LMFDB - Embedded newform 572.2.y.a.79.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(79,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 1, 0]))

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

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

chi := DirichletCharacter("572.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.y (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$72$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			79.14
Character	$\chi$	$=$	572.79
Dual form			572.2.y.a.391.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18418 + 0.773121i) q^{2} +(-0.0644943 - 0.0887688i) q^{3} +(0.804567 - 1.83103i) q^{4} +(-1.31803 - 4.05649i) q^{5} +(0.145002 + 0.0552564i) q^{6} +(-0.673809 - 0.489551i) q^{7} +(0.462856 + 2.79030i) q^{8} +(0.923331 - 2.84172i) q^{9} +O(q^{10})$	\(q+(-1.18418 + 0.773121i) q^{2} +(-0.0644943 - 0.0887688i) q^{3} +(0.804567 - 1.83103i) q^{4} +(-1.31803 - 4.05649i) q^{5} +(0.145002 + 0.0552564i) q^{6} +(-0.673809 - 0.489551i) q^{7} +(0.462856 + 2.79030i) q^{8} +(0.923331 - 2.84172i) q^{9} +(4.69695 + 3.78462i) q^{10} +(-3.07432 + 1.24440i) q^{11} +(-0.214428 + 0.0466706i) q^{12} +(-0.951057 - 0.309017i) q^{13} +(1.17639 + 0.0587805i) q^{14} +(-0.275084 + 0.378621i) q^{15} +(-2.70534 - 2.94637i) q^{16} +(-0.301881 + 0.0980872i) q^{17} +(1.10360 + 4.07896i) q^{18} +(4.60076 - 3.34265i) q^{19} +(-8.48801 - 0.850359i) q^{20} +0.0913865i q^{21} +(2.67848 - 3.85042i) q^{22} +8.65398i q^{23} +(0.217840 - 0.221046i) q^{24} +(-10.6728 + 7.75426i) q^{25} +(1.36513 - 0.369350i) q^{26} +(-0.624868 + 0.203032i) q^{27} +(-1.43851 + 0.839888i) q^{28} +(-4.91240 + 6.76134i) q^{29} +(0.0330295 - 0.661029i) q^{30} +(-4.71670 - 1.53255i) q^{31} +(5.48152 + 1.39748i) q^{32} +(0.308741 + 0.192647i) q^{33} +(0.281649 - 0.349544i) q^{34} +(-1.09776 + 3.37854i) q^{35} +(-4.46039 - 3.97700i) q^{36} +(-1.04933 - 0.762385i) q^{37} +(-2.86386 + 7.51524i) q^{38} +(0.0339067 + 0.104354i) q^{39} +(10.7088 - 5.55528i) q^{40} +(-3.10225 - 4.26988i) q^{41} +(-0.0706528 - 0.108218i) q^{42} +5.60860 q^{43} +(-0.194964 + 6.63038i) q^{44} -12.7444 q^{45} +(-6.69058 - 10.2479i) q^{46} +(-0.974102 - 1.34074i) q^{47} +(-0.0870668 + 0.430175i) q^{48} +(-1.94876 - 5.99767i) q^{49} +(6.64357 - 17.4338i) q^{50} +(0.0281767 + 0.0204716i) q^{51} +(-1.33101 + 1.49279i) q^{52} +(1.14340 - 3.51901i) q^{53} +(0.582988 - 0.723525i) q^{54} +(9.09997 + 10.8308i) q^{55} +(1.05412 - 2.10672i) q^{56} +(-0.593446 - 0.192822i) q^{57} +(0.589834 - 11.8045i) q^{58} +(1.93389 - 2.66177i) q^{59} +(0.471943 + 0.808314i) q^{60} +(10.3500 - 3.36292i) q^{61} +(6.77027 - 1.83177i) q^{62} +(-2.01331 + 1.46276i) q^{63} +(-7.57153 + 2.58301i) q^{64} +4.26525i q^{65} +(-0.514544 + 0.0105646i) q^{66} -6.51462i q^{67} +(-0.0632832 + 0.631672i) q^{68} +(0.768204 - 0.558133i) q^{69} +(-1.31208 - 4.84950i) q^{70} +(-11.1015 + 3.60711i) q^{71} +(8.35661 + 1.26106i) q^{72} +(0.213233 - 0.293490i) q^{73} +(1.83202 + 0.0915399i) q^{74} +(1.37667 + 0.447308i) q^{75} +(-2.41887 - 11.1135i) q^{76} +(2.68070 + 0.666549i) q^{77} +(-0.120830 - 0.0973600i) q^{78} +(-1.74509 + 5.37083i) q^{79} +(-8.38620 + 14.8576i) q^{80} +(-7.19361 - 5.22646i) q^{81} +(6.97476 + 2.65789i) q^{82} +(-4.57335 - 14.0753i) q^{83} +(0.167331 + 0.0735265i) q^{84} +(0.795780 + 1.09530i) q^{85} +(-6.64160 + 4.33613i) q^{86} +0.917018 q^{87} +(-4.89522 - 8.00230i) q^{88} -0.695560 q^{89} +(15.0917 - 9.85296i) q^{90} +(0.489551 + 0.673809i) q^{91} +(15.8457 + 6.96271i) q^{92} +(0.168158 + 0.517537i) q^{93} +(2.19006 + 0.834575i) q^{94} +(-19.6234 - 14.2572i) q^{95} +(-0.229474 - 0.576718i) q^{96} +(-1.57639 + 4.85163i) q^{97} +(6.94461 + 5.59569i) q^{98} +(0.697621 + 9.88536i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) $ 288 * q - 4 * q^4 + 80 * q^9	$ 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) $ 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−1.18418	+	0.773121i	−0.837342	+	0.546679i
$2$	−1.18418	+	0.773121i	−0.837342	+	0.546679i
$3$	−0.0644943	−	0.0887688i	−0.0372358	−	0.0512507i	0.789993	−	0.613116i	$-0.210084\pi$
$3$	−0.0644943	−	0.0887688i	−0.0372358	−	0.0512507i	−0.827229	+	0.561865i	$0.810084\pi$
$4$	0.804567	−	1.83103i	0.402284	−	0.915515i
$5$	−1.31803	−	4.05649i	−0.589443	−	1.81412i	−0.580645	−	0.814157i	$-0.697200\pi$
$5$	−1.31803	−	4.05649i	−0.589443	−	1.81412i	−0.00879782	−	0.999961i	$-0.502800\pi$
$6$	0.145002	+	0.0552564i	0.0591968	+	0.0225583i
$7$	−0.673809	−	0.489551i	−0.254676	−	0.185033i	0.453121	−	0.891449i	$-0.350311\pi$
$7$	−0.673809	−	0.489551i	−0.254676	−	0.185033i	−0.707796	+	0.706416i	$0.750311\pi$
$8$	0.462856	+	2.79030i	0.163644	+	0.986519i
$9$	0.923331	−	2.84172i	0.307777	−	0.947240i
$10$	4.69695	+	3.78462i	1.48531	+	1.19680i
$11$	−3.07432	+	1.24440i	−0.926943	+	0.375201i
$11$	−3.07432	+	1.24440i	−0.926943	+	0.375201i
$12$	−0.214428	+	0.0466706i	−0.0619002	+	0.0134726i
$13$	−0.951057	−	0.309017i	−0.263776	−	0.0857059i
$13$	−0.951057	−	0.309017i	−0.263776	−	0.0857059i
$14$	1.17639	+	0.0587805i	0.314404	+	0.0157098i
$15$	−0.275084	+	0.378621i	−0.0710265	+	0.0977595i
$16$	−2.70534	−	2.94637i	−0.676336	−	0.736593i
$17$	−0.301881	+	0.0980872i	−0.0732170	+	0.0237896i	−0.345396	−	0.938457i	$-0.612256\pi$
$17$	−0.301881	+	0.0980872i	−0.0732170	+	0.0237896i	0.272179	+	0.962246i	$0.412256\pi$
$18$	1.10360	+	4.07896i	0.260122	+	0.961419i
$19$	4.60076	−	3.34265i	1.05549	−	0.766856i	0.0822382	−	0.996613i	$-0.473793\pi$
$19$	4.60076	−	3.34265i	1.05549	−	0.766856i	0.973248	+	0.229757i	$0.0737932\pi$
$20$	−8.48801	−	0.850359i	−1.89798	−	0.190146i
$21$			0.0913865i			0.0199422i
$22$	2.67848	−	3.85042i	0.571054	−	0.820912i
$23$			8.65398i			1.80448i	0.431234	+	0.902240i	$0.358078\pi$
$23$			8.65398i			1.80448i	−0.431234	+	0.902240i	$0.641922\pi$
$24$	0.217840	−	0.221046i	0.0444664	−	0.0451207i
$25$	−10.6728	+	7.75426i	−2.13457	+	1.55085i
$26$	1.36513	−	0.369350i	0.267724	−	0.0724355i
$27$	−0.624868	+	0.203032i	−0.120256	+	0.0390735i
$28$	−1.43851	+	0.839888i	−0.271852	+	0.158724i
$29$	−4.91240	+	6.76134i	−0.912210	+	1.25555i	0.0541965	+	0.998530i	$0.482740\pi$
$29$	−4.91240	+	6.76134i	−0.912210	+	1.25555i	−0.966406	+	0.257019i	$0.917260\pi$
$30$	0.0330295	−	0.661029i	0.00603033	−	0.120687i
$31$	−4.71670	−	1.53255i	−0.847144	−	0.275254i	−0.146895	−	0.989152i	$-0.546928\pi$
$31$	−4.71670	−	1.53255i	−0.847144	−	0.275254i	−0.700249	+	0.713898i	$0.746928\pi$
$32$	5.48152	+	1.39748i	0.969005	+	0.247042i
$33$	0.308741	+	0.192647i	0.0537448	+	0.0335356i
$34$	0.281649	−	0.349544i	0.0483024	−	0.0599463i
$35$	−1.09776	+	3.37854i	−0.185555	+	0.571078i
$36$	−4.46039	−	3.97700i	−0.743399	−	0.662833i
