LMFDB - Embedded newform 756.2.be.c.107.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(107,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.107"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.be (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,0,-4,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.5
Character	$\chi$	$=$	756.107
Dual form			756.2.be.c.431.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.687910 - 1.23563i) q^{2} +(-1.05356 + 1.70000i) q^{4} +(0.303357 + 0.175143i) q^{5} +(-2.63538 - 0.234036i) q^{7} +(2.82533 + 0.132362i) q^{8} +(0.00772994 - 0.495319i) q^{10} +(0.356330 + 0.617181i) q^{11} +0.127465 q^{13} +(1.52372 + 3.41735i) q^{14} +(-1.78002 - 3.58211i) q^{16} +(5.30564 - 3.06321i) q^{17} +(-2.91768 - 1.68453i) q^{19} +(-0.617349 + 0.331184i) q^{20} +(0.517485 - 0.864856i) q^{22} +(2.38776 - 4.13571i) q^{23} +(-2.43865 - 4.22387i) q^{25} +(-0.0876844 - 0.157499i) q^{26} +(3.17439 - 4.23358i) q^{28} +3.39607i q^{29} +(-0.00202473 + 0.00116898i) q^{31} +(-3.20167 + 4.66362i) q^{32} +(-7.43480 - 4.44859i) q^{34} +(-0.758471 - 0.532565i) q^{35} +(2.17085 - 3.76003i) q^{37} +(-0.0743466 + 4.76398i) q^{38} +(0.833900 + 0.534990i) q^{40} -8.22678i q^{41} -7.55045i q^{43} +(-1.42462 - 0.0444762i) q^{44} +(-6.75277 - 0.105384i) q^{46} +(1.33348 - 2.30966i) q^{47} +(6.89045 + 1.23355i) q^{49} +(-3.54156 + 5.91891i) q^{50} +(-0.134292 + 0.216691i) q^{52} +(10.1596 - 5.86566i) q^{53} +0.249635i q^{55} +(-7.41484 - 1.01005i) q^{56} +(4.19629 - 2.33619i) q^{58} +(-5.13898 - 8.90098i) q^{59} +(-2.83849 + 4.91641i) q^{61} +(0.00283726 + 0.00169767i) q^{62} +(7.96496 + 0.747932i) q^{64} +(0.0386674 + 0.0223246i) q^{65} +(-7.79435 + 4.50007i) q^{67} +(-0.382342 + 12.2469i) q^{68} +(-0.136294 + 1.30355i) q^{70} -9.61361 q^{71} +(-2.15337 - 3.72974i) q^{73} +(-6.13935 - 0.0958106i) q^{74} +(5.93766 - 3.18532i) q^{76} +(-0.794621 - 1.70990i) q^{77} +(1.92240 + 1.10990i) q^{79} +(0.0874011 - 1.39842i) q^{80} +(-10.1653 + 5.65928i) q^{82} -5.12311 q^{83} +2.14600 q^{85} +(-9.32956 + 5.19403i) q^{86} +(0.925057 + 1.79090i) q^{88} +(7.79048 + 4.49784i) q^{89} +(-0.335919 - 0.0298314i) q^{91} +(4.51508 + 8.41642i) q^{92} +(-3.77120 - 0.0588532i) q^{94} +(-0.590066 - 1.02203i) q^{95} -17.3426 q^{97} +(-3.21580 - 9.36262i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) $ 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−0.687910	−	1.23563i	−0.486426	−	0.873722i
$2$	−0.687910	−	1.23563i	−0.486426	−	0.873722i
$3$		0			0
$3$		0			0
$4$	−1.05356	+	1.70000i	−0.526780	+	0.850001i
$5$	0.303357	+	0.175143i	0.135665	+	0.0783264i	0.566297	−	0.824202i	$-0.308376\pi$
$5$	0.303357	+	0.175143i	0.135665	+	0.0783264i	−0.430631	+	0.902528i	$0.641709\pi$
$6$		0			0
$7$	−2.63538	−	0.234036i	−0.996080	−	0.0884574i
$7$	−2.63538	−	0.234036i	−0.996080	−	0.0884574i
$8$	2.82533	+	0.132362i	0.998904	+	0.0467970i
$9$		0			0
$10$	0.00772994	−	0.495319i	0.00244442	−	0.156634i
$11$	0.356330	+	0.617181i	0.107437	+	0.186087i	0.914731	−	0.404062i	$-0.132402\pi$
$11$	0.356330	+	0.617181i	0.107437	+	0.186087i	−0.807294	+	0.590149i	$0.799069\pi$
$12$		0			0
$13$	0.127465			0.0353524			0.0176762	−	0.999844i	$-0.494373\pi$
$13$	0.127465			0.0353524			0.0176762	+	0.999844i	$0.494373\pi$
$14$	1.52372	+	3.41735i	0.407232	+	0.913325i
$15$		0			0
$16$	−1.78002	−	3.58211i	−0.445005	−	0.895528i
$17$	5.30564	−	3.06321i	1.28681	−	0.742938i	0.308723	−	0.951152i	$-0.400098\pi$
$17$	5.30564	−	3.06321i	1.28681	−	0.742938i	0.978083	+	0.208214i	$0.0667649\pi$
$18$		0			0
$19$	−2.91768	−	1.68453i	−0.669363	−	0.386457i	0.126472	−	0.991970i	$-0.459634\pi$
$19$	−2.91768	−	1.68453i	−0.669363	−	0.386457i	−0.795835	+	0.605513i	$0.792968\pi$
$20$	−0.617349	+	0.331184i	−0.138043	+	0.0740549i
$21$		0			0
$22$	0.517485	−	0.864856i	0.110328	−	0.184388i
$23$	2.38776	−	4.13571i	0.497881	−	0.862356i	−0.502116	−	0.864801i	$-0.667445\pi$
$23$	2.38776	−	4.13571i	0.497881	−	0.862356i	0.999997	+	0.00244454i	$0.000778122\pi$
$24$		0			0
$25$	−2.43865	−	4.22387i	−0.487730	−	0.844773i
$26$	−0.0876844	−	0.157499i	−0.0171963	−	0.0308882i
$27$		0			0
$28$	3.17439	−	4.23358i	0.599904	−	0.800072i
$29$			3.39607i			0.630635i	0.948986	+	0.315318i	$0.102111\pi$
$29$			3.39607i			0.630635i	−0.948986	+	0.315318i	$0.897889\pi$
$30$		0			0
$31$	−0.00202473	+	0.00116898i	−0.000363652	+	0.000209955i	−0.500182	−	0.865920i	$-0.666733\pi$
$31$	−0.00202473	+	0.00116898i	−0.000363652	+	0.000209955i	0.499818	+	0.866130i	$0.333400\pi$
$32$	−3.20167	+	4.66362i	−0.565981	+	0.824418i
$33$		0			0
$34$	−7.43480	−	4.44859i	−1.27506	−	0.762927i
$35$	−0.758471	−	0.532565i	−0.128205	−	0.0900200i
$36$		0			0
$37$	2.17085	−	3.76003i	0.356886	−	0.618145i	−0.630553	−	0.776146i	$-0.717172\pi$
$37$	2.17085	−	3.76003i	0.356886	−	0.618145i	0.987439	+	0.158001i	$0.0505051\pi$
$38$	−0.0743466	+	4.76398i	−0.0120606	+	0.772819i
$39$		0			0
$40$	0.833900	+	0.534990i	0.131851	+	0.0845893i
$41$		−	8.22678i		−	1.28481i	−0.766367	−	0.642404i	$-0.777937\pi$
$41$		−	8.22678i		−	1.28481i	0.766367	−	0.642404i	$-0.222063\pi$
$42$		0			0
$43$		−	7.55045i		−	1.15143i	−0.817649	−	0.575717i	$-0.804723\pi$
$43$		−	7.55045i		−	1.15143i	0.817649	−	0.575717i	$-0.195277\pi$
$44$	−1.42462	−	0.0444762i	−0.214770	−	0.00670503i
$45$		0			0
$46$	−6.75277	−	0.105384i	−0.995642	−	0.0155380i
$47$	1.33348	−	2.30966i	0.194508	−	0.336898i	−0.752231	−	0.658900i	$-0.771022\pi$
$47$	1.33348	−	2.30966i	0.194508	−	0.336898i	0.946739	+	0.322001i	$0.104356\pi$
$48$		0			0
$49$	6.89045	+	1.23355i	0.984351	+	0.176221i
$50$	−3.54156	+	5.91891i	−0.500852	+	0.837060i
$51$		0			0
$52$	−0.134292	+	0.216691i	−0.0186230	+	0.0300496i
$53$	10.1596	−	5.86566i	1.39553	−	0.805710i	0.401610	−	0.915811i	$-0.368451\pi$
$53$	10.1596	−	5.86566i	1.39553	−	0.805710i	0.993920	+	0.110101i	$0.0351175\pi$
$54$		0			0
$55$			0.249635i			0.0336608i
$56$	−7.41484	−	1.01005i	−0.990849	−	0.134974i
$57$		0			0
$58$	4.19629	−	2.33619i	0.551000	−	0.306757i
$59$	−5.13898	−	8.90098i	−0.669039	−	1.15881i	−0.978173	−	0.207791i	$-0.933373\pi$
$59$	−5.13898	−	8.90098i	−0.669039	−	1.15881i	0.309134	−	0.951018i	$-0.399961\pi$
$60$		0			0
$61$	−2.83849	+	4.91641i	−0.363432	+	0.629482i	−0.988523	−	0.151069i	$-0.951728\pi$
$61$	−2.83849	+	4.91641i	−0.363432	+	0.629482i	0.625091	+	0.780552i	$0.285062\pi$
$62$	0.00283726	+	0.00169767i	0.000360332	+	0.000215604i
$63$		0			0
$64$	7.96496	+	0.747932i	0.995620	+	0.0934915i
$65$	0.0386674	+	0.0223246i	0.00479610	+	0.00276903i
$66$		0			0
$67$	−7.79435	+	4.50007i	−0.952231	+	0.549771i	−0.893773	−	0.448519i	$-0.851952\pi$
$67$	−7.79435	+	4.50007i	−0.952231	+	0.549771i	−0.0584577	+	0.998290i	$0.518618\pi$
$68$	−0.382342	+	12.2469i	−0.0463658	+	1.48515i
$69$		0			0
$70$	−0.136294	+	1.30355i	−0.0162903	+	0.155803i
$71$	−9.61361			−1.14093			−0.570463	−	0.821323i	$-0.693236\pi$
$71$	−9.61361			−1.14093			−0.570463	+	0.821323i	$0.693236\pi$
$72$		0			0
$73$	−2.15337	−	3.72974i	−0.252033	−	0.436534i	0.712053	−	0.702126i	$-0.247766\pi$
$73$	−2.15337	−	3.72974i	−0.252033	−	0.436534i	−0.964085	+	0.265593i	$0.914432\pi$
$74$	−6.13935	−	0.0958106i	−0.713685	−	0.0111378i
$75$		0			0
$76$	5.93766	−	3.18532i	0.681096	−	0.365382i
$77$	−0.794621	−	1.70990i	−0.0905555	−	0.194861i
$78$		0			0
$79$	1.92240	+	1.10990i	0.216287	+	0.124874i	0.604230	−	0.796810i	$-0.293481\pi$
$79$	1.92240	+	1.10990i	0.216287	+	0.124874i	−0.387943	+	0.921684i	$0.626814\pi$
