LMFDB - Embedded newform 936.2.be.a.685.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(685,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.685"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24,1,0,-1,0,0,-2,10,0,-3,0,0,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 104)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			685.7
Character	$\chi$	$=$	936.685
Dual form			936.2.be.a.757.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.262058 + 1.38972i) q^{2} +(-1.86265 + 0.728375i) q^{4} -0.497079i q^{5} +(-0.845740 - 1.46486i) q^{7} +(-1.50036 - 2.39769i) q^{8} +(0.690801 - 0.130263i) q^{10} +(3.29345 + 1.90148i) q^{11} +(-1.15864 - 3.41432i) q^{13} +(1.81412 - 1.55922i) q^{14} +(2.93894 - 2.71342i) q^{16} +(1.69983 + 2.94419i) q^{17} +(-1.05470 + 0.608933i) q^{19} +(0.362060 + 0.925884i) q^{20} +(-1.77945 + 5.07528i) q^{22} +(4.43183 - 7.67616i) q^{23} +4.75291 q^{25} +(4.44132 - 2.50493i) q^{26} +(2.64229 + 2.11252i) q^{28} +(-0.342961 - 0.198009i) q^{29} +2.08430 q^{31} +(4.54107 + 3.37323i) q^{32} +(-3.64615 + 3.13383i) q^{34} +(-0.728152 + 0.420399i) q^{35} +(8.53399 + 4.92710i) q^{37} +(-1.12264 - 1.30617i) q^{38} +(-1.19184 + 0.745797i) q^{40} +(2.30090 - 3.98527i) q^{41} +(-2.68011 + 1.54736i) q^{43} +(-7.51955 - 1.14292i) q^{44} +(11.8291 + 4.14741i) q^{46} +3.97467 q^{47} +(2.06945 - 3.58439i) q^{49} +(1.24554 + 6.60522i) q^{50} +(4.64504 + 5.51576i) q^{52} +5.68458i q^{53} +(0.945183 - 1.63711i) q^{55} +(-2.24337 + 4.22565i) q^{56} +(0.185301 - 0.528511i) q^{58} +(-5.36063 + 3.09496i) q^{59} +(3.53620 - 2.04163i) q^{61} +(0.546207 + 2.89659i) q^{62} +(-3.49783 + 7.19480i) q^{64} +(-1.69718 + 0.575933i) q^{65} +(-6.67080 - 3.85139i) q^{67} +(-5.31066 - 4.24588i) q^{68} +(-0.775056 - 0.901760i) q^{70} +(-3.83307 - 6.63908i) q^{71} +6.02464 q^{73} +(-4.61090 + 13.1511i) q^{74} +(1.52101 - 1.90245i) q^{76} -6.43262i q^{77} -9.36611 q^{79} +(-1.34878 - 1.46088i) q^{80} +(6.14138 + 2.15323i) q^{82} +7.17235i q^{83} +(1.46349 - 0.844947i) q^{85} +(-2.85275 - 3.31911i) q^{86} +(-0.382219 - 10.7496i) q^{88} +(6.31322 - 10.9348i) q^{89} +(-4.02161 + 4.58487i) q^{91} +(-2.66383 + 17.5260i) q^{92} +(1.04159 + 5.52368i) q^{94} +(0.302688 + 0.524270i) q^{95} +(0.832515 + 1.44196i) q^{97} +(5.52362 + 1.93664i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) $ 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.262058	+	1.38972i	0.185303	+	0.982681i
$2$	0.262058	+	1.38972i	0.185303	+	0.982681i
$3$		0			0
$3$		0			0
$4$	−1.86265	+	0.728375i	−0.931326	+	0.364188i
$5$		−	0.497079i		−	0.222300i	−0.993804	−	0.111150i	$-0.964547\pi$
$5$		−	0.497079i		−	0.222300i	0.993804	−	0.111150i	$-0.0354534\pi$
$6$		0			0
$7$	−0.845740	−	1.46486i	−0.319660	−	0.553667i	0.660757	−	0.750600i	$-0.270235\pi$
$7$	−0.845740	−	1.46486i	−0.319660	−	0.553667i	−0.980417	+	0.196933i	$0.936902\pi$
$8$	−1.50036	−	2.39769i	−0.530458	−	0.847711i
$9$		0			0
$10$	0.690801	−	0.130263i	0.218450	−	0.0411929i
$11$	3.29345	+	1.90148i	0.993014	+	0.573317i	0.906174	−	0.422905i	$-0.138990\pi$
$11$	3.29345	+	1.90148i	0.993014	+	0.573317i	0.0868401	+	0.996222i	$0.472323\pi$
$12$		0			0
$13$	−1.15864	−	3.41432i	−0.321348	−	0.946961i
$13$	−1.15864	−	3.41432i	−0.321348	−	0.946961i
$14$	1.81412	−	1.55922i	0.484844	−	0.416720i
$15$		0			0
$16$	2.93894	−	2.71342i	0.734735	−	0.678354i
$17$	1.69983	+	2.94419i	0.412269	+	0.714070i	0.995137	−	0.0984962i	$-0.0314032\pi$
$17$	1.69983	+	2.94419i	0.412269	+	0.714070i	−0.582869	+	0.812566i	$0.698070\pi$
$18$		0			0
$19$	−1.05470	+	0.608933i	−0.241966	+	0.139699i	−0.616080	−	0.787684i	$-0.711280\pi$
$19$	−1.05470	+	0.608933i	−0.241966	+	0.139699i	0.374114	+	0.927383i	$0.377947\pi$
$20$	0.362060	+	0.925884i	0.0809590	+	0.207034i
$21$		0			0
$22$	−1.77945	+	5.07528i	−0.379379	+	1.08205i
$23$	4.43183	−	7.67616i	0.924101	−	1.60059i	0.131099	−	0.991369i	$-0.458149\pi$
$23$	4.43183	−	7.67616i	0.924101	−	1.60059i	0.793001	−	0.609220i	$-0.208517\pi$
$24$		0			0
$25$	4.75291			0.950583
$26$	4.44132	−	2.50493i	0.871015	−	0.491257i
$27$		0			0
$28$	2.64229	+	2.11252i	0.499346	+	0.399228i
$29$	−0.342961	−	0.198009i	−0.0636863	−	0.0367693i	0.467819	−	0.883824i	$-0.345040\pi$
$29$	−0.342961	−	0.198009i	−0.0636863	−	0.0367693i	−0.531505	+	0.847055i	$0.678373\pi$
$30$		0			0
$31$	2.08430			0.374351			0.187176	−	0.982326i	$-0.440067\pi$
$31$	2.08430			0.374351			0.187176	+	0.982326i	$0.440067\pi$
$32$	4.54107	+	3.37323i	0.802755	+	0.596309i
$33$		0			0
$34$	−3.64615	+	3.13383i	−0.625309	+	0.537448i
$35$	−0.728152	+	0.420399i	−0.123080	+	0.0710604i
$36$		0			0
$37$	8.53399	+	4.92710i	1.40298	+	0.810011i	0.994697	−	0.102845i	$-0.0327944\pi$
$37$	8.53399	+	4.92710i	1.40298	+	0.810011i	0.408283	+	0.912856i	$0.366128\pi$
$38$	−1.12264	−	1.30617i	−0.182116	−	0.211888i
$39$		0			0
$40$	−1.19184	+	0.745797i	−0.188446	+	0.117921i
$41$	2.30090	−	3.98527i	0.359339	−	0.622394i	−0.628511	−	0.777801i	$-0.716335\pi$
$41$	2.30090	−	3.98527i	0.359339	−	0.622394i	0.987851	+	0.155406i	$0.0496687\pi$
$42$		0			0
$43$	−2.68011	+	1.54736i	−0.408713	+	0.235971i	−0.690237	−	0.723584i	$-0.742494\pi$
$43$	−2.68011	+	1.54736i	−0.408713	+	0.235971i	0.281524	+	0.959554i	$0.409160\pi$
$44$	−7.51955	−	1.14292i	−1.13361	−	0.172301i
$45$		0			0
$46$	11.8291	+	4.14741i	1.74411	+	0.611503i
$47$	3.97467			0.579765			0.289882	−	0.957062i	$-0.406384\pi$
$47$	3.97467			0.579765			0.289882	+	0.957062i	$0.406384\pi$
$48$		0			0
$49$	2.06945	−	3.58439i	0.295636	−	0.512056i
$50$	1.24554	+	6.60522i	0.176146	+	0.934120i
$51$		0			0
$52$	4.64504	+	5.51576i	0.644151	+	0.764899i
$53$			5.68458i			0.780837i	0.920637	+	0.390419i	$0.127670\pi$
$53$			5.68458i			0.780837i	−0.920637	+	0.390419i	$0.872330\pi$
$54$		0			0
$55$	0.945183	−	1.63711i	0.127449	−	0.220747i
$56$	−2.24337	+	4.22565i	−0.299784	+	0.564676i
$57$		0			0
$58$	0.185301	−	0.528511i	0.0243313	−	0.0693968i
$59$	−5.36063	+	3.09496i	−0.697895	+	0.402930i	−0.806563	−	0.591148i	$-0.798675\pi$
$59$	−5.36063	+	3.09496i	−0.697895	+	0.402930i	0.108668	+	0.994078i	$0.465341\pi$
$60$		0			0
$61$	3.53620	−	2.04163i	0.452764	−	0.261404i	−0.256233	−	0.966615i	$-0.582481\pi$
$61$	3.53620	−	2.04163i	0.452764	−	0.261404i	0.708997	+	0.705211i	$0.249148\pi$
$62$	0.546207	+	2.89659i	0.0693684	+	0.367868i
$63$		0			0
$64$	−3.49783	+	7.19480i	−0.437229	+	0.899350i
$65$	−1.69718	+	0.575933i	−0.210510	+	0.0714357i
$66$		0			0
$67$	−6.67080	−	3.85139i	−0.814969	−	0.470522i	0.0337098	−	0.999432i	$-0.489268\pi$
$67$	−6.67080	−	3.85139i	−0.814969	−	0.470522i	−0.848678	+	0.528909i	$0.822601\pi$
$68$	−5.31066	−	4.24588i	−0.644012	−	0.514889i
$69$		0			0
$70$	−0.775056	−	0.901760i	−0.0926369	−	0.107781i
$71$	−3.83307	−	6.63908i	−0.454902	−	0.787913i	0.543781	−	0.839227i	$-0.316992\pi$
$71$	−3.83307	−	6.63908i	−0.454902	−	0.787913i	−0.998683	+	0.0513141i	$0.983659\pi$
$72$		0			0
$73$	6.02464			0.705131			0.352566	−	0.935787i	$-0.385309\pi$
$73$	6.02464			0.705131			0.352566	+	0.935787i	$0.385309\pi$
$74$	−4.61090	+	13.1511i	−0.536006	+	1.52878i
$75$		0			0
$76$	1.52101	−	1.90245i	0.174472	−	0.218226i
$77$		−	6.43262i		−	0.733065i
$78$		0			0
$79$	−9.36611			−1.05377			−0.526885	−	0.849937i	$-0.676640\pi$
$79$	−9.36611			−1.05377			−0.526885	+	0.849937i	$0.676640\pi$
$80$	−1.34878	−	1.46088i	−0.150798	−	0.163332i
$81$		0			0
$82$	6.14138	+	2.15323i	0.678202	+	0.237785i
$83$			7.17235i			0.787268i	0.919267	+	0.393634i	$0.128782\pi$