$37$	−1.04933	−	0.762385i	−0.172509	−	0.125335i	0.498180	−	0.867073i	$-0.334002\pi$
$37$	−1.04933	−	0.762385i	−0.172509	−	0.125335i	−0.670690	+	0.741738i	$0.734002\pi$
$38$	−2.86386	+	7.51524i	−0.464579	+	1.21913i
$39$	0.0339067	+	0.104354i	0.00542941	+	0.0167100i
$40$	10.7088	−	5.55528i	1.69320	−	0.878367i
$41$	−3.10225	−	4.26988i	−0.484490	−	0.666843i	0.494870	−	0.868967i	$-0.335216\pi$
$41$	−3.10225	−	4.26988i	−0.484490	−	0.666843i	−0.979360	+	0.202124i	$0.935216\pi$
$42$	−0.0706528	−	0.108218i	−0.0109020	−	0.0166984i
$43$	5.60860			0.855304			0.427652	−	0.903943i	$-0.359341\pi$
$43$	5.60860			0.855304			0.427652	+	0.903943i	$0.359341\pi$
$44$	−0.194964	+	6.63038i	−0.0293919	+	0.999568i
$45$	−12.7444			−1.89982
$46$	−6.69058	−	10.2479i	−0.986472	−	1.51097i
$47$	−0.974102	−	1.34074i	−0.142087	−	0.195566i	0.732042	−	0.681259i	$-0.238567\pi$
$47$	−0.974102	−	1.34074i	−0.142087	−	0.195566i	−0.874130	+	0.485693i	$0.838567\pi$
$48$	−0.0870668	+	0.430175i	−0.0125670	+	0.0620904i
$49$	−1.94876	−	5.99767i	−0.278394	−	0.856810i
$50$	6.64357	−	17.4338i	0.939542	−	2.46552i
$51$	0.0281767	+	0.0204716i	0.00394553	+	0.00286660i
$52$	−1.33101	+	1.49279i	−0.184578	+	0.207013i
$53$	1.14340	−	3.51901i	0.157058	−	0.483374i	−0.841306	−	0.540559i	$-0.818213\pi$
$53$	1.14340	−	3.51901i	0.157058	−	0.483374i	0.998364	+	0.0571855i	$0.0182126\pi$
$54$	0.582988	−	0.723525i	0.0793346	−	0.0984593i
$55$	9.09997	+	10.8308i	1.22704	+	1.46043i
$56$	1.05412	−	2.10672i	0.140862	−	0.281522i
$57$	−0.593446	−	0.192822i	−0.0786038	−	0.0255399i
$58$	0.589834	−	11.8045i	0.0774490	−	1.55001i
$59$	1.93389	−	2.66177i	0.251771	−	0.346533i	−0.664359	−	0.747413i	$-0.731296\pi$
$59$	1.93389	−	2.66177i	0.251771	−	0.346533i	0.916131	+	0.400880i	$0.131296\pi$
$60$	0.471943	+	0.808314i	0.0609276	+	0.104353i
$61$	10.3500	−	3.36292i	1.32518	−	0.430577i	0.440910	−	0.897551i	$-0.354656\pi$
$61$	10.3500	−	3.36292i	1.32518	−	0.430577i	0.884271	+	0.466974i	$0.154656\pi$
$62$	6.77027	−	1.83177i	0.859825	−	0.232635i
$63$	−2.01331	+	1.46276i	−0.253654	+	0.184290i
$64$	−7.57153	+	2.58301i	−0.946441	+	0.322876i
$65$			4.26525i			0.529039i
$66$	−0.514544	+	0.0105646i	−0.0633360	+	0.00130041i
$67$		−	6.51462i		−	0.795888i	−0.917410	−	0.397944i	$-0.869724\pi$
$67$		−	6.51462i		−	0.795888i	0.917410	−	0.397944i	$-0.130276\pi$
$68$	−0.0632832	+	0.631672i	−0.00767421	+	0.0766014i
$69$	0.768204	−	0.558133i	0.0924809	−	0.0671913i
$70$	−1.31208	−	4.84950i	−0.156824	−	0.579626i
$71$	−11.1015	+	3.60711i	−1.31751	+	0.428085i	−0.881639	−	0.471924i	$-0.843560\pi$
$71$	−11.1015	+	3.60711i	−1.31751	+	0.428085i	−0.435871	+	0.900009i	$0.643560\pi$
$72$	8.35661	+	1.26106i	0.984836	+	0.148618i
$73$	0.213233	−	0.293490i	0.0249571	−	0.0343504i	−0.796356	−	0.604828i	$-0.793242\pi$
$73$	0.213233	−	0.293490i	0.0249571	−	0.0343504i	0.821313	+	0.570478i	$0.193242\pi$
$74$	1.83202	+	0.0915399i	0.212967	+	0.0106413i
$75$	1.37667	+	0.447308i	0.158965	+	0.0516507i
$76$	−2.41887	−	11.1135i	−0.277463	−	1.27481i
$77$	2.68070	+	0.666549i	0.305494	+	0.0759603i
$78$	−0.120830	−	0.0973600i	−0.0136813	−	0.0110239i
$79$	−1.74509	+	5.37083i	−0.196338	+	0.604265i	0.803621	+	0.595142i	$0.202904\pi$
$79$	−1.74509	+	5.37083i	−0.196338	+	0.604265i	−0.999958	+	0.00912334i	$0.997096\pi$
$80$	−8.38620	+	14.8576i	−0.937606	+	1.66113i
$81$	−7.19361	−	5.22646i	−0.799290	−	0.580718i