$80$	0.0874011	−	1.39842i	0.00977174	−	0.156348i
$81$		0			0
$82$	−10.1653	+	5.65928i	−1.12256	+	0.624963i
$83$	−5.12311			−0.562334			−0.281167	−	0.959659i	$-0.590722\pi$
$83$	−5.12311			−0.562334			−0.281167	+	0.959659i	$0.590722\pi$
$84$		0			0
$85$	2.14600			0.232767
$86$	−9.32956	+	5.19403i	−1.00603	+	0.560087i
$87$		0			0
$88$	0.925057	+	1.79090i	0.0986114	+	0.190911i
$89$	7.79048	+	4.49784i	0.825789	+	0.476770i	0.852409	−	0.522876i	$-0.175141\pi$
$89$	7.79048	+	4.49784i	0.825789	+	0.476770i	−0.0266194	+	0.999646i	$0.508474\pi$
$90$		0			0
$91$	−0.335919	−	0.0298314i	−0.0352138	−	0.00312718i
$92$	4.51508	+	8.41642i	0.470730	+	0.877472i
$93$		0			0
$94$	−3.77120	−	0.0588532i	−0.388969	−	0.00607024i
$95$	−0.590066	−	1.02203i	−0.0605395	−	0.104858i
$96$		0			0
$97$	−17.3426			−1.76087			−0.880436	−	0.474165i	$-0.842750\pi$
$97$	−17.3426			−1.76087			−0.880436	+	0.474165i	$0.842750\pi$
$98$	−3.21580	−	9.36262i	−0.324845	−	0.945767i
$99$		0			0
$100$	9.74985	+	0.304386i	0.974985	+	0.0304386i
$101$	9.20243	−	5.31302i	0.915676	−	0.528666i	0.0334227	−	0.999441i	$-0.489359\pi$
$101$	9.20243	−	5.31302i	0.915676	−	0.528666i	0.882253	+	0.470776i	$0.156026\pi$
$102$		0			0
$103$	9.00546	+	5.19931i	0.887335	+	0.512303i	0.873070	−	0.487595i	$-0.162126\pi$
$103$	9.00546	+	5.19931i	0.887335	+	0.512303i	0.0142649	+	0.999898i	$0.495459\pi$
$104$	0.360130	+	0.0168715i	0.0353137	+	0.00165439i
$105$		0			0
$106$	−14.2367	−	8.51848i	−1.38279	−	0.827388i
$107$	−4.46519	+	7.73394i	−0.431666	+	0.747668i	−0.997017	−	0.0771828i	$-0.975407\pi$
$107$	−4.46519	+	7.73394i	−0.431666	+	0.747668i	0.565351	+	0.824851i	$0.308741\pi$
$108$		0			0
$109$	8.15380	+	14.1228i	0.780993	+	1.35272i	0.931364	+	0.364089i	$0.118620\pi$
$109$	8.15380	+	14.1228i	0.780993	+	1.35272i	−0.150371	+	0.988630i	$0.548047\pi$
$110$	0.308456	−	0.171726i	0.0294101	−	0.0163735i
$111$		0			0
$112$	3.85269	+	9.85682i	0.364045	+	0.931382i
$113$			8.44061i			0.794025i	0.917813	+	0.397013i	$0.129953\pi$
$113$			8.44061i			0.794025i	−0.917813	+	0.397013i	$0.870047\pi$
$114$		0			0
$115$	1.44868	−	0.836398i	0.135090	−	0.0779945i
$116$	−5.77334	−	3.57797i	−0.536041	−	0.332206i
$117$		0			0
$118$	−7.46316	+	12.4730i	−0.687040	+	1.14823i
$119$	−14.6993	+	6.83102i	−1.34748	+	0.626198i
$120$		0			0
$121$	5.24606	−	9.08644i	0.476914	−	0.826040i
$122$	8.02749	+	0.125277i	0.726775	+	0.0113420i
$123$		0			0
$124$	0.000145909	−	0.00467364i	1.31030e−5	−	0.000419705i
$125$		−	3.45988i		−	0.309461i
$126$		0			0
$127$			9.21826i			0.817988i	0.912537	+	0.408994i	$0.134120\pi$
$127$			9.21826i			0.817988i	−0.912537	+	0.408994i	$0.865880\pi$
$128$	−4.55501	−	10.3563i	−0.402609	−	0.915372i
$129$		0			0
$130$	0.000985297	−	0.0631359i	8.64162e−5	−	0.00553738i
$131$	9.60458	−	16.6356i	0.839156	−	1.45346i	−0.0514445	−	0.998676i	$-0.516383\pi$
$131$	9.60458	−	16.6356i	0.839156	−	1.45346i	0.890601	−	0.454786i	$-0.150284\pi$
$132$		0			0
$133$	7.29497	+	5.12221i	0.632554	+	0.444152i
$134$	10.9222	+	6.53528i	0.943536	+	0.564563i
$135$		0			0
$136$	15.3956	−	7.95232i	1.32016	−	0.681906i
$137$	9.16525	−	5.29156i	0.783040	−	0.452088i	−0.0544666	−	0.998516i	$-0.517346\pi$
$137$	9.16525	−	5.29156i	0.783040	−	0.452088i	0.837507	+	0.546427i	$0.184013\pi$
$138$		0			0
$139$		−	11.6495i		−	0.988101i	−0.869433	−	0.494050i	$-0.835516\pi$
$139$		−	11.6495i		−	0.988101i	0.869433	−	0.494050i	$-0.164484\pi$
$140$	1.70446	−	0.728313i	0.144053	−	0.0615537i
$141$		0			0
$142$	6.61329	+	11.8789i	0.554975	+	0.996852i
$143$	0.0454195	+	0.0786690i	0.00379817	+	0.00657863i
$144$		0			0
$145$	−0.594799	+	1.03022i	−0.0493954	+	0.0855553i
$146$	−3.12726	+	5.22649i	−0.258814	+	0.432548i
$147$		0			0
$148$	4.10493	+	7.65188i	0.337424	+	0.628980i
$149$	−13.7343	−	7.92950i	−1.12516	−	0.649610i	−0.182445	−	0.983216i	$-0.558401\pi$
$149$	−13.7343	−	7.92950i	−1.12516	−	0.649610i	−0.942712	+	0.333606i	$0.891734\pi$
$150$		0			0
$151$	3.21821	−	1.85804i	0.261895	−	0.151205i	−0.363304	−	0.931671i	$-0.618351\pi$
$151$	3.21821	−	1.85804i	0.261895	−	0.151205i	0.625199	+	0.780466i	$0.285018\pi$
$152$	−8.02045	−	5.14553i	−0.650544	−	0.417358i
$153$		0			0
$154$	−1.56618	+	2.15812i	−0.126206	+	0.173906i
$155$	−0.000818955	0		−6.57800e−5	0
$156$		0			0
$157$	1.00586	+	1.74221i	0.0802766	+	0.139043i	0.903369	−	0.428865i	$-0.141086\pi$
$157$	1.00586	+	1.74221i	0.0802766	+	0.139043i	−0.823092	+	0.567908i	$0.807753\pi$
$158$	0.0489855	−	3.13889i	0.00389707	−	0.249717i
$159$		0			0
$160$	−1.78805	+	0.853989i	−0.141358	+	0.0675138i
$161$	−7.26055	+	10.3404i	−0.572212	+	0.814934i
$162$		0			0
$163$	14.0550	+	8.11468i	1.10088	+	0.635590i	0.936451	−	0.350799i	$-0.114090\pi$
$163$	14.0550	+	8.11468i	1.10088	+	0.635590i	0.164424	+	0.986390i	$0.447423\pi$
$164$	13.9855	+	8.66741i	1.09209	+	0.676811i
$165$		0			0
$166$	3.52424	+	6.33027i	0.273534	+	0.491324i
$167$	24.8179			1.92047			0.960235	−	0.279193i	$-0.0900670\pi$
$167$	24.8179			1.92047			0.960235	+	0.279193i	$0.0900670\pi$
$168$		0			0
$169$	−12.9838			−0.998750
$170$	−1.47626	−	2.65166i	−0.113224	−	0.203373i
$171$		0			0
$172$	12.8358	+	7.95486i	0.978720	+	0.606552i
$173$	−4.32404	−	2.49649i	−0.328751	−	0.189804i	0.326536	−	0.945185i	$-0.394119\pi$
$173$	−4.32404	−	2.49649i	−0.328751	−	0.189804i	−0.655286	+	0.755381i	$0.727452\pi$
$174$		0			0
$175$	5.43823	+	11.7022i	0.411092	+	0.884605i
$176$	1.57654	−	2.37501i	0.118836	−	0.179023i
$177$		0			0
$178$	0.198512	−	12.7203i	0.0148791	−	0.953423i
$179$	9.75634	+	16.8985i	0.729223	+	1.26305i	0.957212	+	0.289388i	$0.0934517\pi$
$179$	9.75634	+	16.8985i	0.729223	+	1.26305i	−0.227989	+	0.973664i	$0.573215\pi$
$180$		0			0
$181$	−7.80817			−0.580377			−0.290188	−	0.956970i	$-0.593718\pi$
$181$	−7.80817			−0.580377			−0.290188	+	0.956970i	$0.593718\pi$
$182$	0.194221	+	0.435592i	0.0143966	+	0.0322882i
$183$		0			0
$184$	7.29361	−	11.3687i	0.537692	−	0.838112i
$185$	1.31709	−	0.760420i	0.0968341	−	0.0559072i
$186$		0			0
$187$	3.78111	+	2.18303i	0.276502	+	0.159639i
$188$	2.52152	+	4.70029i	0.183901	+	0.342804i
$189$		0			0
$190$	−0.856932	+	1.43216i	−0.0621684	+	0.103900i
$191$	6.21530	−	10.7652i	0.449723	−	0.778944i	−0.548644	−	0.836056i	$-0.684856\pi$
$191$	6.21530	−	10.7652i	0.449723	−	0.778944i	0.998368	+	0.0571120i	$0.0181892\pi$
$192$		0			0
$193$	0.669942	+	1.16037i	0.0482235	+	0.0835256i	0.889130	−	0.457656i	$-0.151311\pi$
$193$	0.669942	+	1.16037i	0.0482235	+	0.0835256i	−0.840906	+	0.541181i	$0.817977\pi$
$194$	11.9301	+	21.4290i	0.856533	+	1.53851i
$195$		0			0
$196$	−9.35655	+	10.4142i	−0.668325	+	0.743870i
$197$			12.0610i			0.859312i	0.902993	+	0.429656i	$0.141365\pi$
$197$			12.0610i			0.859312i	−0.902993	+	0.429656i	$0.858635\pi$
$198$		0			0
$199$	10.2777	−	5.93383i	0.728566	−	0.420638i	−0.0893311	−	0.996002i	$-0.528473\pi$
$199$	10.2777	−	5.93383i	0.728566	−	0.420638i	0.817897	+	0.575364i	$0.195140\pi$
$200$	−6.33091	−	12.2566i	−0.447663	−	0.866672i
$201$		0			0
$202$	−12.8954	−	7.71591i	−0.907315	−	0.542889i
$203$	0.794805	−	8.94995i	0.0557844	−	0.628163i
$204$		0			0
$205$	1.44086	−	2.49565i	0.100634	−	0.174304i
$206$	0.229471	−	14.7041i	0.0159880	−	1.02448i
$207$		0			0
$208$	−0.226890	−	0.456594i	−0.0157320	−	0.0316591i
$209$		−	2.40099i		−	0.166080i
$210$		0			0
$211$			2.47485i			0.170376i	0.996365	+	0.0851878i	$0.0271490\pi$
$211$			2.47485i			0.170376i	−0.996365	+	0.0851878i	$0.972851\pi$
$212$	−0.732136	+	23.4512i	−0.0502833	+	1.61063i
$213$		0			0
