LMFDB - Embedded newform 756.2.be.c.431.10

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			431.10
Character	$\chi$	$=$	756.431
Dual form			756.2.be.c.107.10

$q$-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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

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	$-0.691624\pi$
$5$	−0.303357	+	0.175143i	−0.135665	+	0.0783264i	0.430631	+	0.902528i	$0.358291\pi$
$6$		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	$-0.867598\pi$
$11$	−0.356330	+	0.617181i	−0.107437	+	0.186087i	0.807294	+	0.590149i	$0.200931\pi$
$12$		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	$-0.599902\pi$
$17$	−5.30564	−	3.06321i	−1.28681	−	0.742938i	−0.978083	+	0.208214i	$0.933235\pi$
$18$		0			0
$19$	−2.91768	+	1.68453i	−0.669363	+	0.386457i	−0.795835	−	0.605513i	$-0.792968\pi$
$19$	−2.91768	+	1.68453i	−0.669363	+	0.386457i	0.126472	+	0.991970i	$0.459634\pi$
$20$	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	$-0.332555\pi$
$23$	−2.38776	−	4.13571i	−0.497881	−	0.862356i	−0.999997	+	0.00244454i	$0.999222\pi$
$24$		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	0.499818	−	0.866130i	$-0.333400\pi$
$31$	−0.00202473	−	0.00116898i	−0.000363652	−	0.000209955i	−0.500182	+	0.865920i	$0.666733\pi$
$32$	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	0.987439	−	0.158001i	$-0.0505051\pi$
$37$	2.17085	+	3.76003i	0.356886	+	0.618145i	−0.630553	+	0.776146i	$0.717172\pi$
$38$	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	$0.195277\pi$
$43$			7.55045i			1.15143i	−0.817649	+	0.575717i	$0.804723\pi$
$44$	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	$-0.228978\pi$
$47$	−1.33348	−	2.30966i	−0.194508	−	0.336898i	−0.946739	+	0.322001i	$0.895644\pi$
$48$		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	$-0.631549\pi$
$53$	−10.1596	−	5.86566i	−1.39553	−	0.805710i	−0.993920	+	0.110101i	$0.964883\pi$
$54$		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	−0.309134	−	0.951018i	$-0.600039\pi$
$59$	5.13898	−	8.90098i	0.669039	−	1.15881i	0.978173	−	0.207791i	$-0.0666274\pi$
$60$		0			0
$61$	−2.83849	−	4.91641i	−0.363432	−	0.629482i	0.625091	−	0.780552i	$-0.285062\pi$
$61$	−2.83849	−	4.91641i	−0.363432	−	0.629482i	−0.988523	+	0.151069i	$0.951728\pi$
$62$	−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	−0.0584577	−	0.998290i	$-0.518618\pi$
$67$	−7.79435	−	4.50007i	−0.952231	−	0.549771i	−0.893773	+	0.448519i	$0.851952\pi$
$68$	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	$-0.306764\pi$
$71$	9.61361			1.14093			0.570463	+	0.821323i	$0.306764\pi$
$72$		0			0
$73$	−2.15337	+	3.72974i	−0.252033	+	0.436534i	−0.964085	−	0.265593i	$-0.914432\pi$
$73$	−2.15337	+	3.72974i	−0.252033	+	0.436534i	0.712053	+	0.702126i	$0.247766\pi$
$74$	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	−0.387943	−	0.921684i	$-0.626814\pi$
$79$	1.92240	−	1.10990i	0.216287	−	0.124874i	0.604230	+	0.796810i	$0.293481\pi$
$80$	−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	$-0.409278\pi$
$83$	5.12311			0.562334			0.281167	+	0.959659i	$0.409278\pi$
$84$		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	$-0.824859\pi$
$89$	−7.79048	+	4.49784i	−0.825789	+	0.476770i	0.0266194	+	0.999646i	$0.491526\pi$
$90$		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	$-0.510641\pi$
$101$	−9.20243	−	5.31302i	−0.915676	−	0.528666i	−0.882253	+	0.470776i	$0.843974\pi$
$102$		0			0