$82$	6.97476	+	2.65789i	0.770233	+	0.293515i
$83$	−4.57335	−	14.0753i	−0.501990	−	1.54497i	−0.805772	−	0.592226i	$-0.798249\pi$
$83$	−4.57335	−	14.0753i	−0.501990	−	1.54497i	0.303782	−	0.952742i	$-0.401751\pi$
$84$	0.167331	+	0.0735265i	0.0182573	+	0.00802240i
$85$	0.795780	+	1.09530i	0.0863144	+	0.118802i
$86$	−6.64160	+	4.33613i	−0.716182	+	0.467577i
$87$	0.917018			0.0983147
$88$	−4.89522	−	8.00230i	−0.521832	−	0.853048i
$89$	−0.695560			−0.0737293			−0.0368646	−	0.999320i	$-0.511737\pi$
$89$	−0.695560			−0.0737293			−0.0368646	+	0.999320i	$0.511737\pi$
$90$	15.0917	−	9.85296i	1.59080	−	1.03859i
$91$	0.489551	+	0.673809i	0.0513188	+	0.0706343i
$92$	15.8457	+	6.96271i	1.65203	+	0.725913i
$93$	0.168158	+	0.517537i	0.0174372	+	0.0536660i
$94$	2.19006	+	0.834575i	0.225888	+	0.0860798i
$95$	−19.6234	−	14.2572i	−2.01332	−	1.46276i
$96$	−0.229474	−	0.576718i	−0.0234206	−	0.0588610i
$97$	−1.57639	+	4.85163i	−0.160058	+	0.492608i	−0.998638	−	0.0521701i	$-0.983386\pi$
$97$	−1.57639	+	4.85163i	−0.160058	+	0.492608i	0.838580	+	0.544778i	$0.183386\pi$
$98$	6.94461	+	5.59569i	0.701512	+	0.565250i
$99$	0.697621	+	9.88536i	0.0701135	+	0.993516i
$100$	5.61128	+	25.7811i	0.561128	+	2.57811i
$101$	−2.73427	−	0.888417i	−0.272070	−	0.0884008i	0.169805	−	0.985478i	$-0.445686\pi$
$101$	−2.73427	−	0.888417i	−0.272070	−	0.0884008i	−0.441874	+	0.897077i	$0.645686\pi$
$102$	−0.0491933	−	0.00245803i	−0.00487087	−	0.000243381i
$103$	−4.49435	+	6.18594i	−0.442842	+	0.609519i	−0.970841	−	0.239726i	$-0.922942\pi$
$103$	−4.49435	+	6.18594i	−0.442842	+	0.609519i	0.527999	+	0.849245i	$0.322942\pi$
$104$	0.422048	−	2.79676i	0.0413852	−	0.274245i
$105$	0.370708	−	0.120450i	0.0361774	−	0.0117548i
$106$	1.36664	+	5.05113i	0.132739	+	0.490609i
$107$	−7.43033	+	5.39845i	−0.718317	+	0.521888i	−0.885846	−	0.463979i	$-0.846421\pi$
$107$	−7.43033	+	5.39845i	−0.718317	+	0.521888i	0.167529	+	0.985867i	$0.446421\pi$
$108$	−0.130991	+	1.30750i	−0.0126046	+	0.125815i
$109$			1.02944i			0.0986020i	0.998784	+	0.0493010i	$0.0156994\pi$
$109$			1.02944i			0.0986020i	−0.998784	+	0.0493010i	$0.984301\pi$
$110$	−19.1495	−	5.79025i	−1.82584	−	0.552079i
$111$			0.142318i			0.0135082i
$112$	0.380485	+	3.30969i	0.0359525	+	0.312737i
$113$	6.27445	−	4.55865i	0.590250	−	0.428842i	−0.252155	−	0.967687i	$-0.581139\pi$
$113$	6.27445	−	4.55865i	0.590250	−	0.428842i	0.842405	+	0.538845i	$0.181139\pi$
$114$	0.851822	−	0.230469i	0.0797804	−	0.0215854i
$115$	35.1048	−	11.4062i	3.27354	−	1.06364i
$116$	8.42786	+	14.4347i	0.782507	+	1.34023i
$117$	−1.75628	+	2.41731i	−0.162368	+	0.223480i
$118$	−0.232203	+	4.64715i	−0.0213760	+	0.427805i
$119$	0.251429	+	0.0816942i	0.0230484	+	0.00748890i
$120$	−1.18379	−	0.592320i	−0.108065	−	0.0540712i
$121$	7.90293	−	7.65138i	0.718448	−	0.695580i
$122$	−9.65632	+	11.9841i	−0.874242	+	1.08499i
$123$	−0.178955	+	0.550766i	−0.0161358	+	0.0496609i
$124$	−6.60104	+	7.40338i	−0.592791	+	0.664843i
$125$	28.2690	+	20.5386i	2.52845	+	1.83703i
$126$	1.25324	−	3.28870i	0.111647	−	0.292981i
$127$	4.48036	+	13.7891i	0.397567	+	1.22359i	0.926944	+	0.375200i	$0.122426\pi$
$127$	4.48036	+	13.7891i	0.397567	+	1.22359i	−0.529376	+	0.848387i	$0.677574\pi$
$128$	6.96908	−	8.91246i	0.615985	−	0.787758i
$129$	−0.361723	−	0.497869i	−0.0318480	−	0.0438350i
$130$	−3.29755	−	5.05082i	−0.289215	−	0.442987i