$214$	12.6279	+	0.197071i	0.863227	+	0.0134715i
$215$	1.32241	−	2.29048i	0.0901876	−	0.156210i
$216$		0			0
$217$	0.00560952	−	0.00260684i	0.000380799	−	0.000176964i
$218$	11.8415	−	19.7903i	0.802006	−	1.34037i
$219$		0			0
$220$	−0.424380	−	0.263005i	−0.0286117	−	0.0177318i
$221$	0.676283	−	0.390452i	0.0454917	−	0.0262647i
$222$		0			0
$223$		−	7.76582i		−	0.520038i	−0.965604	−	0.260019i	$-0.916271\pi$
$223$		−	7.76582i		−	0.520038i	0.965604	−	0.260019i	$-0.0837288\pi$
$224$	9.52907	−	11.5411i	0.636688	−	0.771122i
$225$		0			0
$226$	10.4295	−	5.80637i	0.693757	−	0.386234i
$227$	8.03290	+	13.9134i	0.533163	+	0.923465i	0.999250	+	0.0387259i	$0.0123299\pi$
$227$	8.03290	+	13.9134i	0.533163	+	0.923465i	−0.466087	+	0.884739i	$0.654337\pi$
$228$		0			0
$229$	−5.54735	+	9.60830i	−0.366579	+	0.634934i	−0.989028	−	0.147726i	$-0.952805\pi$
$229$	−5.54735	+	9.60830i	−0.366579	+	0.634934i	0.622449	+	0.782660i	$0.286138\pi$
$230$	−2.03004	−	1.21467i	−0.133857	−	0.0800930i
$231$		0			0
$232$	−0.449511	+	9.59503i	−0.0295119	+	0.629944i
$233$	−3.11180	−	1.79660i	−0.203861	−	0.117699i	0.394594	−	0.918855i	$-0.370885\pi$
$233$	−3.11180	−	1.79660i	−0.203861	−	0.117699i	−0.598455	+	0.801156i	$0.704218\pi$
$234$		0			0
$235$	0.809041	−	0.467100i	0.0527760	−	0.0304703i
$236$	20.5459	+	0.641435i	1.33743	+	0.0417539i
$237$		0			0
$238$	18.5524	+	13.4637i	1.20257	+	0.872725i
$239$	−6.15253			−0.397974			−0.198987	−	0.980002i	$-0.563765\pi$
$239$	−6.15253			−0.397974			−0.198987	+	0.980002i	$0.563765\pi$
$240$		0			0
$241$	−6.27143	−	10.8624i	−0.403978	−	0.699711i	0.590224	−	0.807240i	$-0.299040\pi$
$241$	−6.27143	−	10.8624i	−0.403978	−	0.699711i	−0.994202	+	0.107529i	$0.965706\pi$
$242$	−14.8363	−	0.231535i	−0.953713	−	0.0148836i
$243$		0			0
$244$	−5.36739	−	10.0052i	−0.343612	−	0.640516i
$245$	1.87422	+	1.58102i	0.119739	+	0.101008i
$246$		0			0
$247$	−0.371903	−	0.214718i	−0.0236636	−	0.0136622i
$248$	−0.00587526	+	0.00303475i	−0.000373079	+	0.000192707i
$249$		0			0
$250$	−4.27513	+	2.38009i	−0.270383	+	0.150530i
$251$	−0.485661			−0.0306547			−0.0153273	−	0.999883i	$-0.504879\pi$
$251$	−0.485661			−0.0306547			−0.0153273	+	0.999883i	$0.504879\pi$
$252$		0			0
$253$	3.40331			0.213964
$254$	11.3904	−	6.34133i	0.714694	−	0.397890i
$255$		0			0
$256$	−9.66306	+	12.7525i	−0.603941	+	0.797029i
$257$	−25.2361	−	14.5701i	−1.57418	−	0.908855i	−0.995648	−	0.0931975i	$-0.970291\pi$
$257$	−25.2361	−	14.5701i	−1.57418	−	0.908855i	−0.578535	−	0.815657i	$-0.696375\pi$
$258$		0			0
$259$	−6.60101	+	9.40105i	−0.410167	+	0.584153i
$260$	−0.0786903	+	0.0422143i	−0.00488017	+	0.00261802i
$261$		0			0
$262$	−27.1626	−	0.423898i	−1.67811	−	0.0261885i
$263$	11.6832	+	20.2359i	0.720416	+	1.24780i	0.960833	+	0.277127i	$0.0893823\pi$
$263$	11.6832	+	20.2359i	0.720416	+	1.24780i	−0.240418	+	0.970670i	$0.577284\pi$
$264$		0			0
$265$	4.10932			0.252433
$266$	1.31088	−	12.5375i	0.0803749	−	0.768723i
$267$		0			0
$268$	0.561687	−	17.9915i	0.0343105	−	1.09901i
$269$	−24.1233	+	13.9276i	−1.47082	+	0.849180i	−0.999463	−	0.0327619i	$-0.989570\pi$
$269$	−24.1233	+	13.9276i	−1.47082	+	0.849180i	−0.471359	+	0.881941i	$0.656236\pi$
$270$		0			0
$271$	−24.8590	−	14.3523i	−1.51008	−	0.871843i	−0.999931	−	0.0117552i	$-0.996258\pi$
$271$	−24.8590	−	14.3523i	−1.51008	−	0.871843i	−0.510146	−	0.860088i	$-0.670409\pi$
$272$	−20.4169	−	13.5528i	−1.23796	−	0.821760i
$273$		0			0
$274$	−12.8433	−	7.68474i	−0.775890	−	0.464252i
$275$	1.73793	−	3.01018i	0.104801	−	0.181521i
$276$		0			0
$277$	13.4773	+	23.3434i	0.809773	+	1.40257i	0.913021	+	0.407912i	$0.133743\pi$
$277$	13.4773	+	23.3434i	0.809773	+	1.40257i	−0.103248	+	0.994656i	$0.532924\pi$
$278$	−14.3945	+	8.01383i	−0.863325	+	0.480637i
$279$		0			0
$280$	−2.07244	−	1.60506i	−0.123852	−	0.0959209i
$281$			25.3505i			1.51228i	0.654409	+	0.756141i	$0.272918\pi$
$281$			25.3505i			1.51228i	−0.654409	+	0.756141i	$0.727082\pi$
$282$		0			0
$283$	−2.20500	+	1.27306i	−0.131074	+	0.0756754i	−0.564103	−	0.825704i	$-0.690778\pi$
$283$	−2.20500	+	1.27306i	−0.131074	+	0.0756754i	0.433029	+	0.901380i	$0.357445\pi$
$284$	10.1285	−	16.3432i	0.601017	−	0.969788i
$285$		0			0
$286$	0.0659611	−	0.110239i	0.00390036	−	0.00651856i
$287$	−1.92537	+	21.6807i	−0.113651	+	1.27977i
$288$		0			0
$289$	10.2665	−	17.7822i	0.603914	−	1.04601i
$290$	1.68214	+	0.0262515i	0.0987787	+	0.00154154i
$291$		0			0
$292$	8.60928	+	0.268778i	0.503820	+	0.0157290i
$293$			4.66529i			0.272549i	0.990671	+	0.136274i	$0.0435129\pi$
$293$			4.66529i			0.272549i	−0.990671	+	0.136274i	$0.956487\pi$
$294$		0			0
$295$		−	3.60023i		−	0.209614i
$296$	6.63106	−	10.3360i	0.385422	−	0.600766i
$297$		0			0
$298$	−0.349968	+	22.4253i	−0.0202731	+	1.29906i
$299$	0.304355	−	0.527159i	0.0176013	−	0.0304864i
$300$		0			0
$301$	−1.76708	+	19.8983i	−0.101853	+	1.14692i
$302$	−4.50969	−	2.69836i	−0.259503	−	0.155273i
$303$		0			0
$304$	−0.840623	+	13.4500i	−0.0482130	+	0.771408i
$305$	−1.72215	+	0.994285i	−0.0986101	+	0.0569326i
$306$		0			0
$307$			16.7333i			0.955020i	0.878626	+	0.477510i	$0.158461\pi$
$307$			16.7333i			0.955020i	−0.878626	+	0.477510i	$0.841539\pi$
$308$	3.74402	+	0.450626i	0.213335	+	0.0256768i
$309$		0			0
$310$	0.000563367		0.00101192i	3.19971e−5		5.74734e-5i
$311$	−15.6845	−	27.1664i	−0.889389	−	1.54047i	−0.840599	−	0.541657i	$-0.817797\pi$
$311$	−15.6845	−	27.1664i	−0.889389	−	1.54047i	−0.0487894	−	0.998809i	$-0.515536\pi$
$312$		0			0
$313$	11.3777	−	19.7068i	0.643107	−	1.11389i	−0.341629	−	0.939835i	$-0.610979\pi$
$313$	11.3777	−	19.7068i	0.643107	−	1.11389i	0.984735	−	0.174058i	$-0.0556882\pi$
$314$	1.46078	−	2.44135i	0.0824364	−	0.137774i
$315$		0			0
$316$	−3.91220	+	2.09875i	−0.220079	+	0.118064i
$317$	5.10594	+	2.94792i	0.286778	+	0.165572i	0.636488	−	0.771287i	$-0.280386\pi$
$317$	5.10594	+	2.94792i	0.286778	+	0.165572i	−0.349710	+	0.936858i	$0.613720\pi$
$318$		0			0
$319$	−2.09599	+	1.21012i	−0.117353	+	0.0677538i
$320$	2.28523	+	1.62190i	0.127748	+	0.0906669i
$321$		0			0
$322$	17.7715	+	1.85812i	0.990364	+	0.103549i
$323$	−20.6402			−1.14845
$324$		0			0
$325$	−0.310842	−	0.538395i	−0.0172424	−	0.0298648i
$326$	0.358141	−	22.9490i	0.0198356	−	1.27103i
$327$		0			0
$328$	1.08891	−	23.2434i	0.0601252	−	1.28340i
$329$	−4.05477	+	5.77474i	−0.223547	+	0.318372i
$330$		0			0
$331$	7.41160	+	4.27909i	0.407378	+	0.235200i	0.689663	−	0.724131i	$-0.257759\pi$
$331$	7.41160	+	4.27909i	0.407378	+	0.235200i	−0.282284	+	0.959331i	$0.591092\pi$
$332$	5.39751	−	8.70930i	0.296227	−	0.477985i
$333$		0			0
$334$	−17.0725	−	30.6658i	−0.934166	−	1.67796i
$335$	−3.15262			−0.172246
$336$		0			0
$337$	−26.1588			−1.42496			−0.712479	−	0.701693i	$-0.752428\pi$
$337$	−26.1588			−1.42496			−0.712479	+	0.701693i	$0.752428\pi$
$338$	8.93165	+	16.0431i	0.485818	+	0.872630i
$339$		0			0
$340$	−2.26094	+	3.64821i	−0.122617	+	0.197852i
$341$	−0.00144294		0.000833084i	−7.81398e−5		4.51140e-5i
$342$		0			0
$343$	−17.8703	−	4.86349i	−0.964904	−	0.262604i
$344$	0.999393	−	21.3325i	0.0538837	−	1.15017i
$345$		0			0
$346$	−0.110182	+	7.06027i	−0.00592344	+	0.379562i
$347$	18.3826	+	31.8396i	0.986830	+	1.70924i	0.633505	+	0.773738i	$0.281615\pi$
$347$	18.3826	+	31.8396i	0.986830	+	1.70924i	0.353324	+	0.935501i	$0.385051\pi$
$348$		0			0
$349$	9.93465			0.531790			0.265895	−	0.964002i	$-0.414333\pi$
$349$	9.93465			0.531790			0.265895	+	0.964002i	$0.414333\pi$
$350$	10.7186	−	14.7697i	0.572933	−	0.789474i
