LMFDB - Embedded newform 768.2.z.a.349.57

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			349.57
Character	$\chi$	$=$	768.349
Dual form			768.2.z.a.757.57

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.32657 - 0.490103i) q^{2} +(0.0490677 - 0.998795i) q^{3} +(1.51960 - 1.30031i) q^{4} +(0.251949 - 0.420352i) q^{5} +(-0.424420 - 1.34902i) q^{6} +(-0.848315 + 1.03368i) q^{7} +(1.37857 - 2.46972i) q^{8} +(-0.995185 - 0.0980171i) q^{9} +O(q^{10})$	\(q+(1.32657 - 0.490103i) q^{2} +(0.0490677 - 0.998795i) q^{3} +(1.51960 - 1.30031i) q^{4} +(0.251949 - 0.420352i) q^{5} +(-0.424420 - 1.34902i) q^{6} +(-0.848315 + 1.03368i) q^{7} +(1.37857 - 2.46972i) q^{8} +(-0.995185 - 0.0980171i) q^{9} +(0.128214 - 0.681109i) q^{10} +(2.04313 + 0.731044i) q^{11} +(-1.22419 - 1.58157i) q^{12} +(1.09435 - 4.36890i) q^{13} +(-0.618747 + 1.78701i) q^{14} +(-0.407483 - 0.272272i) q^{15} +(0.618362 - 3.95191i) q^{16} +(-0.860261 + 0.574808i) q^{17} +(-1.36822 + 0.357716i) q^{18} +(-0.938177 - 6.32468i) q^{19} +(-0.163728 - 0.966380i) q^{20} +(0.990805 + 0.898014i) q^{21} +(3.06865 - 0.0315595i) q^{22} +(-0.210299 - 0.693263i) q^{23} +(-2.39911 - 1.49810i) q^{24} +(2.24377 + 4.19779i) q^{25} +(-0.689469 - 6.33202i) q^{26} +(-0.146730 + 0.989177i) q^{27} +(0.0550041 + 2.67385i) q^{28} +(1.09514 - 2.31549i) q^{29} +(-0.673998 - 0.161480i) q^{30} +(2.91728 + 7.04294i) q^{31} +(-1.11654 - 5.54557i) q^{32} +(0.830415 - 2.00480i) q^{33} +(-0.859485 + 1.18414i) q^{34} +(0.220775 + 0.617025i) q^{35} +(-1.63973 + 1.14511i) q^{36} +(-4.33455 + 3.21472i) q^{37} +(-4.34430 - 7.93035i) q^{38} +(-4.30994 - 1.30741i) q^{39} +(-0.690823 - 1.20173i) q^{40} +(4.47418 - 8.37061i) q^{41} +(1.75450 + 0.705686i) q^{42} +(-10.2452 + 0.503314i) q^{43} +(4.05533 - 1.54582i) q^{44} +(-0.291938 + 0.393633i) q^{45} +(-0.618747 - 0.816597i) q^{46} +(-1.74273 + 8.76132i) q^{47} +(-3.91681 - 0.811529i) q^{48} +(1.01679 + 5.11173i) q^{49} +(5.03387 + 4.46901i) q^{50} +(0.531904 + 0.887429i) q^{51} +(-4.01797 - 8.06198i) q^{52} +(0.564547 + 1.19364i) q^{53} +(0.290149 + 1.38413i) q^{54} +(0.822062 - 0.674649i) q^{55} +(1.38343 + 3.52010i) q^{56} +(-6.36309 + 0.626710i) q^{57} +(0.317964 - 3.60840i) q^{58} +(0.794013 + 3.16988i) q^{59} +(-0.973250 + 0.116113i) q^{60} +(2.79985 - 2.53764i) q^{61} +(7.32176 + 7.91322i) q^{62} +(0.945548 - 0.945548i) q^{63} +(-4.19907 - 6.80939i) q^{64} +(-1.56076 - 1.56076i) q^{65} +(0.119050 - 3.06651i) q^{66} +(9.82060 + 10.8354i) q^{67} +(-0.559820 + 1.99209i) q^{68} +(-0.702747 + 0.176029i) q^{69} +(0.595280 + 0.710327i) q^{70} +(0.649809 + 6.59762i) q^{71} +(-1.61401 + 2.32271i) q^{72} +(0.148558 + 0.181018i) q^{73} +(-4.17456 + 6.38894i) q^{74} +(4.30283 - 2.03509i) q^{75} +(-9.64973 - 8.39105i) q^{76} +(-2.48888 + 1.49178i) q^{77} +(-6.35822 + 0.377941i) q^{78} +(-6.19628 + 1.23252i) q^{79} +(-1.50540 - 1.25561i) q^{80} +(0.980785 + 0.195090i) q^{81} +(1.83288 - 13.2970i) q^{82} +(13.8002 + 10.2349i) q^{83} +(2.67333 + 0.0762617i) q^{84} +(0.0248795 + 0.506435i) q^{85} +(-13.3443 + 5.68888i) q^{86} +(-2.25896 - 1.20744i) q^{87} +(4.62208 - 4.03817i) q^{88} +(4.07160 - 13.4223i) q^{89} +(-0.194357 + 0.665262i) q^{90} +(3.58767 + 4.83741i) q^{91} +(-1.22103 - 0.780027i) q^{92} +(7.17760 - 2.56819i) q^{93} +(1.98208 + 12.4767i) q^{94} +(-2.89497 - 1.19913i) q^{95} +(-5.59368 + 0.843086i) q^{96} +(9.41706 - 3.90067i) q^{97} +(3.85412 + 6.28276i) q^{98} +(-1.96164 - 0.927786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{43}{64}\right)$

Coefficient data

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

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

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

$2$	1.32657	−	0.490103i	0.938030	−	0.346555i
$2$	1.32657	−	0.490103i	0.938030	−	0.346555i
$3$	0.0490677	−	0.998795i	0.0283292	−	0.576655i
$3$	0.0490677	−	0.998795i	0.0283292	−	0.576655i
$4$	1.51960	−	1.30031i	0.759800	−	0.650157i
$5$	0.251949	−	0.420352i	0.112675	−	0.187987i	−0.796225	−	0.605000i	$-0.793173\pi$
$5$	0.251949	−	0.420352i	0.112675	−	0.187987i	0.908901	+	0.417013i	$0.136923\pi$
$6$	−0.424420	−	1.34902i	−0.173269	−	0.550737i
$7$	−0.848315	+	1.03368i	−0.320633	+	0.390693i	−0.908237	−	0.418456i	$-0.862571\pi$
$7$	−0.848315	+	1.03368i	−0.320633	+	0.390693i	0.587604	+	0.809149i	$0.300071\pi$
$8$	1.37857	−	2.46972i	0.487399	−	0.873179i
$9$	−0.995185	−	0.0980171i	−0.331728	−	0.0326724i
$10$	0.128214	−	0.681109i	0.0405448	−	0.215386i
$11$	2.04313	+	0.731044i	0.616027	+	0.220418i	0.626367	−	0.779528i	$-0.284541\pi$
$11$	2.04313	+	0.731044i	0.616027	+	0.220418i	−0.0103395	+	0.999947i	$0.503291\pi$
$12$	−1.22419	−	1.58157i	−0.353392	−	0.456561i
$13$	1.09435	−	4.36890i	0.303519	−	1.21172i	−0.605800	−	0.795617i	$-0.707147\pi$
$13$	1.09435	−	4.36890i	0.303519	−	1.21172i	0.909319	−	0.416099i	$-0.136603\pi$
$14$	−0.618747	+	1.78701i	−0.165367	+	0.477598i
$15$	−0.407483	−	0.272272i	−0.105212	−	0.0703002i
$16$	0.618362	−	3.95191i	0.154591	−	0.987979i
$17$	−0.860261	+	0.574808i	−0.208644	+	0.139411i	−0.655502	−	0.755193i	$-0.727543\pi$
$17$	−0.860261	+	0.574808i	−0.208644	+	0.139411i	0.446858	+	0.894605i	$0.352543\pi$
$18$	−1.36822	+	0.357716i	−0.322494	+	0.0843144i
$19$	−0.938177	−	6.32468i	−0.215233	−	1.45098i	−0.780025	−	0.625748i	$-0.784794\pi$
$19$	−0.938177	−	6.32468i	−0.215233	−	1.45098i	0.564793	−	0.825233i	$-0.308956\pi$
$20$	−0.163728	−	0.966380i	−0.0366107	−	0.216089i
$21$	0.990805	+	0.898014i	0.216211	+	0.195963i
$22$	3.06865	−	0.0315595i	0.654239	−	0.00672851i
$23$	−0.210299	−	0.693263i	−0.0438504	−	0.144555i	0.932282	−	0.361733i	$-0.117815\pi$
$23$	−0.210299	−	0.693263i	−0.0438504	−	0.144555i	−0.976132	+	0.217178i	$0.930315\pi$
$24$	−2.39911	−	1.49810i	−0.489715	−	0.305798i
$25$	2.24377	+	4.19779i	0.448753	+	0.839558i
$26$	−0.689469	−	6.33202i	−0.135216	−	1.24181i
$27$	−0.146730	+	0.989177i	−0.0282383	+	0.190367i
$28$	0.0550041	+	2.67385i	0.0103948	+	0.505310i
$29$	1.09514	−	2.31549i	0.203363	−	0.429976i	−0.776371	−	0.630276i	$-0.782942\pi$
$29$	1.09514	−	2.31549i	0.203363	−	0.429976i	0.979735	+	0.200300i	$0.0641918\pi$
$30$	−0.673998	−	0.161480i	−0.123055	−	0.0294821i
$31$	2.91728	+	7.04294i	0.523959	+	1.26495i	0.935425	+	0.353525i	$0.115017\pi$
$31$	2.91728	+	7.04294i	0.523959	+	1.26495i	−0.411466	+	0.911425i	$0.634983\pi$
$32$	−1.11654	−	5.54557i	−0.197378	−	0.980327i
$33$	0.830415	−	2.00480i	0.144557	−	0.348991i
$34$	−0.859485	+	1.18414i	−0.147400	+	0.203079i
$35$	0.220775	+	0.617025i	0.0373178	+	0.104296i
$36$	−1.63973	+	1.14511i	−0.273289	+	0.190851i
$37$	−4.33455	+	3.21472i	−0.712595	+	0.528497i	−0.890180	−	0.455609i	$-0.849422\pi$
$37$	−4.33455	+	3.21472i	−0.712595	+	0.528497i	0.177585	+	0.984106i	$0.443172\pi$
$38$	−4.34430	−	7.93035i	−0.704739	−	1.28647i
$39$	−4.30994	−	1.30741i	−0.690143	−	0.209353i
$40$	−0.690823	−	1.20173i	−0.109229	−	0.190010i
$41$	4.47418	−	8.37061i	0.698750	−	1.30727i	−0.242695	−	0.970103i	$-0.578031\pi$
$41$	4.47418	−	8.37061i	0.698750	−	1.30727i	0.941445	−	0.337167i	$-0.109469\pi$
$42$	1.75450	+	0.705686i	0.270725	+	0.108890i
$43$	−10.2452	+	0.503314i	−1.56238	+	0.0767547i	−0.811763	−	0.583987i	$-0.801492\pi$
$43$	−10.2452	+	0.503314i	−1.56238	+	0.0767547i	−0.750614	+	0.660741i	$0.770242\pi$
$44$	4.05533	−	1.54582i	0.611364	−	0.233041i
$45$	−0.291938	+	0.393633i	−0.0435195	+	0.0586793i
$46$	−0.618747	−	0.816597i	−0.0912293	−	0.120401i
$47$	−1.74273	+	8.76132i	−0.254204	+	1.27797i	0.616967	+	0.786989i	$0.288361\pi$
$47$	−1.74273	+	8.76132i	−0.254204	+	1.27797i	−0.871171	+	0.490980i	$0.836639\pi$
$48$	−3.91681	−	0.811529i	−0.565343	−	0.117134i
$49$	1.01679	+	5.11173i	0.145255	+	0.730247i
$50$	5.03387	+	4.46901i	0.711897	+	0.632013i
$51$	0.531904	+	0.887429i	0.0744815	+	0.124265i
$52$	−4.01797	−	8.06198i	−0.557192	−	1.11800i
$53$	0.564547	+	1.19364i	0.0775466	+	0.163958i	0.939038	−	0.343814i	$-0.111719\pi$
$53$	0.564547	+	1.19364i	0.0775466	+	0.163958i	−0.861491	+	0.507773i	$0.830469\pi$
$54$	0.290149	+	1.38413i	0.0394843	+	0.188356i
$55$	0.822062	−	0.674649i	0.110847	−	0.0909696i
$56$	1.38343	+	3.52010i	0.184868	+	0.470393i
$57$	−6.36309	+	0.626710i	−0.842812	+	0.0830098i
$58$	0.317964	−	3.60840i	0.0417507	−	0.473806i
$59$	0.794013	+	3.16988i	0.103372	+	0.412683i	0.999517	−	0.0310780i	$-0.00989401\pi$
$59$	0.794013	+	3.16988i	0.103372	+	0.412683i	−0.896145	+	0.443761i	$0.853644\pi$
$60$	−0.973250	+	0.116113i	−0.125646	+	0.0149901i
$61$	2.79985	−	2.53764i	0.358484	−	0.324911i	−0.472371	−	0.881400i	$-0.656602\pi$
$61$	2.79985	−	2.53764i	0.358484	−	0.324911i	0.830855	+	0.556489i	$0.187852\pi$
$62$	7.32176	+	7.91322i	0.929864	+	1.00498i
$63$	0.945548	−	0.945548i	0.119128	−	0.119128i
$64$	−4.19907	−	6.80939i	−0.524884	−	0.851174i
$65$	−1.56076	−	1.56076i	−0.193588	−	0.193588i
$66$	0.119050	−	3.06651i	0.0146541	−	0.377461i
$67$	9.82060	+	10.8354i	1.19978	+	1.32375i	0.932950	+	0.360007i	$0.117226\pi$
$67$	9.82060	+	10.8354i	1.19978	+	1.32375i	0.266828	+	0.963744i	$0.414024\pi$
$68$	−0.559820	+	1.99209i	−0.0678882	+	0.241576i
$69$	−0.702747	+	0.176029i	−0.0846008	+	0.0211914i
$70$	0.595280	+	0.710327i	0.0711496	+	0.0849003i
$71$	0.649809	+	6.59762i	0.0771181	+	0.782993i	0.953503	+	0.301383i	$0.0974481\pi$
$71$	0.649809	+	6.59762i	0.0771181	+	0.782993i	−0.876385	+	0.481611i	$0.840052\pi$
$72$	−1.61401	+	2.32271i	−0.190213	+	0.273734i
$73$	0.148558	+	0.181018i	0.0173874	+	0.0211866i	0.781632	−	0.623740i	$-0.214388\pi$