$83$			7.17235i			0.787268i	−0.919267	+	0.393634i	$0.871218\pi$
$84$		0			0
$85$	1.46349	−	0.844947i	0.158738	−	0.0916474i
$86$	−2.85275	−	3.31911i	−0.307620	−	0.357909i
$87$		0			0
$88$	−0.382219	−	10.7496i	−0.0407447	−	1.14591i
$89$	6.31322	−	10.9348i	0.669200	−	1.15909i	−0.308929	−	0.951085i	$-0.599970\pi$
$89$	6.31322	−	10.9348i	0.669200	−	1.15909i	0.978128	−	0.208003i	$-0.0666963\pi$
$90$		0			0
$91$	−4.02161	+	4.58487i	−0.421579	+	0.480625i
$92$	−2.66383	+	17.5260i	−0.277724	+	1.82722i
$93$		0			0
$94$	1.04159	+	5.52368i	0.107432	+	0.569724i
$95$	0.302688	+	0.524270i	0.0310551	+	0.0537890i
$96$		0			0
$97$	0.832515	+	1.44196i	0.0845291	+	0.146409i	0.905190	−	0.425006i	$-0.139728\pi$
$97$	0.832515	+	1.44196i	0.0845291	+	0.146409i	−0.820661	+	0.571415i	$0.806395\pi$
$98$	5.52362	+	1.93664i	0.557970	+	0.195630i
$99$		0			0
$100$	−8.85302	+	3.46190i	−0.885302	+	0.346190i
$101$	−6.79643	−	3.92392i	−0.676270	−	0.390444i	0.122178	−	0.992508i	$-0.461012\pi$
$101$	−6.79643	−	3.92392i	−0.676270	−	0.390444i	−0.798448	+	0.602064i	$0.794345\pi$
$102$		0			0
$103$	13.2316			1.30375			0.651873	−	0.758328i	$-0.273983\pi$
$103$	13.2316			1.30375			0.651873	+	0.758328i	$0.273983\pi$
$104$	−6.44810	+	7.90076i	−0.632289	+	0.774733i
$105$		0			0
$106$	−7.89998	+	1.48969i	−0.767314	+	0.144691i
$107$	−7.63683	−	4.40913i	−0.738281	−	0.426247i	0.0831632	−	0.996536i	$-0.473498\pi$
$107$	−7.63683	−	4.40913i	−0.738281	−	0.426247i	−0.821444	+	0.570289i	$0.806831\pi$
$108$		0			0
$109$			3.65580i			0.350162i	0.984554	+	0.175081i	$0.0560188\pi$
$109$			3.65580i			0.350162i	−0.984554	+	0.175081i	$0.943981\pi$
$110$	2.52281	+	0.884525i	0.240541	+	0.0843362i
$111$		0			0
$112$	−6.46037	−	2.01030i	−0.610447	−	0.189956i
$113$	5.71030	+	9.89054i	0.537180	+	0.930423i	0.999054	+	0.0434779i	$0.0138438\pi$
$113$	5.71030	+	9.89054i	0.537180	+	0.930423i	−0.461874	+	0.886945i	$0.652823\pi$
$114$		0			0
$115$	−3.81565	−	2.20297i	−0.355811	−	0.205428i
$116$	0.783042	+	0.119017i	0.0727036	+	0.0110504i
$117$		0			0
$118$	−5.70593	−	6.63872i	−0.525274	−	0.611144i
$119$	2.87522	−	4.98003i	0.263571	−	0.456519i
$120$		0			0
$121$	1.73123	+	2.99858i	0.157384	+	0.272598i
$122$	3.76398	+	4.37931i	0.340775	+	0.396484i
$123$		0			0
$124$	−3.88232	+	1.51815i	−0.348643	+	0.136334i
$125$		−	4.84796i		−	0.433615i
$126$		0			0
$127$	6.38026	−	11.0509i	0.566157	−	0.980612i	−0.430784	−	0.902455i	$-0.641763\pi$
$127$	6.38026	−	11.0509i	0.566157	−	0.980612i	0.996941	−	0.0781574i	$-0.0249037\pi$
$128$	−10.9154	−	2.97556i	−0.964795	−	0.263005i
$129$		0			0
$130$	−1.24515	−	2.20769i	−0.109207	−	0.193627i
$131$		−	11.2798i		−	0.985523i	−0.870165	−	0.492761i	$-0.835988\pi$
$131$		−	11.2798i		−	0.985523i	0.870165	−	0.492761i	$-0.164012\pi$
$132$		0			0
$133$	1.78401	+	1.03000i	0.154693	+	0.0893121i
$134$	3.60422	−	10.2798i	0.311357	−	0.888044i
$135$		0			0
$136$	4.50889	−	8.49300i	0.386634	−	0.728269i
$137$	3.69961	+	6.40791i	0.316079	+	0.547465i	0.979666	−	0.200634i	$-0.0643002\pi$
$137$	3.69961	+	6.40791i	0.316079	+	0.547465i	−0.663587	+	0.748099i	$0.730967\pi$
$138$		0			0
$139$	−10.2330	+	5.90805i	−0.867956	+	0.501115i	−0.866668	−	0.498885i	$-0.833743\pi$
$139$	−10.2330	+	5.90805i	−0.867956	+	0.501115i	−0.00128744	+	0.999999i	$0.500410\pi$
$140$	1.05009	−	1.31342i	0.0887485	−	0.111005i
$141$		0			0
$142$	8.22198	−	7.06673i	0.689973	−	0.593026i
$143$	2.67633	−	13.4480i	0.223806	−	1.12458i
$144$		0			0
$145$	−0.0984260	+	0.170479i	−0.00817383	+	0.0141575i
$146$	1.57881	+	8.37258i	0.130663	+	0.692919i
$147$		0			0
$148$	−19.4846	−	2.96153i	−1.60163	−	0.243436i
$149$	10.6954	−	6.17498i	0.876199	−	0.505874i	0.00679591	−	0.999977i	$-0.497837\pi$
$149$	10.6954	−	6.17498i	0.876199	−	0.505874i	0.869403	+	0.494103i	$0.164503\pi$
$150$		0			0
$151$	−17.6993			−1.44035			−0.720175	−	0.693792i	$-0.755939\pi$
$151$	−17.6993			−1.44035			−0.720175	+	0.693792i	$0.755939\pi$
$152$	3.04247	+	1.61523i	0.246777	+	0.131013i
$153$		0			0
$154$	8.93955	−	1.68572i	0.720369	−	0.135839i
$155$		−	1.03606i		−	0.0832184i
$156$		0			0
$157$		−	2.70138i		−	0.215594i	−0.994173	−	0.107797i	$-0.965620\pi$
$157$		−	2.70138i		−	0.215594i	0.994173	−	0.107797i	$-0.0343796\pi$
$158$	−2.45446	−	13.0163i	−0.195267	−	1.03552i
$159$		0			0
$160$	1.67676	−	2.25727i	0.132560	−	0.178453i
$161$	−14.9927			−1.18159
$162$		0			0
$163$	1.86997	−	1.07963i	0.146467	−	0.0845630i	−0.424975	−	0.905205i	$-0.639717\pi$
$163$	1.86997	−	1.07963i	0.146467	−	0.0845630i	0.571443	+	0.820642i	$0.306384\pi$
$164$	−1.38300	+	9.09908i	−0.107994	+	0.710519i
$165$		0			0
$166$	−9.96757	+	1.87957i	−0.773634	+	0.145883i
$167$	−3.70257	+	6.41303i	−0.286513	+	0.496255i	−0.972975	−	0.230910i	$-0.925830\pi$
$167$	−3.70257	+	6.41303i	−0.286513	+	0.496255i	0.686462	+	0.727166i	$0.259163\pi$
$168$		0			0
$169$	−10.3151	+	7.91190i	−0.793471	+	0.608607i
$170$	1.55776	+	1.81242i	0.119475	+	0.139006i
$171$		0			0
$172$	3.86505	−	4.83432i	0.294707	−	0.368614i
$173$	−3.65801	+	2.11195i	−0.278113	+	0.160569i	−0.632569	−	0.774504i	$-0.718000\pi$
$173$	−3.65801	+	2.11195i	−0.278113	+	0.160569i	0.354456	+	0.935073i	$0.384666\pi$
$174$		0			0
$175$	−4.01973	−	6.96237i	−0.303863	−	0.526306i
$176$	14.8388	−	3.34819i	1.11851	−	0.252379i
$177$		0			0
$178$	16.8508	+	5.90806i	1.26302	+	0.442828i
$179$	0.388283	+	0.224175i	0.0290216	+	0.0167557i	0.514441	−	0.857526i	$-0.328000\pi$
$179$	0.388283	+	0.224175i	0.0290216	+	0.0167557i	−0.485419	+	0.874282i	$0.661333\pi$
$180$		0			0
$181$			1.46266i			0.108718i	0.998521	+	0.0543592i	$0.0173116\pi$
$181$			1.46266i			0.108718i	−0.998521	+	0.0543592i	$0.982688\pi$
$182$	−7.42558	−	4.38741i	−0.550421	−	0.325217i
$183$		0			0
$184$	−25.0544	+	0.890850i	−1.84703	+	0.0656743i
$185$	2.44916	−	4.24207i	0.180066	−	0.311883i
$186$		0			0
$187$			12.9287i			0.945442i
$188$	−7.40342	+	2.89505i	−0.539950	+	0.211143i
$189$		0			0
$190$	−0.649268	+	0.558041i	−0.0471029	+	0.0404845i
$191$	4.12331	+	7.14178i	0.298352	+	0.516761i	0.975759	−	0.218847i	$-0.0702297\pi$
$191$	4.12331	+	7.14178i	0.298352	+	0.516761i	−0.677407	+	0.735609i	$0.736896\pi$
$192$		0			0
$193$	−6.31137	+	10.9316i	−0.454302	+	0.786875i	−0.998648	−	0.0519863i	$-0.983445\pi$
$193$	−6.31137	+	10.9316i	−0.454302	+	0.786875i	0.544345	+	0.838861i	$0.316778\pi$
$194$	−1.78575	+	1.53484i	−0.128210	+	0.110195i
$195$		0			0
$196$	−1.24388	+	8.18381i	−0.0888486	+	0.584558i
$197$	15.2949	+	8.83050i	1.08971	+	0.629147i	0.933500	−	0.358576i	$-0.116738\pi$
$197$	15.2949	+	8.83050i	1.08971	+	0.629147i	0.156214	+	0.987723i	$0.450071\pi$
$198$		0			0
$199$	−9.92096	−	17.1836i	−0.703278	−	1.21811i	−0.967309	−	0.253599i	$-0.918386\pi$
$199$	−9.92096	−	17.1836i	−0.703278	−	1.21811i	0.264032	−	0.964514i	$-0.414948\pi$
$200$	−7.13109	−	11.3960i	−0.504244	−	0.805820i
$201$		0			0
$202$	3.67210	−	10.4734i	0.258368	−	0.736908i
$203$			0.669856i			0.0470147i
$204$		0			0
$205$	−1.98099	−	1.14373i	−0.138358	−	0.0798813i
$206$	3.46744	+	18.3882i	0.241588	+	1.28117i
$207$		0			0
$208$	−12.6696	−	6.89061i	−0.878481	−	0.477778i
$209$	−4.63149			−0.320367
$210$		0			0
$211$	13.0695	+	7.54568i	0.899742	+	0.519466i	0.877116	−	0.480278i	$-0.159464\pi$
$211$	13.0695	+	7.54568i	0.899742	+	0.519466i	0.0226255	+	0.999744i	$0.492797\pi$
$212$	−4.14051	−	10.5884i	−0.284371	−	0.727214i
$213$		0			0
$214$	4.12617	−	11.7685i	0.282059	−	0.804479i
$215$	0.769161	+	1.33223i	0.0524563	+	0.0908570i