$103$	9.00546	−	5.19931i	0.887335	−	0.512303i	0.0142649	−	0.999898i	$-0.495459\pi$
$103$	9.00546	−	5.19931i	0.887335	−	0.512303i	0.873070	+	0.487595i	$0.162126\pi$
$104$	−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	$-0.0245925\pi$
$107$	4.46519	+	7.73394i	0.431666	+	0.747668i	−0.565351	+	0.824851i	$0.691259\pi$
$108$		0			0
$109$	8.15380	−	14.1228i	0.780993	−	1.35272i	−0.150371	−	0.988630i	$-0.548047\pi$
$109$	8.15380	−	14.1228i	0.780993	−	1.35272i	0.931364	−	0.364089i	$-0.118620\pi$
$110$	−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	$-0.865880\pi$
$127$		−	9.21826i		−	0.817988i	0.912537	−	0.408994i	$-0.134120\pi$
$128$	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	−0.890601	−	0.454786i	$-0.849716\pi$
$131$	−9.60458	−	16.6356i	−0.839156	−	1.45346i	0.0514445	−	0.998676i	$-0.483617\pi$
$132$		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	$-0.482654\pi$
$137$	−9.16525	−	5.29156i	−0.783040	−	0.452088i	−0.837507	+	0.546427i	$0.815987\pi$
$138$		0			0
$139$			11.6495i			0.988101i	0.869433	+	0.494050i	$0.164484\pi$
$139$			11.6495i			0.988101i	−0.869433	+	0.494050i	$0.835516\pi$
$140$	−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	$-0.441599\pi$
$149$	13.7343	−	7.92950i	1.12516	−	0.649610i	0.942712	+	0.333606i	$0.108266\pi$
$150$		0			0
$151$	3.21821	+	1.85804i	0.261895	+	0.151205i	0.625199	−	0.780466i	$-0.285018\pi$
$151$	3.21821	+	1.85804i	0.261895	+	0.151205i	−0.363304	+	0.931671i	$0.618351\pi$
$152$	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	−0.823092	−	0.567908i	$-0.807753\pi$
$157$	1.00586	−	1.74221i	0.0802766	−	0.139043i	0.903369	+	0.428865i	$0.141086\pi$
$158$	−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	0.164424	−	0.986390i	$-0.447423\pi$
$163$	14.0550	−	8.11468i	1.10088	−	0.635590i	0.936451	+	0.350799i	$0.114090\pi$
$164$	−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	$-0.909933\pi$
$167$	−24.8179			−1.92047			−0.960235	+	0.279193i	$0.909933\pi$
$168$		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	$-0.605881\pi$
$173$	4.32404	−	2.49649i	0.328751	−	0.189804i	0.655286	+	0.755381i	$0.272548\pi$
$174$		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	0.227989	+	0.973664i	$0.426785\pi$
$179$	−9.75634	+	16.8985i	−0.729223	+	1.26305i	−0.957212	+	0.289388i	$0.906548\pi$
$180$		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	$-0.315144\pi$
$191$	−6.21530	−	10.7652i	−0.449723	−	0.778944i	−0.998368	+	0.0571120i	$0.981811\pi$
$192$		0			0
$193$	0.669942	−	1.16037i	0.0482235	−	0.0835256i	−0.840906	−	0.541181i	$-0.817977\pi$
$193$	0.669942	−	1.16037i	0.0482235	−	0.0835256i	0.889130	+	0.457656i	$0.151311\pi$
$194$	−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	0.817897	−	0.575364i	$-0.195140\pi$
$199$	10.2777	+	5.93383i	0.728566	+	0.420638i	−0.0893311	+	0.996002i	$0.528473\pi$
$200$	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	$-0.972851\pi$
$211$		−	2.47485i		−	0.170376i	0.996365	−	0.0851878i	$-0.0271490\pi$
$212$	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	$0.0837288\pi$
$223$			7.76582i			0.520038i	−0.965604	+	0.260019i	$0.916271\pi$
$224$	−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	0.466087	+	0.884739i	$0.345663\pi$
$227$	−8.03290	+	13.9134i	−0.533163	+	0.923465i	−0.999250	+	0.0387259i	$0.987670\pi$
$228$		0			0
$229$	−5.54735	−	9.60830i	−0.366579	−	0.634934i	0.622449	−	0.782660i	$-0.286138\pi$
$229$	−5.54735	−	9.60830i	−0.366579	−	0.634934i	−0.989028	+	0.147726i	$0.952805\pi$