$73$	0.148558	+	0.181018i	0.0173874	+	0.0211866i	−0.764244	+	0.644927i	$0.776888\pi$
$74$	−4.17456	+	6.38894i	−0.485283	+	0.742699i
$75$	4.30283	−	2.03509i	0.496848	−	0.234992i
$76$	−9.64973	−	8.39105i	−1.10690	−	0.962519i
$77$	−2.48888	+	1.49178i	−0.283634	+	0.170004i
$78$	−6.35822	+	0.377941i	−0.719927	+	0.0427934i
$79$	−6.19628	+	1.23252i	−0.697135	+	0.138669i	−0.530922	−	0.847421i	$-0.678154\pi$
$79$	−6.19628	+	1.23252i	−0.697135	+	0.138669i	−0.166214	+	0.986090i	$0.553154\pi$
$80$	−1.50540	−	1.25561i	−0.168309	−	0.140382i
$81$	0.980785	+	0.195090i	0.108976	+	0.0216767i
$82$	1.83288	−	13.2970i	0.202408	−	1.46841i
$83$	13.8002	+	10.2349i	1.51476	+	1.12343i	0.955716	+	0.294291i	$0.0950835\pi$
$83$	13.8002	+	10.2349i	1.51476	+	1.12343i	0.559049	+	0.829135i	$0.311167\pi$
$84$	2.67333	+	0.0762617i	0.291684	+	0.00832083i
$85$	0.0248795	+	0.506435i	0.00269857	+	0.0549306i
$86$	−13.3443	+	5.68888i	−1.43896	+	0.613447i
$87$	−2.25896	−	1.20744i	−0.242186	−	0.129451i
$88$	4.62208	−	4.03817i	0.492716	−	0.430471i
$89$	4.07160	−	13.4223i	0.431588	−	1.42276i	−0.424265	−	0.905538i	$-0.639468\pi$
$89$	4.07160	−	13.4223i	0.431588	−	1.42276i	0.855854	−	0.517218i	$-0.173032\pi$
$90$	−0.194357	+	0.665262i	−0.0204870	+	0.0701248i
$91$	3.58767	+	4.83741i	0.376090	+	0.507099i
$92$	−1.22103	−	0.780027i	−0.127301	−	0.0813234i
$93$	7.17760	−	2.56819i	0.744283	−	0.266309i
$94$	1.98208	+	12.4767i	0.204436	+	1.28687i
$95$	−2.89497	−	1.19913i	−0.297017	−	0.123029i
$96$	−5.59368	+	0.843086i	−0.570902	+	0.0860471i
$97$	9.41706	−	3.90067i	0.956158	−	0.396053i	0.150616	−	0.988592i	$-0.451874\pi$
$97$	9.41706	−	3.90067i	0.956158	−	0.396053i	0.805542	+	0.592539i	$0.201874\pi$
$98$	3.85412	+	6.28276i	0.389324	+	0.634655i
$99$	−1.96164	−	0.927786i	−0.197152	−	0.0932460i
$100$	8.86808	+	3.46136i	0.886808	+	0.346136i
$101$	13.0129	+	1.93029i	1.29484	+	0.192071i	0.758355	−	0.651841i	$-0.226003\pi$
$101$	13.0129	+	1.93029i	1.29484	+	0.192071i	0.536481	+	0.843912i	$0.319753\pi$
$102$	1.14054	+	0.916553i	0.112930	+	0.0907523i
$103$	−14.5128	+	7.75723i	−1.42999	+	0.764343i	−0.990963	−	0.134134i	$-0.957175\pi$
$103$	−14.5128	+	7.75723i	−1.42999	+	0.764343i	−0.439022	+	0.898476i	$0.644675\pi$
$104$	−9.28134	−	8.72560i	−0.910110	−	0.855616i
$105$	0.627115	−	0.190233i	0.0612001	−	0.0185649i
$106$	1.33392	+	1.30676i	0.129562	+	0.126924i
$107$	6.18099	−	6.81968i	0.597539	−	0.659283i	−0.364815	−	0.931080i	$-0.618868\pi$
$107$	6.18099	−	6.81968i	0.597539	−	0.659283i	0.962355	+	0.271797i	$0.0876179\pi$
$108$	1.06327	+	1.69395i	0.102313	+	0.163000i
$109$	−13.9471	+	2.06886i	−1.33589	+	0.198161i	−0.776173	−	0.630521i	$-0.782841\pi$
$109$	−13.9471	+	2.06886i	−1.33589	+	0.198161i	−0.559720	+	0.828682i	$0.689091\pi$
$110$	0.759879	−	1.29787i	0.0724516	−	0.123747i
$111$	2.99816	+	4.48707i	0.284573	+	0.425893i
$112$	3.56043	+	3.99166i	0.336429	+	0.377176i
$113$	3.84790	−	5.75879i	0.361980	−	0.541741i	−0.605121	−	0.796133i	$-0.706875\pi$
$113$	3.84790	−	5.75879i	0.361980	−	0.541741i	0.967101	+	0.254392i	$0.0818754\pi$
$114$	−8.13397	+	3.94995i	−0.761816	+	0.369946i
$115$	−0.344399	−	0.0862675i	−0.0321154	−	0.00804449i
$116$	−1.34668	−	4.94265i	−0.125036	−	0.458913i
$117$	−1.51731	+	4.24060i	−0.140275	+	0.392044i
$118$	2.60688	+	3.81593i	0.239983	+	0.351285i
$119$	0.135608	−	1.37685i	0.0124311	−	0.126215i
$120$	−1.23418	+	0.631025i	−0.112665	+	0.0576044i
$121$	−4.86315	−	3.99109i	−0.442105	−	0.362826i
$122$	2.47051	−	4.73858i	0.223669	−	0.429011i
$123$	−8.14099	−	4.87952i	−0.734048	−	0.439972i
$124$	13.5911	+	6.90906i	1.22052	+	0.620452i
$125$	4.77729	+	0.234693i	0.427294	+	0.0209916i
$126$	0.790925	−	1.71776i	0.0704612	−	0.153030i
$127$		−	4.30658i		−	0.382148i	−0.981576	−	0.191074i	$-0.938803\pi$
$127$		−	4.30658i		−	0.382148i	0.981576	−	0.191074i	$-0.0611970\pi$
$128$	−8.90768	−	6.97519i	−0.787335	−	0.616525i
$129$			10.2575i			0.903127i
$130$	−2.83539	−	1.30553i	−0.248680	−	0.114502i
$131$	−4.76877	−	0.234274i	−0.416649	−	0.0204687i	−0.160336	−	0.987062i	$-0.551258\pi$
$131$	−4.76877	−	0.234274i	−0.416649	−	0.0204687i	−0.256313	+	0.966594i	$0.582508\pi$
$132$	−1.34497	−	4.12629i	−0.117065	−	0.359148i
$133$	7.33353	+	4.39555i	0.635898	+	0.381143i
$134$	18.3382	+	9.56082i	1.58418	+	0.825929i
$135$	0.378834	+	0.310901i	0.0326048	+	0.0267581i
$136$	0.233684	+	2.91702i	0.0200382	+	0.250132i
$137$	−1.82115	+	18.4904i	−0.155591	+	1.57974i	0.527594	+	0.849497i	$0.323094\pi$
$137$	−1.82115	+	18.4904i	−0.155591	+	1.57974i	−0.683185	+	0.730246i	$0.739406\pi$
$138$	−0.845974	+	0.577934i	−0.0720141	+	0.0491970i
$139$	0.811234	−	2.26725i	0.0688080	−	0.192305i	−0.902218	−	0.431281i	$-0.858062\pi$
$139$	0.811234	−	2.26725i	0.0688080	−	0.192305i	0.971026	+	0.238976i	$0.0768117\pi$
$140$	1.13782	+	0.650553i	0.0961630	+	0.0549818i
$141$	8.66525	+	2.17053i	0.729746	+	0.182792i
$142$	4.09553	+	8.43376i	0.343689	+	0.707745i
$143$	5.42977	−	8.12622i	0.454060	−	0.679549i
$144$	−1.00274	+	3.87227i	−0.0835617	+	0.322690i
$145$	−0.697400	−	1.04373i	−0.0579159	−	0.0866772i
$146$	0.285790	+	0.167325i	0.0236522	+	0.0138480i
$147$	5.15547	−	0.764741i	0.425216	−	0.0630748i
$148$	−2.40663	+	10.5214i	−0.197824	+	0.864851i
$149$	2.88445	−	3.18250i	0.236303	−	0.260720i	−0.611242	−	0.791444i	$-0.709330\pi$
$149$	2.88445	−	3.18250i	0.236303	−	0.260720i	0.847545	+	0.530724i	$0.178080\pi$
$150$	4.71062	−	4.80852i	0.384621	−	0.392614i
$151$	−17.3353	+	5.25862i	−1.41073	+	0.427940i	−0.901533	−	0.432709i	$-0.857558\pi$
$151$	−17.3353	+	5.25862i	−1.41073	+	0.427940i	−0.509197	+	0.860650i	$0.670058\pi$
$152$	−16.9136	−	6.40200i	−1.37187	−	0.519270i
$153$	0.912459	−	0.487720i	0.0737680	−	0.0394298i
$154$	−2.57056	+	3.19876i	−0.207142	+	0.257764i
$155$	3.69552	+	0.548179i	0.296832	+	0.0440308i
$156$	−8.24943	+	3.61755i	−0.660483	+	0.289636i
$157$	15.2505	+	7.21295i	1.21712	+	0.575656i	0.924723	−	0.380640i	$-0.124296\pi$
$157$	15.2505	+	7.21295i	1.21712	+	0.575656i	0.292399	+	0.956296i	$0.405546\pi$
$158$	−7.61576	+	4.67183i	−0.605877	+	0.371671i
$159$	1.21990	−	0.505298i	0.0967442	−	0.0400728i
$160$	−2.61240	−	0.927863i	−0.206529	−	0.0733540i
$161$	0.895009	+	0.370725i	0.0705366	+	0.0292172i
$162$	1.39670	−	0.221884i	0.109735	−	0.0174328i
$163$	2.41185	−	0.862974i	0.188911	−	0.0675933i	−0.240735	−	0.970591i	$-0.577388\pi$
$163$	2.41185	−	0.862974i	0.188911	−	0.0675933i	0.429646	+	0.902998i	$0.358638\pi$
$164$	−4.08546	−	18.5378i	−0.319021	−	1.44756i
$165$	−0.633499	−	0.854175i	−0.0493179	−	0.0664974i
$166$	23.3231	+	6.81386i	1.81022	+	0.528858i
$167$	−4.38961	+	14.4706i	−0.339678	+	1.11977i	0.606217	+	0.795299i	$0.292686\pi$
$167$	−4.38961	+	14.4706i	−0.339678	+	1.11977i	−0.945896	+	0.324470i	$0.894814\pi$
$168$	3.58374	−	1.20904i	0.276492	−	0.0932793i
$169$	−6.42472	−	3.43409i	−0.494210	−	0.264161i
$170$	0.281210	+	0.659630i	0.0215678	+	0.0505913i
$171$	0.313733	+	6.38618i	0.0239918	+	0.488363i
$172$	−14.9141	+	14.0868i	−1.13719	+	1.07411i
$173$	−3.75769	−	2.78689i	−0.285692	−	0.211883i	0.443357	−	0.896345i	$-0.353787\pi$
$173$	−3.75769	−	2.78689i	−0.285692	−	0.211883i	−0.729049	+	0.684462i	$0.760037\pi$
$174$	−3.58845	−	0.494637i	−0.272040	−	0.0374983i
$175$	−6.24257	−	1.24173i	−0.471894	−	0.0938656i
$176$	4.15242	−	7.62223i	0.313000	−	0.574547i
$177$	3.20502	−	0.637518i	0.240904	−	0.0479188i
$178$	−1.17701	−	19.8011i	−0.0882203	−	1.48416i
$179$	2.47461	−	1.48323i	0.184961	−	0.110861i	−0.418625	−	0.908159i	$-0.637488\pi$
$179$	2.47461	−	1.48323i	0.184961	−	0.110861i	0.603586	+	0.797298i	$0.293738\pi$
$180$	0.0682179	+	0.977775i	0.00508466	+	0.0728790i
$181$	−8.40432	+	3.97495i	−0.624688	+	0.295456i	−0.713567	−	0.700587i	$-0.752922\pi$
$181$	−8.40432	+	3.97495i	−0.624688	+	0.295456i	0.0888788	+	0.996042i	$0.471672\pi$
$182$	7.13014	+	4.65886i	0.528521	+	0.345338i
$183$	−2.39720	−	2.92099i	−0.177206	−	0.215926i
$184$	−2.00208	−	0.436334i	−0.147595	−	0.0321669i
$185$	0.259228	+	2.63198i	0.0190588	+	0.193507i
$186$	8.26295	−	6.92465i	0.605869	−	0.507740i
$187$	−2.17784	+	0.545520i	−0.159259	+	0.0398923i
$188$	8.74422	+	15.5798i	0.637737	+	1.13627i
$189$	−0.898014	−	0.990805i	−0.0653209	−	0.0720705i
$190$	−4.42808	−	0.171910i	−0.321247	−	0.0124717i
$191$	4.13780	+	4.13780i	0.299400	+	0.299400i	0.840779	−	0.541379i	$-0.182097\pi$
$191$	4.13780	+	4.13780i	0.299400	+	0.299400i	−0.541379	+	0.840779i	$0.682097\pi$
$192$	−7.00723	+	3.85989i	−0.505703	+	0.278564i
$193$	−4.02921	+	4.02921i	−0.290029	+	0.290029i	−0.837092	−	0.547063i	$-0.815746\pi$
$193$	−4.02921	+	4.02921i	−0.290029	+	0.290029i	0.547063	+	0.837092i	$0.315746\pi$
$194$	10.5807	−	9.78986i	0.759650	−	0.702871i
$195$	−1.63546	+	1.48229i	−0.117118	+	0.106149i
$196$	8.19197	+	6.44564i	0.585141	+	0.460403i
$197$	0.865681	+	3.45599i	0.0616772	+	0.246229i	0.993025	−	0.117901i	$-0.0376164\pi$
$197$	0.865681	+	3.45599i	0.0616772	+	0.246229i	−0.931348	+	0.364130i	$0.881366\pi$
$198$	−3.05697	−	0.269373i	−0.217249	−	0.0191435i
$199$	−11.5929	+	1.14181i	−0.821802	+	0.0809405i	−0.500173	−	0.865925i	$-0.666730\pi$
$199$	−11.5929	+	1.14181i	−0.821802	+	0.0809405i	−0.321629	+	0.946866i	$0.604230\pi$
$200$	13.4606	+	0.245481i	0.951807	+	0.0173582i
$201$	11.3042	−	9.27711i	0.797336	−	0.654357i
$202$	18.2087	−	3.81701i	1.28116	−	0.268564i
$203$	1.46444	+	3.09629i	0.102783	+	0.217317i
$204$	1.96222	+	0.656893i	0.137383	+	0.0459917i
$205$	−2.39134	−	3.98970i	−0.167018	−	0.278653i