$351$		0			0
$352$	−4.01915	−	0.314226i	−0.214221	−	0.0167483i
$353$	−10.7415	+	6.20163i	−0.571715	+	0.330080i	−0.757834	−	0.652447i	$-0.773742\pi$
$353$	−10.7415	+	6.20163i	−0.571715	+	0.330080i	0.186119	+	0.982527i	$0.440409\pi$
$354$		0			0
$355$	−2.91635	−	1.68376i	−0.154784	−	0.0893646i
$356$	−15.8541	+	8.50510i	−0.840265	+	0.450769i
$357$		0			0
$358$	14.1688	−	23.6799i	0.748843	−	1.25152i
$359$	−8.25328	+	14.2951i	−0.435592	+	0.754467i	−0.997344	−	0.0728388i	$-0.976794\pi$
$359$	−8.25328	+	14.2951i	−0.435592	+	0.754467i	0.561752	+	0.827306i	$0.310127\pi$
$360$		0			0
$361$	−3.82474	−	6.62465i	−0.201302	−	0.348666i
$362$	5.37132	+	9.64801i	0.282310	+	0.507088i
$363$		0			0
$364$	0.404624	−	0.539633i	0.0212081	−	0.0282845i
$365$		−	1.50859i		−	0.0789633i
$366$		0			0
$367$	−10.7204	+	6.18944i	−0.559602	+	0.323086i	−0.752986	−	0.658037i	$-0.771387\pi$
$367$	−10.7204	+	6.18944i	−0.559602	+	0.323086i	0.193384	+	0.981123i	$0.438054\pi$
$368$	−19.0648	−	1.19155i	−0.993824	−	0.0621140i
$369$		0			0
$370$	−1.84563	−	1.10433i	−0.0959500	−	0.0574114i
$371$	−28.1472	+	13.0805i	−1.46133	+	0.679106i
$372$		0			0
$373$	10.5698	−	18.3074i	0.547282	−	0.947920i	−0.451178	−	0.892434i	$-0.648996\pi$
$373$	10.5698	−	18.3074i	0.547282	−	0.947920i	0.998459	−	0.0554855i	$-0.0176707\pi$
$374$	0.0963479	−	6.17378i	0.00498203	−	0.319239i
$375$		0			0
$376$	4.07323	−	6.34904i	0.210061	−	0.327427i
$377$			0.432880i			0.0222945i
$378$		0			0
$379$		−	18.9297i		−	0.972352i	−0.873861	−	0.486176i	$-0.838391\pi$
$379$		−	18.9297i		−	0.972352i	0.873861	−	0.486176i	$-0.161609\pi$
$380$	2.35912	+	0.0736506i	0.121020	+	0.00377819i
$381$		0			0
$382$	−17.5774	−	0.274312i	−0.899337	−	0.0140350i
$383$	3.25973	−	5.64601i	0.166564	−	0.288498i	−0.770645	−	0.637264i	$-0.780066\pi$
$383$	3.25973	−	5.64601i	0.166564	−	0.288498i	0.937210	+	0.348766i	$0.113399\pi$
$384$		0			0
$385$	0.0584236	−	0.657883i	0.00297754	−	0.0335288i
$386$	0.972933	−	1.62603i	0.0495210	−	0.0827629i
$387$		0			0
$388$	18.2715	−	29.4824i	0.927593	−	1.49674i
$389$	−14.7537	+	8.51806i	−0.748043	+	0.431883i	−0.824986	−	0.565153i	$-0.808817\pi$
$389$	−14.7537	+	8.51806i	−0.748043	+	0.431883i	0.0769436	+	0.997035i	$0.475484\pi$
$390$		0			0
$391$		−	29.2568i		−	1.47958i
$392$	19.3045	+	4.39722i	0.975025	+	0.222093i
$393$		0			0
$394$	14.9030	−	8.29689i	0.750800	−	0.417991i
$395$	0.388783	+	0.673392i	0.0195618	+	0.0338820i
$396$		0			0
$397$	−7.32945	+	12.6950i	−0.367854	+	0.637142i	−0.989230	−	0.146370i	$-0.953241\pi$
$397$	−7.32945	+	12.6950i	−0.367854	+	0.637142i	0.621375	+	0.783513i	$0.286574\pi$
$398$	−14.4021	−	8.61748i	−0.721914	−	0.431955i
$399$		0			0
$400$	−10.7895	+	16.2541i	−0.539476	+	0.812704i
$401$	5.41239	+	3.12484i	0.270282	+	0.156047i	0.629016	−	0.777393i	$-0.283458\pi$
$401$	5.41239	+	3.12484i	0.270282	+	0.156047i	−0.358734	+	0.933440i	$0.616791\pi$
$402$		0			0
$403$	−0.000258082	0	0.000149004i	−1.28560e−5	0	7.42241e-6i
$404$	−0.663158	+	21.2417i	−0.0329933	+	1.05682i
$405$		0			0
$406$	−11.6056	+	5.17467i	−0.575975	+	0.256815i
$407$	3.09416			0.153372
$408$		0			0
$409$	−14.5140	−	25.1389i	−0.717670	−	1.24304i	−0.961921	−	0.273329i	$-0.911875\pi$
$409$	−14.5140	−	25.1389i	−0.717670	−	1.24304i	0.244251	−	0.969712i	$-0.421458\pi$
$410$	−4.07488	−	0.0635925i	−0.201244	−	0.00314061i
$411$		0			0
$412$	−18.3266	+	9.83153i	−0.902889	+	0.484365i
$413$	11.4600	+	24.6602i	0.563911	+	1.21345i
$414$		0			0
$415$	−1.55413	−	0.897278i	−0.0762893	−	0.0440456i
$416$	−0.408101	+	0.594447i	−0.0200088	+	0.0291452i
$417$		0			0
$418$	−2.96673	+	1.65166i	−0.145108	+	0.0807854i
$419$	5.94826			0.290591			0.145296	−	0.989388i	$-0.453587\pi$
$419$	5.94826			0.290591			0.145296	+	0.989388i	$0.453587\pi$
$420$		0			0
$421$	26.2986			1.28172			0.640858	−	0.767660i	$-0.278579\pi$
$421$	26.2986			1.28172			0.640858	+	0.767660i	$0.278579\pi$
$422$	3.05799	−	1.70247i	0.148861	−	0.0828750i
$423$		0			0
$424$	29.4806	−	15.2277i	1.43171	−	0.739520i
$425$	−25.8772	−	14.9402i	−1.25523	−	0.724706i
$426$		0			0
$427$	8.63112	−	12.2923i	0.417689	−	0.594866i
$428$	−8.44337	−	15.7390i	−0.408126	−	0.760774i
$429$		0			0
$430$	−3.73989	−	0.0583646i	−0.180353	−	0.00281459i
$431$	3.94092	+	6.82587i	0.189827	+	0.328790i	0.945193	−	0.326514i	$-0.105874\pi$
$431$	3.94092	+	6.82587i	0.189827	+	0.328790i	−0.755365	+	0.655304i	$0.772541\pi$
$432$		0			0
$433$	−28.8906			−1.38839			−0.694196	−	0.719786i	$-0.744240\pi$
$433$	−28.8906			−1.38839			−0.694196	+	0.719786i	$0.744240\pi$
$434$	−0.00707993	−	0.00513801i	−0.000339848	−	0.000246633i
$435$		0			0
$436$	−32.5993	−	1.01774i	−1.56122	−	0.0487407i
$437$	−13.9334	+	8.04447i	−0.666527	+	0.384819i
$438$		0			0
$439$	−22.8209	−	13.1757i	−1.08918	−	0.628840i	−0.155824	−	0.987785i	$-0.549803\pi$
$439$	−22.8209	−	13.1757i	−1.08918	−	0.628840i	−0.933359	+	0.358945i	$0.883136\pi$
$440$	−0.0330422	+	0.705300i	−0.00157522	+	0.0336239i
$441$		0			0
$442$	−0.947676	−	0.567040i	−0.0450764	−	0.0269713i
$443$	11.8798	−	20.5764i	0.564425	−	0.977613i	−0.432678	−	0.901549i	$-0.642431\pi$
$443$	11.8798	−	20.5764i	0.564425	−	0.977613i	0.997103	−	0.0760641i	$-0.0242354\pi$
$444$		0			0
$445$	1.57553	+	2.72890i	0.0746873	+	0.129362i
$446$	−9.59567	+	5.34218i	−0.454368	+	0.252960i
$447$		0			0
$448$	−20.8157	−	3.83518i	−0.983447	−	0.181195i
$449$		−	36.0964i		−	1.70350i	−0.523951	−	0.851748i	$-0.675543\pi$
$449$		−	36.0964i		−	1.70350i	0.523951	−	0.851748i	$-0.324457\pi$
$450$		0			0
$451$	5.07741	−	2.93145i	0.239086	−	0.138036i
$452$	−14.3491	−	8.89269i	−0.674923	−	0.418277i
$453$		0			0
$454$	11.6659	−	19.4969i	0.547507	−	0.915033i
$455$	−0.0966784	−	0.0678834i	−0.00453235	−	0.00318242i
$456$		0			0
$457$	9.98422	−	17.2932i	0.467042	−	0.808941i	−0.532249	−	0.846588i	$-0.678653\pi$
$457$	9.98422	−	17.2932i	0.467042	−	0.808941i	0.999291	+	0.0376473i	$0.0119863\pi$
$458$	15.6884	+	0.244832i	0.733070	+	0.0114403i
$459$		0			0
$460$	−0.104397	+	3.34396i	−0.00486754	+	0.155913i
$461$			3.90222i			0.181744i	0.995863	+	0.0908722i	$0.0289655\pi$
$461$			3.90222i			0.181744i	−0.995863	+	0.0908722i	$0.971035\pi$
$462$		0			0
$463$			11.0279i			0.512510i	0.966609	+	0.256255i	$0.0824887\pi$
$463$			11.0279i			0.512510i	−0.966609	+	0.256255i	$0.917511\pi$
$464$	12.1651	−	6.04508i	0.564752	−	0.280636i
$465$		0			0
$466$	−0.0792928	+	5.08092i	−0.00367317	+	0.235369i
$467$	19.2572	−	33.3545i	0.891119	−	1.54346i	0.0525832	−	0.998617i	$-0.483255\pi$
$467$	19.2572	−	33.3545i	0.891119	−	1.54346i	0.838536	−	0.544847i	$-0.183412\pi$
$468$		0			0
$469$	21.5942	−	10.0352i	0.997129	−	0.463384i
$470$	−1.13371	−	0.678353i	−0.0522942	−	0.0312901i
$471$		0			0
$472$	−13.3412	−	25.8284i	−0.614077	−	1.18885i
$473$	4.66000	−	2.69045i	0.214267	−	0.123707i
$474$		0			0
$475$			16.4319i			0.753946i
$476$	3.87383	−	32.1857i	0.177557	−	1.47523i
$477$		0			0
$478$	4.23239	+	7.60225i	0.193585	+	0.347719i
$479$	7.41054	+	12.8354i	0.338596	+	0.586466i	0.984169	−	0.177233i	$-0.0567146\pi$
$479$	7.41054	+	12.8354i	0.338596	+	0.586466i	−0.645573	+	0.763699i	$0.723381\pi$
$480$		0			0
$481$	0.276708	−	0.479272i	0.0126168	−	0.0218529i
$482$	−9.10777	+	15.2215i	−0.414847	+	0.693322i
$483$		0			0
$484$	9.91993	+	18.4914i	0.450906	+	0.840519i
$485$	−5.26099	−	3.03743i	−0.238889	−	0.137923i
$486$		0			0
$487$	7.45460	−	4.30391i	0.337800	−	0.195029i	−0.321499	−	0.946910i	$-0.604187\pi$
$487$	7.45460	−	4.30391i	0.337800	−	0.195029i	0.659299	+	0.751881i	$0.270853\pi$