$230$	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	$-0.629115\pi$
$233$	3.11180	−	1.79660i	0.203861	−	0.117699i	0.598455	+	0.801156i	$0.295782\pi$
$234$		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	$-0.436235\pi$
$239$	6.15253			0.397974			0.198987	+	0.980002i	$0.436235\pi$
$240$		0			0
$241$	−6.27143	+	10.8624i	−0.403978	+	0.699711i	−0.994202	−	0.107529i	$-0.965706\pi$
$241$	−6.27143	+	10.8624i	−0.403978	+	0.699711i	0.590224	+	0.807240i	$0.299040\pi$
$242$	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	$-0.495121\pi$
$251$	0.485661			0.0306547			0.0153273	+	0.999883i	$0.495121\pi$
$252$		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	0.578535	−	0.815657i	$-0.303625\pi$
$257$	25.2361	−	14.5701i	1.57418	−	0.908855i	0.995648	−	0.0931975i	$-0.0297088\pi$
$258$		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	0.240418	+	0.970670i	$0.422716\pi$
$263$	−11.6832	+	20.2359i	−0.720416	+	1.24780i	−0.960833	+	0.277127i	$0.910618\pi$
$264$		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	$-0.0104303\pi$
$269$	24.1233	+	13.9276i	1.47082	+	0.849180i	0.471359	+	0.881941i	$0.343764\pi$
$270$		0			0
$271$	−24.8590	+	14.3523i	−1.51008	+	0.871843i	−0.510146	+	0.860088i	$0.670409\pi$
$271$	−24.8590	+	14.3523i	−1.51008	+	0.871843i	−0.999931	+	0.0117552i	$0.996258\pi$
$272$	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	−0.103248	−	0.994656i	$-0.532924\pi$
$277$	13.4773	−	23.3434i	0.809773	−	1.40257i	0.913021	−	0.407912i	$-0.133743\pi$
$278$	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	0.433029	−	0.901380i	$-0.357445\pi$
$283$	−2.20500	−	1.27306i	−0.131074	−	0.0756754i	−0.564103	+	0.825704i	$0.690778\pi$
$284$	−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	$-0.841539\pi$
$307$		−	16.7333i		−	0.955020i	0.878626	−	0.477510i	$-0.158461\pi$
$308$	−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	0.0487894	−	0.998809i	$-0.484464\pi$
$311$	15.6845	−	27.1664i	0.889389	−	1.54047i	0.840599	−	0.541657i	$-0.182203\pi$
$312$		0			0
$313$	11.3777	+	19.7068i	0.643107	+	1.11389i	0.984735	+	0.174058i	$0.0556882\pi$
$313$	11.3777	+	19.7068i	0.643107	+	1.11389i	−0.341629	+	0.939835i	$0.610979\pi$
$314$	−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	$-0.719614\pi$
$317$	−5.10594	+	2.94792i	−0.286778	+	0.165572i	0.349710	+	0.936858i	$0.386280\pi$
$318$		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	−0.282284	−	0.959331i	$-0.591092\pi$
$331$	7.41160	−	4.27909i	0.407378	−	0.235200i	0.689663	+	0.724131i	$0.257759\pi$
$332$	−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	−0.353324	+	0.935501i	$0.614949\pi$
$347$	−18.3826	+	31.8396i	−0.986830	+	1.70924i	−0.633505	+	0.773738i	$0.718385\pi$
$348$		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	$-0.226258\pi$
$353$	10.7415	+	6.20163i	0.571715	+	0.330080i	−0.186119	+	0.982527i	$0.559591\pi$
$354$		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	$-0.0232059\pi$
$359$	8.25328	+	14.2951i	0.435592	+	0.754467i	−0.561752	+	0.827306i	$0.689873\pi$
$360$		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	0.193384	−	0.981123i	$-0.438054\pi$
$367$	−10.7204	−	6.18944i	−0.559602	−	0.323086i	−0.752986	+	0.658037i	$0.771387\pi$
$368$	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	0.998459	+	0.0554855i	$0.0176707\pi$
$373$	10.5698	+	18.3074i	0.547282	+	0.947920i	−0.451178	+	0.892434i	$0.648996\pi$
$374$	−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	$0.161609\pi$