$206$	−15.4504	+	17.4033i	−1.07648	+	1.21254i
$207$	0.141335	+	0.710538i	0.00982345	+	0.0493858i
$208$	−16.5888	−	7.02636i	−1.15023	−	0.487190i
$209$	2.70680	−	13.6080i	0.187233	−	0.941285i
$210$	0.738680	−	0.559709i	0.0509738	−	0.0386236i
$211$	−2.03681	+	2.74632i	−0.140220	+	0.189065i	−0.867735	−	0.497027i	$-0.834425\pi$
$211$	−2.03681	+	2.74632i	−0.140220	+	0.189065i	0.727515	+	0.686091i	$0.240675\pi$
$212$	2.40999	+	1.07976i	0.165519	+	0.0741581i
$213$	6.62156	−	0.325296i	0.453702	−	0.0222889i
$214$	4.85721	−	12.0761i	0.332032	−	0.825507i
$215$	−2.36970	+	4.43340i	−0.161612	+	0.302355i
$216$	2.24071	+	1.72604i	0.152461	+	0.117442i
$217$	−9.75489	−	2.95911i	−0.662205	−	0.200878i
$218$	−17.4880	+	9.58002i	−1.18443	+	0.648841i
$219$	0.188089	−	0.139497i	0.0127099	−	0.00942631i
$220$	0.371949	−	2.09413i	0.0250768	−	0.141187i
$221$	1.56985	+	4.38744i	0.105600	+	0.295131i
$222$	6.17641	+	4.48302i	0.414533	+	0.300881i
$223$	−3.89142	+	9.39473i	−0.260589	+	0.629117i	−0.998975	−	0.0452606i	$-0.985588\pi$
$223$	−3.89142	+	9.39473i	−0.260589	+	0.629117i	0.738386	+	0.674378i	$0.235588\pi$
$224$	6.67950	+	3.55025i	0.446293	+	0.237211i
$225$	−1.82151	−	4.39751i	−0.121434	−	0.293167i
$226$	2.28213	−	9.52533i	0.151805	−	0.633615i
$227$	−5.79073	+	12.2435i	−0.384344	+	0.812628i	0.615358	+	0.788247i	$0.289011\pi$
$227$	−5.79073	+	12.2435i	−0.384344	+	0.812628i	−0.999703	+	0.0243804i	$0.992239\pi$
$228$	−8.85443	+	9.22637i	−0.586399	+	0.611032i
$229$	0.149885	−	1.01044i	0.00990470	−	0.0667720i	−0.983661	−	0.180033i	$-0.942380\pi$
$229$	0.149885	−	1.01044i	0.00990470	−	0.0667720i	0.993565	+	0.113261i	$0.0361296\pi$
$230$	−0.499151	+	0.0543507i	−0.0329131	+	0.00358378i
$231$	1.36786	+	2.55908i	0.0899985	+	0.168375i
$232$	−4.20888	−	5.89678i	−0.276327	−	0.387142i
$233$	−4.06852	−	13.4121i	−0.266537	−	0.878656i	−0.983401	−	0.181443i	$-0.941923\pi$
$233$	−4.06852	−	13.4121i	−0.266537	−	0.878656i	0.716864	−	0.697213i	$-0.245577\pi$
$234$	0.0655030	+	6.36911i	0.00428206	+	0.416362i
$235$	3.24376	+	2.93997i	0.211599	+	0.191783i
$236$	5.32842	+	3.78447i	0.346850	+	0.246348i
$237$	0.926994	+	6.24929i	0.0602148	+	0.405935i
$238$	−0.494903	−	1.89295i	−0.0320798	−	0.122702i
$239$	5.45840	−	3.64718i	0.353074	−	0.235917i	−0.366366	−	0.930471i	$-0.619398\pi$
$239$	5.45840	−	3.64718i	0.353074	−	0.235917i	0.719441	+	0.694554i	$0.244398\pi$
$240$	−1.32797	+	1.44198i	−0.0857198	+	0.0930792i
$241$	−9.95074	−	6.64887i	−0.640983	−	0.428291i	0.192148	−	0.981366i	$-0.438455\pi$
$241$	−9.95074	−	6.64887i	−0.640983	−	0.428291i	−0.833132	+	0.553074i	$0.813455\pi$
$242$	−8.40738	−	2.91103i	−0.540447	−	0.187128i
$243$	0.242980	−	0.970031i	0.0155872	−	0.0622275i
$244$	0.954924	−	7.49688i	0.0611327	−	0.479939i
$245$	2.40491	+	0.860489i	0.153644	+	0.0549746i
$246$	−13.1911	−	2.48313i	−0.841033	−	0.158318i
$247$	−28.6586	−	2.82263i	−1.82350	−	0.179599i
$248$	21.4158	+	2.50433i	1.35991	+	0.159025i
$249$	10.8997	−	13.2813i	0.690741	−	0.841670i
$250$	6.45246	−	2.03003i	0.408089	−	0.128390i
$251$	12.0456	−	20.0969i	0.760313	−	1.26851i	−0.197270	−	0.980349i	$-0.563208\pi$
$251$	12.0456	−	20.0969i	0.760313	−	1.26851i	0.957583	−	0.288156i	$-0.0930423\pi$
$252$	0.207344	−	2.66636i	0.0130614	−	0.167965i
$253$	0.0771373	−	1.57017i	0.00484958	−	0.0987155i
$254$	−2.11067	−	5.71300i	−0.132435	−	0.358466i
$255$	0.507046			0.0317524
$256$	−15.2353	−	4.88743i	−0.952203	−	0.305464i
$257$	−2.00998			−0.125379			−0.0626896	−	0.998033i	$-0.519968\pi$
$257$	−2.00998			−0.125379			−0.0626896	+	0.998033i	$0.519968\pi$
$258$	5.02725	+	13.6074i	0.312983	+	0.847160i
$259$	0.354087	−	7.20761i	0.0220019	−	0.447859i
$260$	−4.40120	−	0.342249i	−0.272951	−	0.0212254i
$261$	−1.31683	+	2.19700i	−0.0815097	+	0.135991i
$262$	−6.44094	+	2.02640i	−0.397923	+	0.125192i
$263$	10.9163	−	13.3016i	0.673130	−	0.820211i	−0.318689	−	0.947859i	$-0.603243\pi$
$263$	10.9163	−	13.3016i	0.673130	−	0.820211i	0.991820	+	0.127648i	$0.0407427\pi$
$264$	−3.80651	−	4.81466i	−0.234275	−	0.296322i
$265$	0.643984	+	0.0634269i	0.0395596	+	0.00389629i
$266$	11.8827	+	2.23684i	0.728578	+	0.137150i
$267$	−13.2063	−	4.72529i	−0.808213	−	0.289183i
$268$	29.0128	+	3.69554i	1.77224	+	0.225741i
$269$	−0.275370	+	1.09934i	−0.0167896	+	0.0670279i	−0.977847	−	0.209321i	$-0.932875\pi$
$269$	−0.275370	+	1.09934i	−0.0167896	+	0.0670279i	0.961057	+	0.276349i	$0.0891246\pi$
$270$	0.654924	+	0.226766i	0.0398574	+	0.0138005i
$271$	−5.83653	−	3.89984i	−0.354544	−	0.236899i	0.365525	−	0.930802i	$-0.380890\pi$
$271$	−5.83653	−	3.89984i	−0.354544	−	0.236899i	−0.720068	+	0.693903i	$0.755890\pi$
$272$	1.73964	+	3.75512i	0.105481	+	0.227687i
$273$	5.00762	−	3.34599i	0.303075	−	0.202508i
$274$	6.64631	+	25.4215i	0.401518	+	1.53577i
$275$	1.51554	+	10.2169i	0.0913904	+	0.616104i
$276$	−0.839001	+	1.18129i	−0.0505019	+	0.0711051i
$277$	−6.63360	−	6.01234i	−0.398574	−	0.361247i	0.447526	−	0.894271i	$-0.352305\pi$
$277$	−6.63360	−	6.01234i	−0.398574	−	0.361247i	−0.846100	+	0.533025i	$0.821055\pi$
$278$	−0.0350213	−	3.40526i	−0.00210044	−	0.204234i
$279$	−2.21291	−	7.29497i	−0.132483	−	0.436739i
$280$	1.82824	+	0.305361i	0.109258	+	0.0182488i
$281$	−12.4772	−	23.3432i	−0.744327	−	1.39254i	−0.913453	−	0.406944i	$-0.866594\pi$
$281$	−12.4772	−	23.3432i	−0.744327	−	1.39254i	0.169126	−	0.985594i	$-0.445906\pi$
$282$	12.5589	−	1.36749i	0.747871	−	0.0814328i
$283$	2.24323	−	15.1226i	0.133346	−	0.898945i	−0.814488	−	0.580180i	$-0.802982\pi$
$283$	2.24323	−	15.1226i	0.133346	−	0.898945i	0.947834	−	0.318765i	$-0.103268\pi$
$284$	9.56643	+	9.18078i	0.567663	+	0.544779i
$285$	−1.33974	+	2.83264i	−0.0793593	+	0.167791i
$286$	3.22031	−	13.4412i	0.190421	−	0.794794i
$287$	4.85697	+	11.7258i	0.286698	+	0.692150i
$288$	0.567602	+	5.62831i	0.0334463	+	0.331651i
$289$	−6.09597	+	14.7170i	−0.358587	+	0.865705i
$290$	−1.43669	−	1.04279i	−0.0843652	−	0.0612348i
$291$	−3.43390	−	9.59711i	−0.201299	−	0.562593i
$292$	0.461129	+	0.0819031i	0.0269855	+	0.00479302i
$293$	−20.2047	+	14.9848i	−1.18037	+	0.875424i	−0.994248	−	0.107102i	$-0.965843\pi$
$293$	−20.2047	+	14.9848i	−1.18037	+	0.875424i	−0.186124	+	0.982526i	$0.559593\pi$
$294$	6.46431	−	3.54119i	0.377006	−	0.206527i
$295$	1.53252	+	0.464883i	0.0892265	+	0.0270666i
$296$	1.96398	+	15.1369i	0.114154	+	0.879812i
$297$	−1.02292	+	1.91375i	−0.0593559	+	0.111047i
$298$	2.26668	−	5.63549i	0.131305	−	0.326455i
$299$	−3.25894	+	0.160101i	−0.188469	+	0.00925891i
$300$	3.89232	−	8.68755i	0.224723	−	0.501576i
$301$	8.17089	−	11.0172i	0.470962	−	0.635019i
$302$	−20.4194	+	15.4720i	−1.17500	+	0.890316i
$303$	2.56648	−	12.9026i	0.147440	−	0.741233i
$304$	−25.5747	−	0.203347i	−1.46681	−	0.0116627i
$305$	−0.361280	−	1.81628i	−0.0206869	−	0.104000i
$306$	0.971413	−	1.09420i	0.0555320	−	0.0625510i
$307$	−9.78959	−	16.3329i	−0.558721	−	0.932170i	−0.999404	−	0.0345073i	$-0.989014\pi$
$307$	−9.78959	−	16.3329i	−0.558721	−	0.932170i	0.440683	−	0.897663i	$-0.354736\pi$
$308$	−1.84232	+	5.50324i	−0.104976	+	0.313576i
$309$	7.03578	+	14.8759i	0.400252	+	0.846261i
$310$	5.17105	−	1.08399i	0.293696	−	0.0615662i
$311$	1.04220	−	0.855308i	0.0590975	−	0.0485001i	−0.604381	−	0.796696i	$-0.706579\pi$
$311$	1.04220	−	0.855308i	0.0590975	−	0.0485001i	0.663478	+	0.748195i	$0.269079\pi$
$312$	−9.17051	+	8.84201i	−0.519178	+	0.500580i
$313$	28.5159	−	2.80857i	1.61181	−	0.158750i	0.748400	−	0.663248i	$-0.230823\pi$
$313$	28.5159	−	2.80857i	1.61181	−	0.158750i	0.863413	+	0.504498i	$0.168323\pi$
$314$	23.7660	+	2.09420i	1.34119	+	0.118183i
$315$	−0.159233	−	0.635693i	−0.00897176	−	0.0358173i
$316$	−7.81320	+	9.93004i	−0.439527	+	0.558608i
$317$	18.1871	−	16.4838i	1.02149	−	0.925823i	0.0242210	−	0.999707i	$-0.492289\pi$
$317$	18.1871	−	16.4838i	1.02149	−	0.925823i	0.997267	+	0.0738840i	$0.0235394\pi$
$318$	1.37064	−	1.26819i	0.0768616	−	0.0711166i
$319$	3.93025	−	3.93025i	0.220052	−	0.220052i
$320$	−3.92029	+	0.0494662i	−0.219151	+	0.00276525i
$321$	−6.50817	−	6.50817i	−0.363251	−	0.363251i
$322$	1.36899	+	0.0531479i	0.0762908	+	0.00296182i
$323$	4.44255	+	4.90160i	0.247190	+	0.272732i
$324$	1.74408	−	0.978871i	0.0968933	−	0.0543817i
$325$	20.7952	−	5.20893i	1.15351	−	0.288939i
$326$	2.77655	−	2.32685i	0.153779	−	0.128872i
$327$	1.38202	+	14.0318i	0.0764257	+	0.775963i
$328$	−14.5051	−	22.5895i	−0.800910	−	1.24730i
$329$	−7.57797	−	9.23378i	−0.417787	−	0.509075i
$330$	−1.25902	−	0.822647i	−0.0693066	−	0.0452852i
$331$	−19.6653	+	9.30102i	−1.08091	+	0.511230i	−0.883183	−	0.469028i	$-0.844604\pi$
$331$	−19.6653	+	9.30102i	−1.08091	+	0.511230i	−0.197722	+	0.980258i	$0.563354\pi$
$332$	34.2793	−	2.39162i	1.88132	−	0.131257i
$333$	4.62877	−	2.77438i	0.253655	−	0.152035i
$334$	1.26894	+	21.3477i	0.0694331	+	1.16809i
$335$	7.02896	−	1.39815i	0.384033	−	0.0763890i
$336$	4.16155	−	3.36028i	0.227031	−	0.183318i
$337$	0.0954499	+	0.0189862i	0.00519949	+	0.00103424i	0.197689	−	0.980265i	$-0.436656\pi$
$337$	0.0954499	+	0.0189862i	0.00519949	+	0.00103424i	−0.192490	+	0.981299i	$0.561656\pi$
$338$	−10.2059	−	1.40680i	−0.555129	−	0.0765197i
$339$	−5.56304	−	4.12584i	−0.302143	−	0.224085i
$340$	0.696332	+	0.737227i	0.0377639	+	0.0399817i
$341$	0.811690	+	16.5223i	0.0439555	+	0.894734i
$342$	3.54607	+	8.31798i	0.191750	+	0.449785i
$343$	−14.4016	−	7.69782i	−0.777614	−	0.415643i
$344$	−12.8807	+	25.9966i	−0.694481	+	1.40165i
$345$	−0.103063	+	0.339752i	−0.00554870	+	0.0182916i
$346$	−6.35072	−	1.85537i	−0.341417	−	0.0997451i