$131$	5.88784			0.514423			0.257211	−	0.966355i	$-0.417196\pi$
$131$	5.88784			0.514423			0.257211	+	0.966355i	$0.417196\pi$
$132$	0.601146	−	0.410315i	0.0523230	−	0.0357134i
$133$	−4.73642			−0.410700
$134$	5.03659	+	7.71449i	0.435095	+	0.666431i
$135$	1.64719	+	2.26717i	0.141768	+	0.195127i
$136$	−0.413420	−	0.796939i	−0.0354505	−	0.0683369i
$137$	−4.59179	−	14.1321i	−0.392303	−	1.20739i	−0.931042	−	0.364912i	$-0.881099\pi$
$137$	−4.59179	−	14.1321i	−0.392303	−	1.20739i	0.538739	−	0.842473i	$-0.318901\pi$
$138$	−0.478188	+	1.25484i	−0.0407061	+	0.106819i
$139$	−12.2105	−	8.87146i	−1.03568	−	0.752468i	−0.0662449	−	0.997803i	$-0.521102\pi$
$139$	−12.2105	−	8.87146i	−1.03568	−	0.752468i	−0.969438	+	0.245336i	$0.921102\pi$
$140$	5.30300	+	4.72829i	0.448185	+	0.399613i
$141$	−0.0561915	+	0.172940i	−0.00473218	+	0.0145642i
$142$	10.3575	−	12.8543i	0.869182	−	1.07871i
$143$	3.30840	−	0.233477i	0.276662	−	0.0195244i
$144$	−10.8707	+	4.96735i	−0.905891	+	0.413946i
$145$	33.9020	+	11.0154i	2.81541	+	0.914782i
$146$	−0.0256030	+	0.512401i	−0.00211892	+	0.0424066i
$147$	−0.406722	+	0.559805i	−0.0335459	+	0.0461719i
$148$	−2.24021	+	1.30797i	−0.184144	+	0.107515i
$149$	−4.94880	+	1.60796i	−0.405421	+	0.131729i	−0.504627	−	0.863338i	$-0.668370\pi$
$149$	−4.94880	+	1.60796i	−0.405421	+	0.131729i	0.0992056	+	0.995067i	$0.468370\pi$
$150$	−1.97605	+	0.534642i	−0.161344	+	0.0436533i
$151$	−6.50124	+	4.72343i	−0.529063	+	0.384387i	−0.820007	−	0.572353i	$-0.806031\pi$
$151$	−6.50124	+	4.72343i	−0.529063	+	0.384387i	0.290944	+	0.956740i	$0.406031\pi$
$152$	11.4565	+	11.2903i	0.929242	+	0.915766i
$153$			0.948429i			0.0766759i
$154$	−3.68976	+	1.28319i	−0.297329	+	0.103403i
$155$			21.1532i			1.69907i
$156$	0.218356	+	0.0218757i	0.0174824	+	0.00175145i
$157$	13.5260	−	9.82720i	1.07949	−	0.784296i	0.101896	−	0.994795i	$-0.467509\pi$
$157$	13.5260	−	9.82720i	1.07949	−	0.784296i	0.977594	+	0.210499i	$0.0675090\pi$
$158$	−2.08580	−	7.70919i	−0.165937	−	0.613310i
$159$	−0.386121	+	0.125458i	−0.0306214	+	0.00994950i
$160$	−1.55597	−	24.0777i	−0.123010	−	1.90351i
$161$	4.23656	−	5.83113i	0.333888	−	0.459557i
$162$	12.5592	+	0.627544i	0.986746	+	0.0493045i
$163$	3.41244	+	1.10877i	0.267283	+	0.0868454i	0.439592	−	0.898197i	$-0.355123\pi$
$163$	3.41244	+	1.10877i	0.267283	+	0.0868454i	−0.172310	+	0.985043i	$0.555123\pi$
$164$	−10.3142	+	2.24491i	−0.805407	+	0.175298i
$165$	0.374542	−	1.50632i	0.0291580	−	0.117267i
$166$	16.2976	+	13.1320i	1.26494	+	1.01924i
$167$	−4.87309	+	14.9978i	−0.377091	+	1.16057i	0.564967	+	0.825114i	$0.308889\pi$
$167$	−4.87309	+	14.9978i	−0.377091	+	1.16057i	−0.942057	+	0.335452i	$0.891111\pi$
$168$	−0.254995	+	0.0422987i	−0.0196733	+	0.00326342i
$169$	0.809017	+	0.587785i	0.0622321	+	0.0452143i
$170$	−1.78914	−	0.681795i	−0.137221	−	0.0522913i
$171$	−5.25084	−	16.1604i	−0.401542	−	1.23582i
$172$	4.51250	−	10.2695i	0.344075	−	0.783044i
$173$	−6.04951	−	8.32643i	−0.459936	−	0.633047i	0.514560	−	0.857455i	$-0.327955\pi$
$173$	−6.04951	−	8.32643i	−0.459936	−	0.633047i	−0.974495	+	0.224407i	$0.927955\pi$
$174$	−1.08592	+	0.708966i	−0.0823230	+	0.0537466i
$175$	10.9875			0.830580
$176$	11.9836	+	5.69157i	0.903296	+	0.429018i
$177$	−0.361007			−0.0271350
$178$	0.823669	−	0.537753i	0.0617366	−	0.0403063i
$179$	−7.20941	−	9.92290i	−0.538856	−	0.741672i	0.449591	−	0.893234i	$-0.351570\pi$