$216$		0			0
$217$	−1.76277	−	3.05321i	−0.119665	−	0.207266i
$218$	−5.08055	+	0.958032i	−0.344098	+	0.0648861i
$219$		0			0
$220$	−0.568120	+	3.73781i	−0.0383026	+	0.252003i
$221$	8.08291	−	9.21499i	0.543715	−	0.619867i
$222$		0			0
$223$	4.97902	−	8.62392i	0.333420	−	0.577500i	−0.649760	−	0.760139i	$-0.725131\pi$
$223$	4.97902	−	8.62392i	0.333420	−	0.577500i	0.983180	+	0.182639i	$0.0584640\pi$
$224$	1.10077	−	9.50492i	0.0735483	−	0.635074i
$225$		0			0
$226$	−12.2487	+	10.5276i	−0.814769	+	0.700287i
$227$	−1.19973	+	0.692666i	−0.0796291	+	0.0459739i	−0.539286	−	0.842123i	$-0.681306\pi$
$227$	−1.19973	+	0.692666i	−0.0796291	+	0.0459739i	0.459657	+	0.888097i	$0.347972\pi$
$228$		0			0
$229$		−	22.8190i		−	1.50793i	−0.656917	−	0.753963i	$-0.728140\pi$
$229$		−	22.8190i		−	1.50793i	0.656917	−	0.753963i	$-0.271860\pi$
$230$	2.06159	−	5.88000i	0.135937	−	0.387716i
$231$		0			0
$232$	0.0398021	+	1.11940i	0.00261313	+	0.0734922i
$233$	−4.47546			−0.293197			−0.146599	−	0.989196i	$-0.546833\pi$
$233$	−4.47546			−0.293197			−0.146599	+	0.989196i	$0.546833\pi$
$234$		0			0
$235$		−	1.97572i		−	0.128882i
$236$	7.73069	−	9.66939i	0.503225	−	0.629423i
$237$		0			0
$238$	7.67433	+	2.69070i	0.497453	+	0.174412i
$239$	−18.4932			−1.19623			−0.598114	−	0.801411i	$-0.704083\pi$
$239$	−18.4932			−1.19623			−0.598114	+	0.801411i	$0.704083\pi$
$240$		0			0
$241$	6.87454	+	11.9070i	0.442828	+	0.767000i	0.997898	−	0.0648032i	$-0.0206420\pi$
$241$	6.87454	+	11.9070i	0.442828	+	0.767000i	−0.555070	+	0.831803i	$0.687309\pi$
$242$	−3.71350	+	3.19173i	−0.238713	+	0.205172i
$243$		0			0
$244$	−5.09964	+	6.37852i	−0.326471	+	0.408343i
$245$	−1.78172	−	1.02868i	−0.113830	−	0.0657199i
$246$		0			0
$247$	3.30111	+	2.89556i	0.210044	+	0.184240i
$248$	−3.12720	−	4.99750i	−0.198577	−	0.317342i
$249$		0			0
$250$	6.73732	−	1.27045i	0.426105	−	0.0803502i
$251$	3.45759	−	1.99624i	0.218241	−	0.126002i	−0.386894	−	0.922124i	$-0.626452\pi$
$251$	3.45759	−	1.99624i	0.218241	−	0.126002i	0.605136	+	0.796122i	$0.293119\pi$
$252$		0			0
$253$	29.1921	−	16.8540i	1.83529	−	1.05960i
$254$	17.0297	+	5.97080i	1.06854	+	0.374641i
$255$		0			0
$256$	1.27473	−	15.9491i	0.0796706	−	0.996821i
$257$	3.41417	−	5.91352i	0.212970	−	0.368875i	−0.739673	−	0.672967i	$-0.765020\pi$
$257$	3.41417	−	5.91352i	0.212970	−	0.368875i	0.952643	+	0.304092i	$0.0983530\pi$
$258$		0			0
$259$		−	16.6682i		−	1.03571i
$260$	2.74177	−	2.30895i	0.170037	−	0.143195i
$261$		0			0
$262$	15.6758	−	2.95597i	0.968455	−	0.182620i
$263$	−5.96177	+	10.3261i	−0.367619	+	0.636734i	−0.989193	−	0.146621i	$-0.953160\pi$
$263$	−5.96177	+	10.3261i	−0.367619	+	0.636734i	0.621574	+	0.783355i	$0.286493\pi$
$264$		0			0
$265$	2.82568			0.173580
$266$	−0.963896	+	2.74919i	−0.0591003	+	0.168564i
$267$		0			0
$268$	15.2306	+	2.31495i	0.930359	+	0.141408i
$269$	18.3269	−	10.5811i	1.11741	−	0.645139i	0.176674	−	0.984270i	$-0.443466\pi$
$269$	18.3269	−	10.5811i	1.11741	−	0.645139i	0.940739	+	0.339131i	$0.110133\pi$
$270$		0			0
$271$	−10.8551	+	18.8016i	−0.659402	+	1.14212i	0.321368	+	0.946954i	$0.395857\pi$
$271$	−10.8551	+	18.8016i	−0.659402	+	1.14212i	−0.980771	+	0.195164i	$0.937476\pi$
$272$	12.9845	+	4.04045i	0.787301	+	0.244988i
$273$		0			0
$274$	−7.93570	+	6.82067i	−0.479413	+	0.412052i
$275$	15.6535	+	9.03755i	0.943942	+	0.544985i
$276$		0			0
$277$	−1.51540	+	0.874918i	−0.0910517	+	0.0525687i	−0.544835	−	0.838544i	$-0.683408\pi$
$277$	−1.51540	+	0.874918i	−0.0910517	+	0.0525687i	0.453783	+	0.891112i	$0.350074\pi$
$278$	−10.8922	−	12.6728i	−0.653271	−	0.760066i
$279$		0			0
$280$	2.10048	+	1.11513i	0.125528	+	0.0666420i
$281$	16.9779			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$281$	16.9779			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$282$		0			0
$283$	−14.3699	−	8.29645i	−0.854200	−	0.493173i	0.00786548	−	0.999969i	$-0.497496\pi$
$283$	−14.3699	−	8.29645i	−0.854200	−	0.493173i	−0.862066	+	0.506796i	$0.830830\pi$
$284$	11.9754	+	9.57437i	0.710610	+	0.568134i
$285$		0			0
$286$	19.3904	+	0.195198i	1.14658	+	0.0115423i
$287$	−7.78383			−0.459465
$288$		0			0
$289$	2.72118	−	4.71322i	0.160069	−	0.277248i
$290$	−0.262711	−	0.0921093i	−0.0154269	−	0.00540885i
$291$		0			0
$292$	−11.2218	+	4.38820i	−0.656707	+	0.256800i
$293$	−19.9026	+	11.4908i	−1.16272	+	0.671299i	−0.951955	−	0.306237i	$-0.900930\pi$
$293$	−19.9026	+	11.4908i	−1.16272	+	0.671299i	−0.210769	+	0.977536i	$0.567597\pi$
$294$		0			0
$295$	1.53844	+	2.66465i	0.0895714	+	0.155142i
$296$	−0.990405	−	27.8543i	−0.0575661	−	1.61900i
$297$		0			0
$298$	11.3843	+	13.2454i	0.659475	+	0.767285i
$299$	−31.3437	−	6.23781i	−1.81265	−	0.360742i
$300$		0			0
$301$	4.53335	+	2.61733i	0.261298	+	0.150860i
$302$	−4.63825	−	24.5971i	−0.266901	−	1.41541i
$303$		0			0
$304$	−1.44742	+	4.65147i	−0.0830152	+	0.266780i
$305$	−1.01485	−	1.75777i	−0.0581101	−	0.100650i
$306$		0			0
$307$			14.1283i			0.806346i	0.915124	+	0.403173i	$0.132093\pi$
$307$			14.1283i			0.806346i	−0.915124	+	0.403173i	$0.867907\pi$
$308$	4.68536	+	11.9817i	0.266973	+	0.682722i
$309$		0			0
$310$	1.43983	−	0.271508i	0.0817771	−	0.0154206i
$311$	−18.5022			−1.04917			−0.524583	−	0.851359i	$-0.675779\pi$
$311$	−18.5022			−1.04917			−0.524583	+	0.851359i	$0.675779\pi$
$312$		0			0
$313$	−30.0763			−1.70001			−0.850007	−	0.526772i	$-0.823402\pi$
$313$	−30.0763			−1.70001			−0.850007	+	0.526772i	$0.823402\pi$
$314$	3.75417	−	0.707918i	0.211860	−	0.0399501i
$315$		0			0
$316$	17.4458	−	6.82204i	0.981403	−	0.383770i
$317$			29.4608i			1.65469i	0.561698	+	0.827343i	$0.310148\pi$
$317$			29.4608i			1.65469i	−0.561698	+	0.827343i	$0.689852\pi$
$318$		0			0
$319$	−0.753019	−	1.30427i	−0.0421609	−	0.0730249i
$320$	3.57638	+	1.73870i	0.199926	+	0.0971962i
$321$		0			0
$322$	−3.92896	−	20.8357i	−0.218952	−	1.16113i
$323$	−3.58563	−	2.07016i	−0.199510	−	0.115187i
$324$		0			0
$325$	−5.50689	−	16.2280i	−0.305467	−	0.900165i
$326$	1.99042	+	2.31581i	0.110239	+	0.128261i
$327$		0			0
$328$	−13.0076	+	0.462507i	−0.718225	+	0.0255377i
$329$	−3.36153	−	5.82234i	−0.185327	−	0.320996i
$330$		0			0
$331$	5.82316	−	3.36200i	0.320070	−	0.184792i	−0.331354	−	0.943507i	$-0.607505\pi$
$331$	5.82316	−	3.36200i	0.320070	−	0.184792i	0.651424	+	0.758714i	$0.274172\pi$
$332$	−5.22416	−	13.3596i	−0.286713	−	0.733203i
$333$		0			0
$334$	−9.88262	−	3.46495i	−0.540753	−	0.189594i
$335$	−1.91444	+	3.31591i	−0.104597	+	0.181168i
$336$		0			0
$337$	24.6061			1.34038			0.670191	−	0.742189i	$-0.266212\pi$
$337$	24.6061			1.34038			0.670191	+	0.742189i	$0.266212\pi$
$338$	−13.6985	−	12.2618i	−0.745100	−	0.666953i
$339$		0			0
$340$	−2.11054	+	2.63981i	−0.114460	+	0.143164i
$341$	6.86454	+	3.96325i	0.371736	+	0.214622i
$342$		0			0
$343$	−18.8412			−1.01733
$344$	7.73123	+	4.10447i	0.416840	+	0.221298i
$345$		0			0
$346$	−3.89364	−	4.53016i	−0.209323	−	0.243543i
$347$	−24.0795	+	13.9023i	−1.29265	+	0.746314i	−0.979124	−	0.203264i	$-0.934845\pi$
$347$	−24.0795	+	13.9023i	−1.29265	+	0.746314i	−0.313530	+	0.949578i	$0.601512\pi$
$348$		0			0
$349$	−1.80201	−	1.04039i	−0.0964596	−	0.0556910i	0.450994	−	0.892527i	$-0.351069\pi$
$349$	−1.80201	−	1.04039i	−0.0964596	−	0.0556910i	−0.547454	+	0.836836i	$0.684403\pi$
$350$	8.62235	−	7.41084i	0.460884	−	0.396126i
$351$		0			0
$352$	8.54167	+	19.7443i	0.455273	+	1.05238i
$353$	−9.53154	+	16.5091i	−0.507312	+	0.878691i	0.492652	+	0.870227i	$0.336028\pi$
