0.860812	+	0.496990i	0.00347239	+	0.999994i	$0.498895\pi$
$728$		0			0
$729$	5.67568	+	26.3967i	0.210210	+	0.977656i
$730$		0			0
$731$	−0.621920	+	2.32104i	−0.0230025	+	0.0858466i
$732$		0			0
$733$	−6.44950	−	24.0699i	−0.238218	−	0.889041i	−0.976672	−	0.214737i	$-0.931110\pi$
$733$	−6.44950	−	24.0699i	−0.238218	−	0.889041i	0.738454	−	0.674304i	$-0.235556\pi$
$734$		0			0
$735$	4.67954	−	8.80926i	0.172607	−	0.324935i
$736$		0			0
$737$	−71.7313			−2.64226
$738$		0			0
$739$	9.91976	−	9.91976i	0.364904	−	0.364904i	−0.500711	−	0.865615i	$-0.666928\pi$
$739$	9.91976	−	9.91976i	0.364904	−	0.364904i	0.865615	+	0.500711i	$0.166928\pi$
$740$		0			0
$741$	14.3040	+	13.3282i	0.525469	+	0.489623i
$742$		0			0
$743$	15.1283	+	8.73432i	0.555003	+	0.320431i	0.751137	−	0.660146i	$-0.229506\pi$
$743$	15.1283	+	8.73432i	0.555003	+	0.320431i	−0.196134	+	0.980577i	$0.562839\pi$
$744$		0			0
$745$	15.0257	−	8.67507i	0.550497	−	0.317830i
$746$		0			0
$747$	−12.5922	−	10.9289i	−0.460725	−	0.399868i
$748$		0			0
$749$	−6.50048	−	1.74180i	−0.237522	−	0.0636439i
$750$		0			0
$751$	1.95134	−	3.37983i	0.0712056	−	0.123332i	−0.828224	−	0.560397i	$-0.810649\pi$
$751$	1.95134	−	3.37983i	0.0712056	−	0.123332i	0.899430	+	0.437065i	$0.143982\pi$
$752$		0			0
$753$	18.1331	+	28.9938i	0.660807	+	1.05659i
$754$		0			0
$755$	3.64548	−	3.64548i	0.132673	−	0.132673i
$756$		0			0
$757$	16.8568	+	16.8568i	0.612670	+	0.612670i	0.943641	−	0.330971i	$-0.107376\pi$
$757$	16.8568	+	16.8568i	0.612670	+	0.612670i	−0.330971	+	0.943641i	$0.607376\pi$
$758$		0			0
$759$	35.4256	−	22.1557i	1.28587	−	0.804200i
$760$		0			0
$761$	34.1207	+	19.6996i	1.23688	+	0.714111i	0.968454	−	0.249191i	$-0.0801647\pi$
$761$	34.1207	+	19.6996i	1.23688	+	0.714111i	0.268422	+	0.963302i	$0.413498\pi$
$762$		0			0
$763$	1.37373	−	5.12685i	0.0497325	−	0.185604i
$764$		0			0
$765$	−7.11968	−	1.37814i	−0.257413	−	0.0498266i
$766$		0			0
$767$	−16.2730	−	28.1857i	−0.587584	−	1.01773i
$768$		0			0
$769$	10.1180	−	17.5249i	0.364866	−	0.631966i	−0.623889	−	0.781513i	$-0.714448\pi$
$769$	10.1180	−	17.5249i	0.364866	−	0.631966i	0.988755	+	0.149547i	$0.0477816\pi$
$770$		0			0
$771$	−20.6029	+	22.1113i	−0.741996	+	0.796318i
$772$		0			0
$773$	−2.34590	−	2.34590i	−0.0843761	−	0.0843761i	0.663659	−	0.748035i	$-0.269003\pi$
$773$	−2.34590	−	2.34590i	−0.0843761	−	0.0843761i	−0.748035	+	0.663659i	$0.769003\pi$
$774$		0			0
$775$		−	17.6725i		−	0.634816i
$776$		0			0
$777$	−6.09883	−	3.23974i	−0.218794	−	0.116225i
$778$		0			0
$779$	16.8527	−	4.51566i	0.603810	−	0.161790i
$780$		0			0
$781$	−25.0166	−	6.70318i	−0.895164	−	0.239859i