$179$	−7.20941	−	9.92290i	−0.538856	−	0.741672i	−0.988448	+	0.151562i	$0.951570\pi$
$180$	−10.2537	+	23.3354i	−0.764267	+	1.73932i
$181$	−5.62011	−	17.2969i	−0.417740	−	1.28567i	−0.909777	−	0.415096i	$-0.863748\pi$
$181$	−5.62011	−	17.2969i	−0.417740	−	1.28567i	0.492038	−	0.870574i	$-0.336252\pi$
$182$	−1.10065	−	0.419429i	−0.0815858	−	0.0310902i
$183$	−0.966038	−	0.701868i	−0.0714116	−	0.0518836i
$184$	−24.1472	+	4.00555i	−1.78015	+	0.295293i
$185$	−1.70955	+	5.26146i	−0.125689	+	0.386830i
$186$	−0.599248	−	0.482850i	−0.0439390	−	0.0354043i
$187$	0.806021	−	0.677213i	0.0589421	−	0.0495227i
$188$	−3.23866	+	0.704898i	−0.236203	+	0.0514099i
$189$	0.520436	+	0.169100i	0.0378561	+	0.0123002i
$190$	34.2602	+	1.71187i	2.48549	+	0.124192i
$191$	−2.42528	+	3.33811i	−0.175487	+	0.241537i	−0.887696	−	0.460431i	$-0.847695\pi$
$191$	−2.42528	+	3.33811i	−0.175487	+	0.241537i	0.712209	+	0.701968i	$0.247695\pi$
$192$	0.717612	+	0.505526i	0.0517892	+	0.0364832i
$193$	−4.43318	+	1.44043i	−0.319108	+	0.103684i	−0.464191	−	0.885735i	$-0.653655\pi$
$193$	−4.43318	+	1.44043i	−0.319108	+	0.103684i	0.145083	+	0.989419i	$0.453655\pi$
$194$	−1.88417	−	6.96394i	−0.135275	−	0.499982i
$195$	0.378621	−	0.275084i	0.0271136	−	0.0196992i
$196$	−12.5498	−	1.25729i	−0.896416	−	0.0898062i
$197$		−	11.6968i		−	0.833365i	−0.909052	−	0.416682i	$-0.863193\pi$
$197$		−	11.6968i		−	0.833365i	0.909052	−	0.416682i	$-0.136807\pi$
$198$	−8.46869	−	11.1667i	−0.601844	−	0.793583i
$199$		−	15.8639i		−	1.12456i	−0.826946	−	0.562281i	$-0.809924\pi$
$199$		−	15.8639i		−	1.12456i	0.826946	−	0.562281i	$-0.190076\pi$
$200$	−26.5767	−	26.1913i	−1.87926	−	1.85200i
$201$	−0.578296	+	0.420156i	−0.0407898	+	0.0296355i
$202$	3.92472	−	1.06187i	0.276142	−	0.0747131i
$203$	6.62004	−	2.15098i	0.464635	−	0.150969i
$204$	0.0601542	−	0.0351217i	0.00421163	−	0.00245901i
$205$	−13.2319	+	18.2121i	−0.924153	+	1.27199i
$206$	0.539639	−	10.8000i	0.0375984	−	0.752468i
$207$	24.5922	+	7.99049i	1.70928	+	0.555377i
$208$	1.66246	+	3.63816i	0.115271	+	0.252261i
$209$	−9.98463	+	16.0016i	−0.690651	+	1.10685i
$210$	−0.345863	+	0.429238i	−0.0238668	+	0.0296202i
$211$	5.14906	−	15.8472i	0.354476	−	1.09097i	−0.601836	−	0.798619i	$-0.705564\pi$
$211$	5.14906	−	15.8472i	0.354476	−	1.09097i	0.956313	−	0.292346i	$-0.0944359\pi$
$212$	−5.52348	−	4.92488i	−0.379354	−	0.338242i
$213$	1.03619	+	0.752833i	0.0709983	+	0.0515833i
$214$	4.62519	−	12.1373i	0.316172	−	0.829688i
$215$	−7.39233	−	22.7513i	−0.504153	−	1.55162i
$216$	−0.855743	−	1.64959i	−0.0582259	−	0.112241i
$217$	2.42789	+	3.34171i	0.164816	+	0.226850i
$218$	−0.795878	−	1.21904i	−0.0539037	−	0.0825636i
$219$	−0.0398051			−0.00268978
$220$	27.1531	−	7.94820i	1.83066	−	0.535868i
$221$	0.317417			0.0213518
$222$	−0.110029	−	0.168530i	−0.00738465	−	0.0113110i
$223$	4.88844	+	6.72836i	0.327354	+	0.450564i	0.940695	−	0.339254i	$-0.110175\pi$
$223$	4.88844	+	6.72836i	0.327354	+	0.450564i	−0.613341	+	0.789818i	$0.710175\pi$
$224$	−3.00936	−	3.62511i	−0.201071	−	0.242213i
$225$	12.1809	+	37.4889i	0.812059	+	2.49926i
$226$	−3.90569	+	10.2492i	−0.259802	+	0.681765i
$227$	−10.2124	−	7.41977i	−0.677824	−	0.492468i	0.194811	−	0.980841i	$-0.437591\pi$
$227$	−10.2124	−	7.41977i	−0.677824	−	0.492468i	−0.872635	+	0.488373i	$0.837591\pi$
$228$	−0.830530	+	0.931479i	−0.0550032	+	0.0616887i