$488$	−8.67042	+	13.5148i	−0.392491	+	0.611785i
$489$		0			0
$490$	0.664264	−	3.40344i	0.0300084	−	0.153752i
$491$	−8.74870			−0.394823			−0.197412	−	0.980321i	$-0.563254\pi$
$491$	−8.74870			−0.394823			−0.197412	+	0.980321i	$0.563254\pi$
$492$		0			0
$493$	10.4029	+	18.0184i	0.468523	+	0.811506i
$494$	−0.00947658	+	0.607240i	−0.000426371	+	0.0273210i
$495$		0			0
$496$	0.00779148	+	0.00517201i	0.000349848	+	0.000232230i
$497$	25.3355	+	2.24993i	1.13645	+	0.100923i
$498$		0			0
$499$	−25.1145	−	14.4998i	−1.12428	−	0.649102i	−0.181788	−	0.983338i	$-0.558189\pi$
$499$	−25.1145	−	14.4998i	−1.12428	−	0.649102i	−0.942490	+	0.334236i	$0.891522\pi$
$500$	5.88181	+	3.64520i	0.263043	+	0.163018i
$501$		0			0
$502$	0.334091	+	0.600097i	0.0149112	+	0.0267837i
$503$	27.7583			1.23768			0.618841	−	0.785516i	$-0.287603\pi$
$503$	27.7583			1.23768			0.618841	+	0.785516i	$0.287603\pi$
$504$		0			0
$505$	3.72216			0.165634
$506$	−2.34117	−	4.20523i	−0.104078	−	0.186945i
$507$		0			0
$508$	−15.6711	−	9.71199i	−0.695291	−	0.430900i
$509$	−18.3756	−	10.6092i	−0.814484	−	0.470243i	0.0340265	−	0.999421i	$-0.489167\pi$
$509$	−18.3756	−	10.6092i	−0.814484	−	0.470243i	−0.848511	+	0.529178i	$0.822500\pi$
$510$		0			0
$511$	4.80205	+	10.3333i	0.212430	+	0.457117i
$512$	22.4046	+	3.16741i	0.990154	+	0.139981i
$513$		0			0
$514$	−0.643049	+	41.2053i	−0.0283637	+	1.81749i
$515$	1.82125	+	3.15449i	0.0802537	+	0.139003i
$516$		0			0
$517$	1.90064			0.0835899
$518$	16.1571	+	1.68933i	0.709902	+	0.0742249i
$519$		0			0
$520$	0.106293	+	0.0681925i	0.00466126	+	0.00299044i
$521$	−20.9834	+	12.1148i	−0.919300	+	0.530758i	−0.883412	−	0.468598i	$-0.844759\pi$
$521$	−20.9834	+	12.1148i	−0.919300	+	0.530758i	−0.0358883	+	0.999356i	$0.511426\pi$
$522$		0			0
$523$	18.7115	+	10.8031i	0.818195	+	0.472385i	0.849794	−	0.527116i	$-0.176727\pi$
$523$	18.7115	+	10.8031i	0.818195	+	0.472385i	−0.0315989	+	0.999501i	$0.510060\pi$
$524$	18.1616	+	33.8545i	0.793393	+	1.47894i
$525$		0			0
$526$	16.9671	−	28.3565i	0.739799	−	1.23640i
$527$	−0.00716166	+	0.0124044i	−0.000311967	+	0.000540343i
$528$		0			0
$529$	0.0972459	+	0.168435i	0.00422808	+	0.00732325i
$530$	−2.82684	−	5.07759i	−0.122790	−	0.220557i
$531$		0			0
$532$	−16.3935	+	7.00491i	−0.710747	+	0.303701i
$533$		−	1.04863i		−	0.0454210i
$534$		0			0
$535$	−2.70909	+	1.56409i	−0.117124	+	0.0676217i
$536$	−22.6172	+	11.6825i	−0.976915	+	0.504607i
$537$		0			0
$538$	33.8040	+	20.2265i	1.45739	+	0.872027i
$539$	1.69395	+	4.69221i	0.0729636	+	0.202108i
$540$		0			0
$541$	−20.2054	+	34.9967i	−0.868696	+	1.50463i	−0.00536596	+	0.999986i	$0.501708\pi$
$541$	−20.2054	+	34.9967i	−0.868696	+	1.50463i	−0.863330	+	0.504640i	$0.831625\pi$
$542$	−0.633441	+	40.5896i	−0.0272086	+	1.74347i
$543$		0			0
$544$	−2.70126	+	34.5509i	−0.115816	+	1.48136i
$545$			5.71233i			0.244689i
$546$		0			0
$547$			21.7198i			0.928670i	0.885660	+	0.464335i	$0.153707\pi$
$547$			21.7198i			0.928670i	−0.885660	+	0.464335i	$0.846293\pi$
$548$	−0.660479	+	21.1559i	−0.0282143	+	0.903736i
$549$		0			0
$550$	−4.91500	−	0.0767034i	−0.209576	−	0.00327064i
$551$	5.72078	−	9.90868i	0.243713	−	0.422124i
$552$		0			0
$553$	−4.80651	−	3.37492i	−0.204394	−	0.143516i
$554$	19.5726	−	32.7111i	0.831560	−	1.38976i
$555$		0			0
$556$	19.8042	+	12.2735i	0.839887	+	0.520512i
$557$	36.2866	−	20.9501i	1.53751	−	0.887684i	0.538530	−	0.842606i	$-0.318980\pi$
$557$	36.2866	−	20.9501i	1.53751	−	0.887684i	0.998983	−	0.0450775i	$-0.0143535\pi$
$558$		0			0
$559$		−	0.962418i		−	0.0407059i
$560$	−0.557615	+	3.66490i	−0.0235635	+	0.154870i
$561$		0			0
$562$	31.3238	−	17.4388i	1.32131	−	0.735613i
$563$	1.21907	+	2.11148i	0.0513775	+	0.0889885i	0.890570	−	0.454845i	$-0.150305\pi$
$563$	1.21907	+	2.11148i	0.0513775	+	0.0889885i	−0.839193	+	0.543834i	$0.816972\pi$
$564$		0			0
$565$	−1.47831	+	2.56052i	−0.0621932	+	0.107722i
$566$	3.08987	+	1.84881i	0.129877	+	0.0777114i
$567$		0			0
$568$	−27.1616	−	1.27248i	−1.13968	−	0.0533919i
$569$	−7.19227	−	4.15246i	−0.301515	−	0.174080i	0.341608	−	0.939843i	$-0.389028\pi$
$569$	−7.19227	−	4.15246i	−0.301515	−	0.174080i	−0.643123	+	0.765762i	$0.722362\pi$
$570$		0			0
$571$	−40.3829	+	23.3151i	−1.68997	+	0.975705i	−0.735442	+	0.677588i	$0.763025\pi$
$571$	−40.3829	+	23.3151i	−1.68997	+	0.975705i	−0.954529	+	0.298117i	$0.903641\pi$
$572$	−0.181590	−	0.00566915i	−0.00759265	−	0.000237039i
$573$		0			0
$574$	28.1138	−	12.5353i	1.17345	−	0.523214i
$575$	−23.2916			−0.971327
$576$		0			0
$577$	−4.32922	−	7.49843i	−0.180228	−	0.312164i	0.761730	−	0.647894i	$-0.224350\pi$
$577$	−4.32922	−	7.49843i	−0.180228	−	0.312164i	−0.941958	+	0.335730i	$0.891017\pi$
$578$	−29.0346	−	0.453114i	−1.20768	−	0.0188471i
$579$		0			0
$580$	−1.12472	−	2.09656i	−0.0467016	−	0.0870550i
$581$	13.5013	+	1.19899i	0.560130	+	0.0497426i
$582$		0			0
$583$	7.24034	+	4.18021i	0.299864	+	0.173127i
$584$	−5.59030	−	10.8228i	−0.231328	−	0.447850i
$585$		0			0
$586$	5.76457	−	3.20930i	0.238132	−	0.132575i
$587$	16.5890			0.684700			0.342350	−	0.939573i	$-0.388777\pi$
$587$	16.5890			0.684700			0.342350	+	0.939573i	$0.388777\pi$
$588$		0			0
$589$	0.00787670			0.000324554
$590$	−4.44855	+	2.47663i	−0.183144	+	0.101961i
$591$		0			0
$592$	−17.3330	−	1.08331i	−0.712382	−	0.0445239i
$593$	35.4794	+	20.4840i	1.45696	+	0.841178i	0.998861	−	0.0477210i	$-0.0151958\pi$
$593$	35.4794	+	20.4840i	1.45696	+	0.841178i	0.458103	+	0.888899i	$0.348529\pi$
$594$		0			0
$595$	−5.65553	−	0.502243i	−0.231854	−	0.0205899i
$596$	27.9501	−	14.9941i	1.14488	−	0.614184i
$597$		0			0
$598$	−0.860742	−	0.0134327i	−0.0351983	−	0.000549305i
$599$	10.5150	+	18.2125i	0.429632	+	0.744144i	0.996840	−	0.0794302i	$-0.0253101\pi$
$599$	10.5150	+	18.2125i	0.429632	+	0.744144i	−0.567209	+	0.823574i	$0.691977\pi$
$600$		0			0
$601$	−1.20122			−0.0489988			−0.0244994	−	0.999700i	$-0.507799\pi$
$601$	−1.20122			−0.0489988			−0.0244994	+	0.999700i	$0.507799\pi$
$602$	25.8025	−	11.5048i	1.05163	−	0.468900i
$603$		0			0
$604$	−0.231915	+	7.42853i	−0.00943650	+	0.302263i
$605$	3.18286	−	1.83762i	0.129401	−	0.0747100i
$606$		0			0
$607$	26.7657	+	15.4532i	1.08638	+	0.627224i	0.932612	−	0.360882i	$-0.117524\pi$
$607$	26.7657	+	15.4532i	1.08638	+	0.627224i	0.153773	+	0.988106i	$0.450858\pi$
$608$	17.1974	−	8.21366i	0.697449	−	0.333108i
$609$		0			0
$610$	2.41325	+	1.44396i	0.0977098	+	0.0584644i
$611$	0.169972	−	0.294400i	0.00687634	−	0.0119102i
$612$		0			0
$613$	2.49089	+	4.31434i	0.100606	+	0.174255i	0.911934	−	0.410336i	$-0.134589\pi$
$613$	2.49089	+	4.31434i	0.100606	+	0.174255i	−0.811329	+	0.584590i	$0.801255\pi$
$614$	20.6762	−	11.5110i	0.834422	−	0.464546i
$615$		0			0
$616$	−2.01874	−	4.93621i	−0.0813374	−	0.198886i
$617$			15.4858i			0.623435i	0.950175	+	0.311718i	$0.100904\pi$
$617$			15.4858i			0.623435i	−0.950175	+	0.311718i	$0.899096\pi$
$618$		0			0
$619$	21.9439	−	12.6693i	0.881998	−	0.509222i	0.0106814	−	0.999943i	$-0.496600\pi$
$619$	21.9439	−	12.6693i	0.881998	−	0.509222i	0.871317	+	0.490721i	$0.163267\pi$
$620$	0.000862818	−	0.00139223i	3.46516e−5	−	5.59131e-5i
$621$		0			0
$622$	−22.7781	+	38.0683i	−0.913318	+	1.52640i
$623$	−19.4782	−	13.6768i	−0.780379	−	0.547948i
$624$		0			0
$625$	−11.5873	+	20.0697i	−0.463491	+	0.802790i
$626$	−32.1771	−	0.502156i	−1.28606	−	0.0200702i
$627$		0			0
$628$	−4.02149	−	0.125549i	−0.160475	−	0.00500996i
$629$		−	26.5991i		−	1.06058i
$630$		0			0