$379$			18.9297i			0.972352i	−0.873861	+	0.486176i	$0.838391\pi$
$380$	−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	$-0.219934\pi$
$383$	−3.25973	−	5.64601i	−0.166564	−	0.288498i	−0.937210	+	0.348766i	$0.886601\pi$
$384$		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	$-0.191183\pi$
$389$	14.7537	+	8.51806i	0.748043	+	0.431883i	−0.0769436	+	0.997035i	$0.524516\pi$
$390$		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	0.621375	−	0.783513i	$-0.286574\pi$
$397$	−7.32945	−	12.6950i	−0.367854	−	0.637142i	−0.989230	+	0.146370i	$0.953241\pi$
$398$	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	$-0.716542\pi$
$401$	−5.41239	+	3.12484i	−0.270282	+	0.156047i	0.358734	+	0.933440i	$0.383209\pi$
$402$		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	0.244251	+	0.969712i	$0.421458\pi$
$409$	−14.5140	+	25.1389i	−0.717670	+	1.24304i	−0.961921	+	0.273329i	$0.911875\pi$
$410$	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	$-0.546413\pi$
$419$	−5.94826			−0.290591			−0.145296	+	0.989388i	$0.546413\pi$
$420$		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	$-0.894126\pi$
$431$	−3.94092	+	6.82587i	−0.189827	+	0.328790i	0.755365	+	0.655304i	$0.227459\pi$
$432$		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	−0.933359	−	0.358945i	$-0.883136\pi$
$439$	−22.8209	+	13.1757i	−1.08918	+	0.628840i	−0.155824	+	0.987785i	$0.549803\pi$
$440$	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	−0.997103	−	0.0760641i	$-0.975765\pi$
$443$	−11.8798	−	20.5764i	−0.564425	−	0.977613i	0.432678	−	0.901549i	$-0.357569\pi$
$444$		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	0.999291	−	0.0376473i	$-0.0119863\pi$
$457$	9.98422	+	17.2932i	0.467042	+	0.808941i	−0.532249	+	0.846588i	$0.678653\pi$
$458$	−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	$-0.917511\pi$
$463$		−	11.0279i		−	0.512510i	0.966609	−	0.256255i	$-0.0824887\pi$
$464$	−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	−0.838536	−	0.544847i	$-0.816588\pi$
$467$	−19.2572	−	33.3545i	−0.891119	−	1.54346i	−0.0525832	−	0.998617i	$-0.516745\pi$
$468$		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	$-0.943285\pi$
$479$	−7.41054	+	12.8354i	−0.338596	+	0.586466i	0.645573	+	0.763699i	$0.276619\pi$
$480$		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	0.659299	−	0.751881i	$-0.270853\pi$
$487$	7.45460	+	4.30391i	0.337800	+	0.195029i	−0.321499	+	0.946910i	$0.604187\pi$
$488$	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	$-0.436746\pi$
$491$	8.74870			0.394823			0.197412	+	0.980321i	$0.436746\pi$
$492$		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	−0.942490	−	0.334236i	$-0.891522\pi$
$499$	−25.1145	+	14.4998i	−1.12428	+	0.649102i	−0.181788	+	0.983338i	$0.558189\pi$
$500$	−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	$-0.712397\pi$
$503$	−27.7583			−1.23768			−0.618841	+	0.785516i	$0.712397\pi$
$504$		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	$-0.510833\pi$
$509$	18.3756	−	10.6092i	0.814484	−	0.470243i	0.848511	+	0.529178i	$0.177500\pi$
$510$		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	$-0.155241\pi$
$521$	20.9834	+	12.1148i	0.919300	+	0.530758i	0.0358883	+	0.999356i	$0.488574\pi$
$522$		0			0
$523$	18.7115	−	10.8031i	0.818195	−	0.472385i	−0.0315989	−	0.999501i	$-0.510060\pi$
$523$	18.7115	−	10.8031i	0.818195	−	0.472385i	0.849794	+	0.527116i	$0.176727\pi$