$347$	−20.0351	−	27.0142i	−1.07554	−	1.45020i	−0.883277	−	0.468852i	$-0.844668\pi$
$347$	−20.0351	−	27.0142i	−1.07554	−	1.45020i	−0.192262	−	0.981344i	$-0.561582\pi$
$348$	−5.00277	+	1.10254i	−0.268177	+	0.0591022i
$349$	3.10184	−	1.10985i	0.166037	−	0.0594092i	−0.252559	−	0.967581i	$-0.581272\pi$
$349$	3.10184	−	1.10985i	0.166037	−	0.0594092i	0.418596	+	0.908172i	$0.362522\pi$
$350$	−8.88981	+	1.41226i	−0.475180	+	0.0754885i
$351$	4.16104	+	1.72356i	0.222100	+	0.0919968i
$352$	1.77282	−	12.1466i	0.0944916	−	0.647414i
$353$	9.55320	−	3.95707i	0.508466	−	0.210613i	−0.113676	−	0.993518i	$-0.536263\pi$
$353$	9.55320	−	3.95707i	0.508466	−	0.210613i	0.622142	+	0.782904i	$0.286263\pi$
$354$	3.93925	−	2.41650i	0.209369	−	0.128436i
$355$	2.93704	+	1.38912i	0.155882	+	0.0737267i
$356$	−11.2660	−	25.6908i	−0.597095	−	1.36161i
$357$	−1.36854	−	0.203003i	−0.0724306	−	0.0107441i
$358$	2.55582	−	3.18042i	0.135080	−	0.168091i
$359$	−15.6440	+	8.36189i	−0.825659	+	0.441324i	−0.829391	−	0.558669i	$-0.811312\pi$
$359$	−15.6440	+	8.36189i	−0.825659	+	0.441324i	0.00373187	+	0.999993i	$0.498812\pi$
$360$	0.569706	+	1.26366i	0.0300261	+	0.0666006i
$361$	−20.9395	+	6.35193i	−1.10208	+	0.334312i
$362$	−9.20083	+	9.39204i	−0.483585	+	0.493635i
$363$	−4.22490	+	4.66146i	−0.221750	+	0.244663i
$364$	11.7420	+	2.68583i	0.615447	+	0.140776i
$365$	0.113520	−	0.0168392i	0.00594193	−	0.000881402i
$366$	−4.61165	−	2.70004i	−0.241055	−	0.141134i
$367$	−15.4018	−	23.0505i	−0.803969	−	1.20322i	−0.975922	−	0.218120i	$-0.930008\pi$
$367$	−15.4018	−	23.0505i	−0.803969	−	1.20322i	0.171953	−	0.985105i	$-0.444992\pi$
$368$	−2.86976	+	0.402396i	−0.149596	+	0.0209763i
$369$	−5.27310	+	7.89176i	−0.274507	+	0.410828i
$370$	1.63383	+	3.36447i	0.0849386	+	0.174911i
$371$	−1.71275	−	0.429020i	−0.0889213	−	0.0222736i
$372$	7.56763	−	13.2358i	0.392363	−	0.686242i
$373$	−8.92625	+	24.9472i	−0.462184	+	1.29172i	0.454015	+	0.890994i	$0.349991\pi$
$373$	−8.92625	+	24.9472i	−0.462184	+	1.29172i	−0.916199	+	0.400723i	$0.868759\pi$
$374$	−2.62170	+	1.79104i	−0.135565	+	0.0926122i
$375$	0.468821	−	4.76002i	0.0242098	−	0.245807i
$376$	19.2355	+	16.3822i	0.991998	+	0.844847i
$377$	−8.91767	−	7.31854i	−0.459283	−	0.376924i
$378$	−1.67688	−	0.874258i	−0.0862493	−	0.0449670i
$379$	12.2788	+	7.35961i	0.630718	+	0.378038i	0.793452	−	0.608632i	$-0.208281\pi$
$379$	12.2788	+	7.35961i	0.630718	+	0.378038i	−0.162735	+	0.986670i	$0.552031\pi$
$380$	−5.95844	+	1.94216i	−0.305661	+	0.0996309i
$381$	−4.30140	−	0.211314i	−0.220367	−	0.0108259i
$382$	7.51704	+	3.46115i	0.384605	+	0.177088i
$383$			22.8583i			1.16800i	0.811752	+	0.584002i	$0.198514\pi$
$383$			22.8583i			1.16800i	−0.811752	+	0.584002i	$0.801486\pi$
$384$	−7.40387	+	8.55469i	−0.377827	+	0.436555i
$385$			1.42206i			0.0724749i
$386$	−3.37032	+	7.31977i	−0.171545	+	0.372567i
$387$	10.2452	+	0.503314i	0.520792	+	0.0255849i
$388$	9.23805	−	18.1726i	0.468991	−	0.922574i
$389$	−5.58844	−	3.34958i	−0.283345	−	0.169831i	0.365369	−	0.930863i	$-0.380943\pi$
$389$	−5.58844	−	3.34958i	−0.283345	−	0.169831i	−0.648714	+	0.761032i	$0.724693\pi$
$390$	−1.44308	+	2.76791i	−0.0730733	+	0.140159i
$391$	0.579405	+	0.475506i	0.0293018	+	0.0240473i
$392$	14.0263	+	4.53572i	0.708434	+	0.229088i
$393$	−0.467985	+	4.75153i	−0.0236067	+	0.239683i
$394$	2.84218	+	4.16036i	0.143187	+	0.209596i
$395$	−1.04306	+	2.91515i	−0.0524819	+	0.146677i
$396$	−4.18732	+	1.14089i	−0.210421	+	0.0573316i
$397$	−26.9731	−	6.75641i	−1.35374	−	0.339094i	−0.502821	−	0.864391i	$-0.667705\pi$
$397$	−26.9731	−	6.75641i	−1.35374	−	0.339094i	−0.850919	+	0.525296i	$0.823955\pi$
$398$	−14.8193	+	7.19642i	−0.742825	+	0.360724i
$399$	4.75010	−	7.10902i	0.237802	−	0.355896i
$400$	17.9768	−	6.27142i	0.898839	−	0.313571i
$401$	−10.5675	−	15.8153i	−0.527713	−	0.789779i	0.467856	−	0.883804i	$-0.345026\pi$
$401$	−10.5675	−	15.8153i	−0.527713	−	0.789779i	−0.995570	+	0.0940256i	$0.970026\pi$
$402$	10.4491	−	17.8470i	0.521154	−	0.890127i
$403$	33.9625	−	5.03786i	1.69179	−	0.250954i
$404$	22.2844	−	13.9877i	1.10869	−	0.695912i
$405$	0.329115	−	0.363122i	0.0163538	−	0.0180437i
$406$	3.46018	+	3.38973i	0.171726	+	0.168230i
$407$	−11.2062	+	3.39935i	−0.555469	+	0.168500i
$408$	2.92497	−	0.0902710i	0.144808	−	0.00446908i
$409$	11.6935	−	6.25029i	0.578205	−	0.309057i	−0.156246	−	0.987718i	$-0.549939\pi$
$409$	11.6935	−	6.25029i	0.578205	−	0.309057i	0.734452	+	0.678661i	$0.237439\pi$
$410$	−5.12765	−	4.12064i	−0.253236	−	0.203504i
$411$	18.3788	+	2.72623i	0.906558	+	0.134475i
$412$	−11.9667	+	30.6590i	−0.589559	+	1.51046i
$413$	−3.95020	−	1.86830i	−0.194376	−	0.0919332i
$414$	0.535727	+	0.873313i	0.0263296	+	0.0429210i
$415$	7.77920	−	3.22225i	0.381866	−	0.158174i
$416$	−25.4499	−	1.19076i	−1.24779	−	0.0583818i
$417$	−2.22471	−	0.921505i	−0.108945	−	0.0451263i
$418$	−3.07854	−	19.3786i	−0.150577	−	0.947840i
$419$	−0.721680	+	0.258221i	−0.0352564	+	0.0126149i	−0.354459	−	0.935072i	$-0.615335\pi$
$419$	−0.721680	+	0.258221i	−0.0352564	+	0.0126149i	0.319203	+	0.947686i	$0.396585\pi$
$420$	0.705600	−	1.10452i	0.0344297	−	0.0538953i
$421$	8.40367	+	11.3310i	0.409570	+	0.552241i	0.959039	−	0.283273i	$-0.0914202\pi$
$421$	8.40367	+	11.3310i	0.409570	+	0.552241i	−0.549470	+	0.835514i	$0.685170\pi$
$422$	−1.35600	+	4.64145i	−0.0660092	+	0.225942i
$423$	2.59310	−	8.54831i	0.126081	−	0.415633i
$424$	3.72622	+	0.251238i	0.180961	+	0.0122012i
$425$	−4.34315	−	2.32146i	−0.210674	−	0.112607i
$426$	8.62456	−	3.67677i	0.417861	−	0.178140i
$427$	0.247936	+	5.04685i	0.0119985	+	0.244234i
$428$	0.524906	−	18.4004i	0.0253723	−	0.889418i
$429$	−7.85001	−	5.82196i	−0.379002	−	0.281087i
$430$	−0.970764	+	7.04263i	−0.0468144	+	0.339626i
$431$	−5.25351	−	1.04499i	−0.253053	−	0.0503353i	0.0669338	−	0.997757i	$-0.478678\pi$
$431$	−5.25351	−	1.04499i	−0.253053	−	0.0503353i	−0.319986	+	0.947422i	$0.603678\pi$
$432$	3.81841	+	1.19154i	0.183713	+	0.0573278i
$433$	6.18907	−	1.23108i	0.297428	−	0.0591620i	−0.0441208	−	0.999026i	$-0.514049\pi$
$433$	6.18907	−	1.23108i	0.297428	−	0.0591620i	0.341548	+	0.939864i	$0.389049\pi$
$434$	−14.3909	+	0.855412i	−0.690783	+	0.0410611i
$435$	−1.07669	+	0.645346i	−0.0516236	+	0.0309420i
$436$	−18.5039	+	21.2795i	−0.886175	+	1.01910i
$437$	−4.18737	+	1.98048i	−0.200309	+	0.0947391i
$438$	0.181147	−	0.277236i	0.00865554	−	0.0132468i
$439$	20.5225	+	25.0068i	0.979486	+	1.19351i	0.981099	+	0.193509i	$0.0619868\pi$
$439$	20.5225	+	25.0068i	0.979486	+	1.19351i	−0.00161214	+	0.999999i	$0.500513\pi$
$440$	−0.532923	−	2.96032i	−0.0254061	−	0.141128i
$441$	−0.510853	−	5.18678i	−0.0243263	−	0.246990i
$442$	4.23282	+	5.05088i	0.201335	+	0.240246i
$443$	29.3735	−	7.35769i	1.39558	−	0.349574i	0.529003	−	0.848620i	$-0.322566\pi$
$443$	29.3735	−	7.35769i	1.39558	−	0.349574i	0.866576	+	0.499046i	$0.166316\pi$
$444$	10.3906	+	2.91999i	0.493116	+	0.138576i
$445$	−4.61624	−	5.09323i	−0.218831	−	0.241442i
$446$	−0.557883	+	14.3700i	−0.0264165	+	0.680439i
$447$	−3.03713	−	3.03713i	−0.143651	−	0.143651i
$448$	10.6008	+	1.43604i	0.500842	+	0.0678463i
$449$	24.8265	−	24.8265i	1.17164	−	1.17164i	0.189818	−	0.981819i	$-0.439210\pi$
$449$	24.8265	−	24.8265i	1.17164	−	1.17164i	0.981819	−	0.189818i	$-0.0607897\pi$
$450$	−4.57159	−	4.94089i	−0.215507	−	0.232916i
$451$	15.2606	−	13.8314i	0.718595	−	0.651297i
$452$	−1.64097	−	13.7545i	−0.0771849	−	0.646959i
$453$	4.40168	+	17.5725i	0.206809	+	0.825628i
$454$	−1.68128	+	19.0799i	−0.0789063	+	0.895465i
$455$	2.93733	−	0.289302i	0.137704	−	0.0135627i
$456$	−7.22419	+	16.5791i	−0.338304	+	0.776385i
$457$	−18.9684	+	15.5669i	−0.887302	+	0.728190i	−0.963160	−	0.268929i	$-0.913330\pi$
$457$	−18.9684	+	15.5669i	−0.887302	+	0.728190i	0.0758581	+	0.997119i	$0.475830\pi$
$458$	−0.296387	−	1.41389i	−0.0138493	−	0.0660667i
$459$	−0.442360	−	0.935292i	−0.0206476	−	0.0436557i
$460$	−0.635524	+	0.316736i	−0.0296315	+	0.0147679i
$461$	−3.33196	−	5.55905i	−0.155185	−	0.258911i	0.770311	−	0.637669i	$-0.220101\pi$
$461$	−3.33196	−	5.55905i	−0.155185	−	0.258911i	−0.925496	+	0.378758i	$0.876351\pi$
$462$	3.06878	+	2.72442i	0.142772	+	0.126752i
$463$	−3.47520	−	17.4710i	−0.161506	−	0.811947i	−0.973572	−	0.228381i	$-0.926657\pi$
$463$	−3.47520	−	17.4710i	−0.161506	−	0.811947i	0.812066	−	0.583566i	$-0.198343\pi$
$464$	−8.47342	−	5.75973i	−0.393369	−	0.267389i
$465$	0.728850	−	3.66417i	0.0337996	−	0.169922i
$466$	−11.9705	−	15.7982i	−0.554522	−	0.731836i
$467$	−16.8262	+	22.6875i	−0.778623	+	1.04985i	0.218632	+	0.975807i	$0.429841\pi$
$467$	−16.8262	+	22.6875i	−0.778623	+	1.04985i	−0.997255	+	0.0740445i	$0.976409\pi$
$468$	3.20841	+	8.41699i	0.148309	+	0.389076i
$469$	−19.5312	+	0.959507i	−0.901868	+	0.0443059i
$470$	5.74397	+	2.31032i	0.264950	+	0.106567i
$471$	7.95257	−	14.8782i	0.366435	−	0.685552i
$472$	8.92332	+	2.40892i	0.410729	+	0.110879i
$473$	−21.3002	−	6.46135i	−0.979385	−	0.297093i
$474$	4.29252	+	7.83582i	0.197162	+	0.359911i
$475$	24.4446	−	18.1294i	1.12160	−	0.831833i
$476$	−1.58427	−	2.26859i	−0.0726148	−	0.103981i
$477$	−0.444832	−	1.24322i	−0.0203675	−	0.0569233i
$478$	5.45348	−	7.51344i	0.249436	−	0.343657i
$479$	14.7235	−	35.5456i	0.672733	−	1.62412i	−0.104213	−	0.994555i	$-0.533232\pi$
$479$	14.7235	−	35.5456i	0.672733	−	1.62412i	0.776946	−	0.629567i	$-0.216768\pi$
$480$	−1.05493	+	2.56373i	−0.0481507	+	0.117018i
$481$	9.30127	+	22.4553i	0.424102	+	1.02387i
$482$	−16.4590	−	3.94334i	−0.749688	−	0.179614i