$631$		−	12.6823i		−	0.504876i	−0.967613	−	0.252438i	$-0.918768\pi$
$631$		−	12.6823i		−	0.504876i	0.967613	−	0.252438i	$-0.0812323\pi$
$632$	5.28452	+	3.39029i	0.210207	+	0.134858i
$633$		0			0
$634$	0.130106	−	8.33695i	0.00516718	−	0.331103i
$635$	−1.61451	+	2.79642i	−0.0640701	+	0.110973i
$636$		0			0
$637$	0.878291	+	0.157234i	0.0347992	+	0.00622985i
$638$	2.93712	+	1.75742i	0.116282	+	0.0695768i
$639$		0			0
$640$	0.432034	−	3.93942i	0.0170776	−	0.155719i
$641$	14.7613	−	8.52242i	0.583035	−	0.336615i	−0.179304	−	0.983794i	$-0.557385\pi$
$641$	14.7613	−	8.52242i	0.583035	−	0.336615i	0.762338	+	0.647179i	$0.224051\pi$
$642$		0			0
$643$		−	37.1996i		−	1.46701i	−0.679685	−	0.733504i	$-0.737883\pi$
$643$		−	37.1996i		−	1.46701i	0.679685	−	0.733504i	$-0.262117\pi$
$644$	−9.92921	−	23.2371i	−0.391266	−	0.915672i
$645$		0			0
$646$	14.1986	+	25.5037i	0.558637	+	1.00343i
$647$	−7.31238	−	12.6654i	−0.287479	−	0.497929i	0.685728	−	0.727858i	$-0.259484\pi$
$647$	−7.31238	−	12.6654i	−0.287479	−	0.497929i	−0.973207	+	0.229929i	$0.926151\pi$
$648$		0			0
$649$	3.66235	−	6.34337i	0.143760	−	0.248999i
$650$	−0.451425	+	0.754453i	−0.0177063	+	0.0295921i
$651$		0			0
$652$	−28.6028	+	15.3443i	−1.12017	+	0.600929i
$653$	35.1095	+	20.2705i	1.37394	+	0.793245i	0.991422	−	0.130703i	$-0.0417235\pi$
$653$	35.1095	+	20.2705i	1.37394	+	0.793245i	0.382519	+	0.923948i	$0.375057\pi$
$654$		0			0
$655$	5.82723	−	3.36435i	0.227689	−	0.131456i
$656$	−29.4692	+	14.6438i	−1.15058	+	0.571746i
$657$		0			0
$658$	9.92476	+	1.03770i	0.386907	+	0.0404537i
$659$	−2.98301			−0.116201			−0.0581007	−	0.998311i	$-0.518504\pi$
$659$	−2.98301			−0.116201			−0.0581007	+	0.998311i	$0.518504\pi$
$660$		0			0
$661$	15.4040	+	26.6805i	0.599146	+	1.03775i	0.992947	+	0.118556i	$0.0378264\pi$
$661$	15.4040	+	26.6805i	0.599146	+	1.03775i	−0.393801	+	0.919196i	$0.628840\pi$
$662$	0.188858	−	12.1016i	0.00734016	−	0.470343i
$663$		0			0
$664$	−14.4745	−	0.678105i	−0.561718	−	0.0263156i
$665$	1.31586	+	2.83152i	0.0510268	+	0.109802i
$666$		0			0
$667$	14.0452	+	8.10900i	0.543832	+	0.313982i
$668$	−26.1472	+	42.1906i	−1.01167	+	1.63240i
$669$		0			0
$670$	2.16872	+	3.89548i	0.0837850	+	0.150495i
$671$	−4.04576			−0.156185
$672$		0			0
$673$	15.4848			0.596894			0.298447	−	0.954426i	$-0.403531\pi$
$673$	15.4848			0.596894			0.298447	+	0.954426i	$0.403531\pi$
$674$	17.9949	+	32.3225i	0.693136	+	1.24502i
$675$		0			0
$676$	13.6792	−	22.0724i	0.526122	−	0.848939i
$677$	−25.3739	−	14.6496i	−0.975199	−	0.563032i	−0.0743819	−	0.997230i	$-0.523698\pi$
$677$	−25.3739	−	14.6496i	−0.975199	−	0.563032i	−0.900817	+	0.434198i	$0.857032\pi$
$678$		0			0
$679$	45.7043	+	4.05879i	1.75397	+	0.155762i
$680$	6.06316	+	0.284049i	0.232512	+	0.0108928i
$681$		0			0
$682$	−3.67682e−5		0.00235603i	−1.40793e−6		9.02171e-5i
$683$	−1.53968	−	2.66681i	−0.0589143	−	0.102043i	0.835064	−	0.550153i	$-0.185431\pi$
$683$	−1.53968	−	2.66681i	−0.0589143	−	0.102043i	−0.893978	+	0.448110i	$0.852097\pi$
$684$		0			0
$685$	3.70712			0.141642
$686$	6.28366	+	25.4267i	0.239911	+	0.970795i
$687$		0			0
$688$	−27.0466	+	13.4400i	−1.03114	+	0.512394i
$689$	1.29499	−	0.747665i	0.0493354	−	0.0284838i
$690$		0			0
$691$	19.1882	+	11.0783i	0.729952	+	0.421438i	0.818405	−	0.574642i	$-0.194859\pi$
$691$	19.1882	+	11.0783i	0.729952	+	0.421438i	−0.0884525	+	0.996080i	$0.528192\pi$
$692$	8.79967	−	4.72068i	0.334513	−	0.179453i
$693$		0			0
$694$	26.6964	−	44.6169i	1.01338	−	1.69363i
$695$	2.04034	−	3.53397i	0.0773944	−	0.134051i
$696$		0			0
$697$	−25.2004	−	43.6483i	−0.954532	−	1.65330i
$698$	−6.83414	−	12.2756i	−0.258676	−	0.464636i
$699$		0			0
$700$	−25.6233	−	3.08399i	−0.968470	−	0.116564i
$701$		−	33.1595i		−	1.25242i	−0.779656	−	0.626208i	$-0.784606\pi$
$701$		−	33.1595i		−	1.25242i	0.779656	−	0.626208i	$-0.215394\pi$
$702$		0			0
$703$	−12.6677	+	7.31372i	−0.477773	+	0.275842i
$704$	2.37654	+	5.18233i	0.0895693	+	0.195317i
$705$		0			0
$706$	15.0521	+	9.00641i	0.566495	+	0.338961i
$707$	−25.4953	+	11.8481i	−0.958850	+	0.445595i
$708$		0			0
$709$	−7.67372	+	13.2913i	−0.288193	+	0.499164i	−0.973378	−	0.229204i	$-0.926388\pi$
$709$	−7.67372	+	13.2913i	−0.288193	+	0.499164i	0.685186	+	0.728368i	$0.259721\pi$
$710$	−0.0743126	+	4.76181i	−0.00278890	+	0.178707i
$711$		0			0
$712$	21.4153	+	13.7390i	0.802573	+	0.514892i
$713$			0.0111649i			0.000418130i
$714$		0			0
$715$			0.0318197i			0.00118999i
$716$	−39.0064	−	1.21776i	−1.45774	−	0.0455099i
$717$		0			0
$718$	23.3410	+	0.364259i	0.871077	+	0.0135940i
$719$	14.9962	−	25.9742i	0.559264	−	0.968674i	−0.438294	−	0.898832i	$-0.644417\pi$
$719$	14.9962	−	25.9742i	0.559264	−	0.968674i	0.997558	−	0.0698422i	$-0.0222496\pi$
$720$		0			0
$721$	−22.5160	−	15.8098i	−0.838539	−	0.588786i
$722$	−5.55454	+	9.28313i	−0.206718	+	0.345482i
$723$		0			0
$724$	8.22638	−	13.2739i	0.305731	−	0.493321i
$725$	14.3446	−	8.28184i	0.532744	−	0.307580i
$726$		0			0
$727$			41.1692i			1.52688i	0.645879	+	0.763440i	$0.276491\pi$
$727$			41.1692i			1.52688i	−0.645879	+	0.763440i	$0.723509\pi$
$728$	−0.945132	−	0.128746i	−0.0350289	−	0.00477166i
$729$		0			0
$730$	−1.86406	+	1.03777i	−0.0689920	+	0.0384098i
$731$	−23.1286	−	40.0600i	−0.855444	−	1.48167i
$732$		0			0
$733$	−16.3313	+	28.2866i	−0.603209	+	1.04479i	0.389123	+	0.921186i	$0.372778\pi$
$733$	−16.3313	+	28.2866i	−0.603209	+	1.04479i	−0.992332	+	0.123603i	$0.960555\pi$
$734$	15.0225	+	8.98870i	0.554492	+	0.331779i
$735$		0			0
$736$	11.6426	+	24.3768i	0.429151	+	0.898540i
$737$	−5.55471	−	3.20702i	−0.204611	−	0.118132i
$738$		0			0
$739$	15.9487	−	9.20799i	0.586683	−	0.338721i	−0.177102	−	0.984192i	$-0.556672\pi$
$739$	15.9487	−	9.20799i	0.586683	−	0.338721i	0.763785	+	0.645471i	$0.223339\pi$
$740$	−0.0949137	+	3.04020i	−0.00348910	+	0.111760i
$741$		0			0
$742$	35.5254	+	25.7813i	1.30418	+	0.946462i
$743$	−22.5175			−0.826088			−0.413044	−	0.910711i	$-0.635534\pi$
$743$	−22.5175			−0.826088			−0.413044	+	0.910711i	$0.635534\pi$
$744$		0			0
$745$	−2.77759	−	4.81093i	−0.101763	−	0.176259i
$746$	−29.8922	−	0.466496i	−1.09443	−	0.0170797i
$747$		0			0
$748$	−7.69479	+	4.12795i	−0.281349	+	0.150933i
$749$	13.5775	−	19.3368i	0.496111	−	0.706553i
$750$		0			0
$751$	27.5078	+	15.8816i	1.00377	+	0.579529i	0.909362	−	0.416005i	$-0.136570\pi$
$751$	27.5078	+	15.8816i	1.00377	+	0.579529i	0.0944107	+	0.995533i	$0.469903\pi$
$752$	−10.6471	−	0.665443i	−0.388259	−	0.0242662i
$753$		0			0
$754$	0.534880	−	0.297783i	0.0194792	−	0.0108446i
$755$	1.30169			0.0473733
$756$		0			0
$757$	−7.32709			−0.266308			−0.133154	−	0.991095i	$-0.542510\pi$
$757$	−7.32709			−0.266308			−0.133154	+	0.991095i	$0.542510\pi$
$758$	−23.3901	+	13.0219i	−0.849565	+	0.472977i
$759$		0			0
$760$	−1.53185	−	2.96566i	−0.0555662	−	0.107576i
$761$	4.23458	+	2.44483i	0.153503	+	0.0886252i	0.574784	−	0.818305i	$-0.305086\pi$
$761$	4.23458	+	2.44483i	0.153503	+	0.0886252i	−0.421281	+	0.906930i	$0.638419\pi$
$762$		0			0
$763$	−18.1831	−	39.1272i	−0.658273	−	1.41650i
$764$	11.7527	+	21.9078i	0.425198	+	0.792598i
$765$		0			0
$766$	−9.21877	−	0.143868i	−0.333088	−	0.00519816i
$767$	−0.655040	−	1.13456i	−0.0236521	−	0.0409667i
$768$		0			0
$769$	10.3531			0.373343			0.186672	−	0.982422i	$-0.440230\pi$
$769$	10.3531			0.373343			0.186672	+	0.982422i	$0.440230\pi$
$770$	−0.853089	+	0.380374i	−0.0307432	+	0.0137077i
$771$		0			0
$772$	−2.67846	−	0.0836205i	−0.0964000	−	0.00300957i