$524$	−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	−0.863330	−	0.504640i	$-0.831625\pi$
$541$	−20.2054	−	34.9967i	−0.868696	−	1.50463i	−0.00536596	−	0.999986i	$-0.501708\pi$
$542$	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	$-0.846293\pi$
$547$		−	21.7198i		−	0.928670i	0.885660	−	0.464335i	$-0.153707\pi$
$548$	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	−0.998983	−	0.0450775i	$-0.985647\pi$
$557$	−36.2866	−	20.9501i	−1.53751	−	0.887684i	−0.538530	−	0.842606i	$-0.681020\pi$
$558$		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	$-0.849695\pi$
$563$	−1.21907	+	2.11148i	−0.0513775	+	0.0889885i	0.839193	+	0.543834i	$0.183028\pi$
$564$		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	$-0.610972\pi$
$569$	7.19227	−	4.15246i	0.301515	−	0.174080i	0.643123	+	0.765762i	$0.277638\pi$
$570$		0			0
$571$	−40.3829	−	23.3151i	−1.68997	−	0.975705i	−0.954529	−	0.298117i	$-0.903641\pi$
$571$	−40.3829	−	23.3151i	−1.68997	−	0.975705i	−0.735442	−	0.677588i	$-0.763025\pi$
$572$	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	−0.941958	−	0.335730i	$-0.891017\pi$
$577$	−4.32922	+	7.49843i	−0.180228	+	0.312164i	0.761730	+	0.647894i	$0.224350\pi$
$578$	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	$-0.611223\pi$
$587$	−16.5890			−0.684700			−0.342350	+	0.939573i	$0.611223\pi$
$588$		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	$-0.984804\pi$
$593$	−35.4794	+	20.4840i	−1.45696	+	0.841178i	−0.458103	+	0.888899i	$0.651471\pi$
$594$		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	$-0.974690\pi$
$599$	−10.5150	+	18.2125i	−0.429632	+	0.744144i	0.567209	+	0.823574i	$0.308023\pi$
$600$		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	0.153773	−	0.988106i	$-0.450858\pi$
$607$	26.7657	−	15.4532i	1.08638	−	0.627224i	0.932612	+	0.360882i	$0.117524\pi$
$608$	−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	−0.811329	−	0.584590i	$-0.801255\pi$
$613$	2.49089	−	4.31434i	0.100606	−	0.174255i	0.911934	+	0.410336i	$0.134589\pi$
$614$	−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	0.871317	−	0.490721i	$-0.163267\pi$
$619$	21.9439	+	12.6693i	0.881998	+	0.509222i	0.0106814	+	0.999943i	$0.496600\pi$
$620$	−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	$0.0812323\pi$
$631$			12.6823i			0.504876i	−0.967613	+	0.252438i	$0.918768\pi$
$632$	−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	$-0.442615\pi$
$641$	−14.7613	−	8.52242i	−0.583035	−	0.336615i	−0.762338	+	0.647179i	$0.775949\pi$
$642$		0			0
$643$			37.1996i			1.46701i	0.679685	+	0.733504i	$0.262117\pi$
$643$			37.1996i			1.46701i	−0.679685	+	0.733504i	$0.737883\pi$
$644$	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	$-0.740516\pi$
$647$	7.31238	−	12.6654i	0.287479	−	0.497929i	0.973207	+	0.229929i	$0.0738494\pi$
$648$		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	$-0.958277\pi$
$653$	−35.1095	+	20.2705i	−1.37394	+	0.793245i	−0.382519	+	0.923948i	$0.624943\pi$
$654$		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	$-0.481496\pi$
$659$	2.98301			0.116201			0.0581007	+	0.998311i	$0.481496\pi$
$660$		0			0
$661$	15.4040	−	26.6805i	0.599146	−	1.03775i	−0.393801	−	0.919196i	$-0.628840\pi$
$661$	15.4040	−	26.6805i	0.599146	−	1.03775i	0.992947	−	0.118556i	$-0.0378264\pi$
$662$	−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	$-0.476302\pi$
$677$	25.3739	−	14.6496i	0.975199	−	0.563032i	0.900817	+	0.434198i	$0.142968\pi$
$678$		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	$-0.814569\pi$