$782$		0			0
$783$	7.83255	+	10.7540i	0.279912	+	0.384316i
$784$		0			0
$785$	−8.61946	−	14.9293i	−0.307642	−	0.532851i
$786$		0			0
$787$	8.00353	+	29.8696i	0.285295	+	1.06474i	0.948623	+	0.316407i	$0.102477\pi$
$787$	8.00353	+	29.8696i	0.285295	+	1.06474i	−0.663328	+	0.748328i	$0.730857\pi$
$788$		0			0
$789$	17.3341	−	5.30701i	0.617112	−	0.188934i
$790$		0			0
$791$		−	1.18908i		−	0.0422790i
$792$		0			0
$793$		−	17.9914i		−	0.638893i
$794$		0			0
$795$	12.0086	+	11.1894i	0.425902	+	0.396848i
$796$		0			0
$797$	5.59514	+	20.8814i	0.198190	+	0.739655i	0.991418	+	0.130730i	$0.0417323\pi$
$797$	5.59514	+	20.8814i	0.198190	+	0.739655i	−0.793228	+	0.608925i	$0.791601\pi$
$798$		0			0
$799$	−12.8398	−	22.2392i	−0.454240	−	0.786767i
$800$		0			0
$801$	−6.71049	+	13.7859i	−0.237103	+	0.487102i
$802$		0			0
$803$	−3.77741	−	1.01215i	−0.133302	−	0.0357181i
$804$		0			0
$805$	−2.24513	+	0.601580i	−0.0791303	+	0.0212029i
$806$		0			0
$807$	30.9193	−	19.3374i	1.08841	−	0.680709i
$808$		0			0
$809$		−	16.4138i		−	0.577078i	−0.957468	−	0.288539i	$-0.906831\pi$
$809$		−	16.4138i		−	0.577078i	0.957468	−	0.288539i	$-0.0931695\pi$
$810$		0			0
$811$	−2.03580	−	2.03580i	−0.0714865	−	0.0714865i	0.670460	−	0.741946i	$-0.266097\pi$
$811$	−2.03580	−	2.03580i	−0.0714865	−	0.0714865i	−0.741946	+	0.670460i	$0.766097\pi$
$812$		0			0
$813$	2.78146	+	0.641002i	0.0975499	+	0.0224809i
$814$		0			0
$815$	3.10301	−	5.37456i	0.108694	−	0.188263i
$816$		0			0
$817$	1.06881	+	1.85123i	0.0373928	+	0.0647663i
$818$		0			0
$819$	2.94888	+	8.54242i	0.103042	+	0.298496i
$820$		0			0
$821$	2.92634	−	10.9213i	0.102130	−	0.381155i	−0.895874	−	0.444309i	$-0.853449\pi$
$821$	2.92634	−	10.9213i	0.102130	−	0.381155i	0.998004	+	0.0631541i	$0.0201160\pi$
$822$		0			0
$823$	9.22371	+	5.32531i	0.321518	+	0.185629i	0.652069	−	0.758159i	$-0.273901\pi$
$823$	9.22371	+	5.32531i	0.321518	+	0.185629i	−0.330551	+	0.943788i	$0.607234\pi$
$824$		0			0
$825$	1.54071	+	43.6302i	0.0536407	+	1.51901i
$826$		0			0
$827$	−25.0775	−	25.0775i	−0.872029	−	0.872029i	0.120665	−	0.992693i	$-0.461497\pi$
$827$	−25.0775	−	25.0775i	−0.872029	−	0.872029i	−0.992693	+	0.120665i	$0.961497\pi$
$828$		0			0
$829$	21.3779	−	21.3779i	0.742484	−	0.742484i	−0.230571	−	0.973055i	$-0.574059\pi$
$829$	21.3779	−	21.3779i	0.742484	−	0.742484i	0.973055	+	0.230571i	$0.0740594\pi$
$830$		0			0
$831$	9.85097	−	18.5445i	0.341726	−	0.643302i
$832$		0			0
$833$	−9.06227	+	15.6963i	−0.313989	+	0.543845i
$834$		0			0
$835$	14.1761	+	3.79848i	0.490584	+	0.131452i
$836$		0			0
$837$	−20.2488	+	7.80011i	−0.699902	+	0.269611i