$353$	−9.53154	+	16.5091i	−0.507312	+	0.878691i	−0.999964	+	0.00846439i	$0.997306\pi$
$354$		0			0
$355$	−3.30014	+	1.90534i	−0.175153	+	0.101125i
$356$	−3.79468	+	24.9661i	−0.201117	+	1.32320i
$357$		0			0
$358$	−0.209789	+	0.598352i	−0.0110877	+	0.0316239i
$359$	6.51007			0.343588			0.171794	−	0.985133i	$-0.445044\pi$
$359$	6.51007			0.343588			0.171794	+	0.985133i	$0.445044\pi$
$360$		0			0
$361$	−8.75840	+	15.1700i	−0.460968	+	0.798421i
$362$	−2.03268	+	0.383301i	−0.106836	+	0.0201458i
$363$		0			0
$364$	4.15135	−	11.4692i	0.217590	−	0.601152i
$365$		−	2.99472i		−	0.156751i
$366$		0			0
$367$	2.78509	−	4.82392i	0.145381	−	0.251806i	−0.784134	−	0.620591i	$-0.786893\pi$
$367$	2.78509	−	4.82392i	0.145381	−	0.251806i	0.929515	+	0.368785i	$0.120226\pi$
$368$	−7.80373	−	34.5852i	−0.406798	−	1.80288i
$369$		0			0
$370$	6.53711	+	2.29198i	0.339848	+	0.119154i
$371$	8.32714	−	4.80768i	0.432323	−	0.249602i
$372$		0			0
$373$	−14.8322	+	8.56338i	−0.767982	+	0.443395i	−0.832154	−	0.554544i	$-0.812893\pi$
$373$	−14.8322	+	8.56338i	−0.767982	+	0.443395i	0.0641721	+	0.997939i	$0.479559\pi$
$374$	−17.9673	+	3.38808i	−0.929068	+	0.175193i
$375$		0			0
$376$	−5.96343	−	9.53002i	−0.307541	−	0.491473i
$377$	−0.278698	+	1.40040i	−0.0143537	+	0.0721242i
$378$		0			0
$379$	10.6206	+	6.13180i	0.545543	+	0.314969i	0.747322	−	0.664462i	$-0.231339\pi$
$379$	10.6206	+	6.13180i	0.545543	+	0.314969i	−0.201780	+	0.979431i	$0.564672\pi$
$380$	−0.945667	−	0.756063i	−0.0485117	−	0.0387852i
$381$		0			0
$382$	−8.84454	+	7.60181i	−0.452526	+	0.388943i
$383$	1.62701	+	2.81807i	0.0831365	+	0.143997i	0.904596	−	0.426271i	$-0.140173\pi$
$383$	1.62701	+	2.81807i	0.0831365	+	0.143997i	−0.821459	+	0.570267i	$0.806840\pi$
$384$		0			0
$385$	−3.19752			−0.162961
$386$	−16.8458	−	5.90633i	−0.857431	−	0.300624i
$387$		0			0
$388$	−2.60097	−	2.07948i	−0.132044	−	0.105570i
$389$		−	17.9829i		−	0.911769i	−0.890039	−	0.455884i	$-0.849323\pi$
$389$		−	17.9829i		−	0.911769i	0.890039	−	0.455884i	$-0.150677\pi$
$390$		0			0
$391$	30.1334			1.52391
$392$	−11.6992	+	0.415983i	−0.590898	+	0.0210103i
$393$		0			0
$394$	−8.26379	+	23.5697i	−0.416324	+	1.18743i
$395$			4.65569i			0.234253i
$396$		0			0
$397$	−17.9828	+	10.3824i	−0.902532	+	0.521077i	−0.878021	−	0.478622i	$-0.841136\pi$
$397$	−17.9828	+	10.3824i	−0.902532	+	0.521077i	−0.0245115	+	0.999700i	$0.507803\pi$
$398$	21.2806	−	18.2905i	1.06670	−	0.916818i
$399$		0			0
$400$	13.9685	−	12.8966i	0.698426	−	0.644832i
$401$	−1.17622	+	2.03728i	−0.0587377	+	0.101737i	−0.893899	−	0.448268i	$-0.852041\pi$
$401$	−1.17622	+	2.03728i	−0.0587377	+	0.101737i	0.835161	+	0.550005i	$0.185374\pi$
$402$		0			0
$403$	−2.41494	−	7.11646i	−0.120297	−	0.354496i
$404$	15.5175	+	2.35854i	0.772022	+	0.117342i
$405$		0			0
$406$	−0.930913	+	0.175541i	−0.0462004	+	0.00871195i
$407$	18.7376	+	32.4544i	0.928786	+	1.60870i
$408$		0			0
$409$	18.1089	+	31.3655i	0.895426	+	1.55092i	0.833276	+	0.552857i	$0.186462\pi$
$409$	18.1089	+	31.3655i	0.895426	+	1.55092i	0.0621499	+	0.998067i	$0.480204\pi$
$410$	1.07033	−	3.05275i	0.0528596	−	0.150764i
$411$		0			0
$412$	−24.6458	+	9.63755i	−1.21421	+	0.474808i
$413$	9.06740	+	5.23506i	0.446177	+	0.257601i
$414$		0			0
$415$	3.56522			0.175010
$416$	6.25585	−	19.4130i	0.306718	−	0.951800i
$417$		0			0
$418$	−1.21372	−	6.43648i	−0.0593649	−	0.314819i
$419$	20.6067	+	11.8973i	1.00671	+	0.581222i	0.910225	−	0.414113i	$-0.135908\pi$
$419$	20.6067	+	11.8973i	1.00671	+	0.581222i	0.0964800	+	0.995335i	$0.469242\pi$
$420$		0			0
$421$			19.8220i			0.966067i	0.875602	+	0.483033i	$0.160465\pi$
$421$			19.8220i			0.966067i	−0.875602	+	0.483033i	$0.839535\pi$
$422$	−7.06143	+	20.1404i	−0.343745	+	0.980418i
$423$		0			0
$424$	13.6299	−	8.52892i	0.661925	−	0.414201i
$425$	8.07913	+	13.9935i	0.391895	+	0.678783i
$426$		0			0
$427$	−5.98141	−	3.45337i	−0.289461	−	0.167120i
$428$	17.4363	+	2.65019i	0.842813	+	0.128102i
$429$		0			0
$430$	−1.64986	+	1.41804i	−0.0795632	+	0.0683839i
$431$	−0.190576	+	0.330088i	−0.00917975	+	0.0158998i	−0.870579	−	0.492029i	$-0.836255\pi$
$431$	−0.190576	+	0.330088i	−0.00917975	+	0.0158998i	0.861399	+	0.507929i	$0.169589\pi$
$432$		0			0
$433$	−1.76379	−	3.05497i	−0.0847622	−	0.146813i	0.820528	−	0.571607i	$-0.193680\pi$
$433$	−1.76379	−	3.05497i	−0.0847622	−	0.146813i	−0.905290	+	0.424794i	$0.860346\pi$
$434$	3.78117	−	3.24988i	0.181502	−	0.155999i
$435$		0			0
$436$	−2.66280	−	6.80949i	−0.127525	−	0.326115i
$437$			10.7948i			0.516383i
$438$		0			0
$439$	3.20727	−	5.55516i	0.153075	−	0.265133i	−0.779282	−	0.626674i	$-0.784416\pi$
$439$	3.20727	−	5.55516i	0.153075	−	0.265133i	0.932356	+	0.361541i	$0.117749\pi$
$440$	−5.34339	+	0.189993i	−0.254736	+	0.00905756i
$441$		0			0
$442$	14.9245	+	8.81813i	0.709884	+	0.419436i
$443$			17.5752i			0.835023i	0.908672	+	0.417512i	$0.137098\pi$
$443$			17.5752i			0.835023i	−0.908672	+	0.417512i	$0.862902\pi$
$444$		0			0
$445$	−5.43546	−	3.13816i	−0.257666	−	0.148763i
$446$	13.2896	+	4.65949i	0.629283	+	0.220633i
$447$		0			0
$448$	13.4977	−	0.961078i	0.637705	−	0.0454067i
$449$	18.1700	+	31.4714i	0.857498	+	1.48523i	0.874308	+	0.485371i	$0.161315\pi$
$449$	18.1700	+	31.4714i	0.857498	+	1.48523i	−0.0168107	+	0.999859i	$0.505351\pi$
$450$		0			0
$451$	15.1558	−	8.75020i	0.713658	−	0.412031i
$452$	−17.8403	−	14.2634i	−0.839138	−	0.670893i
$453$		0			0
$454$	−1.27701	−	1.48578i	−0.0599332	−	0.0697309i
$455$	2.27904	+	1.99905i	0.106843	+	0.0937171i
$456$		0			0
$457$	−6.58332	+	11.4026i	−0.307955	+	0.533393i	−0.977915	−	0.209004i	$-0.932978\pi$
$457$	−6.58332	+	11.4026i	−0.307955	+	0.533393i	0.669960	+	0.742397i	$0.266311\pi$
$458$	31.7121	−	5.97991i	1.48181	−	0.279423i
$459$		0			0
$460$	8.71182	+	1.32413i	0.406191	+	0.0617381i
$461$	−12.7594	+	7.36666i	−0.594266	+	0.343099i	−0.766782	−	0.641907i	$-0.778143\pi$
$461$	−12.7594	+	7.36666i	−0.594266	+	0.343099i	0.172517	+	0.985007i	$0.444810\pi$
$462$		0			0
$463$	−5.65151			−0.262648			−0.131324	−	0.991339i	$-0.541923\pi$
$463$	−5.65151			−0.262648			−0.131324	+	0.991339i	$0.541923\pi$
$464$	−1.54522	+	0.348661i	−0.0717352	+	0.0161862i
$465$		0			0
$466$	−1.17283	−	6.21965i	−0.0543303	−	0.288120i
$467$		−	29.5883i		−	1.36918i	−0.728926	−	0.684592i	$-0.759980\pi$
$467$		−	29.5883i		−	1.36918i	0.728926	−	0.684592i	$-0.240020\pi$
$468$		0			0
$469$			13.0291i			0.601628i
$470$	2.74570	−	0.517753i	0.126650	−	0.0238822i
$471$		0			0
$472$	15.4636	+	8.20957i	0.711772	+	0.377876i
$473$	−11.7691			−0.541144
$474$		0			0
$475$	−5.01291	+	2.89421i	−0.230008	+	0.132795i
$476$	−1.72821	+	11.3703i	−0.0792122	+	0.521157i
$477$		0			0
$478$	−4.84630	−	25.7004i	−0.221665	−	1.17551i
$479$	−7.57479	+	13.1199i	−0.346101	+	0.599464i	−0.985553	−	0.169367i	$-0.945828\pi$
$479$	−7.57479	+	13.1199i	−0.346101	+	0.599464i	0.639452	+	0.768831i	$0.279161\pi$
$480$		0			0
$481$	6.93491	−	34.8465i	0.316205	−	1.58886i
$482$	−14.7459	+	12.6740i	−0.671660	+	0.577286i
$483$		0			0
$484$	−5.40877	−	4.32432i	−0.245853	−	0.196560i
$485$	0.716766	−	0.413825i	0.0325467	−	0.0187908i
$486$		0			0
$487$	15.0531	+	26.0728i	0.682122	+	1.18147i	0.974332	+	0.225116i	$0.0722761\pi$
$487$	15.0531	+	26.0728i	0.682122	+	1.18147i	−0.292210	+	0.956354i	$0.594391\pi$
$488$	−10.2008	−	5.41554i	−0.461767	−	0.245150i
$489$		0			0
$490$	0.962662	−	2.74567i	0.0434886	−	0.124037i
$491$	23.2315	+	13.4127i	1.04842	+	0.605307i	0.922208	−	0.386695i	$-0.126383\pi$