$483$	0.414194	−	0.875740i	0.0188465	−	0.0398476i
$484$	−12.5797	+	0.258779i	−0.571805	+	0.0117627i
$485$	0.732966	−	4.94125i	0.0332823	−	0.224371i
$486$	−0.153083	−	1.40590i	−0.00694401	−	0.0637731i
$487$	−14.1352	−	26.4451i	−0.640528	−	1.19834i	−0.967395	−	0.253273i	$-0.918493\pi$
$487$	−14.1352	−	26.4451i	−0.640528	−	1.19834i	0.326867	−	0.945070i	$-0.394007\pi$
$488$	−2.40746	−	10.4132i	−0.108981	−	0.471382i
$489$	−0.743590	−	2.45129i	−0.0336263	−	0.110851i
$490$	3.61201	−	0.0371477i	0.163174	−	0.00167816i
$491$	−8.97367	−	8.13326i	−0.404976	−	0.367049i	0.443507	−	0.896271i	$-0.353734\pi$
$491$	−8.97367	−	8.13326i	−0.404976	−	0.367049i	−0.848484	+	0.529222i	$0.822484\pi$
$492$	−18.7160	+	3.17093i	−0.843780	+	0.142957i
$493$	0.388851	+	2.62142i	0.0175130	+	0.118063i
$494$	−39.4011	+	10.3012i	−1.77274	+	0.463474i
$495$	−0.884230	+	0.590824i	−0.0397432	+	0.0265556i
$496$	29.6371	−	7.17376i	1.33074	−	0.322111i
$497$	−7.37104	−	4.92517i	−0.330636	−	0.220924i
$498$	7.95006	−	22.9607i	0.356251	−	1.02889i
$499$	1.18707	−	4.73905i	0.0531406	−	0.212149i	−0.937644	−	0.347598i	$-0.886998\pi$
$499$	1.18707	−	4.73905i	0.0531406	−	0.212149i	0.990784	+	0.135449i	$0.0432475\pi$
$500$	7.56475	−	5.85535i	0.338306	−	0.261859i
$501$	14.2378	+	5.09436i	0.636098	+	0.227599i
$502$	6.12987	−	32.5636i	0.273589	−	1.45339i
$503$	30.7044	+	3.02412i	1.36904	+	0.134839i	0.755668	−	0.654955i	$-0.227312\pi$
$503$	30.7044	+	3.02412i	1.36904	+	0.134839i	0.613373	+	0.789794i	$0.289812\pi$
$504$	−1.03174	−	3.63875i	−0.0459571	−	0.162083i
$505$	4.09000	−	4.98368i	0.182003	−	0.221771i
$506$	−0.667214	−	2.12075i	−0.0296613	−	0.0942787i
$507$	−3.74520	+	6.24848i	−0.166330	+	0.277505i
$508$	−5.59992	−	6.54428i	−0.248456	−	0.290356i
$509$	−0.00866283	+	0.176336i	−0.000383973	+	0.00781595i	−0.998980	−	0.0451593i	$-0.985620\pi$
$509$	−0.00866283	+	0.176336i	−0.000383973	+	0.00781595i	0.998596	+	0.0529753i	$0.0168705\pi$
$510$	0.672634	−	0.248504i	0.0297847	−	0.0110040i
$511$	−0.313138			−0.0138524
$512$	−22.6060	+	0.983297i	−0.999055	+	0.0434560i
$513$	6.39388			0.282297
$514$	−2.66639	+	0.985097i	−0.117609	+	0.0434507i
$515$	−0.395712	+	8.05490i	−0.0174371	+	0.354941i
$516$	13.3380	+	15.5874i	0.587175	+	0.686195i
$517$	−9.96555	+	16.6265i	−0.438284	+	0.731233i
$518$	−3.06275	−	9.73497i	−0.134569	−	0.427730i
$519$	−2.96792	+	3.61642i	−0.130277	+	0.158743i
$520$	−6.00625	+	1.70302i	−0.263392	+	0.0746823i
$521$	−21.9498	−	2.16187i	−0.961639	−	0.0947131i	−0.395001	−	0.918681i	$-0.629256\pi$
$521$	−21.9498	−	2.16187i	−0.961639	−	0.0947131i	−0.566637	+	0.823967i	$0.691756\pi$
$522$	−0.670118	+	3.55986i	−0.0293303	+	0.155811i
$523$	4.68774	+	1.67730i	0.204981	+	0.0733433i	0.437378	−	0.899278i	$-0.355907\pi$
$523$	4.68774	+	1.67730i	0.204981	+	0.0733433i	−0.232398	+	0.972621i	$0.574657\pi$
$524$	−7.55124	+	5.84489i	−0.329878	+	0.255335i
$525$	−1.54654	+	6.17413i	−0.0674965	+	0.269461i
$526$	7.96219	−	22.9957i	0.347168	−	1.00266i
$527$	−6.55796	−	4.38189i	−0.285669	−	0.190878i
$528$	−7.40930	−	4.52142i	−0.322448	−	0.196770i
$529$	18.6874	−	12.4865i	0.812496	−	0.542893i
$530$	0.885379	−	0.231478i	0.0384584	−	0.0100548i
$531$	−0.479487	−	3.23244i	−0.0208080	−	0.140276i
$532$	16.8596	−	2.85643i	0.730958	−	0.123842i
$533$	−31.6740	−	28.7077i	−1.37196	−	1.24347i
$534$	−19.8350	+	0.203993i	−0.858345	+	0.00882763i
$535$	−1.30937	−	4.31641i	−0.0566089	−	0.186615i
$536$	40.2988	−	9.31683i	1.74064	−	0.402426i
$537$	−1.36002	−	2.54441i	−0.0586890	−	0.109799i
$538$	0.173490	+	1.59332i	0.00747969	+	0.0686927i
$539$	−1.65947	+	11.1873i	−0.0714786	+	0.481869i
$540$	0.979944	−	0.0201586i	0.0421701	−	0.000867487i
$541$	11.5938	−	24.5131i	0.498458	−	1.05390i	−0.485291	−	0.874353i	$-0.661286\pi$
$541$	11.5938	−	24.5131i	0.498458	−	1.05390i	0.983749	−	0.179548i	$-0.0574637\pi$
$542$	−9.65391	−	2.31294i	−0.414671	−	0.0993491i
$543$	3.55778	+	8.58924i	0.152679	+	0.368600i
$544$	4.14815	+	4.12884i	0.177851	+	0.177023i
$545$	−2.64432	+	6.38395i	−0.113270	+	0.273459i
$546$	5.00311	−	6.89295i	0.214113	−	0.294991i
$547$	7.89563	+	22.0668i	0.337593	+	0.943508i	0.983630	+	0.180202i	$0.0576752\pi$
$547$	7.89563	+	22.0668i	0.337593	+	0.943508i	−0.646037	+	0.763306i	$0.723575\pi$
$548$	21.2759	+	30.4661i	0.908863	+	1.30145i
$549$	−3.03510	+	2.25098i	−0.129535	+	0.0960697i
$550$	7.01782	+	12.8108i	0.299241	+	0.546252i
$551$	−15.6722	−	4.75410i	−0.667657	−	0.202531i
$552$	−0.534046	+	1.97826i	−0.0227305	+	0.0842003i
$553$	3.98237	−	7.45050i	0.169348	−	0.316827i
$554$	−11.7466	−	4.72468i	−0.499066	−	0.200732i
$555$	2.64153	−	0.129770i	0.112127	−	0.00550844i
$556$	−1.71538	−	4.50017i	−0.0727485	−	0.190850i
$557$	−15.5913	+	21.0224i	−0.660623	+	0.890748i	−0.998731	−	0.0503598i	$-0.983963\pi$
$557$	−15.5913	+	21.0224i	−0.660623	+	0.890748i	0.338108	+	0.941107i	$0.390213\pi$
$558$	−6.51087	−	8.59277i	−0.275627	−	0.363761i
$559$	−9.01293	+	45.3110i	−0.381206	+	1.91645i
$560$	2.57495	−	0.490939i	0.108811	−	0.0207460i
$561$	0.438001	+	2.20198i	0.0184924	+	0.0929677i
$562$	−27.9925	−	24.8514i	−1.18079	−	1.04829i
$563$	−3.63326	−	6.06172i	−0.153124	−	0.255471i	0.771602	−	0.636105i	$-0.219456\pi$
$563$	−3.63326	−	6.06172i	−0.153124	−	0.255471i	−0.924726	+	0.380634i	$0.875706\pi$
$564$	15.9901	−	7.96922i	0.673304	−	0.335565i
$565$	−1.45124	−	3.06840i	−0.0610543	−	0.129088i
$566$	−4.43582	−	21.1607i	−0.186451	−	0.889449i
$567$	−1.03368	+	0.848315i	−0.0434103	+	0.0356259i
$568$	17.1901	+	7.49045i	0.721281	+	0.314293i
$569$	−32.1867	+	3.17011i	−1.34934	+	0.132898i	−0.746723	−	0.665135i	$-0.768374\pi$
$569$	−32.1867	+	3.17011i	−1.34934	+	0.132898i	−0.602613	+	0.798033i	$0.705874\pi$
$570$	−0.388979	+	4.41432i	−0.0162925	+	0.184895i
$571$	−8.61203	−	34.3811i	−0.360402	−	1.43881i	−0.830908	−	0.556409i	$-0.812179\pi$
$571$	−8.61203	−	34.3811i	−0.360402	−	1.43881i	0.470506	−	0.882397i	$-0.344071\pi$
$572$	−2.31558	−	19.4090i	−0.0968192	−	0.811531i
$573$	4.33584	−	3.92978i	0.181132	−	0.164169i
$574$	12.1900	+	13.1747i	0.508799	+	0.549901i
$575$	2.43831	−	2.43831i	0.101685	−	0.101685i
$576$	3.51141	+	7.18818i	0.146309	+	0.299508i
$577$	10.1687	+	10.1687i	0.423329	+	0.423329i	0.886348	−	0.463019i	$-0.153234\pi$
$577$	10.1687	+	10.1687i	0.423329	+	0.423329i	−0.463019	+	0.886348i	$0.653234\pi$
$578$	−0.873932	+	22.5108i	−0.0363508	+	0.936327i
$579$	3.82665	+	4.22206i	0.159030	+	0.175463i
$580$	−2.41695	−	0.679215i	−0.100358	−	0.0282029i
$581$	−22.2864	+	5.58246i	−0.924598	+	0.231600i
$582$	−9.25890	−	11.0483i	−0.383794	−	0.457968i
$583$	0.280845	+	2.85146i	0.0116314	+	0.118096i
$584$	0.651862	−	0.117350i	0.0269743	−	0.00485597i
$585$	1.40026	+	1.70622i	0.0578936	+	0.0705436i
$586$	−19.4590	+	29.7809i	−0.803842	+	1.23024i
$587$	4.53140	−	2.14319i	0.187031	−	0.0884591i	−0.331746	−	0.943369i	$-0.607638\pi$
$587$	4.53140	−	2.14319i	0.187031	−	0.0884591i	0.518777	+	0.854910i	$0.326388\pi$
$588$	6.83984	−	7.86583i	0.282070	−	0.324381i
$589$	41.8074	−	25.0584i	1.72265	−	1.03251i
$590$	2.26084	−	0.134387i	0.0930771	−	0.00553263i
$591$	3.49431	−	0.695060i	0.143737	−	0.0285910i
$592$	10.0240	+	19.1176i	0.411983	+	0.785730i
$593$	4.18164	+	0.831780i	0.171719	+	0.0341571i	0.280201	−	0.959941i	$-0.409599\pi$
$593$	4.18164	+	0.831780i	0.171719	+	0.0341571i	−0.108482	+	0.994098i	$0.534599\pi$
$594$	−0.419047	+	3.04007i	−0.0171937	+	0.124736i
$595$	−0.544595	−	0.403899i	−0.0223262	−	0.0165582i
$596$	0.244955	−	8.58681i	0.0100337	−	0.351729i
$597$	0.571591	+	11.6350i	0.0233937	+	0.476189i
$598$	−4.24476	+	1.80960i	−0.173581	+	0.0740001i
$599$	−8.94817	−	4.78289i	−0.365612	−	0.195424i	0.278353	−	0.960479i	$-0.410212\pi$
$599$	−8.94817	−	4.78289i	−0.365612	−	0.195424i	−0.643965	+	0.765055i	$0.722712\pi$
$600$	0.905665	−	13.4323i	0.0369736	−	0.548372i
$601$	−4.30962	+	14.2069i	−0.175793	+	0.579512i	0.824121	+	0.566414i	$0.191670\pi$
$601$	−4.30962	+	14.2069i	−0.175793	+	0.579512i	−0.999914	+	0.0130985i	$0.995830\pi$
$602$	5.43975	−	18.6197i	0.221708	−	0.758881i
$603$	−8.71126	−	11.7458i	−0.354750	−	0.478325i
$604$	−19.5049	+	30.5324i	−0.793644	+	1.24235i
$605$	−2.90293	+	1.03868i	−0.118021	+	0.0422285i
$606$	−2.91895	−	18.3740i	−0.118574	−	0.746394i
$607$	30.5806	+	12.6669i	1.24123	+	0.514133i	0.904098	−	0.427325i	$-0.140544\pi$
$607$	30.5806	+	12.6669i	1.24123	+	0.514133i	0.337129	+	0.941458i	$0.390544\pi$
$608$	−34.0264	+	12.2645i	−1.37995	+	0.497390i
$609$	3.16442	−	1.31074i	0.128229	−	0.0531140i
$610$	−1.36943	−	2.23237i	−0.0554465	−	0.0903858i
$611$	36.3702	+	17.2018i	1.47138	+	0.695911i
$612$	0.752383	−	1.92762i	0.0304133	−	0.0779195i
$613$	−12.3874	−	1.83750i	−0.500324	−	0.0742161i	−0.108201	−	0.994129i	$-0.534509\pi$
$613$	−12.3874	−	1.83750i	−0.500324	−	0.0742161i	−0.392123	+	0.919913i	$0.628259\pi$
$614$	−20.9914	−	16.8690i	−0.847145	−	0.680776i
$615$	−4.10223	+	2.19269i	−0.165418	+	0.0884178i
$616$	0.253174	+	8.20338i	0.0102007	+	0.330524i
$617$	−44.8890	+	13.6169i	−1.80716	+	0.548197i	−0.999160	−	0.0409831i	$-0.986951\pi$
$617$	−44.8890	+	13.6169i	−1.80716	+	0.548197i	−0.808002	+	0.589180i	$0.799451\pi$
$618$	16.6242	+	16.2857i	0.668724	+	0.655109i
$619$	27.7734	−	30.6432i	1.11631	−	1.23165i	0.146126	−	0.989266i	$-0.453319\pi$
$619$	27.7734	−	30.6432i	1.11631	−	1.23165i	0.970179	−	0.242388i	$-0.0779306\pi$
$620$	6.32852	−	3.97233i	0.254159	−	0.159533i
$621$	0.716617	−	0.106300i	0.0287568	−	0.00426568i
$622$	0.963361	−	1.64541i	0.0386273	−	0.0659750i