$838$		0			0
$839$	26.6311	−	15.3755i	0.919407	−	0.530820i	0.0359612	−	0.999353i	$-0.488551\pi$
$839$	26.6311	−	15.3755i	0.919407	−	0.530820i	0.883446	+	0.468533i	$0.155217\pi$
$840$		0			0
$841$	−19.4376	−	11.2223i	−0.670261	−	0.386975i
$842$		0			0
$843$	4.36245	−	1.33560i	0.150251	−	0.0460006i
$844$		0			0
$845$	5.05928	−	5.05928i	0.174045	−	0.174045i
$846$		0			0
$847$	−16.0262			−0.550665
$848$		0			0
$849$	18.6054	−	0.657012i	0.638535	−	0.0225486i
$850$		0			0
$851$	−6.38307	−	23.8220i	−0.218809	−	0.816606i
$852$		0			0
$853$	−10.3808	+	38.7416i	−0.355431	+	1.32649i	0.524511	+	0.851404i	$0.324248\pi$
$853$	−10.3808	+	38.7416i	−0.355431	+	1.32649i	−0.879942	+	0.475082i	$0.842418\pi$
$854$		0			0
$855$	−5.34544	+	3.61165i	−0.182810	+	0.123516i
$856$		0			0
$857$	47.6428	−	27.5066i	1.62745	−	0.939606i	0.642594	−	0.766206i	$-0.277858\pi$
$857$	47.6428	−	27.5066i	1.62745	−	0.939606i	0.984851	−	0.173400i	$-0.0554753\pi$
$858$		0			0
$859$	−30.6273	+	8.20655i	−1.04499	+	0.280004i	−0.740179	−	0.672409i	$-0.765259\pi$
$859$	−30.6273	+	8.20655i	−1.04499	+	0.280004i	−0.304809	+	0.952413i	$0.598593\pi$
$860$		0			0
$861$	7.85862	+	1.81106i	0.267821	+	0.0617208i
$862$		0			0
$863$	−3.26635			−0.111188			−0.0555940	−	0.998453i	$-0.517705\pi$
$863$	−3.26635			−0.111188			−0.0555940	+	0.998453i	$0.517705\pi$
$864$		0			0
$865$	14.7756			0.502386
$866$		0			0
$867$	−15.8528	−	3.65337i	−0.538390	−	0.124075i
$868$		0			0
$869$	93.9109	−	25.1634i	3.18571	−	0.853608i
$870$		0			0
$871$	47.9818	−	27.7023i	1.62580	−	0.938657i
$872$		0			0
$873$	1.29368	+	18.2945i	0.0437844	+	0.619173i
$874$		0			0
$875$	1.37121	−	5.11741i	0.0463553	−	0.173000i
$876$		0			0
$877$	9.53436	+	35.5827i	0.321952	+	1.20154i	0.917340	+	0.398104i	$0.130332\pi$
$877$	9.53436	+	35.5827i	0.321952	+	1.20154i	−0.595388	+	0.803439i	$0.703002\pi$
$878$		0			0
$879$	7.09579	−	0.250574i	0.239335	−	0.00845165i
$880$		0			0
$881$	−24.2794			−0.817994			−0.408997	−	0.912536i	$-0.634121\pi$
$881$	−24.2794			−0.817994			−0.408997	+	0.912536i	$0.634121\pi$
$882$		0			0
$883$	−17.8136	+	17.8136i	−0.599475	+	0.599475i	−0.940173	−	0.340698i	$-0.889337\pi$
$883$	−17.8136	+	17.8136i	−0.599475	+	0.599475i	0.340698	+	0.940173i	$0.389337\pi$
$884$		0			0
$885$	10.2686	−	3.14383i	0.345175	−	0.105679i
$886$		0			0
$887$	−3.04467	−	1.75784i	−0.102230	−	0.0590225i	0.448013	−	0.894027i	$-0.352132\pi$
$887$	−3.04467	−	1.75784i	−0.102230	−	0.0590225i	−0.550243	+	0.835004i	$0.685465\pi$
$888$		0			0
$889$	−10.8893	+	6.28692i	−0.365214	+	0.210857i
$890$		0			0