$491$	23.2315	+	13.4127i	1.04842	+	0.605307i	0.126216	+	0.992003i	$0.459717\pi$
$492$		0			0
$493$		−	1.34632i		−	0.0606353i
$494$	−3.15894	+	5.34642i	−0.142127	+	0.240547i
$495$		0			0
$496$	6.12563	−	5.65557i	0.275049	−	0.253943i
$497$	−6.48356	+	11.2299i	−0.290828	+	0.503728i
$498$		0			0
$499$			18.5109i			0.828660i	0.910127	+	0.414330i	$0.135984\pi$
$499$			18.5109i			0.828660i	−0.910127	+	0.414330i	$0.864016\pi$
$500$	3.53114	+	9.03007i	0.157917	+	0.403837i
$501$		0			0
$502$	3.68031	+	4.28196i	0.164260	+	0.191113i
$503$	−7.36468	−	12.7560i	−0.328375	−	0.568762i	0.653815	−	0.756655i	$-0.273168\pi$
$503$	−7.36468	−	12.7560i	−0.328375	−	0.568762i	−0.982190	+	0.187893i	$0.939834\pi$
$504$		0			0
$505$	−1.95050	+	3.37836i	−0.0867959	+	0.150335i
$506$	31.0724	+	36.1521i	1.38134	+	1.60716i
$507$		0			0
$508$	−3.83498	+	25.2313i	−0.170150	+	1.11946i
$509$	−28.9656	−	16.7233i	−1.28388	−	0.741248i	−0.306324	−	0.951927i	$-0.599099\pi$
$509$	−28.9656	−	16.7233i	−1.28388	−	0.741248i	−0.977555	+	0.210680i	$0.932432\pi$
$510$		0			0
$511$	−5.09528	−	8.82528i	−0.225402	−	0.390408i
$512$	22.4989	−	2.40808i	0.994321	−	0.106423i
$513$		0			0
$514$	9.11285	+	3.19506i	0.401951	+	0.140928i
$515$		−	6.57713i		−	0.289823i
$516$		0			0
$517$	13.0904	+	7.55773i	0.575714	+	0.332389i
$518$	23.1641	−	4.36803i	1.01777	−	0.191920i
$519$		0			0
$520$	3.92730	+	3.20521i	0.172223	+	0.140558i
$521$	−29.7885			−1.30506			−0.652530	−	0.757763i	$-0.726292\pi$
$521$	−29.7885			−1.30506			−0.652530	+	0.757763i	$0.726292\pi$
$522$		0			0
$523$	−1.49190	−	0.861351i	−0.0652364	−	0.0376642i	0.467027	−	0.884243i	$-0.345325\pi$
$523$	−1.49190	−	0.861351i	−0.0652364	−	0.0376642i	−0.532263	+	0.846579i	$0.678658\pi$
$524$	8.21594	+	21.0104i	0.358915	+	0.917843i
$525$		0			0
$526$	−15.9127	−	5.57917i	−0.693828	−	0.243263i
$527$	3.54295	+	6.13656i	0.154333	+	0.267313i
$528$		0			0
$529$	−27.7822	−	48.1203i	−1.20792	−	2.09218i
$530$	0.740493	+	3.92691i	0.0321650	+	0.170574i
$531$		0			0
$532$	−4.07321	−	0.619099i	−0.176596	−	0.0268414i
$533$	−16.2729	−	3.23852i	−0.704856	−	0.140276i
$534$		0			0
$535$	−2.19168	+	3.79611i	−0.0947547	+	0.164120i
$536$	0.774174	+	21.7730i	0.0334392	+	0.940450i
$537$		0			0
$538$	19.5074	+	22.6965i	0.841026	+	0.978515i
$539$	13.6313	−	7.87002i	0.587141	−	0.338986i
$540$		0			0
$541$			36.6856i			1.57724i	0.614883	+	0.788618i	$0.289203\pi$
$541$			36.6856i			1.57724i	−0.614883	+	0.788618i	$0.710797\pi$
$542$	−28.9737	−	10.1585i	−1.24453	−	0.436345i
$543$		0			0
$544$	−2.21240	+	19.1037i	−0.0948560	+	0.819063i
$545$	1.81722			0.0778412
$546$		0			0
$547$			33.7227i			1.44188i	0.692999	+	0.720939i	$0.256289\pi$
$547$			33.7227i			1.44188i	−0.692999	+	0.720939i	$0.743711\pi$
$548$	−11.5584	−	9.24100i	−0.493752	−	0.394756i
$549$		0			0
$550$	−8.45756	+	24.1224i	−0.360631	+	1.02858i
$551$	0.482297			0.0205465
$552$		0			0
$553$	7.92129	+	13.7201i	0.336848	+	0.583437i
$554$	−1.61302	−	1.87671i	−0.0685305	−	0.0797337i
$555$		0			0
$556$	14.7573	−	18.4581i	0.625850	−	0.782800i
$557$	−2.44793	−	1.41331i	−0.103722	−	0.0598839i	0.447242	−	0.894413i	$-0.352406\pi$
$557$	−2.44793	−	1.41331i	−0.103722	−	0.0598839i	−0.550964	+	0.834529i	$0.685740\pi$
$558$		0			0
$559$	8.38846	+	7.35792i	0.354794	+	0.311207i
$560$	−0.999278	+	3.21131i	−0.0422272	+	0.135703i
$561$		0			0
$562$	4.44919	+	23.5945i	0.187678	+	0.995275i
$563$	7.06225	−	4.07739i	0.297638	−	0.171842i	−0.343743	−	0.939064i	$-0.611695\pi$
$563$	7.06225	−	4.07739i	0.297638	−	0.171842i	0.641381	+	0.767222i	$0.278362\pi$
$564$		0			0
$565$	4.91637	−	2.83847i	0.206833	−	0.119415i
$566$	7.76402	−	22.1443i	0.326346	−	0.930793i
$567$		0			0
$568$	−10.1675	+	19.1515i	−0.426617	+	0.803580i
$569$	15.0669	−	26.0967i	0.631638	−	1.09403i	−0.355579	−	0.934646i	$-0.615716\pi$
$569$	15.0669	−	26.0967i	0.631638	−	1.09403i	0.987217	−	0.159382i	$-0.0509503\pi$
$570$		0			0
$571$		−	32.3914i		−	1.35554i	−0.735276	−	0.677768i	$-0.762947\pi$
$571$		−	32.3914i		−	1.35554i	0.735276	−	0.677768i	$-0.237053\pi$
$572$	4.81012	+	26.9983i	0.201121	+	1.12886i
$573$		0			0
$574$	−2.03982	−	10.8174i	−0.0851402	−	0.451508i
$575$	21.0641	−	36.4841i	0.878434	−	1.52149i
$576$		0			0
$577$	15.3547			0.639225			0.319612	−	0.947548i	$-0.396447\pi$
$577$	15.3547			0.639225			0.319612	+	0.947548i	$0.396447\pi$
$578$	7.26317	+	2.54654i	0.302108	+	0.105922i
$579$		0			0
$580$	0.0591608	−	0.389233i	0.00245652	−	0.0161620i
$581$	10.5065	−	6.06594i	0.435884	−	0.251658i
$582$		0			0
$583$	−10.8091	+	18.7219i	−0.447667	+	0.775382i
$584$	−9.03914	−	14.4452i	−0.374042	−	0.597748i
$585$		0			0
$586$	−21.1846	−	24.6479i	−0.875129	−	1.01819i
$587$	0.529297	+	0.305590i	0.0218464	+	0.0126130i	0.510883	−	0.859650i	$-0.329318\pi$
$587$	0.529297	+	0.305590i	0.0218464	+	0.0126130i	−0.489037	+	0.872263i	$0.662652\pi$
$588$		0			0
$589$	−2.19832	+	1.26920i	−0.0905800	+	0.0522964i
$590$	−3.29997	+	2.83630i	−0.135858	+	0.116768i
$591$		0			0
$592$	38.4502	−	8.67583i	1.58029	−	0.356574i
$593$	−39.5530			−1.62425			−0.812123	−	0.583486i	$-0.801688\pi$
$593$	−39.5530			−1.62425			−0.812123	+	0.583486i	$0.801688\pi$
$594$		0			0
$595$	−2.47547	−	1.42921i	−0.101484	−	0.0585919i
$596$	−15.4241	+	19.2921i	−0.631794	+	0.790234i
$597$		0			0
$598$	0.454955	−	45.1937i	0.0186045	−	1.84811i
$599$	18.3132			0.748257			0.374128	−	0.927377i	$-0.377942\pi$
$599$	18.3132			0.748257			0.374128	+	0.927377i	$0.377942\pi$
$600$		0			0
$601$	5.87056	−	10.1681i	0.239465	−	0.414766i	−0.721096	−	0.692836i	$-0.756361\pi$
$601$	5.87056	−	10.1681i	0.239465	−	0.414766i	0.960561	+	0.278069i	$0.0896945\pi$
$602$	−2.44936	+	6.98599i	−0.0998285	+	0.284728i
$603$		0			0
$604$	32.9677	−	12.8917i	1.34144	−	0.524558i
$605$	1.49053	−	0.860557i	0.0605986	−	0.0349866i
$606$		0			0
$607$	17.0834	+	29.5893i	0.693393	+	1.20099i	0.970719	+	0.240216i	$0.0772184\pi$
$607$	17.0834	+	29.5893i	0.693393	+	1.20099i	−0.277326	+	0.960776i	$0.589448\pi$
$608$	−6.84355	−	0.792555i	−0.277543	−	0.0321423i
$609$		0			0
$610$	2.17686	−	1.87100i	0.0881386	−	0.0757544i
$611$	−4.60519	−	13.5708i	−0.186306	−	0.549015i
$612$		0			0
$613$	−17.1561	−	9.90507i	−0.692928	−	0.400062i	0.111780	−	0.993733i	$-0.464345\pi$
$613$	−17.1561	−	9.90507i	−0.692928	−	0.400062i	−0.804708	+	0.593671i	$0.797678\pi$
$614$	−19.6344	+	3.70244i	−0.792381	+	0.149418i
$615$		0			0
$616$	−15.4234	+	9.65125i	−0.621427	+	0.388860i
$617$	−3.28645	−	5.69230i	−0.132308	−	0.229164i	0.792258	−	0.610186i	$-0.208905\pi$
$617$	−3.28645	−	5.69230i	−0.132308	−	0.229164i	−0.924566	+	0.381023i	$0.875572\pi$
$618$		0			0
$619$			12.1233i			0.487277i	0.969866	+	0.243638i	$0.0783410\pi$
$619$			12.1233i			0.487277i	−0.969866	+	0.243638i	$0.921659\pi$
$620$	0.754640	+	1.92982i	0.0303071	+	0.0775034i
$621$		0			0
$622$	−4.84866	−	25.7130i	−0.194414	−	1.03100i
$623$	−21.3574			−0.855664
$624$		0			0
$625$	21.3547			0.854190
$626$	−7.88174	−	41.7977i	−0.315017	−	1.67057i
$627$		0			0
$628$	1.96762	+	5.03173i	0.0785165	+	0.200788i
$629$			33.5009i			1.33577i
$630$		0			0
$631$	7.76063	+	13.4418i	0.308946	+	0.535110i	0.978132	−	0.207985i	$-0.0666905\pi$
$631$	7.76063	+	13.4418i	0.308946	+	0.535110i	−0.669186	+	0.743095i	$0.733357\pi$
$632$	14.0526	+	22.4570i	0.558980	+	0.893293i
$633$		0			0
$634$	−40.9424	+	7.72045i	−1.62603	+	0.306618i
$635$	−5.49319	−	3.17149i	−0.217990	−	0.125857i
$636$		0			0