$683$	1.53968	−	2.66681i	0.0589143	−	0.102043i	0.893978	+	0.448110i	$0.147903\pi$
$684$		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	−0.0884525	−	0.996080i	$-0.528192\pi$
$691$	19.1882	−	11.0783i	0.729952	−	0.421438i	0.818405	+	0.574642i	$0.194859\pi$
$692$	−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	0.685186	−	0.728368i	$-0.259721\pi$
$709$	−7.67372	−	13.2913i	−0.288193	−	0.499164i	−0.973378	+	0.229204i	$0.926388\pi$
$710$	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	−0.997558	−	0.0698422i	$-0.977750\pi$
$719$	−14.9962	−	25.9742i	−0.559264	−	0.968674i	0.438294	−	0.898832i	$-0.355583\pi$
$720$		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	$-0.723509\pi$
$727$		−	41.1692i		−	1.52688i	0.645879	−	0.763440i	$-0.276491\pi$
$728$	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	−0.992332	−	0.123603i	$-0.960555\pi$
$733$	−16.3313	−	28.2866i	−0.603209	−	1.04479i	0.389123	−	0.921186i	$-0.372778\pi$
$734$	−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	0.763785	−	0.645471i	$-0.223339\pi$
$739$	15.9487	+	9.20799i	0.586683	+	0.338721i	−0.177102	+	0.984192i	$0.556672\pi$
$740$	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	$-0.364466\pi$
$743$	22.5175			0.826088			0.413044	+	0.910711i	$0.364466\pi$
$744$		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	0.0944107	−	0.995533i	$-0.469903\pi$
$751$	27.5078	−	15.8816i	1.00377	−	0.579529i	0.909362	+	0.416005i	$0.136570\pi$
$752$	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	$-0.694914\pi$
$761$	−4.23458	+	2.44483i	−0.153503	+	0.0886252i	0.421281	+	0.906930i	$0.361581\pi$
$762$		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	$-0.369671\pi$
$773$	−5.48545	−	3.16703i	−0.197298	−	0.113910i	−0.595395	+	0.803433i	$0.703004\pi$
$774$		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	0.473222	−	0.880943i	$-0.343091\pi$
$787$	−1.48926	−	0.859826i	−0.0530865	−	0.0306495i	−0.526308	+	0.850294i	$0.676424\pi$
$788$	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	$-0.396017\pi$
$809$	−9.63889	−	5.56502i	−0.338885	−	0.195656i	−0.659779	+	0.751460i	$0.729350\pi$
$810$		0			0
$811$		−	40.8908i		−	1.43587i	−0.696110	−	0.717936i	$-0.745087\pi$
$811$		−	40.8908i		−	1.43587i	0.696110	−	0.717936i	$-0.254913\pi$
$812$	−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	$-0.858106\pi$
$821$	−28.0807	+	16.2124i	−0.980024	+	0.565817i	−0.0777465	+	0.996973i	$0.524772\pi$
$822$		0			0
$823$	8.66266	+	5.00139i	0.301961	+	0.174337i	0.643324	−	0.765594i	$-0.277555\pi$
$823$	8.66266	+	5.00139i	0.301961	+	0.174337i	−0.341362	+	0.939932i	$0.610888\pi$
$824$	−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	$-0.337631\pi$
$827$	28.0825			0.976525			0.488263	+	0.872697i	$0.337631\pi$
$828$		0			0
$829$	22.9592	−	39.7666i	0.797407	−	1.38115i	−0.123892	−	0.992296i	$-0.539538\pi$
$829$	22.9592	−	39.7666i	0.797407	−	1.38115i	0.921299	−	0.388854i	$-0.127129\pi$
$830$	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	$-0.370630\pi$
$839$	22.9019			0.790662			0.395331	+	0.918539i	$0.370630\pi$
$840$		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	$-0.513157\pi$
$857$	−27.1454	−	15.6724i	−0.927268	−	0.535358i	−0.885946	+	0.463788i	$0.846490\pi$
$858$		0			0
$859$	8.41769	−	4.85995i	0.287208	−	0.165819i	−0.349474	−	0.936946i	$-0.613640\pi$
$859$	8.41769	−	4.85995i	0.287208	−	0.165819i	0.636682	+	0.771127i	$0.280306\pi$