$623$	10.4203	+	15.5950i	0.417479	+	0.624801i
$624$	−7.83187	+	16.2241i	−0.313526	+	0.649483i
$625$	−11.9198	+	17.8392i	−0.476792	+	0.713570i
$626$	36.4519	−	17.7015i	1.45691	−	0.707493i
$627$	−13.4588	−	3.37125i	−0.537492	−	0.134635i
$628$	32.5537	−	8.86966i	1.29904	−	0.353938i
$629$	1.88100	−	5.25703i	0.0750002	−	0.209612i
$630$	−0.522789	−	0.765254i	−0.0208284	−	0.0304885i
$631$	0.915328	−	9.29348i	0.0364386	−	0.369967i	−0.959622	−	0.281293i	$-0.909237\pi$
$631$	0.915328	−	9.29348i	0.0364386	−	0.369967i	0.996061	−	0.0886748i	$-0.0282632\pi$
$632$	−5.49805	+	17.0022i	−0.218701	+	0.676311i
$633$	2.64307	+	2.16911i	0.105053	+	0.0862145i
$634$	16.0478	−	30.7805i	0.637338	−	1.22245i
$635$	−1.81028	−	1.08504i	−0.0718388	−	0.0430585i
$636$	1.19671	−	2.35410i	0.0474526	−	0.0933463i
$637$	23.4454	+	1.15180i	0.928940	+	0.0456359i
$638$	3.28754	−	7.13999i	0.130155	−	0.282675i
$639$		−	6.62954i		−	0.262261i
$640$	−5.17632	+	1.98697i	−0.204612	+	0.0785418i
$641$			25.9476i			1.02487i	0.858726	+	0.512435i	$0.171256\pi$
$641$			25.9476i			1.02487i	−0.858726	+	0.512435i	$0.828744\pi$
$642$	−11.8233	−	5.44390i	−0.466626	−	0.214854i
$643$	−14.5652	−	0.715544i	−0.574397	−	0.0282183i	−0.240203	−	0.970723i	$-0.577214\pi$
$643$	−14.5652	−	0.715544i	−0.574397	−	0.0282183i	−0.334194	+	0.942504i	$0.608464\pi$
$644$	1.84211	−	0.600440i	0.0725895	−	0.0236607i
$645$	4.31178	+	2.58438i	0.169776	+	0.101760i
$646$	8.29566	+	4.32503i	0.326388	+	0.170166i
$647$	19.0323	+	15.6194i	0.748238	+	0.614063i	0.929264	−	0.369416i	$-0.120442\pi$
$647$	19.0323	+	15.6194i	0.748238	+	0.614063i	−0.181027	+	0.983478i	$0.557942\pi$
$648$	1.83390	−	2.15332i	0.0720425	−	0.0845905i
$649$	−0.695047	+	7.05693i	−0.0272830	+	0.277009i
$650$	25.0335	−	17.1018i	0.981894	−	0.670789i
$651$	−3.43420	+	9.59795i	−0.134597	+	0.376173i
$652$	2.54291	−	4.44754i	0.0995879	−	0.174179i
$653$	15.0918	+	3.78031i	0.590589	+	0.147935i	0.526742	−	0.850025i	$-0.323413\pi$
$653$	15.0918	+	3.78031i	0.590589	+	0.147935i	0.0638463	+	0.997960i	$0.479663\pi$
$654$	8.71039	+	17.9370i	0.340603	+	0.701391i
$655$	−1.29997	+	1.94554i	−0.0507938	+	0.0760184i
$656$	−30.3133	−	22.8577i	−1.18353	−	0.892442i
$657$	−0.130099	−	0.194708i	−0.00507566	−	0.00759627i
$658$	−14.5782	−	8.53532i	−0.568319	−	0.332741i
$659$	−0.0424980	+	0.00630398i	−0.00165549	+	0.000245568i	−0.147558	−	0.989053i	$-0.547141\pi$
$659$	−0.0424980	+	0.00630398i	−0.00165549	+	0.000245568i	0.145903	+	0.989299i	$0.453391\pi$
$660$	−2.07336	−	0.474255i	−0.0807055	−	0.0184603i
$661$	1.20933	−	1.33429i	0.0470374	−	0.0518977i	−0.716978	−	0.697096i	$-0.754475\pi$
$661$	1.20933	−	1.33429i	0.0470374	−	0.0518977i	0.764015	+	0.645198i	$0.223225\pi$
$662$	−21.5291	+	21.9765i	−0.836752	+	0.854142i
$663$	4.45918	−	1.35268i	0.173180	−	0.0525337i
$664$	44.3019	−	19.9730i	1.71925	−	0.775104i
$665$	3.69536	−	1.97521i	0.143300	−	0.0765954i
$666$	4.78068	−	5.94900i	0.185248	−	0.230519i
$667$	−1.83555	−	0.272278i	−0.0710728	−	0.0105427i
$668$	12.1459	+	27.6974i	0.469939	+	1.07164i
$669$	9.19247	+	4.34771i	0.355401	+	0.168092i
$670$	8.63921	−	5.29966i	0.333762	−	0.204744i
$671$	7.57559	−	3.13791i	0.292452	−	0.121138i
$672$	3.87372	−	6.49725i	0.149432	−	0.250637i
$673$	3.63090	+	1.50397i	0.139961	+	0.0579737i	0.451565	−	0.892238i	$-0.350866\pi$
$673$	3.63090	+	1.50397i	0.139961	+	0.0579737i	−0.311604	+	0.950212i	$0.600866\pi$
$674$	0.135927	−	0.0215937i	0.00523569	−	0.000831757i
$675$	−4.48159	+	1.60354i	−0.172496	+	0.0617202i
$676$	−14.2284	+	3.13573i	−0.547246	+	0.120605i
$677$	11.1103	+	14.9805i	0.427003	+	0.575747i	0.963349	−	0.268251i	$-0.0864457\pi$
$677$	11.1103	+	14.9805i	0.427003	+	0.575747i	−0.536346	+	0.843998i	$0.680196\pi$
$678$	−9.40187	−	2.74676i	−0.361077	−	0.105489i
$679$	−3.95661	+	13.0432i	−0.151841	+	0.500551i
$680$	1.28505	+	0.636712i	0.0492795	+	0.0244168i
$681$	11.9446	+	6.38452i	0.457718	+	0.244655i
$682$	9.17440	+	21.5203i	0.351306	+	0.824054i
$683$	0.685421	+	13.9521i	0.0262269	+	0.533861i	0.975579	+	0.219648i	$0.0704908\pi$
$683$	0.685421	+	13.9521i	0.0262269	+	0.533861i	−0.949352	+	0.314213i	$0.898259\pi$
$684$	8.78079	+	9.29648i	0.335742	+	0.355460i
$685$	7.31365	+	5.42417i	0.279440	+	0.207247i
$686$	−22.8775	−	3.15347i	−0.873468	−	0.120400i
$687$	−1.00187	−	0.199285i	−0.0382238	−	0.00760319i
$688$	−4.34619	+	40.7994i	−0.165697	+	1.55546i
$689$	5.83269	−	1.16019i	0.222208	−	0.0441999i
$690$	0.0297930	+	0.501217i	0.00113420	+	0.0190810i
$691$	12.4101	−	7.43834i	0.472103	−	0.282968i	−0.258199	−	0.966092i	$-0.583129\pi$
$691$	12.4101	−	7.43834i	0.472103	−	0.282968i	0.730303	+	0.683124i	$0.239379\pi$
$692$	−9.33402	+	0.651220i	−0.354826	+	0.0247557i
$693$	2.62312	−	1.24064i	0.0996440	−	0.0471281i
$694$	−39.8177	−	26.0170i	−1.51146	−	0.987594i
$695$	−0.748652	−	0.912235i	−0.0283980	−	0.0346031i
$696$	−6.09619	+	3.91447i	−0.231076	+	0.148378i
$697$	0.962527	+	9.77270i	0.0364583	+	0.370168i
$698$	3.57087	−	2.99252i	0.135160	−	0.113269i
$699$	−13.5956	+	3.40551i	−0.514232	+	0.128808i
$700$	−11.1008	+	6.23039i	−0.419572	+	0.235487i
$701$	12.4224	+	13.7060i	0.469188	+	0.517669i	0.928866	−	0.370417i	$-0.120785\pi$
$701$	12.4224	+	13.7060i	0.469188	+	0.517669i	−0.459678	+	0.888086i	$0.652035\pi$
$702$	6.36465	+	0.247093i	0.240218	+	0.00932593i
$703$	24.3986	+	24.3986i	0.920212	+	0.920212i
$704$	−3.60129	−	16.9822i	−0.135729	−	0.640040i
$705$	3.09559	−	3.09559i	0.116587	−	0.116587i
$706$	10.7337	−	9.93139i	0.403967	−	0.373773i
$707$	−13.0344	+	11.8137i	−0.490208	+	0.444299i
$708$	4.04137	−	5.13630i	0.151884	−	0.193034i
$709$	9.72482	+	38.8236i	0.365223	+	1.45805i	0.822519	+	0.568738i	$0.192568\pi$
$709$	9.72482	+	38.8236i	0.365223	+	1.45805i	−0.457296	+	0.889315i	$0.651182\pi$
$710$	4.57701	+	0.403316i	0.171772	+	0.0151362i
$711$	6.28725	−	0.619240i	0.235790	−	0.0232233i
$712$	−27.5363	−	28.5593i	−1.03197	−	1.07030i
$713$	4.26911	−	3.50357i	0.159880	−	0.131210i
$714$	−1.91496	+	0.401424i	−0.0716655	+	0.0150229i
$715$	−2.04785	−	4.32981i	−0.0765852	−	0.161926i
$716$	1.83176	−	5.47168i	0.0684560	−	0.204486i
$717$	−3.37496	−	5.63078i	−0.126040	−	0.210285i
$718$	−16.6547	+	18.7598i	−0.621549	+	0.700111i
$719$	−10.3147	−	51.8555i	−0.384673	−	1.93388i	−0.356540	−	0.934280i	$-0.616044\pi$
$719$	−10.3147	−	51.8555i	−0.384673	−	1.93388i	−0.0281333	−	0.999604i	$-0.508956\pi$
$720$	1.37508	+	1.39712i	0.0512462	+	0.0520676i
$721$	4.29294	−	21.5821i	0.159877	−	0.803758i
$722$	−24.6647	+	18.6888i	−0.917926	+	0.695526i
$723$	−7.12912	+	9.61251i	−0.265135	+	0.357493i
$724$	−7.60251	+	16.9686i	−0.282545	+	0.630633i
$725$	12.1772	−	0.598227i	0.452249	−	0.0222176i
$726$	−3.32005	+	8.25441i	−0.123219	+	0.306350i
$727$	12.1607	−	22.7510i	0.451014	−	0.843788i	−0.548954	−	0.835852i	$-0.684974\pi$
$727$	12.1607	−	22.7510i	0.451014	−	0.843788i	0.999969	−	0.00793604i	$-0.00252615\pi$
$728$	16.8929	−	2.19182i	0.626094	−	0.0812344i
$729$	−0.956940	−	0.290285i	−0.0354422	−	0.0107513i
$730$	0.142340	−	0.0779750i	0.00526825	−	0.00288598i
$731$	8.52423	−	6.32200i	0.315280	−	0.233828i
$732$	−7.44099	−	1.32163i	−0.275027	−	0.0488488i
$733$	−1.47209	−	4.11421i	−0.0543728	−	0.151962i	0.911287	−	0.411772i	$-0.135090\pi$
$733$	−1.47209	−	4.11421i	−0.0543728	−	0.151962i	−0.965660	+	0.259810i	$0.916340\pi$
$734$	−31.7288	−	23.0297i	−1.17113	−	0.850041i
$735$	0.977456	−	2.35979i	0.0360540	−	0.0870421i
$736$	−3.60973	+	1.94028i	−0.133056	+	0.0715198i
$737$	12.1437	+	29.3174i	0.447317	+	1.07992i
$738$	−3.12739	+	13.0534i	−0.115121	+	0.480501i
$739$	−16.0824	+	34.0034i	−0.591602	+	1.25084i	0.356923	+	0.934134i	$0.383826\pi$
$739$	−16.0824	+	34.0034i	−0.591602	+	1.25084i	−0.948525	+	0.316703i	$0.897424\pi$
$740$	3.81633	+	3.66248i	0.140291	+	0.134635i
$741$	−4.22544	+	28.4856i	−0.155225	+	1.04644i
$742$	−2.48235	+	0.270293i	−0.0911299	+	0.00992278i
$743$	16.2015	+	30.3110i	0.594377	+	1.11200i	0.981767	+	0.190086i	$0.0608766\pi$
$743$	16.2015	+	30.3110i	0.594377	+	1.11200i	−0.387390	+	0.921916i	$0.626623\pi$
$744$	3.55214	−	21.2671i	0.130228	−	0.779691i
$745$	−0.611035	−	2.01431i	−0.0223866	−	0.0737987i
$746$	0.385350	+	37.4691i	0.0141087	+	1.37184i
$747$	−12.7305	−	11.5383i	−0.465785	−	0.422163i
$748$	−2.60009	+	3.66084i	−0.0950687	+	0.133854i
$749$	1.80590	+	12.1744i	0.0659861	+	0.444842i
$750$	−1.71097	−	6.54430i	−0.0624759	−	0.238964i
$751$	7.81963	−	5.22491i	0.285343	−	0.190660i	−0.404659	−	0.914468i	$-0.632610\pi$
$751$	7.81963	−	5.22491i	0.285343	−	0.190660i	0.690002	+	0.723808i	$0.257610\pi$
$752$	33.5463	+	12.3048i	1.22331	+	0.448710i
$753$	−19.4816	−	13.0172i	−0.709951	−	0.474374i
$754$	−15.4168	−	5.33802i	−0.561446	−	0.194399i
$755$	−2.15716	+	8.61186i	−0.0785070	+	0.313418i
$756$	−2.65298	−	0.337926i	−0.0964879	−	0.0122903i
$757$	19.3248	+	6.91451i	0.702371	+	0.251312i	0.663764	−	0.747942i	$-0.268958\pi$
$757$	19.3248	+	6.91451i	0.702371	+	0.251312i	0.0386069	+	0.999254i	$0.487708\pi$
$758$	19.8957	+	3.74521i	0.722643	+	0.136032i
$759$	−1.56449	−	0.154089i	−0.0567874	−	0.00559307i
$760$	−6.95245	+	5.49667i	−0.252192	+	0.199385i
$761$	2.49148	−	3.03588i	0.0903160	−	0.110050i	−0.725892	−	0.687809i	$-0.758573\pi$
$761$	2.49148	−	3.03588i	0.0903160	−	0.110050i	0.816208	+	0.577759i	$0.196073\pi$
$762$	−5.80969	+	1.82780i	−0.210463	+	0.0662143i
$763$	9.69303	−	16.1719i	0.350911	−	0.585460i
$764$	11.6682	+	0.907353i	0.422142	+	0.0328269i
$765$	0.0248795	−	0.506435i	0.000899522	−	0.0183102i