$773$	5.48545	−	3.16703i	0.197298	−	0.113910i	−0.398097	−	0.917344i	$-0.630329\pi$
$773$	5.48545	−	3.16703i	0.197298	−	0.113910i	0.595395	+	0.803433i	$0.296996\pi$
$774$		0			0
$775$	0.00987522	+	0.00570146i	0.000354728	+	0.000204802i
$776$	−48.9985	−	2.29550i	−1.75894	−	0.0824036i
$777$		0			0
$778$	20.6744	+	12.3705i	0.741212	+	0.443503i
$779$	−13.8582	+	24.0031i	−0.496522	+	0.860002i
$780$		0			0
$781$	−3.42561	−	5.93334i	−0.122578	−	0.212312i
$782$	−36.1506	+	20.1260i	−1.29274	+	0.719706i
$783$		0			0
$784$	−7.84644	−	26.8781i	−0.280230	−	0.959933i
$785$			0.704680i			0.0251511i
$786$		0			0
$787$	−1.48926	+	0.859826i	−0.0530865	+	0.0306495i	−0.526308	−	0.850294i	$-0.676424\pi$
$787$	−1.48926	+	0.859826i	−0.0530865	+	0.0306495i	0.473222	+	0.880943i	$0.343091\pi$
$788$	−20.5038	−	12.7070i	−0.730417	−	0.452669i
$789$		0			0
$790$	0.564615	−	0.943625i	0.0200881	−	0.0335727i
$791$	1.97541	−	22.2442i	0.0702374	−	0.790913i
$792$		0			0
$793$	−0.361808	+	0.626670i	−0.0128482	+	0.0222537i
$794$	20.7283	+	0.323485i	0.735619	+	0.0114801i
$795$		0			0
$796$	−0.740645	+	23.7238i	−0.0262515	+	0.840866i
$797$		−	3.60991i		−	0.127870i	−0.997954	−	0.0639348i	$-0.979635\pi$
$797$		−	3.60991i		−	0.127870i	0.997954	−	0.0639348i	$-0.0203650\pi$
$798$		0			0
$799$		−	16.3390i		−	0.578031i
$800$	27.5062	+	2.15050i	0.972492	+	0.0760317i
$801$		0			0
$802$	0.137915	−	8.83732i	0.00486995	−	0.312056i
$803$	1.53462	−	2.65804i	0.0541555	−	0.0938001i
$804$		0			0
$805$	−4.01358	+	1.86518i	−0.141460	+	0.0657390i
$806$	0.000361651	0	0.000216393i	1.27386e−5	0	7.62211e-6i
$807$		0			0
$808$	26.7031	−	13.7930i	0.939412	−	0.485235i
$809$	9.63889	−	5.56502i	0.338885	−	0.195656i	−0.320894	−	0.947115i	$-0.603983\pi$
$809$	9.63889	−	5.56502i	0.338885	−	0.195656i	0.659779	+	0.751460i	$0.270650\pi$
$810$		0			0
$811$			40.8908i			1.43587i	0.696110	+	0.717936i	$0.254913\pi$
$811$			40.8908i			1.43587i	−0.696110	+	0.717936i	$0.745087\pi$
$812$	14.3776	+	10.7805i	0.504553	+	0.378321i
$813$		0			0
$814$	−2.12850	−	3.82323i	−0.0746039	−	0.134004i
$815$	2.84246	+	4.92329i	0.0995670	+	0.172455i
$816$		0			0
$817$	−12.7189	+	22.0298i	−0.444979	+	0.770727i
$818$	−21.0781	+	35.2272i	−0.736979	+	1.23169i
$819$		0			0
$820$	2.72457	+	5.07879i	0.0951463	+	0.177359i
$821$	28.0807	+	16.2124i	0.980024	+	0.565817i	0.902277	−	0.431156i	$-0.141894\pi$
$821$	28.0807	+	16.2124i	0.980024	+	0.565817i	0.0777465	+	0.996973i	$0.475228\pi$
$822$		0			0
$823$	8.66266	−	5.00139i	0.301961	−	0.174337i	−0.341362	−	0.939932i	$-0.610888\pi$
$823$	8.66266	−	5.00139i	0.301961	−	0.174337i	0.643324	+	0.765594i	$0.277555\pi$
$824$	24.7552	+	15.8817i	0.862388	+	0.553266i
$825$		0			0
$826$	22.5874	−	31.1243i	0.785916	−	1.08295i
$827$	−28.0825			−0.976525			−0.488263	−	0.872697i	$-0.662369\pi$
$827$	−28.0825			−0.976525			−0.488263	+	0.872697i	$0.662369\pi$
$828$		0			0
$829$	22.9592	+	39.7666i	0.797407	+	1.38115i	0.921299	+	0.388854i	$0.127129\pi$
$829$	22.9592	+	39.7666i	0.797407	+	1.38115i	−0.123892	+	0.992296i	$0.539538\pi$
$830$	−0.0396013	+	2.53758i	−0.00137458	+	0.0880805i
$831$		0			0
$832$	1.01525	+	0.0953351i	0.0351976	+	0.00330515i
$833$	40.3369	−	14.5622i	1.39759	−	0.504549i
$834$		0			0
$835$	7.52869	+	4.34669i	0.260541	+	0.150423i
$836$	4.08168	+	2.52958i	0.141168	+	0.0874875i
$837$		0			0
$838$	−4.09186	−	7.34984i	−0.141351	−	0.253896i
$839$	−22.9019			−0.790662			−0.395331	−	0.918539i	$-0.629370\pi$
$839$	−22.9019			−0.790662			−0.395331	+	0.918539i	$0.629370\pi$
$840$		0			0
$841$	17.4667			0.602299
$842$	−18.0911	−	32.4953i	−0.623459	−	1.11986i
$843$		0			0
$844$	−4.20725	−	2.60740i	−0.144819	−	0.0897505i
$845$	−3.93871	−	2.27402i	−0.135496	−	0.0782285i
$846$		0			0
$847$	−15.9519	+	22.7185i	−0.548114	+	0.780615i
$848$	−39.0958	−	25.9519i	−1.34255	−	0.891192i
$849$		0			0
$850$	−0.659386	+	42.2521i	−0.0226168	+	1.44924i
$851$	−10.3669	−	17.9561i	−0.355374	−	0.615526i
$852$		0			0
$853$	10.6107			0.363304			0.181652	−	0.983363i	$-0.441856\pi$
$853$	10.6107			0.363304			0.181652	+	0.983363i	$0.441856\pi$
$854$	−21.1262	−	2.20888i	−0.722923	−	0.0755862i
$855$		0			0
$856$	−13.6393	+	21.2599i	−0.466182	+	0.726648i
$857$	27.1454	−	15.6724i	0.927268	−	0.535358i	0.0413213	−	0.999146i	$-0.486843\pi$
$857$	27.1454	−	15.6724i	0.927268	−	0.535358i	0.885946	+	0.463788i	$0.153510\pi$
$858$		0			0
$859$	8.41769	+	4.85995i	0.287208	+	0.165819i	0.636682	−	0.771127i	$-0.280306\pi$
$859$	8.41769	+	4.85995i	0.287208	+	0.165819i	−0.349474	+	0.936946i	$0.613640\pi$
$860$	2.50059	+	4.66126i	0.0852693	+	0.158948i
$861$		0			0
$862$	5.72325	−	9.56509i	0.194935	−	0.325788i
$863$	22.7910	−	39.4752i	0.775815	−	1.34375i	−0.158520	−	0.987356i	$-0.550672\pi$
$863$	22.7910	−	39.4752i	0.775815	−	1.34375i	0.934335	−	0.356395i	$-0.115994\pi$
$864$		0			0
$865$	−0.874485	−	1.51465i	−0.0297334	−	0.0514997i
$866$	19.8741	+	35.6981i	0.675350	+	1.21307i
$867$		0			0
$868$	−0.00147833	+	0.0122827i	−5.01777e−5	+	0.000416901i
$869$			1.58196i			0.0536644i
$870$		0			0
$871$	−0.993506	+	0.573601i	−0.0336637	+	0.0194357i
$872$	21.1678	+	40.9808i	0.716834	+	1.38779i
$873$		0			0
$874$	19.5249	+	11.6827i	0.660441	+	0.395173i
$875$	−0.809738	+	9.11811i	−0.0273741	+	0.308248i
$876$		0			0
$877$	−4.86133	+	8.42007i	−0.164155	+	0.284326i	−0.936355	−	0.351054i	$-0.885823\pi$
$877$	−4.86133	+	8.42007i	−0.164155	+	0.284326i	0.772200	+	0.635380i	$0.219157\pi$
$878$	−0.581507	+	37.2618i	−0.0196249	+	1.25753i
$879$		0			0
$880$	0.894220	−	0.444355i	0.0301442	−	0.0149792i
$881$		−	7.59560i		−	0.255902i	−0.991780	−	0.127951i	$-0.959160\pi$
$881$		−	7.59560i		−	0.255902i	0.991780	−	0.127951i	$-0.0408401\pi$
$882$		0			0
$883$		−	12.2076i		−	0.410817i	−0.978676	−	0.205409i	$-0.934148\pi$
$883$		−	12.2076i		−	0.410817i	0.978676	−	0.205409i	$-0.0658524\pi$
$884$	−0.0487352	+	1.56105i	−0.00163914	+	0.0525037i
$885$		0			0
$886$	−33.5970	−	0.524314i	−1.12871	−	0.0176147i
$887$	−14.1560	+	24.5189i	−0.475312	+	0.823264i	−0.999600	−	0.0282768i	$-0.990998\pi$
$887$	−14.1560	+	24.5189i	−0.475312	+	0.823264i	0.524288	+	0.851541i	$0.324331\pi$
$888$		0			0
$889$	2.15741	−	24.2936i	0.0723571	−	0.814782i
$890$	2.28809	−	3.82401i	0.0766968	−	0.128181i
$891$		0			0
$892$	13.2019	+	8.18176i	0.442033	+	0.273946i
$893$	−7.78136	+	4.49257i	−0.260393	+	0.150338i
$894$		0			0
$895$			6.83503i			0.228470i
$896$	9.58043	+	28.3587i	0.320060	+	0.947397i
$897$		0			0
$898$	−44.6018	+	24.8311i	−1.48838	+	0.828624i
$899$	−0.00396994	−	0.00687614i	−0.000132405	−	0.000229332i
$900$		0			0
$901$	35.9355	−	62.2421i	1.19719	−	2.07359i
$902$	−7.11498	−	4.25723i	−0.236903	−	0.141750i
$903$		0			0
$904$	−1.11722	+	23.8475i	−0.0371580	+	0.793156i
$905$	−2.36866	−	1.36755i	−0.0787370	−	0.0454588i
$906$		0			0
$907$	5.89877	−	3.40566i	0.195865	−	0.113083i	−0.398860	−	0.917012i	$-0.630594\pi$
$907$	5.89877	−	3.40566i	0.195865	−	0.113083i	0.594725	+	0.803929i	$0.297261\pi$
$908$	−32.1160	−	1.00265i	−1.06581	−	0.0332740i
$909$		0			0
$910$	−0.0173727	+	0.166156i	−0.000575900	+	0.00550803i
$911$	33.1107			1.09701			0.548503	−	0.836148i	$-0.315198\pi$
$911$	33.1107			1.09701			0.548503	+	0.836148i	$0.315198\pi$
$912$		0			0
$913$	−1.82552	−	3.16189i	−0.0604158	−	0.104643i
$914$	−28.2362	−	0.440653i	−0.933970	−	0.0145755i
$915$		0			0
$916$	−10.4897	−	19.5534i	−0.346588	−	0.646064i
$917$	−29.2051	+	41.5934i	−0.964436	+	1.37353i
$918$		0			0
$919$	−38.7490	−	22.3718i	−1.27821	−	0.737976i	−0.301693	−	0.953405i	$-0.597552\pi$