$229$	2.40793	−	7.41084i	0.159120	−	0.489722i	−0.839435	−	0.543460i	$-0.817114\pi$
$229$	2.40793	−	7.41084i	0.159120	−	0.489722i	0.998555	+	0.0537386i	$0.0171138\pi$
$230$	−32.7520	+	40.6473i	−2.15960	+	2.68021i
$231$	−0.113721	−	0.280952i	−0.00748232	−	0.0184853i
$232$	−21.1399	−	10.5775i	−1.38790	−	0.694449i
$233$	24.1915	+	7.86030i	1.58484	+	0.514946i	0.963298	−	0.268435i	$-0.0865065\pi$
$233$	24.1915	+	7.86030i	1.58484	+	0.514946i	0.621542	+	0.783381i	$0.286506\pi$
$234$	0.210877	−	4.22035i	0.0137855	−	0.275893i
$235$	−4.15478	+	5.71857i	−0.271028	+	0.373038i
$236$	−3.31784	−	5.68259i	−0.215973	−	0.369905i
$237$	0.589310	−	0.191478i	0.0382798	−	0.0124379i
$238$	−0.360897	+	0.0976443i	−0.0233935	+	0.00632934i
$239$	6.51146	−	4.73085i	0.421191	−	0.306013i	−0.356926	−	0.934133i	$-0.616175\pi$
$239$	6.51146	−	4.73085i	0.421191	−	0.306013i	0.778117	+	0.628120i	$0.216175\pi$
$240$	1.85976	−	0.213799i	0.120047	−	0.0138007i
$241$			13.0733i			0.842128i	0.907031	+	0.421064i	$0.138343\pi$
$241$			13.0733i			0.842128i	−0.907031	+	0.421064i	$0.861657\pi$
$242$	−3.44305	+	15.1705i	−0.221328	+	0.975199i
$243$			2.94672i			0.189032i
$244$	2.16966	−	21.6568i	0.138898	−	1.38644i
$245$	−21.7610	+	15.8103i	−1.39026	+	1.01008i
$246$	−0.213894	−	0.790560i	−0.0136374	−	0.0504043i
$247$	−5.40852	+	1.75733i	−0.344136	+	0.111816i
$248$	2.09312	−	13.8703i	0.132913	−	0.880768i
$249$	−0.954495	+	1.31375i	−0.0604887	+	0.0832555i
$250$	−49.3544	−	2.46608i	−3.12144	−	0.155968i
$251$	13.7309	+	4.46143i	0.866686	+	0.281603i	0.708418	−	0.705793i	$-0.249409\pi$
$251$	13.7309	+	4.46143i	0.866686	+	0.281603i	0.158268	+	0.987396i	$0.449409\pi$
$252$	1.05851	+	4.86332i	0.0666798	+	0.306361i
$253$	−10.7690	−	26.6051i	−0.677043	−	1.67265i
$254$	−15.9662	−	12.8650i	−1.00181	−	0.807219i
$255$	0.0459049	−	0.141281i	0.00287468	−	0.00884735i
$256$	−1.36223	+	15.9419i	−0.0851394	+	0.996369i
$257$	−21.1572	−	15.3716i	−1.31975	−	0.958856i	−0.999935	−	0.0113763i	$-0.996379\pi$
$257$	−21.1572	−	15.3716i	−1.31975	−	0.958856i	−0.319816	−	0.947480i	$-0.603621\pi$
$258$	0.813259	+	0.309911i	0.0506313	+	0.0192942i
$259$	0.333824	+	1.02740i	0.0207428	+	0.0638397i
$260$	7.80980	+	3.43168i	0.484343	+	0.212824i
$261$	14.6781	+	20.2026i	0.908549	+	1.25051i
$262$	−6.97226	+	4.55201i	−0.430748	+	0.281224i
$263$	12.1003			0.746136			0.373068	−	0.927804i	$-0.378306\pi$
$263$	12.1003			0.746136			0.373068	+	0.927804i	$0.378306\pi$
$264$	−0.394641	+	0.950646i	−0.0242885	+	0.0585082i
$265$	−15.7819			−0.969474
$266$	5.60878	−	3.66183i	0.343896	−	0.224521i
$267$	0.0448597	+	0.0617441i	0.00274537	+	0.00377868i
$268$	−11.9285	−	5.24145i	−0.728648	−	0.320173i
$269$	3.44527	+	10.6034i	0.210062	+	0.646503i	0.999467	+	0.0326314i	$0.0103887\pi$
$269$	3.44527	+	10.6034i	0.210062	+	0.646503i	−0.789406	+	0.613872i	$0.789611\pi$
$270$	−3.70337	−	1.41126i	−0.225380	−	0.0858863i
$271$	−22.3611	−	16.2463i	−1.35834	−	0.986893i	−0.998548	−	0.0538616i	$-0.982847\pi$
$271$	−22.3611	−	16.2463i	−1.35834	−	0.986893i	−0.359794	−	0.933032i	$-0.617153\pi$
$272$	1.10569	+	0.624096i	0.0670426	+	0.0378414i
$273$	0.0282400	−	0.0869137i	0.00170916	−	0.00526026i
$274$	16.3633	+	13.1849i	0.988545	+	0.796530i
$275$	23.1623	−	37.1204i	1.39674	−	2.23844i
$276$	−0.403887	−	1.85566i	−0.0243111	−	0.111698i