$891$	49.3105	−	21.0223i	1.65196	−	0.704275i
$892$		0			0
$893$	−22.0660	−	5.91258i	−0.738412	−	0.197857i
$894$		0			0
$895$	4.06883	−	7.04742i	0.136006	−	0.235569i
$896$		0			0
$897$	−15.1401	+	28.5014i	−0.505514	+	0.951633i
$898$		0			0
$899$	−7.56046	+	7.56046i	−0.252155	+	0.252155i
$900$		0			0
$901$	−21.0885	−	21.0885i	−0.702559	−	0.702559i
$902$		0			0
$903$	0.0348700	+	0.987454i	0.00116040	+	0.0328604i
$904$		0			0
$905$	−16.6241	−	9.59793i	−0.552604	−	0.319046i
$906$		0			0
$907$	−7.82207	+	29.1924i	−0.259727	+	0.969316i	0.705672	+	0.708539i	$0.250645\pi$
$907$	−7.82207	+	29.1924i	−0.259727	+	0.969316i	−0.965399	+	0.260777i	$0.916021\pi$
$908$		0			0
$909$	25.1244	−	28.9481i	0.833323	−	0.960147i
$910$		0			0
$911$	25.9833	+	45.0044i	0.860866	+	1.49106i	0.871094	+	0.491116i	$0.163411\pi$
$911$	25.9833	+	45.0044i	0.860866	+	1.49106i	−0.0102283	+	0.999948i	$0.503256\pi$
$912$		0			0
$913$	−16.5514	+	28.6679i	−0.547772	+	0.948769i
$914$		0			0
$915$	5.78492	+	1.33317i	0.191243	+	0.0440731i
$916$		0			0
$917$	5.59735	+	5.59735i	0.184841	+	0.184841i
$918$		0			0
$919$			24.7771i			0.817322i	0.912686	+	0.408661i	$0.134004\pi$
$919$			24.7771i			0.817322i	−0.912686	+	0.408661i	$0.865996\pi$
$920$		0			0
$921$	−11.2218	+	7.01827i	−0.369770	+	0.231260i
$922$		0			0
$923$	19.3226	−	5.17748i	0.636011	−	0.170419i
$924$		0			0
$925$	24.8904	+	6.66936i	0.818391	+	0.219287i
$926$		0			0
$927$	−3.54640	−	5.24888i	−0.116479	−	0.172396i
$928$		0			0
$929$	18.9049	+	32.7442i	0.620249	+	1.07430i	0.989439	+	0.144949i	$0.0463017\pi$
$929$	18.9049	+	32.7442i	0.620249	+	1.07430i	−0.369190	+	0.929354i	$0.620365\pi$
$930$		0			0
$931$	4.17306	+	15.5741i	0.136767	+	0.510420i
$932$		0			0
$933$	19.7448	+	18.3978i	0.646415	+	0.602318i
$934$		0			0
$935$			14.3975i			0.470849i
$936$		0			0
$937$			18.8873i			0.617022i	0.951221	+	0.308511i	$0.0998307\pi$
$937$			18.8873i			0.617022i	−0.951221	+	0.308511i	$0.900169\pi$
$938$		0			0
$939$	48.6880	−	14.9063i	1.58887	−	0.486448i
$940$		0			0
$941$	2.22556	+	8.30590i	0.0725511	+	0.270765i	0.992667	−	0.120882i	$-0.0385723\pi$
$941$	2.22556	+	8.30590i	0.0725511	+	0.270765i	−0.920116	+	0.391647i	$0.871906\pi$
$942$		0			0
$943$	14.4001	+	24.9417i	0.468931	+	0.812213i
$944$		0			0
$945$	−2.96522	+	0.315182i	−0.0964588	+	0.0102529i
$946$		0			0
$947$	29.3101	+	7.85363i	0.952452	+	0.255209i	0.701402	−	0.712766i	$-0.252558\pi$
$947$	29.3101	+	7.85363i	0.952452	+	0.255209i	0.251049	+	0.967974i	$0.419224\pi$
$948$		0			0
$949$	2.91764	−	0.781778i	0.0947105	−	0.0253776i
$950$		0			0
$951$	8.35547	+	4.43849i	0.270945	+	0.143928i