$860$	−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	−0.934335	−	0.356395i	$-0.884006\pi$
$863$	−22.7910	−	39.4752i	−0.775815	−	1.34375i	0.158520	−	0.987356i	$-0.449328\pi$
$864$		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	0.772200	−	0.635380i	$-0.219157\pi$
$877$	−4.86133	−	8.42007i	−0.164155	−	0.284326i	−0.936355	+	0.351054i	$0.885823\pi$
$878$	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	$0.0658524\pi$
$883$			12.2076i			0.410817i	−0.978676	+	0.205409i	$0.934148\pi$
$884$	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	$-0.00900198\pi$
$887$	14.1560	+	24.5189i	0.475312	+	0.823264i	−0.524288	+	0.851541i	$0.675669\pi$
$888$		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	0.594725	−	0.803929i	$-0.297261\pi$
$907$	5.89877	+	3.40566i	0.195865	+	0.113083i	−0.398860	+	0.917012i	$0.630594\pi$
$908$	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	$-0.684802\pi$
$911$	−33.1107			−1.09701			−0.548503	+	0.836148i	$0.684802\pi$
$912$		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	−0.976520	−	0.215429i	$-0.930885\pi$
$919$	−38.7490	+	22.3718i	−1.27821	+	0.737976i	−0.301693	+	0.953405i	$0.597552\pi$
$920$	−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	$-0.434535\pi$
$929$	35.1764	−	20.3091i	1.15410	−	0.666319i	0.949883	+	0.312606i	$0.101202\pi$
$930$		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	$-0.564626\pi$
$941$	−35.2983	−	20.3795i	−1.15069	−	0.664352i	−0.949056	+	0.315109i	$0.897959\pi$
$942$		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	$-0.283007\pi$
$947$	−10.9987	−	19.0503i	−0.357411	−	0.619053i	−0.987527	+	0.157447i	$0.949674\pi$
$948$		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	$-0.673727\pi$
$967$		−	53.1580i		−	1.70945i	0.519084	−	0.854723i	$-0.326273\pi$
$968$	−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	−0.978997	−	0.203876i	$-0.934646\pi$
$971$	−20.7550	−	35.9488i	−0.666060	−	1.15365i	0.312936	−	0.949774i	$-0.398687\pi$
$972$		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	$-0.466795\pi$
$977$	−22.0401	−	12.7249i	−0.705127	−	0.407105i	−0.809254	+	0.587459i	$0.800128\pi$
$978$		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	$-0.711223\pi$
$983$	11.7347	−	20.3252i	0.374280	−	0.648273i	0.990219	+	0.139522i	$0.0445564\pi$
$984$		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	0.998545	+	0.0539326i	$0.0171756\pi$
$991$	48.6218	+	28.0718i	1.54452	+	0.891731i	0.545979	+	0.837799i	$0.316158\pi$
$992$	−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	−0.994914	−	0.100732i	$-0.967882\pi$
$997$	−12.9528	+	22.4350i	−0.410221	+	0.710523i	0.584693	+	0.811255i	$0.301215\pi$
$998$	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.431.10	yes	28
3.2	odd	2	inner	756.2.be.c.431.5	yes	28
4.3	odd	2		756.2.be.d.431.14	yes	28
7.2	even	3		756.2.be.d.107.1	yes	28
12.11	even	2		756.2.be.d.431.1	yes	28
21.2	odd	6		756.2.be.d.107.14	yes	28
28.23	odd	6	inner	756.2.be.c.107.5	✓	28
84.23	even	6	inner	756.2.be.c.107.10	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.be.c.107.5	✓	28	28.23	odd	6	inner
756.2.be.c.107.10	yes	28	84.23	even	6	inner
756.2.be.c.431.5	yes	28	3.2	odd	2	inner
756.2.be.c.431.10	yes	28	1.1	even	1	trivial
756.2.be.d.107.1	yes	28	7.2	even	3
756.2.be.d.107.14	yes	28	21.2	odd	6
756.2.be.d.431.1	yes	28	12.11	even	2
756.2.be.d.431.14	yes	28	4.3	odd	2

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

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