$766$	11.2029	+	30.3232i	0.404778	+	1.09562i
$767$	14.7178			0.531429
$768$	−5.62910	+	14.9771i	−0.203123	+	0.540439i
$769$	−3.29973			−0.118991			−0.0594957	−	0.998229i	$-0.518949\pi$
$769$	−3.29973			−0.118991			−0.0594957	+	0.998229i	$0.518949\pi$
$770$	0.696955	+	1.88647i	0.0251165	+	0.0679836i
$771$	−0.0986251	+	2.00756i	−0.00355190	+	0.0723005i
$772$	−0.883542	+	11.3620i	−0.0317994	+	0.408928i
$773$	−16.3359	+	27.2549i	−0.587563	+	0.980290i	0.410105	+	0.912038i	$0.365492\pi$
$773$	−16.3359	+	27.2549i	−0.587563	+	0.980290i	−0.997668	+	0.0682516i	$0.978258\pi$
$774$	13.8377	−	4.35351i	0.497385	−	0.156484i
$775$	−23.0191	+	28.0489i	−0.826871	+	1.00755i
$776$	3.34852	−	28.6349i	0.120205	−	1.02793i
$777$	−7.18156	−	0.707322i	−0.257637	−	0.0253750i
$778$	−9.05512	−	1.70456i	−0.324642	−	0.0611115i
$779$	−57.1390	−	20.4447i	−2.04722	−	0.732506i
$780$	−0.557793	+	4.37910i	−0.0199722	+	0.156797i
$781$	−3.49551	+	13.9548i	−0.125079	+	0.499344i
$782$	1.00167	+	0.346826i	0.0358197	+	0.0124025i
$783$	2.12974	+	1.42304i	0.0761106	+	0.0508555i
$784$	20.8299	−	0.857351i	0.743924	−	0.0306197i
$785$	6.87433	−	4.59328i	0.245355	−	0.163941i
$786$	1.70792	+	6.53261i	0.0609195	+	0.233011i
$787$	0.961153	+	6.47957i	0.0342614	+	0.230972i	0.999543	−	0.0302412i	$-0.00962755\pi$
$787$	0.961153	+	6.47957i	0.0342614	+	0.230972i	−0.965281	+	0.261213i	$0.915878\pi$
$788$	5.80936	+	4.12606i	0.206950	+	0.146985i
$789$	−12.7499	−	11.5559i	−0.453910	−	0.411400i
$790$	0.0450292	+	4.37837i	0.00160207	+	0.155775i
$791$	2.68849	+	8.86275i	0.0955915	+	0.315123i
$792$	−4.99564	+	3.56568i	−0.177512	+	0.126701i
$793$	−8.02266	−	15.0093i	−0.284893	−	0.532998i
$794$	−39.0931	+	4.25670i	−1.38736	+	0.151065i
$795$	0.0949493	−	0.640096i	0.00336751	−	0.0227019i
$796$	−16.1319	+	16.8096i	−0.571781	+	0.595799i
$797$	−19.9572	+	42.1959i	−0.706920	+	1.49466i	0.155164	+	0.987889i	$0.450410\pi$
$797$	−19.9572	+	42.1959i	−0.706920	+	1.49466i	−0.862083	+	0.506767i	$0.830840\pi$
$798$	2.81721	−	11.7587i	0.0997280	−	0.416253i
$799$	−3.53687	−	8.53876i	−0.125125	−	0.302079i
$800$	20.7739	−	17.1300i	0.734468	−	0.605636i
$801$	−5.36760	+	12.9585i	−0.189655	+	0.457867i
$802$	−21.7696	−	15.8010i	−0.768712	−	0.557954i
$803$	0.171191	+	0.478446i	0.00604119	+	0.0168840i
$804$	5.11467	−	28.7965i	0.180381	−	1.01557i
$805$	0.381332	−	0.282815i	0.0134402	−	0.00996792i
$806$	42.5847	−	23.3282i	1.49998	−	0.821700i
$807$	1.08450	+	0.328981i	0.0381763	+	0.0115807i
$808$	22.7066	−	29.4773i	0.798815	−	1.03701i
$809$	−16.5348	+	30.9344i	−0.581333	+	1.08760i	0.403645	+	0.914916i	$0.367743\pi$
$809$	−16.5348	+	30.9344i	−0.581333	+	1.08760i	−0.984978	+	0.172681i	$0.944757\pi$
$810$	0.258628	−	0.643009i	0.00908727	−	0.0225930i
$811$	28.1416	−	1.38251i	0.988186	−	0.0485464i	0.451450	−	0.892297i	$-0.350907\pi$
$811$	28.1416	−	1.38251i	0.988186	−	0.0485464i	0.536736	+	0.843750i	$0.319657\pi$
$812$	6.25151	+	2.80089i	0.219385	+	0.0982920i
$813$	−4.18153	+	5.63814i	−0.146653	+	0.197738i
$814$	−13.1998	+	10.0017i	−0.462652	+	0.350558i
$815$	0.244911	−	1.23125i	0.00857886	−	0.0431289i
$816$	3.83595	−	1.55329i	0.134285	−	0.0543760i
$817$	12.7951	+	64.3253i	0.447644	+	2.25046i
$818$	12.4490	−	14.0225i	0.435269	−	0.490285i
$819$	−3.09624	−	5.16577i	−0.108192	−	0.180507i
$820$	−8.82174	−	2.95326i	−0.308069	−	0.103132i
$821$	−13.1445	−	27.7918i	−0.458747	−	0.969939i	−0.992264	−	0.124150i	$-0.960380\pi$
$821$	−13.1445	−	27.7918i	−0.458747	−	0.969939i	0.533516	−	0.845790i	$-0.320870\pi$
$822$	25.7170	−	5.39093i	0.896982	−	0.188030i
$823$	−30.1125	+	24.7127i	−1.04965	+	0.861429i	−0.990595	−	0.136825i	$-0.956310\pi$
$823$	−30.1125	+	24.7127i	−1.04965	+	0.861429i	−0.0590595	+	0.998254i	$0.518810\pi$
$824$	−0.848687	+	46.5364i	−0.0295654	+	1.62117i
$825$	10.2790	−	1.01239i	0.357869	−	0.0352470i
$826$	−6.15589	−	0.542443i	−0.214191	−	0.0188740i
$827$	8.49580	+	33.9171i	0.295428	+	1.17941i	0.917913	+	0.396782i	$0.129873\pi$
$827$	8.49580	+	33.9171i	0.295428	+	1.17941i	−0.622485	+	0.782632i	$0.713877\pi$
$828$	1.13870	+	0.895953i	0.0395724	+	0.0311365i
$829$	−30.2129	+	27.3834i	−1.04934	+	0.951065i	−0.998864	−	0.0476602i	$-0.984824\pi$
$829$	−30.2129	+	27.3834i	−1.04934	+	0.951065i	−0.0504751	+	0.998725i	$0.516074\pi$
$830$	8.74046	−	8.08716i	0.303386	−	0.280709i
$831$	−6.33060	+	6.33060i	−0.219606	+	0.219606i
$832$	−34.3448	+	10.8934i	−1.19069	+	0.377662i
$833$	−3.81297	−	3.81297i	−0.132111	−	0.132111i
$834$	−3.40288	−	0.132109i	−0.117832	−	0.00457456i
$835$	4.97679	+	5.49104i	0.172229	+	0.190025i
$836$	−13.5814	−	24.1984i	−0.469724	−	0.836919i
$837$	−7.39477	+	1.85229i	−0.255601	+	0.0640246i
$838$	−0.830807	+	0.696247i	−0.0286998	+	0.0240514i
$839$	2.92727	+	29.7210i	0.101060	+	1.02608i	0.903279	+	0.429053i	$0.141153\pi$
$839$	2.92727	+	29.7210i	0.101060	+	1.02608i	−0.802219	+	0.597030i	$0.796347\pi$
$840$	0.394700	−	1.81105i	0.0136185	−	0.0624872i
$841$	14.2353	+	17.3457i	0.490871	+	0.598128i
$842$	16.7015	+	10.9128i	0.575570	+	0.376080i
$843$	−23.9273	+	11.3168i	−0.824100	+	0.389770i
$844$	0.475947	+	6.82181i	0.0163828	+	0.234816i
$845$	−3.06223	+	1.83543i	−0.105344	+	0.0631407i
$846$	−0.749607	−	12.6109i	−0.0257720	−	0.433570i
$847$	8.25097	−	1.64122i	0.283507	−	0.0563930i
$848$	5.06624	−	1.49294i	0.173975	−	0.0512679i
$849$	−14.9943	−	2.98255i	−0.514603	−	0.102361i
$850$	−6.89926	−	0.951003i	−0.236643	−	0.0326191i
$851$	3.14020	+	2.32893i	0.107645	+	0.0798347i
$852$	9.63912	−	9.10443i	0.330231	−	0.311913i
$853$	−2.52101	−	51.3164i	−0.0863179	−	1.75704i	−0.518337	−	0.855177i	$-0.673449\pi$
$853$	−2.52101	−	51.3164i	−0.0863179	−	1.75704i	0.432019	−	0.901865i	$-0.357801\pi$
$854$	2.80238	+	6.57351i	0.0958955	+	0.224941i
$855$	2.76349	+	1.47712i	0.0945093	+	0.0505163i
$856$	−8.32176	−	24.6668i	−0.284432	−	0.843093i
$857$	2.11725	−	6.97963i	0.0723238	−	0.238420i	−0.913324	−	0.407233i	$-0.866494\pi$
$857$	2.11725	−	6.97963i	0.0723238	−	0.238420i	0.985648	+	0.168814i	$0.0539936\pi$
$858$	−13.2670	−	3.87596i	−0.452927	−	0.132323i
$859$	−4.55946	−	6.14772i	−0.155567	−	0.209758i	0.718547	−	0.695478i	$-0.244807\pi$
$859$	−4.55946	−	6.14772i	−0.155567	−	0.209758i	−0.874114	+	0.485720i	$0.838557\pi$
$860$	2.16382	+	9.81834i	0.0737856	+	0.334803i
$861$	11.9500	−	4.27577i	0.407254	−	0.145718i
$862$	−7.48132	+	1.18850i	−0.254815	+	0.0404806i
$863$	21.0631	+	8.72461i	0.716996	+	0.296989i	0.711196	−	0.702994i	$-0.248154\pi$
$863$	21.0631	+	8.72461i	0.716996	+	0.296989i	0.00579976	+	0.999983i	$0.498154\pi$
$864$	5.64938	−	0.290751i	0.192196	−	0.00989154i
$865$	−2.11822	+	0.877397i	−0.0720217	+	0.0298324i
$866$	7.60690	−	4.66640i	0.258493	−	0.158571i
$867$	14.4001	+	6.81076i	0.489054	+	0.231306i
$868$	−18.6713	+	8.18776i	−0.633745	+	0.277911i
$869$	−13.5608	−	2.01156i	−0.460020	−	0.0682375i
$870$	−1.11203	+	1.38379i	−0.0377013	+	0.0469149i
$871$	58.0859	−	31.0475i	1.96816	−	1.05201i
$872$	−14.1176	+	37.2976i	−0.478083	+	1.26306i
$873$	−9.75405	+	2.95886i	−0.330125	+	0.100142i
$874$	−4.58422	+	4.67949i	−0.155064	+	0.158286i
$875$	−4.29525	+	4.73908i	−0.145206	+	0.160210i
$876$	0.104431	−	0.456554i	0.00352840	−	0.0154255i
$877$	−49.4642	+	7.33732i	−1.67029	+	0.247764i	−0.913777	−	0.406217i	$-0.866848\pi$
$877$	−49.4642	+	7.33732i	−1.67029	+	0.247764i	−0.756511	+	0.653981i	$0.773098\pi$
$878$	39.4805	+	23.1152i	1.33240	+	0.780100i
$879$	13.9754	+	20.9157i	0.471378	+	0.705468i
$880$	−2.15782	−	3.66589i	−0.0727401	−	0.123577i
$881$	−5.60965	+	8.39544i	−0.188994	+	0.282849i	−0.913851	−	0.406050i	$-0.866906\pi$
$881$	−5.60965	+	8.39544i	−0.188994	+	0.282849i	0.724857	+	0.688899i	$0.241906\pi$
$882$	−3.21974	−	6.63028i	−0.108414	−	0.223253i
$883$	21.4710	+	5.37821i	0.722557	+	0.180991i	0.586778	−	0.809748i	$-0.300396\pi$
$883$	21.4710	+	5.37821i	0.722557	+	0.180991i	0.135779	+	0.990739i	$0.456646\pi$
$884$	8.09059	+	4.62585i	0.272116	+	0.155584i
$885$	0.539520	−	1.50786i	0.0181358	−	0.0506861i
$886$	35.3602	−	24.1566i	1.18795	−	0.811556i
$887$	2.92854	−	29.7339i	0.0983307	−	0.998368i	−0.811769	−	0.583979i	$-0.801495\pi$
$887$	2.92854	−	29.7339i	0.0983307	−	0.998368i	0.910100	−	0.414389i	$-0.136005\pi$
$888$	15.2150	−	1.21888i	0.510582	−	0.0409030i
$889$	4.45161	+	3.65334i	0.149302	+	0.122529i
$890$	−8.61999	−	4.49412i	−0.288943	−	0.150643i
$891$	1.86125	+	1.11559i	0.0623544	+	0.0373738i
$892$	6.30270	+	19.3363i	0.211030	+	0.647427i
$893$	57.0475	+	2.80256i	1.90902	+	0.0937843i
$894$	−5.51749	−	2.54047i	−0.184532	−	0.0849662i
$895$		−	1.41391i		−	0.0472617i
$896$	14.7666	−	3.29049i	0.493317	−	0.109927i
$897$			3.26287i			0.108944i
$898$	20.7667	−	45.1018i	0.692994	−	1.50507i
$899$	19.5027	+	0.958107i	0.650452	+	0.0319546i
$900$	−8.48610	−	4.31391i	−0.282870	−	0.143797i
$901$	−1.17177	−	0.702331i	−0.0390373	−	0.0233980i
$902$	13.4655	−	25.8277i	0.448354	−	0.859968i
$903$	−10.6030	−	8.70163i	−0.352845	−	0.289572i
$904$	−8.91800	−	17.4422i	−0.296608	−	0.580118i
$905$	−0.446586	+	4.53426i	−0.0148450	+	0.150724i
$906$	14.4515	+	21.1539i	0.480118	+	0.702793i
$907$	−10.5446	+	29.4701i	−0.350127	+	0.978539i	0.629375	+	0.777102i	$0.283311\pi$
$907$	−10.5446	+	29.4701i	−0.350127	+	0.978539i	−0.979501	+	0.201437i	$0.935439\pi$
$908$	7.12078	+	26.1349i	0.236311	+	0.867319i
$909$	−12.7611	−	3.19649i	−0.423258	−	0.106021i
$910$	3.75480	−	1.82337i	0.124470	−	0.0604442i
$911$	−11.4056	+	17.0697i	−0.377884	+	0.565543i	−0.970851	−	0.239684i	$-0.922956\pi$