$952$		0			0
$953$		−	53.9237i		−	1.74676i	−0.487038	−	0.873381i	$-0.661923\pi$
$953$		−	53.9237i		−	1.74676i	0.487038	−	0.873381i	$-0.338077\pi$
$954$		0			0
$955$	−2.14468	−	2.14468i	−0.0694002	−	0.0694002i
$956$		0			0
$957$	18.0062	−	19.3245i	0.582058	−	0.624672i
$958$		0			0
$959$	−1.08908	+	1.88635i	−0.0351684	+	0.0609134i
$960$		0			0
$961$	6.78043	+	11.7441i	0.218724	+	0.378840i
$962$		0			0
$963$	−10.0610	−	29.1452i	−0.324212	−	0.939190i
$964$		0			0
$965$	−2.23835	+	8.35362i	−0.0720549	+	0.268913i
$966$		0			0
$967$	−17.5688	−	10.1433i	−0.564973	−	0.326187i	0.190166	−	0.981752i	$-0.439097\pi$
$967$	−17.5688	−	10.1433i	−0.564973	−	0.326187i	−0.755139	+	0.655565i	$0.772431\pi$
$968$		0			0
$969$	9.93817	−	6.21547i	0.319260	−	0.199670i
$970$		0			0
$971$	−8.82647	−	8.82647i	−0.283255	−	0.283255i	0.551151	−	0.834406i	$-0.314189\pi$
$971$	−8.82647	−	8.82647i	−0.283255	−	0.283255i	−0.834406	+	0.551151i	$0.814189\pi$
$972$		0			0
$973$	−5.01092	+	5.01092i	−0.160643	+	0.160643i
$974$		0			0
$975$	−17.8804	−	28.5897i	−0.572630	−	0.915602i
$976$		0			0
$977$	21.4183	−	37.0976i	0.685233	−	1.18686i	−0.288131	−	0.957591i	$-0.593034\pi$
$977$	21.4183	−	37.0976i	0.685233	−	1.18686i	0.973364	−	0.229267i	$-0.0736328\pi$
$978$		0			0
$979$	29.4031	+	7.87854i	0.939728	+	0.251799i
$980$		0			0
$981$	22.9864	−	7.93502i	0.733900	−	0.253346i
$982$		0			0
$983$	16.9469	−	9.78431i	0.540523	−	0.312071i	−0.204768	−	0.978811i	$-0.565644\pi$
$983$	16.9469	−	9.78431i	0.540523	−	0.312071i	0.745291	+	0.666740i	$0.232311\pi$
$984$		0			0
$985$	−5.31635	−	3.06940i	−0.169393	−	0.0977991i
$986$		0			0
$987$	−7.72546	−	7.19845i	−0.245904	−	0.229129i
$988$		0			0
$989$	−2.49508	+	2.49508i	−0.0793390	+	0.0793390i
$990$		0			0
$991$	26.7726			0.850459			0.425230	−	0.905086i	$-0.360193\pi$
$991$	26.7726			0.850459			0.425230	+	0.905086i	$0.360193\pi$
$992$		0			0
$993$	20.9867	−	39.5076i	0.665993	−	1.25374i
$994$		0			0
$995$	4.40015	+	16.4216i	0.139494	+	0.520599i
$996$		0			0
$997$	2.37990	−	8.88189i	0.0753720	−	0.281292i	−0.917945	−	0.396707i	$-0.870153\pi$
$997$	2.37990	−	8.88189i	0.0753720	−	0.281292i	0.993317	+	0.115415i	$0.0368196\pi$
$998$		0			0
$999$	−3.34424	−	31.4626i	−0.105807	−	0.995431i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.49.17		72
3.2	odd	2		1728.2.bc.e.1009.12		72
4.3	odd	2		144.2.x.e.85.1	yes	72
9.2	odd	6		1728.2.bc.e.1585.7		72
9.7	even	3	inner	576.2.bb.e.241.9		72
12.11	even	2		432.2.y.e.37.18		72
16.3	odd	4		144.2.x.e.13.11	✓	72
16.13	even	4	inner	576.2.bb.e.337.9		72
36.7	odd	6		144.2.x.e.133.11	yes	72