$637$	−14.6360	−	2.91276i	−0.579899	−	0.115408i
$638$	1.61523	−	1.38828i	0.0639477	−	0.0549625i
$639$		0			0
$640$	−1.47909	+	5.42581i	−0.0584660	+	0.214474i
$641$	5.10157	+	8.83618i	0.201500	+	0.349008i	0.949012	−	0.315240i	$-0.102085\pi$
$641$	5.10157	+	8.83618i	0.201500	+	0.349008i	−0.747512	+	0.664248i	$0.768752\pi$
$642$		0			0
$643$	35.8102	−	20.6750i	1.41222	−	0.815343i	0.416619	−	0.909081i	$-0.363215\pi$
$643$	35.8102	−	20.6750i	1.41222	−	0.815343i	0.995597	+	0.0937380i	$0.0298816\pi$
$644$	27.9262	−	10.9203i	1.10045	−	0.430320i
$645$		0			0
$646$	1.93731	−	5.52552i	0.0762223	−	0.217399i
$647$	2.36752	−	4.10066i	0.0930767	−	0.161214i	−0.815728	−	0.578436i	$-0.803663\pi$
$647$	2.36752	−	4.10066i	0.0930767	−	0.161214i	0.908804	+	0.417223i	$0.136996\pi$
$648$		0			0
$649$	−23.5400			−0.924026
$650$	21.1092	−	11.9057i	0.827971	−	0.466980i
$651$		0			0
$652$	−2.69673	+	3.37301i	−0.105612	+	0.132097i
$653$	11.0711	+	6.39190i	0.433245	+	0.250134i	0.700728	−	0.713428i	$-0.252859\pi$
$653$	11.0711	+	6.39190i	0.433245	+	0.250134i	−0.267483	+	0.963563i	$0.586192\pi$
$654$		0			0
$655$	−5.60696			−0.219082
$656$	−4.05150	−	17.9558i	−0.158185	−	0.701054i
$657$		0			0
$658$	7.21052	−	6.19738i	0.281095	−	0.241599i
$659$	26.7651	−	15.4528i	1.04262	−	0.601957i	0.122046	−	0.992524i	$-0.461054\pi$
$659$	26.7651	−	15.4528i	1.04262	−	0.601957i	0.920574	+	0.390567i	$0.127721\pi$
$660$		0			0
$661$	37.1109	+	21.4260i	1.44345	+	0.833374i	0.998078	−	0.0619739i	$-0.0197396\pi$
$661$	37.1109	+	21.4260i	1.44345	+	0.833374i	0.445368	+	0.895348i	$0.353073\pi$
$662$	6.19825	+	7.21153i	0.240902	+	0.280284i
$663$		0			0
$664$	17.1971	−	10.7611i	0.667376	−	0.417613i
$665$	0.511990	−	0.886792i	0.0198541	−	0.0343883i
$666$		0			0
$667$	−3.03989	+	1.75508i	−0.117705	+	0.0679571i
$668$	2.22550	−	14.6421i	0.0861070	−	0.566520i
$669$		0			0
$670$	−5.10989	−	1.79158i	−0.197412	−	0.0692149i
$671$	15.5284			0.599469
$672$		0			0
$673$	−1.93359	+	3.34907i	−0.0745343	+	0.129097i	−0.900884	−	0.434061i	$-0.857080\pi$
$673$	−1.93359	+	3.34907i	−0.0745343	+	0.129097i	0.826349	+	0.563158i	$0.190414\pi$
$674$	6.44823	+	34.1957i	0.248377	+	1.31717i
$675$		0			0
$676$	13.4507	−	22.2504i	0.517333	−	0.855784i
$677$		−	35.0468i		−	1.34696i	−0.739206	−	0.673479i	$-0.764799\pi$
$677$		−	35.0468i		−	1.34696i	0.739206	−	0.673479i	$-0.235201\pi$
$678$		0			0
$679$	1.40818	−	2.43904i	0.0540411	−	0.0936018i
$680$	−4.22169	−	2.24127i	−0.161894	−	0.0859489i
$681$		0			0
$682$	−3.70890	+	10.5784i	−0.142021	+	0.405068i
$683$	−27.6732	+	15.9771i	−1.05889	+	0.611348i	−0.925124	−	0.379665i	$-0.876039\pi$
$683$	−27.6732	+	15.9771i	−1.05889	+	0.611348i	−0.133763	+	0.991013i	$0.542706\pi$
$684$		0			0
$685$	3.18524	−	1.83900i	0.121702	−	0.0702645i
$686$	−4.93749	−	26.1840i	−0.188514	−	0.999711i
$687$		0			0
$688$	−3.67804	+	11.8199i	−0.140224	+	0.450628i
$689$	19.4090	−	6.58636i	0.739423	−	0.250920i
$690$		0			0
$691$	5.89675	+	3.40449i	0.224323	+	0.129513i	0.607950	−	0.793975i	$-0.291992\pi$
$691$	5.89675	+	3.40449i	0.224323	+	0.129513i	−0.383627	+	0.923488i	$0.625325\pi$
$692$	5.27530	−	6.59824i	0.200537	−	0.250827i
$693$		0			0
$694$	−25.6305	−	29.8206i	−0.972921	−	1.13197i
$695$	2.93677	+	5.08663i	0.111398	+	0.192947i
$696$		0			0
$697$	15.6445			0.592577
$698$	0.973624	−	2.77694i	0.0368522	−	0.105109i
$699$		0			0
$700$	12.5586	+	10.0406i	0.474669	+	0.379499i
$701$		−	39.0001i		−	1.47301i	−0.676431	−	0.736506i	$-0.736474\pi$
$701$		−	39.0001i		−	1.47301i	0.676431	−	0.736506i	$-0.263526\pi$
$702$		0			0
$703$	−12.0011			−0.452630
$704$	−25.2007	+	17.0447i	−0.949787	+	0.642396i
$705$		0			0
$706$	−25.4409	−	8.91984i	−0.957480	−	0.335703i
$707$			13.2745i			0.499237i
$708$		0			0
$709$	−11.4006	+	6.58214i	−0.428159	+	0.247198i	−0.698562	−	0.715550i	$-0.746176\pi$
$709$	−11.4006	+	6.58214i	−0.428159	+	0.247198i	0.270403	+	0.962747i	$0.412843\pi$
$710$	−3.51272	−	4.08697i	−0.131830	−	0.153381i
$711$		0			0
$712$	−35.6904	+	1.26903i	−1.33755	+	0.0475589i
$713$	9.23726	−	15.9994i	0.345938	−	0.599182i
$714$		0			0
$715$	−6.68472	−	1.33035i	−0.249994	−	0.0497522i
$716$	−0.886520	−	0.134745i	−0.0331308	−	0.00503565i
$717$		0			0
$718$	1.70602	+	9.04719i	0.0636680	+	0.337638i
$719$	−4.83129	−	8.36804i	−0.180177	−	0.312075i	0.761764	−	0.647855i	$-0.224334\pi$
$719$	−4.83129	−	8.36804i	−0.180177	−	0.312075i	−0.941941	+	0.335779i	$0.891000\pi$
$720$		0			0
$721$	−11.1905	−	19.3825i	−0.416755	−	0.721841i
$722$	−23.3773	−	8.19632i	−0.870012	−	0.305035i
$723$		0			0
$724$	−1.06536	−	2.72442i	−0.0395939	−	0.101252i
$725$	−1.63007	−	0.941119i	−0.0605391	−	0.0349523i
$726$		0			0
$727$	−34.2293			−1.26949			−0.634747	−	0.772720i	$-0.718896\pi$
$727$	−34.2293			−1.26949			−0.634747	+	0.772720i	$0.718896\pi$
$728$	17.0270	+	2.76361i	0.631061	+	0.102426i
$729$		0			0
$730$	4.16183	−	0.784791i	0.154036	−	0.0290464i
$731$	−9.11145	−	5.26050i	−0.336999	−	0.194566i
$732$		0			0
$733$			4.21648i			0.155739i	0.996964	+	0.0778697i	$0.0248118\pi$
$733$			4.21648i			0.155739i	−0.996964	+	0.0778697i	$0.975188\pi$
$734$	7.43376	+	2.60635i	0.274385	+	0.0962023i
$735$		0			0
$736$	46.0187	−	19.9083i	1.69627	−	0.733831i
$737$	−14.6467	−	25.3688i	−0.539517	−	0.934470i
$738$		0			0
$739$	−36.8643	−	21.2836i	−1.35608	−	0.782931i	−0.366983	−	0.930228i	$-0.619609\pi$
$739$	−36.8643	−	21.2836i	−1.35608	−	0.782931i	−0.989092	+	0.147297i	$0.952943\pi$
$740$	−1.47211	+	9.68540i	−0.0541159	+	0.356042i
$741$		0			0
$742$	8.86352	+	10.3125i	0.325390	+	0.378584i
$743$	−20.6614	+	35.7866i	−0.757994	+	1.31288i	0.185878	+	0.982573i	$0.440487\pi$
$743$	−20.6614	+	35.7866i	−0.757994	+	1.31288i	−0.943872	+	0.330311i	$0.892846\pi$
$744$		0			0
$745$	−3.06945	−	5.31644i	−0.112456	−	0.194779i
$746$	−15.7876	−	18.3685i	−0.578025	−	0.672520i
$747$		0			0
$748$	−9.41696	−	24.0817i	−0.344318	−	0.880514i
$749$			14.9159i			0.545015i
$750$		0			0
$751$	6.54731	−	11.3403i	0.238915	−	0.413812i	−0.721488	−	0.692427i	$-0.756542\pi$
$751$	6.54731	−	11.3403i	0.238915	−	0.413812i	0.960403	+	0.278614i	$0.0898750\pi$
$752$	11.6813	−	10.7849i	0.425973	−	0.393286i
$753$		0			0
$754$	−2.01920	−	0.0203268i	−0.0735349	−	0.000740260i
$755$			8.79795i			0.320190i
$756$		0			0
$757$	−0.284326	−	0.164156i	−0.0103340	−	0.00596635i	0.494824	−	0.868993i	$-0.335232\pi$
$757$	−0.284326	−	0.164156i	−0.0103340	−	0.00596635i	−0.505158	+	0.863027i	$0.668566\pi$
$758$	−5.73828	+	16.3665i	−0.208424	+	0.594459i
$759$		0			0
$760$	0.802897	−	1.51235i	0.0291241	−	0.0548586i
$761$	−8.81782	−	15.2729i	−0.319646	−	0.553642i	0.660768	−	0.750590i	$-0.270231\pi$
$761$	−8.81782	−	15.2729i	−0.319646	−	0.553642i	−0.980414	+	0.196947i	$0.936897\pi$
$762$		0			0
$763$	5.35525	−	3.09186i	0.193873	−	0.111933i
$764$	−12.8822	−	10.2993i	−0.466061	−	0.372617i
$765$		0			0
$766$	−3.48996	+	2.99959i	−0.126097	+	0.108380i
$767$	16.7782	+	14.7170i	0.605826	+	0.531399i
$768$		0			0
$769$	25.0216	−	43.3387i	0.902302	−	1.56283i	0.0778027	−	0.996969i	$-0.475210\pi$
$769$	25.0216	−	43.3387i	0.902302	−	1.56283i	0.824499	−	0.565864i	$-0.191457\pi$
$770$	−0.837935	−	4.44366i	−0.0301971	−	0.160138i
$771$		0			0
$772$	3.79357	−	24.9588i	0.136533	−	0.898288i
$773$	13.1919	−	7.61633i	0.474479	−	0.273940i	−0.243634	−	0.969867i	$-0.578340\pi$
$773$	13.1919	−	7.61633i	0.474479	−	0.273940i	0.718113	+	0.695927i	$0.245006\pi$
$774$		0			0
$775$	9.90649			0.355852
$776$	2.20830	−	4.15957i	0.0792732	−	0.149320i