$919$	−38.7490	−	22.3718i	−1.27821	−	0.737976i	−0.976520	+	0.215429i	$0.930885\pi$
$920$	4.20372	−	2.17135i	0.138592	−	0.0715872i
$921$		0			0
$922$	4.82170	−	2.68437i	0.158794	−	0.0884052i
$923$	−1.22540			−0.0403345
$924$		0			0
$925$	−21.1758			−0.696256
$926$	13.6264	−	7.58620i	0.447791	−	0.249298i
$927$		0			0
$928$	−15.8380	−	10.8731i	−0.519907	−	0.356927i
$929$	−35.1764	−	20.3091i	−1.15410	−	0.666319i	−0.204216	−	0.978926i	$-0.565465\pi$
$929$	−35.1764	−	20.3091i	−1.15410	−	0.666319i	−0.949883	+	0.312606i	$0.898798\pi$
$930$		0			0
$931$	−18.0262	−	15.2063i	−0.590786	−	0.498365i
$932$	6.33268	−	3.39724i	0.207434	−	0.111280i
$933$		0			0
$934$	−54.4611	−	0.849918i	−1.78202	−	0.0278102i
$935$	0.764685	+	1.32447i	0.0250079	+	0.0433149i
$936$		0			0
$937$	15.8390			0.517437			0.258718	−	0.965953i	$-0.416700\pi$
$937$	15.8390			0.517437			0.258718	+	0.965953i	$0.416700\pi$
$938$	−27.2547	−	19.7792i	−0.889898	−	0.645812i
$939$		0			0
$940$	−0.0583023	+	1.86749i	−0.00190161	+	0.0609109i
$941$	35.2983	−	20.3795i	1.15069	−	0.664352i	0.201636	−	0.979461i	$-0.435374\pi$
$941$	35.2983	−	20.3795i	1.15069	−	0.664352i	0.949056	+	0.315109i	$0.102041\pi$
$942$		0			0
$943$	−34.0236	−	19.6435i	−1.10796	−	0.639682i
$944$	−22.7368	+	34.2524i	−0.740021	+	1.11482i
$945$		0			0
$946$	−6.53006	−	3.90724i	−0.212310	−	0.127035i
$947$	10.9987	−	19.0503i	0.357411	−	0.619053i	−0.630117	−	0.776500i	$-0.716993\pi$
$947$	10.9987	−	19.0503i	0.357411	−	0.619053i	0.987527	+	0.157447i	$0.0503264\pi$
$948$		0			0
$949$	−0.274479	−	0.475412i	−0.00890997	−	0.0154325i
$950$	20.3037	−	11.3036i	0.658739	−	0.366739i
$951$		0			0
$952$	−42.4345	+	17.3542i	−1.37531	+	0.562454i
$953$		−	23.9613i		−	0.776184i	−0.921621	−	0.388092i	$-0.873134\pi$
$953$		−	23.9613i		−	0.776184i	0.921621	−	0.388092i	$-0.126866\pi$
$954$		0			0
$955$	3.77091	−	2.17714i	0.122024	−	0.0704504i
$956$	6.48206	−	10.4593i	0.209645	−	0.338279i
$957$		0			0
$958$	10.7621	−	17.9863i	0.347706	−	0.581111i
$959$	−25.3923	+	11.8003i	−0.819961	+	0.381050i
$960$		0			0
$961$	−15.5000	+	26.8468i	−0.500000	+	0.866025i
$962$	−0.782552	−	0.0122125i	−0.0252305	−	0.000393747i
$963$		0			0
$964$	25.0735	+	0.782784i	0.807563	+	0.0252118i
$965$			0.469343i			0.0151087i
$966$		0			0
$967$			53.1580i			1.70945i	0.519084	+	0.854723i	$0.326273\pi$
$967$			53.1580i			1.70945i	−0.519084	+	0.854723i	$0.673727\pi$
$968$	16.0245	−	24.9778i	0.515048	−	0.802817i
$969$		0			0
$970$	−0.134057	+	8.59011i	−0.00430431	+	0.275812i
$971$	20.7550	−	35.9488i	0.666060	−	1.15365i	−0.312936	−	0.949774i	$-0.601313\pi$
$971$	20.7550	−	35.9488i	0.666060	−	1.15365i	0.978997	−	0.203876i	$-0.0653540\pi$
$972$		0			0
$973$	−2.72641	+	30.7010i	−0.0874048	+	0.984227i
$974$	−10.4461	−	6.25042i	−0.334716	−	0.200276i
$975$		0			0
$976$	22.6637	+	1.41648i	0.725448	+	0.0453405i
$977$	22.0401	−	12.7249i	0.705127	−	0.407105i	−0.104127	−	0.994564i	$-0.533205\pi$
$977$	22.0401	−	12.7249i	0.705127	−	0.407105i	0.809254	+	0.587459i	$0.199872\pi$
$978$		0			0
$979$			6.41085i			0.204892i
$980$	−4.66234	+	1.52048i	−0.148933	+	0.0485698i
$981$		0			0
$982$	6.01832	+	10.8102i	0.192052	+	0.344966i
$983$	−11.7347	−	20.3252i	−0.374280	−	0.648273i	0.615939	−	0.787794i	$-0.288777\pi$
$983$	−11.7347	−	20.3252i	−0.374280	−	0.648273i	−0.990219	+	0.139522i	$0.955444\pi$
$984$		0			0
$985$	−2.11241	+	3.65879i	−0.0673068	+	0.116579i
$986$	15.1078	−	25.2491i	0.481129	−	0.804096i
$987$		0			0
$988$	0.756843	−	0.406017i	0.0240784	−	0.0129171i
$989$	−31.2265	−	18.0286i	−0.992945	−	0.573277i
$990$		0			0
$991$	48.6218	−	28.0718i	1.54452	−	0.891731i	0.545979	−	0.837799i	$-0.316158\pi$
$991$	48.6218	−	28.0718i	1.54452	−	0.891731i	0.998545	−	0.0539326i	$-0.0171756\pi$
$992$	0.00103085	−	0.0131853i	3.27296e−5	−	0.000418632i
$993$		0			0
$994$	−14.6485	−	32.8531i	−0.464621	−	1.04204i
$995$	4.15708			0.131788
$996$		0			0
$997$	−12.9528	−	22.4350i	−0.410221	−	0.710523i	0.584693	−	0.811255i	$-0.301215\pi$
$997$	−12.9528	−	22.4350i	−0.410221	−	0.710523i	−0.994914	+	0.100732i	$0.967882\pi$
$998$	−0.639951	+	41.0068i	−0.0202573	+	1.29805i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.be.c.107.5	✓	28
3.2	odd	2	inner	756.2.be.c.107.10	yes	28
4.3	odd	2		756.2.be.d.107.1	yes	28
7.4	even	3		756.2.be.d.431.14	yes	28
12.11	even	2		756.2.be.d.107.14	yes	28
21.11	odd	6		756.2.be.d.431.1	yes	28
28.11	odd	6	inner	756.2.be.c.431.10	yes	28
84.11	even	6	inner	756.2.be.c.431.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.5	✓	28	1.1	even	1	trivial
756.2.be.c.107.10	yes	28	3.2	odd	2	inner
756.2.be.c.431.5	yes	28	84.11	even	6	inner
756.2.be.c.431.10	yes	28	28.11	odd	6	inner
756.2.be.d.107.1	yes	28	4.3	odd	2
756.2.be.d.107.14	yes	28	12.11	even	2
756.2.be.d.431.1	yes	28	21.11	odd	6
756.2.be.d.431.14	yes	28	7.4	even	3

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.687910 - 1.23563i) q^{2} +(-1.05356 + 1.70000i) q^{4} +(0.303357 + 0.175143i) q^{5} +(-2.63538 - 0.234036i) q^{7} +(2.82533 + 0.132362i) q^{8} +(0.00772994 - 0.495319i) q^{10} +(0.356330 + 0.617181i) q^{11} +0.127465 q^{13} +(1.52372 + 3.41735i) q^{14} +(-1.78002 - 3.58211i) q^{16} +(5.30564 - 3.06321i) q^{17} +(-2.91768 - 1.68453i) q^{19} +(-0.617349 + 0.331184i) q^{20} +(0.517485 - 0.864856i) q^{22} +(2.38776 - 4.13571i) q^{23} +(-2.43865 - 4.22387i) q^{25} +(-0.0876844 - 0.157499i) q^{26} +(3.17439 - 4.23358i) q^{28} +3.39607i q^{29} +(-0.00202473 + 0.00116898i) q^{31} +(-3.20167 + 4.66362i) q^{32} +(-7.43480 - 4.44859i) q^{34} +(-0.758471 - 0.532565i) q^{35} +(2.17085 - 3.76003i) q^{37} +(-0.0743466 + 4.76398i) q^{38} +(0.833900 + 0.534990i) q^{40} -8.22678i q^{41} -7.55045i q^{43} +(-1.42462 - 0.0444762i) q^{44} +(-6.75277 - 0.105384i) q^{46} +(1.33348 - 2.30966i) q^{47} +(6.89045 + 1.23355i) q^{49} +(-3.54156 + 5.91891i) q^{50} +(-0.134292 + 0.216691i) q^{52} +(10.1596 - 5.86566i) q^{53} +0.249635i q^{55} +(-7.41484 - 1.01005i) q^{56} +(4.19629 - 2.33619i) q^{58} +(-5.13898 - 8.90098i) q^{59} +(-2.83849 + 4.91641i) q^{61} +(0.00283726 + 0.00169767i) q^{62} +(7.96496 + 0.747932i) q^{64} +(0.0386674 + 0.0223246i) q^{65} +(-7.79435 + 4.50007i) q^{67} +(-0.382342 + 12.2469i) q^{68} +(-0.136294 + 1.30355i) q^{70} -9.61361 q^{71} +(-2.15337 - 3.72974i) q^{73} +(-6.13935 - 0.0958106i) q^{74} +(5.93766 - 3.18532i) q^{76} +(-0.794621 - 1.70990i) q^{77} +(1.92240 + 1.10990i) q^{79} +(0.0874011 - 1.39842i) q^{80} +(-10.1653 + 5.65928i) q^{82} -5.12311 q^{83} +2.14600 q^{85} +(-9.32956 + 5.19403i) q^{86} +(0.925057 + 1.79090i) q^{88} +(7.79048 + 4.49784i) q^{89} +(-0.335919 - 0.0298314i) q^{91} +(4.51508 + 8.41642i) q^{92} +(-3.77120 - 0.0588532i) q^{94} +(-0.590066 - 1.02203i) q^{95} -17.3426 q^{97} +(-3.21580 - 9.36262i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 4 q^{4} - 2 q^{7} - 20 q^{10} + 8 q^{13} + 12 q^{16} + 42 q^{19} + 4 q^{22} + 6 q^{25} - 28 q^{28} - 30 q^{31} + 24 q^{34} + 12 q^{37} + 36 q^{40} - 12 q^{46} - 14 q^{49} + 84 q^{52} + 28 q^{58}+ \cdots - 4 q^{97}+O(q^{100}) \) 28 * q - 4 * q^4 - 2 * q^7 - 20 * q^10 + 8 * q^13 + 12 * q^16 + 42 * q^19 + 4 * q^22 + 6 * q^25 - 28 * q^28 - 30 * q^31 + 24 * q^34 + 12 * q^37 + 36 * q^40 - 12 * q^46 - 14 * q^49 + 84 * q^52 + 28 * q^58 + 6 * q^61 + 8 * q^64 - 24 * q^67 + 128 * q^70 - 22 * q^73 - 48 * q^79 - 36 * q^82 - 24 * q^85 - 16 * q^88 - 16 * q^91 - 12 * q^94 - 4 * q^97

Introduction

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