36.11	even	6		432.2.y.e.181.8		72
48.29	odd	4		1728.2.bc.e.145.7		72
48.35	even	4		432.2.y.e.253.8		72
144.29	odd	12		1728.2.bc.e.721.12		72
144.61	even	12	inner	576.2.bb.e.529.17		72
144.83	even	12		432.2.y.e.397.18		72
144.115	odd	12		144.2.x.e.61.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.11	✓	72	16.3	odd	4
144.2.x.e.61.1	yes	72	144.115	odd	12
144.2.x.e.85.1	yes	72	4.3	odd	2
144.2.x.e.133.11	yes	72	36.7	odd	6
432.2.y.e.37.18		72	12.11	even	2
432.2.y.e.181.8		72	36.11	even	6
432.2.y.e.253.8		72	48.35	even	4
432.2.y.e.397.18		72	144.83	even	12
576.2.bb.e.49.17		72	1.1	even	1	trivial
576.2.bb.e.241.9		72	9.7	even	3	inner
576.2.bb.e.337.9		72	16.13	even	4	inner
576.2.bb.e.529.17		72	144.61	even	12	inner
1728.2.bc.e.145.7		72	48.29	odd	4
1728.2.bc.e.721.12		72	144.29	odd	12
1728.2.bc.e.1009.12		72	3.2	odd	2
1728.2.bc.e.1585.7		72	9.2	odd	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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.68781 + 0.388965i) q^{3} +(-0.846545 + 0.226831i) q^{5} +(0.567074 - 0.327400i) q^{7} +(2.69741 + 1.31300i) q^{9} +O(q^{10})\)	\(q+(1.68781 + 0.388965i) q^{3} +(-0.846545 + 0.226831i) q^{5} +(0.567074 - 0.327400i) q^{7} +(2.69741 + 1.31300i) q^{9} +(1.54155 - 5.75313i) q^{11} +(1.19068 + 4.44367i) q^{13} +(-1.51704 + 0.0535712i) q^{15} +2.75816 q^{17} +(1.73499 - 1.73499i) q^{19} +(1.08446 - 0.332018i) q^{21} +(3.50762 + 2.02512i) q^{23} +(-3.66494 + 2.11595i) q^{25} +(4.04201 + 3.26530i) q^{27} +(2.47312 + 0.662669i) q^{29} +(-2.08801 + 3.61654i) q^{31} +(4.83961 - 9.11059i) q^{33} +(-0.405789 + 0.405789i) q^{35} +(-4.30563 - 4.30563i) q^{37} +(0.281205 + 7.96320i) q^{39} +(6.15806 + 3.55536i) q^{41} +(-0.225483 + 0.841515i) q^{43} +(-2.58131 - 0.499657i) q^{45} +(-4.65521 - 8.06305i) q^{47} +(-3.28562 + 5.69086i) q^{49} +(4.65526 + 1.07283i) q^{51} +(-7.64584 - 7.64584i) q^{53} +5.21996i q^{55} +(3.60318 - 2.25348i) q^{57} +(-6.83351 + 1.83103i) q^{59} +(-3.77755 - 1.01219i) q^{61} +(1.95951 - 0.138565i) q^{63} +(-2.01592 - 3.49168i) q^{65} +(-3.11705 - 11.6330i) q^{67} +(5.13249 + 4.78237i) q^{69} -4.34835i q^{71} -0.656583i q^{73} +(-7.00876 + 2.14580i) q^{75} +(-1.00941 - 3.76715i) q^{77} +(8.16172 + 14.1365i) q^{79} +(5.55206 + 7.08340i) q^{81} +(-5.36845 - 1.43847i) q^{83} +(-2.33491 + 0.625638i) q^{85} +(3.91640 + 2.08042i) q^{87} +5.11081i q^{89} +(2.13006 + 2.13006i) q^{91} +(-4.93087 + 5.29187i) q^{93} +(-1.07520 + 1.86230i) q^{95} +(3.05669 + 5.29434i) q^{97} +(11.7120 - 13.4945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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