$777$		0			0
$778$	24.9912	−	4.71256i	0.895978	−	0.168953i
$779$			5.60437i			0.200797i
$780$		0			0
$781$		−	29.1540i		−	1.04321i
$782$	7.89669	+	41.8770i	0.282385	+	1.49752i
$783$		0			0
$784$	−3.64396	−	16.1496i	−0.130142	−	0.576771i
$785$	−1.34280			−0.0479265
$786$		0			0
$787$	47.6148	−	27.4904i	1.69728	−	0.979927i	0.748963	−	0.662611i	$-0.230552\pi$
$787$	47.6148	−	27.4904i	1.69728	−	0.979927i	0.948320	−	0.317316i	$-0.102781\pi$
$788$	−34.9209	−	5.30774i	−1.24401	−	0.189080i
$789$		0			0
$790$	−6.47012	+	1.22006i	−0.230196	+	0.0434078i
$791$	9.65886	−	16.7296i	0.343429	−	0.594837i
$792$		0			0
$793$	−11.0679	−	9.70822i	−0.393034	−	0.344749i
$794$	−19.1412	−	22.2703i	−0.679295	−	0.790345i
$795$		0			0
$796$	30.9954	+	24.7809i	1.09860	+	0.878335i
$797$	−43.7170	+	25.2400i	−1.54853	+	0.894047i	−0.550281	+	0.834980i	$0.685479\pi$
$797$	−43.7170	+	25.2400i	−1.54853	+	0.894047i	−0.998254	+	0.0590673i	$0.981187\pi$
$798$		0			0
$799$	6.75624	+	11.7022i	0.239019	+	0.413992i
$800$	21.5833	+	16.0327i	0.763085	+	0.566841i
$801$		0			0
$802$	−3.13949	−	1.10074i	−0.110859	−	0.0388684i
$803$	19.8419	+	11.4557i	0.700205	+	0.404264i
$804$		0			0
$805$			7.45255i			0.262668i
$806$	9.25704	−	5.22102i	0.326065	−	0.183903i
$807$		0			0
$808$	0.788753	+	22.1830i	0.0277482	+	0.780396i
$809$	−2.20857	+	3.82536i	−0.0776493	+	0.134493i	−0.902235	−	0.431244i	$-0.858075\pi$
$809$	−2.20857	+	3.82536i	−0.0776493	+	0.134493i	0.824586	+	0.565737i	$0.191408\pi$
$810$		0			0
$811$			2.09970i			0.0737305i	0.999320	+	0.0368652i	$0.0117372\pi$
$811$			2.09970i			0.0737305i	−0.999320	+	0.0368652i	$0.988263\pi$
$812$	−0.487906	−	1.24771i	−0.0171222	−	0.0437860i
$813$		0			0
$814$	−40.1922	+	34.5449i	−1.40874	+	1.21080i
$815$	−0.536660	−	0.929523i	−0.0187984	−	0.0325598i
$816$		0			0
$817$	1.88448	−	3.26402i	0.0659296	−	0.114193i
$818$	−38.8437	+	33.3859i	−1.35814	+	1.16731i
$819$		0			0
$820$	4.52296	+	0.687458i	0.157949	+	0.0240071i
$821$	18.0251	+	10.4068i	0.629079	+	0.363199i	0.780395	−	0.625286i	$-0.215018\pi$
$821$	18.0251	+	10.4068i	0.629079	+	0.363199i	−0.151316	+	0.988485i	$0.548351\pi$
$822$		0			0
$823$	3.91287	+	6.77729i	0.136394	+	0.236241i	0.926129	−	0.377207i	$-0.123115\pi$
$823$	3.91287	+	6.77729i	0.136394	+	0.236241i	−0.789735	+	0.613448i	$0.789782\pi$
$824$	−19.8521	−	31.7252i	−0.691582	−	1.10520i
$825$		0			0
$826$	−4.89910	+	13.9730i	−0.170461	+	0.486184i
$827$		−	25.1308i		−	0.873884i	−0.899490	−	0.436942i	$-0.856062\pi$
$827$		−	25.1308i		−	0.873884i	0.899490	−	0.436942i	$-0.143938\pi$
$828$		0			0
$829$	−43.4669	−	25.0957i	−1.50967	−	0.871608i	−0.999936	−	0.0112755i	$-0.996411\pi$
$829$	−43.4669	−	25.0957i	−1.50967	−	0.871608i	−0.509733	−	0.860333i	$-0.670256\pi$
$830$	0.934295	+	4.95467i	0.0324299	+	0.171979i
$831$		0			0
$832$	28.6180	+	3.60657i	0.992152	+	0.125035i
$833$	14.0708			0.487525
$834$		0			0
$835$	3.18778	+	1.84047i	0.110318	+	0.0636920i
$836$	8.62685	−	3.37346i	0.298366	−	0.116674i
$837$		0			0
$838$	−11.1338	+	31.7554i	−0.384610	+	1.09697i
$839$	−24.4177	−	42.2926i	−0.842991	−	1.46010i	−0.887354	−	0.461088i	$-0.847459\pi$
$839$	−24.4177	−	42.2926i	−0.842991	−	1.46010i	0.0443634	−	0.999015i	$-0.485874\pi$
$840$		0			0
$841$	−14.4216	−	24.9789i	−0.497296	−	0.861342i
$842$	−27.5471	+	5.19452i	−0.949336	+	0.179015i
$843$		0			0
$844$	−29.8400	−	4.53547i	−1.02714	−	0.156117i
$845$	3.93283	+	5.12743i	0.135294	+	0.176389i
$846$		0			0
$847$	2.92834	−	5.07203i	0.100619	−	0.174277i
$848$	15.4246	+	16.7066i	0.529684	+	0.573708i
$849$		0			0
$850$	−17.3298	+	14.8948i	−0.594408	+	0.510889i
$851$	75.6424	−	43.6722i	2.59299	−	1.49706i
$852$		0			0
$853$		−	47.8014i		−	1.63669i	−0.574728	−	0.818345i	$-0.694892\pi$
$853$		−	47.8014i		−	1.63669i	0.574728	−	0.818345i	$-0.305108\pi$
$854$	3.23175	−	9.21748i	0.110588	−	0.315416i
$855$		0			0
$856$	0.886286	+	24.9260i	0.0302926	+	0.851955i
$857$	34.4402			1.17646			0.588228	−	0.808695i	$-0.299826\pi$
$857$	34.4402			1.17646			0.588228	+	0.808695i	$0.299826\pi$
$858$		0			0
$859$			18.3183i			0.625012i	0.949916	+	0.312506i	$0.101168\pi$
$859$			18.3183i			0.625012i	−0.949916	+	0.312506i	$0.898832\pi$
$860$	−2.40304	−	1.92123i	−0.0819429	−	0.0655135i
$861$		0			0
$862$	−0.508673	−	0.178346i	−0.0173255	−	0.00607449i
$863$	24.5989			0.837356			0.418678	−	0.908135i	$-0.362494\pi$
$863$	24.5989			0.837356			0.418678	+	0.908135i	$0.362494\pi$
$864$		0			0
$865$	1.04981	+	1.81832i	0.0356945	+	0.0618247i
$866$	3.78334	−	3.25175i	0.128563	−	0.110499i
$867$		0			0
$868$	5.50732	+	4.40311i	0.186931	+	0.149451i
$869$	−30.8469	−	17.8094i	−1.04641	−	0.604144i
$870$		0			0
$871$	−5.42084	+	27.2386i	−0.183678	+	0.922945i
$872$	8.76548	−	5.48502i	0.296837	−	0.185746i
$873$		0			0
$874$	−15.0017	+	2.82885i	−0.507440	+	0.0956873i
$875$	−7.10161	+	4.10012i	−0.240078	+	0.138609i
$876$		0			0
$877$	−28.4988	+	16.4538i	−0.962337	+	0.555605i	−0.896891	−	0.442251i	$-0.854180\pi$
$877$	−28.4988	+	16.4538i	−0.962337	+	0.555605i	−0.0654453	+	0.997856i	$0.520847\pi$
$878$	8.56061	+	3.00144i	0.288907	+	0.101294i
$879$		0			0
$880$	−1.66431	−	7.37603i	−0.0561040	−	0.248646i
$881$	−18.9830	+	32.8795i	−0.639553	+	1.10774i	0.345978	+	0.938243i	$0.387547\pi$
$881$	−18.9830	+	32.8795i	−0.639553	+	1.10774i	−0.985531	+	0.169495i	$0.945786\pi$
$882$		0			0
$883$		−	57.4770i		−	1.93425i	−0.254295	−	0.967127i	$-0.581843\pi$
$883$		−	57.4770i		−	1.93425i	0.254295	−	0.967127i	$-0.418157\pi$
$884$	−8.34367	+	23.0517i	−0.280628	+	0.775312i
$885$		0			0
$886$	−24.4246	+	4.60572i	−0.820562	+	0.154732i
$887$	−8.29035	+	14.3593i	−0.278363	+	0.482138i	−0.970978	−	0.239169i	$-0.923125\pi$
$887$	−8.29035	+	14.3593i	−0.278363	+	0.482138i	0.692615	+	0.721307i	$0.256458\pi$
$888$		0			0
$889$	−21.5842			−0.723910
$890$	2.93677	−	8.37616i	0.0984407	−	0.280769i
$891$		0			0
$892$	−2.99273	+	19.6899i	−0.100204	+	0.659268i
$893$	−4.19209	+	2.42031i	−0.140283	+	0.0809924i
$894$		0			0
$895$	0.111433	−	0.193007i	0.00372479	−	0.00645152i
$896$	4.87280	+	18.5061i	0.162789	+	0.618246i
$897$		0			0
$898$	−38.9749	+	33.4987i	−1.30061	+	1.11786i
$899$	−0.714834	−	0.412710i	−0.0238410	−	0.0137646i
$900$		0			0
$901$	−16.7365	+	9.66280i	−0.557573	+	0.321915i
$902$	16.1320	+	18.7693i	0.537138	+	0.624948i
$903$		0			0
$904$	15.1469	−	28.5309i	0.503779	−	0.948924i
$905$	0.727055			0.0241681
$906$		0			0
$907$	13.4171	+	7.74635i	0.445507	+	0.257213i	0.705931	−	0.708281i	$-0.250529\pi$
$907$	13.4171	+	7.74635i	0.445507	+	0.257213i	−0.260424	+	0.965494i	$0.583862\pi$
$908$	1.73016	−	2.16405i	0.0574175	−	0.0718166i
$909$		0			0
$910$	−2.18089	+	3.69110i	−0.0722958	+	0.122359i
$911$	3.26320			0.108115			0.0540574	−	0.998538i	$-0.482785\pi$
$911$	3.26320			0.108115			0.0540574	+	0.998538i	$0.482785\pi$
$912$		0			0
$913$	−13.6381	+	23.6218i	−0.451354	+	0.781768i
$914$	−17.5717	−	6.16083i	−0.581221	−	0.203782i
$915$		0			0
$916$	16.6208	+	42.5039i	0.549168	+	1.40437i
$917$	−16.5234	+	9.53979i	−0.545651	+	0.315032i
$918$		0			0
$919$	−12.7268	−	22.0434i	−0.419817	−	0.727144i	0.576104	−	0.817377i	$-0.304572\pi$
$919$	−12.7268	−	22.0434i	−0.419817	−	0.727144i	−0.995921	+	0.0902323i	$0.971239\pi$
$920$	0.442822	+	12.4540i	0.0145994	+	0.410596i
$921$		0			0
$922$	−13.5813	−	15.8016i	−0.447277	−	0.520397i
$923$	−18.2268	+	20.7796i	−0.599942	+	0.683969i
$924$		0			0
$925$	40.5613	+	23.4181i	1.33365	+	0.769982i
$926$	−1.48102	−	7.85403i	−0.0486695	−	0.258099i