$911$	−11.4056	+	17.0697i	−0.377884	+	0.565543i	0.592967	+	0.805226i	$0.297956\pi$
$912$	−1.45799	+	25.5339i	−0.0482790	+	0.845513i
$913$	20.7134	+	30.9998i	0.685513	+	1.02594i
$914$	−17.5335	+	29.9471i	−0.579958	+	0.990563i
$915$	−1.83182	+	0.271725i	−0.0605581	+	0.00898294i
$916$	−1.08613	−	1.73037i	−0.0358868	−	0.0571730i
$917$	4.28758	−	4.73062i	0.141588	−	0.156219i
$918$	−1.04521	−	1.02393i	−0.0344971	−	0.0337948i
$919$	−41.2255	+	12.5056i	−1.35991	+	0.412523i	−0.884211	−	0.467088i	$-0.845303\pi$
$919$	−41.2255	+	12.5056i	−1.35991	+	0.412523i	−0.475694	+	0.879611i	$0.657803\pi$
$920$	−0.687837	+	0.731645i	−0.0226773	+	0.0241216i
$921$	−16.7936	+	8.97637i	−0.553368	+	0.295782i
$922$	−7.14460	−	5.74148i	−0.235295	−	0.189086i
$923$	29.5355	+	4.38117i	0.972172	+	0.144208i
$924$	5.40621	+	2.11013i	0.177851	+	0.0694183i
$925$	−23.2204	−	10.9824i	−0.763483	−	0.361101i
$926$	−13.1727	−	21.4734i	−0.432882	−	0.705660i
$927$	15.2032	−	6.29738i	0.499339	−	0.206833i
$928$	−14.0635	−	3.48787i	−0.461656	−	0.114495i
$929$	31.9861	+	13.2491i	1.04943	+	0.434688i	0.839688	−	0.543069i	$-0.182738\pi$
$929$	31.9861	+	13.2491i	1.04943	+	0.434688i	0.209741	+	0.977757i	$0.432738\pi$
$930$	−0.828948	−	5.21801i	−0.0271823	−	0.171105i
$931$	31.3761	−	11.2266i	1.02831	−	0.367936i
$932$	−23.6225	−	15.0907i	−0.773780	−	0.494311i
$933$	−0.803139	−	1.08291i	−0.0262936	−	0.0354528i
$934$	−11.2020	+	38.3432i	−0.366541	+	1.25463i
$935$	−0.319394	+	1.05290i	−0.0104453	+	0.0344335i
$936$	8.38139	+	9.59332i	0.273954	+	0.313567i
$937$	7.52353	+	4.02141i	0.245783	+	0.131374i	0.589689	−	0.807630i	$-0.299250\pi$
$937$	7.52353	+	4.02141i	0.245783	+	0.131374i	−0.343906	+	0.939004i	$0.611750\pi$
$938$	−25.4394	+	10.8452i	−0.830624	+	0.354107i
$939$	−1.40598	−	28.6193i	−0.0458823	−	0.933957i
$940$	8.75210	+	0.249670i	0.285462	+	0.00814334i
$941$	−38.1506	−	28.2944i	−1.24367	−	0.922372i	−0.244790	−	0.969576i	$-0.578719\pi$
$941$	−38.1506	−	28.2944i	−1.24367	−	0.922372i	−0.998885	+	0.0472042i	$0.984969\pi$
$942$	3.25782	−	23.6346i	0.106146	−	0.770058i
$943$	−6.74395	−	1.34146i	−0.219613	−	0.0436838i
$944$	13.0181	−	1.17774i	0.423702	−	0.0383321i
$945$	−0.642741	+	0.127849i	−0.0209084	+	0.00415893i
$946$	−31.4231	+	1.86783i	−1.02165	+	0.0607284i
$947$	−25.7748	+	15.4488i	−0.837568	+	0.502019i	−0.867444	−	0.497535i	$-0.834239\pi$
$947$	−25.7748	+	15.4488i	−0.837568	+	0.502019i	0.0298761	+	0.999554i	$0.490489\pi$
$948$	9.53470	+	8.29103i	0.309673	+	0.269280i
$949$	0.953425	−	0.450936i	0.0309495	−	0.0146380i
$950$	23.5424	−	36.0303i	0.763815	−	1.16898i
$951$	−15.5716	−	18.9740i	−0.504942	−	0.615274i
$952$	−3.21349	−	2.23300i	−0.104150	−	0.0723720i
$953$	0.400136	+	4.06265i	0.0129617	+	0.131602i	0.999488	−	0.0320015i	$-0.0101881\pi$
$953$	0.400136	+	4.06265i	0.0129617	+	0.131602i	−0.986526	+	0.163604i	$0.947688\pi$
$954$	−1.19941	−	1.43121i	−0.0388323	−	0.0463373i
$955$	2.78185	−	0.696816i	0.0900184	−	0.0225484i
$956$	3.55209	−	12.6399i	0.114883	−	0.408803i
$957$	−3.73267	−	4.11836i	−0.120660	−	0.133128i
$958$	2.11079	−	54.3700i	0.0681966	−	1.75661i
$959$	−17.5682	−	17.5682i	−0.567306	−	0.567306i
$960$	−0.142953	+	3.91800i	−0.00461379	+	0.126453i
$961$	−19.1722	+	19.1722i	−0.618458	+	0.618458i
$962$	23.3442	+	25.2300i	0.752648	+	0.813448i
$963$	−6.81968	+	6.18099i	−0.219761	+	0.199180i
$964$	−23.7668	+	2.83548i	−0.765476	+	0.0913245i
$965$	0.678530	+	2.70884i	0.0218427	+	0.0872008i
$966$	0.120257	−	1.36473i	0.00386921	−	0.0439095i
$967$	2.95763	−	0.291301i	0.0951108	−	0.00936760i	−0.0503498	−	0.998732i	$-0.516034\pi$
$967$	2.95763	−	0.291301i	0.0951108	−	0.00936760i	0.145461	+	0.989364i	$0.453534\pi$
$968$	−16.5611	+	6.50864i	−0.532294	+	0.209196i
$969$	5.11368	−	4.19669i	0.164275	−	0.134817i
$970$	−1.44939	−	6.91417i	−0.0465370	−	0.222001i
$971$	−14.0430	−	29.6915i	−0.450662	−	0.952845i	−0.993588	−	0.113064i	$-0.963934\pi$
$971$	−14.0430	−	29.6915i	−0.450662	−	0.952845i	0.542926	−	0.839781i	$-0.317316\pi$
$972$	−0.892114	−	1.79001i	−0.0286146	−	0.0574146i
$973$	1.65541	+	2.76189i	0.0530702	+	0.0885422i
$974$	−31.7122	−	28.1537i	−1.01613	−	0.902103i
$975$	−4.18228	−	21.0258i	−0.133940	−	0.673363i
$976$	−8.29720	−	12.6340i	−0.265587	−	0.404403i
$977$	9.64614	−	48.4944i	0.308607	−	1.55147i	−0.445840	−	0.895113i	$-0.647095\pi$
$977$	9.64614	−	48.4944i	0.308607	−	1.55147i	0.754447	−	0.656361i	$-0.227905\pi$
$978$	−2.18781	−	2.88738i	−0.0699585	−	0.0923283i
$979$	18.1311	−	24.4469i	0.579471	−	0.781327i
$980$	4.77340	−	1.81954i	0.152481	−	0.0581230i
$981$	14.0828	−	0.691841i	0.449628	−	0.0220888i
$982$	−15.8904	−	6.39136i	−0.507082	−	0.203956i
$983$	5.94350	−	11.1195i	0.189568	−	0.354657i	−0.769125	−	0.639098i	$-0.779308\pi$
$983$	5.94350	−	11.1195i	0.189568	−	0.354657i	0.958694	+	0.284441i	$0.0918078\pi$
$984$	−23.2740	+	13.3792i	−0.741949	+	0.426514i
$985$	1.67084	+	0.506844i	0.0532374	+	0.0161494i
$986$	1.80061	+	3.28693i	0.0573430	+	0.104677i
$987$	−9.59449	+	7.11576i	−0.305396	+	0.226497i
$988$	−47.2199	+	32.9759i	−1.50226	+	1.04910i
$989$	2.50348	+	6.99677i	0.0796061	+	0.222484i
$990$	−0.883433	+	1.21714i	−0.0280773	+	0.0386831i
$991$	10.2335	−	24.7058i	0.325078	−	0.784807i	−0.673866	−	0.738854i	$-0.735367\pi$
$991$	10.2335	−	24.7058i	0.325078	−	0.784807i	0.998944	−	0.0459533i	$-0.0146325\pi$
$992$	35.7999	−	24.0417i	1.13665	−	0.763325i
$993$	8.32488	+	20.0980i	0.264182	+	0.637792i
$994$	−12.1921	−	2.92104i	−0.386709	−	0.0926498i
$995$	−2.44088	+	5.16080i	−0.0773809	+	0.163608i
$996$	−0.706729	−	34.3554i	−0.0223936	−	1.08859i
$997$	3.89230	−	26.2398i	0.123271	−	0.831022i	−0.836040	−	0.548669i	$-0.815135\pi$
$997$	3.89230	−	26.2398i	0.123271	−	0.831022i	0.959310	−	0.282354i	$-0.0911151\pi$
$998$	−0.747883	−	6.86849i	−0.0236738	−	0.217418i
$999$	−2.54392	−	4.75933i	−0.0804859	−	0.150579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.349.57	✓	2048
256.245	even	64	inner	768.2.z.a.757.57	yes	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.349.57	✓	2048	1.1	even	1	trivial
768.2.z.a.757.57	yes	2048	256.245	even	64	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(1.32657 - 0.490103i) q^{2} +(0.0490677 - 0.998795i) q^{3} +(1.51960 - 1.30031i) q^{4} +(0.251949 - 0.420352i) q^{5} +(-0.424420 - 1.34902i) q^{6} +(-0.848315 + 1.03368i) q^{7} +(1.37857 - 2.46972i) q^{8} +(-0.995185 - 0.0980171i) q^{9} +O(q^{10})\)	\(q+(1.32657 - 0.490103i) q^{2} +(0.0490677 - 0.998795i) q^{3} +(1.51960 - 1.30031i) q^{4} +(0.251949 - 0.420352i) q^{5} +(-0.424420 - 1.34902i) q^{6} +(-0.848315 + 1.03368i) q^{7} +(1.37857 - 2.46972i) q^{8} +(-0.995185 - 0.0980171i) q^{9} +(0.128214 - 0.681109i) q^{10} +(2.04313 + 0.731044i) q^{11} +(-1.22419 - 1.58157i) q^{12} +(1.09435 - 4.36890i) q^{13} +(-0.618747 + 1.78701i) q^{14} +(-0.407483 - 0.272272i) q^{15} +(0.618362 - 3.95191i) q^{16} +(-0.860261 + 0.574808i) q^{17} +(-1.36822 + 0.357716i) q^{18} +(-0.938177 - 6.32468i) q^{19} +(-0.163728 - 0.966380i) q^{20} +(0.990805 + 0.898014i) q^{21} +(3.06865 - 0.0315595i) q^{22} +(-0.210299 - 0.693263i) q^{23} +(-2.39911 - 1.49810i) q^{24} +(2.24377 + 4.19779i) q^{25} +(-0.689469 - 6.33202i) q^{26} +(-0.146730 + 0.989177i) q^{27} +(0.0550041 + 2.67385i) q^{28} +(1.09514 - 2.31549i) q^{29} +(-0.673998 - 0.161480i) q^{30} +(2.91728 + 7.04294i) q^{31} +(-1.11654 - 5.54557i) q^{32} +(0.830415 - 2.00480i) q^{33} +(-0.859485 + 1.18414i) q^{34} +(0.220775 + 0.617025i) q^{35} +(-1.63973 + 1.14511i) q^{36} +(-4.33455 + 3.21472i) q^{37} +(-4.34430 - 7.93035i) q^{38} +(-4.30994 - 1.30741i) q^{39} +(-0.690823 - 1.20173i) q^{40} +(4.47418 - 8.37061i) q^{41} +(1.75450 + 0.705686i) q^{42} +(-10.2452 + 0.503314i) q^{43} +(4.05533 - 1.54582i) q^{44} +(-0.291938 + 0.393633i) q^{45} +(-0.618747 - 0.816597i) q^{46} +(-1.74273 + 8.76132i) q^{47} +(-3.91681 - 0.811529i) q^{48} +(1.01679 + 5.11173i) q^{49} +(5.03387 + 4.46901i) q^{50} +(0.531904 + 0.887429i) q^{51} +(-4.01797 - 8.06198i) q^{52} +(0.564547 + 1.19364i) q^{53} +(0.290149 + 1.38413i) q^{54} +(0.822062 - 0.674649i) q^{55} +(1.38343 + 3.52010i) q^{56} +(-6.36309 + 0.626710i) q^{57} +(0.317964 - 3.60840i) q^{58} +(0.794013 + 3.16988i) q^{59} +(-0.973250 + 0.116113i) q^{60} +(2.79985 - 2.53764i) q^{61} +(7.32176 + 7.91322i) q^{62} +(0.945548 - 0.945548i) q^{63} +(-4.19907 - 6.80939i) q^{64} +(-1.56076 - 1.56076i) q^{65} +(0.119050 - 3.06651i) q^{66} +(9.82060 + 10.8354i) q^{67} +(-0.559820 + 1.99209i) q^{68} +(-0.702747 + 0.176029i) q^{69} +(0.595280 + 0.710327i) q^{70} +(0.649809 + 6.59762i) q^{71} +(-1.61401 + 2.32271i) q^{72} +(0.148558 + 0.181018i) q^{73} +(-4.17456 + 6.38894i) q^{74} +(4.30283 - 2.03509i) q^{75} +(-9.64973 - 8.39105i) q^{76} +(-2.48888 + 1.49178i) q^{77} +(-6.35822 + 0.377941i) q^{78} +(-6.19628 + 1.23252i) q^{79} +(-1.50540 - 1.25561i) q^{80} +(0.980785 + 0.195090i) q^{81} +(1.83288 - 13.2970i) q^{82} +(13.8002 + 10.2349i) q^{83} +(2.67333 + 0.0762617i) q^{84} +(0.0248795 + 0.506435i) q^{85} +(-13.3443 + 5.68888i) q^{86} +(-2.25896 - 1.20744i) q^{87} +(4.62208 - 4.03817i) q^{88} +(4.07160 - 13.4223i) q^{89} +(-0.194357 + 0.665262i) q^{90} +(3.58767 + 4.83741i) q^{91} +(-1.22103 - 0.780027i) q^{92} +(7.17760 - 2.56819i) q^{93} +(1.98208 + 12.4767i) q^{94} +(-2.89497 - 1.19913i) q^{95} +(-5.59368 + 0.843086i) q^{96} +(9.41706 - 3.90067i) q^{97} +(3.85412 + 6.28276i) q^{98} +(-1.96164 - 0.927786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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