$927$		0			0
$928$	−0.889480	−	2.05606i	−0.0291986	−	0.0674935i
$929$	−19.1596	−	33.1853i	−0.628605	−	1.08878i	−0.987832	−	0.155525i	$-0.950293\pi$
$929$	−19.1596	−	33.1853i	−0.628605	−	1.08878i	0.359227	−	0.933250i	$-0.383040\pi$
$930$		0			0
$931$			5.04062i			0.165200i
$932$	8.33623	−	3.25982i	0.273062	−	0.106779i
$933$		0			0
$934$	41.1195	−	7.75386i	1.34547	−	0.253714i
$935$	6.42659			0.210172
$936$		0			0
$937$	−33.4565			−1.09298			−0.546488	−	0.837467i	$-0.684035\pi$
$937$	−33.4565			−1.09298			−0.546488	+	0.837467i	$0.684035\pi$
$938$	−18.1068	+	3.41438i	−0.591208	+	0.111483i
$939$		0			0
$940$	1.43907	+	3.68008i	0.0469372	+	0.120031i
$941$		−	3.09842i		−	0.101006i	−0.998724	−	0.0505028i	$-0.983918\pi$
$941$		−	3.09842i		−	0.101006i	0.998724	−	0.0505028i	$-0.0160824\pi$
$942$		0			0
$943$	−20.3944	−	35.3241i	−0.664132	−	1.15031i
$944$	−7.35665	+	23.6415i	−0.239438	+	0.769466i
$945$		0			0
$946$	−3.08418	−	16.3558i	−0.100275	−	0.531772i
$947$	1.23979	+	0.715796i	0.0402879	+	0.0232602i	0.520009	−	0.854161i	$-0.325929\pi$
$947$	1.23979	+	0.715796i	0.0402879	+	0.0232602i	−0.479721	+	0.877421i	$0.659262\pi$
$948$		0			0
$949$	−6.98036	−	20.5700i	−0.226592	−	0.667732i
$950$	−5.33581	−	6.20810i	−0.173117	−	0.201417i
$951$		0			0
$952$	−16.2544	+	0.577953i	−0.526809	+	0.0187316i
$953$	14.0065	+	24.2600i	0.453716	+	0.785859i	0.998613	−	0.0526434i	$-0.0167647\pi$
$953$	14.0065	+	24.2600i	0.453716	+	0.785859i	−0.544897	+	0.838503i	$0.683431\pi$
$954$		0			0
$955$	3.55003	−	2.04961i	0.114876	−	0.0663238i
$956$	34.4465	−	13.4700i	1.11408	−	0.435651i
$957$		0			0
$958$	−20.2181	−	7.08867i	−0.653216	−	0.229024i
$959$	6.25781	−	10.8388i	0.202075	−	0.350005i
$960$		0			0
$961$	−26.6557			−0.859861
$962$	50.2443	+	0.505798i	1.61994	+	0.0163076i
$963$		0			0
$964$	−21.4777	−	17.1714i	−0.691749	−	0.553055i
$965$	5.43387	+	3.13725i	0.174923	+	0.100992i
$966$		0			0
$967$	36.4058			1.17073			0.585366	−	0.810769i	$-0.300951\pi$
$967$	36.4058			1.17073			0.585366	+	0.810769i	$0.300951\pi$
$968$	4.59219	−	8.64990i	0.147599	−	0.278018i
$969$		0			0
$970$	0.762936	+	0.887659i	0.0244964	+	0.0285010i
$971$	−40.8856	+	23.6053i	−1.31208	+	0.757531i	−0.982441	−	0.186575i	$-0.940261\pi$
$971$	−40.8856	+	23.6053i	−1.31208	+	0.757531i	−0.329642	+	0.944106i	$0.606928\pi$
$972$		0			0
$973$	17.3090	+	9.99335i	0.554901	+	0.320372i
$974$	−32.2891	+	27.7522i	−1.03461	+	0.889239i
$975$		0			0
$976$	4.85290	−	15.5954i	0.155337	−	0.499197i
$977$	29.7141	−	51.4663i	0.950638	−	1.64655i	0.206589	−	0.978428i	$-0.433764\pi$
$977$	29.7141	−	51.4663i	0.950638	−	1.64655i	0.744049	−	0.668125i	$-0.232903\pi$
$978$		0			0
$979$	41.5846	−	24.0089i	1.32905	−	0.767327i
$980$	4.06799	+	0.618307i	0.129947	+	0.0197511i
$981$		0			0
$982$	−12.5519	+	35.8002i	−0.400548	+	1.14243i
$983$	30.8865			0.985126			0.492563	−	0.870277i	$-0.336060\pi$
$983$	30.8865			0.985126			0.492563	+	0.870277i	$0.336060\pi$
$984$		0			0
$985$	4.38945	−	7.60275i	0.139860	−	0.242244i
$986$	1.87101	−	0.352815i	0.0595852	−	0.0112359i
$987$		0			0
$988$	−8.25787	−	2.98897i	−0.262718	−	0.0950920i
$989$			27.4306i			0.872242i
$990$		0			0
$991$	−22.5422	+	39.0441i	−0.716075	+	1.24028i	0.246468	+	0.969151i	$0.420730\pi$
$991$	−22.5422	+	39.0441i	−0.716075	+	1.24028i	−0.962543	+	0.271127i	$0.912604\pi$
$992$	9.46494	+	7.03083i	0.300512	+	0.223229i
$993$		0			0
$994$	−17.3054	−	6.06747i	−0.548895	−	0.192449i
$995$	−8.54160	+	4.93149i	−0.270787	+	0.156339i
$996$		0			0
$997$	−45.6473	+	26.3545i	−1.44566	+	0.834655i	−0.998219	−	0.0596564i	$-0.981000\pi$
$997$	−45.6473	+	26.3545i	−1.44566	+	0.834655i	−0.447446	+	0.894311i	$0.647666\pi$
$998$	−25.7249	+	4.85092i	−0.814309	+	0.153553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.be.a.685.7		24
3.2	odd	2		104.2.r.a.61.6	yes	24
8.5	even	2	inner	936.2.be.a.685.1		24
12.11	even	2		416.2.z.a.113.1		24
13.3	even	3	inner	936.2.be.a.757.1		24
24.5	odd	2		104.2.r.a.61.12	yes	24
24.11	even	2		416.2.z.a.113.12		24
39.29	odd	6		104.2.r.a.29.12	yes	24
104.29	even	6	inner	936.2.be.a.757.7		24
156.107	even	6		416.2.z.a.81.12		24
312.29	odd	6		104.2.r.a.29.6	✓	24
312.107	even	6		416.2.z.a.81.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
104.2.r.a.29.6	✓	24	312.29	odd	6
104.2.r.a.29.12	yes	24	39.29	odd	6
104.2.r.a.61.6	yes	24	3.2	odd	2
104.2.r.a.61.12	yes	24	24.5	odd	2
416.2.z.a.81.1		24	312.107	even	6
416.2.z.a.81.12		24	156.107	even	6
416.2.z.a.113.1		24	12.11	even	2
416.2.z.a.113.12		24	24.11	even	2
936.2.be.a.685.1		24	8.5	even	2	inner
936.2.be.a.685.7		24	1.1	even	1	trivial
936.2.be.a.757.1		24	13.3	even	3	inner
936.2.be.a.757.7		24	104.29	even	6	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.262058 + 1.38972i) q^{2} +(-1.86265 + 0.728375i) q^{4} -0.497079i q^{5} +(-0.845740 - 1.46486i) q^{7} +(-1.50036 - 2.39769i) q^{8} +(0.690801 - 0.130263i) q^{10} +(3.29345 + 1.90148i) q^{11} +(-1.15864 - 3.41432i) q^{13} +(1.81412 - 1.55922i) q^{14} +(2.93894 - 2.71342i) q^{16} +(1.69983 + 2.94419i) q^{17} +(-1.05470 + 0.608933i) q^{19} +(0.362060 + 0.925884i) q^{20} +(-1.77945 + 5.07528i) q^{22} +(4.43183 - 7.67616i) q^{23} +4.75291 q^{25} +(4.44132 - 2.50493i) q^{26} +(2.64229 + 2.11252i) q^{28} +(-0.342961 - 0.198009i) q^{29} +2.08430 q^{31} +(4.54107 + 3.37323i) q^{32} +(-3.64615 + 3.13383i) q^{34} +(-0.728152 + 0.420399i) q^{35} +(8.53399 + 4.92710i) q^{37} +(-1.12264 - 1.30617i) q^{38} +(-1.19184 + 0.745797i) q^{40} +(2.30090 - 3.98527i) q^{41} +(-2.68011 + 1.54736i) q^{43} +(-7.51955 - 1.14292i) q^{44} +(11.8291 + 4.14741i) q^{46} +3.97467 q^{47} +(2.06945 - 3.58439i) q^{49} +(1.24554 + 6.60522i) q^{50} +(4.64504 + 5.51576i) q^{52} +5.68458i q^{53} +(0.945183 - 1.63711i) q^{55} +(-2.24337 + 4.22565i) q^{56} +(0.185301 - 0.528511i) q^{58} +(-5.36063 + 3.09496i) q^{59} +(3.53620 - 2.04163i) q^{61} +(0.546207 + 2.89659i) q^{62} +(-3.49783 + 7.19480i) q^{64} +(-1.69718 + 0.575933i) q^{65} +(-6.67080 - 3.85139i) q^{67} +(-5.31066 - 4.24588i) q^{68} +(-0.775056 - 0.901760i) q^{70} +(-3.83307 - 6.63908i) q^{71} +6.02464 q^{73} +(-4.61090 + 13.1511i) q^{74} +(1.52101 - 1.90245i) q^{76} -6.43262i q^{77} -9.36611 q^{79} +(-1.34878 - 1.46088i) q^{80} +(6.14138 + 2.15323i) q^{82} +7.17235i q^{83} +(1.46349 - 0.844947i) q^{85} +(-2.85275 - 3.31911i) q^{86} +(-0.382219 - 10.7496i) q^{88} +(6.31322 - 10.9348i) q^{89} +(-4.02161 + 4.58487i) q^{91} +(-2.66383 + 17.5260i) q^{92} +(1.04159 + 5.52368i) q^{94} +(0.302688 + 0.524270i) q^{95} +(0.832515 + 1.44196i) q^{97} +(5.52362 + 1.93664i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{4} - 2 q^{7} + 10 q^{8} - 3 q^{10} - 8 q^{14} - q^{16} + 11 q^{20} - 2 q^{22} + 14 q^{23} - 12 q^{25} + 3 q^{26} - 4 q^{28} - 8 q^{31} + 21 q^{32} + 14 q^{34} - 12 q^{38} + 54 q^{40}+ \cdots + 17 q^{98}+O(q^{100}) \) 24 * q + q^2 - q^4 - 2 * q^7 + 10 * q^8 - 3 * q^10 - 8 * q^14 - q^16 + 11 * q^20 - 2 * q^22 + 14 * q^23 - 12 * q^25 + 3 * q^26 - 4 * q^28 - 8 * q^31 + 21 * q^32 + 14 * q^34 - 12 * q^38 + 54 * q^40 + 4 * q^41 + 24 * q^46 + 8 * q^47 + 6 * q^49 - 32 * q^50 - 4 * q^52 + 8 * q^55 - 8 * q^56 + 33 * q^58 + 14 * q^62 + 26 * q^64 - 30 * q^65 - 23 * q^68 - 16 * q^70 - 30 * q^71 - 12 * q^73 + 7 * q^74 + 14 * q^76 - 48 * q^79 - 29 * q^80 - q^82 + 96 * q^86 + 4 * q^88 + 22 * q^89 + 80 * q^92 - 42 * q^94 - 60 * q^95 + 2 * q^97 + 17 * q^98

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