$277$	0.781619	+	0.253963i	0.0469629	+	0.0152592i	0.332404	−	0.943137i	$-0.392140\pi$
$277$	0.781619	+	0.253963i	0.0469629	+	0.0152592i	−0.285441	+	0.958396i	$0.592140\pi$
$278$	21.3182	+	1.06520i	1.27858	+	0.0638865i
$279$	−8.71015	+	11.9885i	−0.521463	+	0.717732i
$280$	−9.93525	−	1.49929i	−0.593745	−	0.0895995i
$281$	24.6517	−	8.00982i	1.47060	−	0.477826i	0.539308	−	0.842109i	$-0.318686\pi$
$281$	24.6517	−	8.00982i	1.47060	−	0.477826i	0.931288	+	0.364283i	$0.118686\pi$
$282$	−0.0671625	−	0.248235i	−0.00399947	−	0.0147822i
$283$	−5.28000	+	3.83615i	−0.313864	+	0.228035i	−0.733553	−	0.679633i	$-0.762139\pi$
$283$	−5.28000	+	3.83615i	−0.313864	+	0.228035i	0.419689	+	0.907668i	$0.362139\pi$
$284$	−2.32721	+	23.2294i	−0.138094	+	1.37841i
$285$			2.66145i			0.157651i
$286$	−3.73723	+	2.83427i	−0.220987	+	0.167594i
$287$			4.39579i			0.259475i
$288$	9.03250	−	14.2866i	0.532245	−	0.841846i
$289$	−13.6718	+	9.93313i	−0.804222	+	0.584302i
$290$	−48.6624	+	13.1661i	−2.85755	+	0.773141i
$291$	0.532342	−	0.172968i	0.0312064	−	0.0101396i
$292$	−0.365829	−	0.626569i	−0.0214085	−	0.0366672i
$293$	−5.80301	+	7.98716i	−0.339015	+	0.466615i	−0.944154	−	0.329506i	$-0.893118\pi$
$293$	−5.80301	+	7.98716i	−0.339015	+	0.466615i	0.605138	+	0.796120i	$0.293118\pi$
$294$	0.0488353	−	0.977356i	0.00284813	−	0.0570005i
$295$	−13.3464	−	4.33651i	−0.777057	−	0.252481i
$296$	1.64159	−	3.28083i	0.0954156	−	0.190694i
$297$	1.66839	−	1.40177i	0.0968100	−	0.0813390i
$298$	4.61712	−	5.73014i	0.267462	−	0.331938i
$299$	2.67423	−	8.23043i	0.154655	−	0.475978i
$300$	1.92666	−	2.16084i	0.111236	−	0.124756i
$301$	−3.77913	−	2.74570i	−0.217825	−	0.158259i
$302$	4.04686	−	10.6196i	0.232871	−	0.611091i
$303$	0.0974809	+	0.300015i	0.00560013	+	0.0172354i
$304$	−22.2953	−	4.51254i	−1.27872	−	0.258812i
$305$	−27.2833	−	37.5522i	−1.56224	−	2.15023i
$306$	−0.733251	−	1.12311i	−0.0419171	−	0.0642040i
$307$	16.7060			0.953461			0.476730	−	0.879050i	$-0.341822\pi$
$307$	16.7060			0.953461			0.476730	+	0.879050i	$0.341822\pi$
$308$	3.37728	−	4.37216i	0.192438	−	0.249127i
$309$	0.838979			0.0477279
$310$	−16.3540	−	25.0492i	−0.928844	−	1.42270i
$311$	−19.8930	−	27.3804i	−1.12803	−	1.55260i	−0.791760	−	0.610832i	$-0.790835\pi$
$311$	−19.8930	−	27.3804i	−1.12803	−	1.55260i	−0.336269	−	0.941766i	$-0.609165\pi$
$312$	−0.275485	+	0.142911i	−0.0155963	+	0.00809072i
$313$	3.45141	+	10.6223i	0.195085	+	0.600411i	0.999976	+	0.00698709i	$0.00222408\pi$
$313$	3.45141	+	10.6223i	0.195085	+	0.600411i	−0.804890	+	0.593424i	$0.797776\pi$
$314$	−8.41958	+	22.0944i	−0.475144	+	1.24686i
$315$	8.58728	+	6.23902i	0.483838	+	0.351529i
$316$	8.43010	+	7.51650i	0.474230	+	0.422836i
$317$	7.60396	−	23.4026i	0.427081	−	1.31442i	−0.473906	−	0.880575i	$-0.657157\pi$
$317$	7.60396	−	23.4026i	0.427081	−	1.31442i	0.900987	−	0.433845i	$-0.142843\pi$
$318$	0.360243	−	0.447084i	0.0202014	−	0.0250712i
$319$	6.68849	−	26.8995i	0.374484	−	1.50609i
$320$	20.4575	+	27.3093i	1.14361	+	1.52664i
$321$	0.958428	+	0.311412i	0.0534943	+	0.0173813i
$322$	−0.508686	+	10.1805i	−0.0283480	+	0.567336i
$323$	−1.06101	+	1.46036i	−0.0590363	+	0.0812565i
$324$	−15.3576	+	8.96668i	−0.853197	+	0.498149i
$325$	12.5467	−	4.07666i	0.695963	−	0.226132i
$326$	−4.89815	+	1.32525i	−0.271284	+	0.0733986i
$327$	0.0913818	−	0.0663927i	0.00505342	−	0.00367153i
$328$	10.4783	−	10.6325i	0.578570	−	0.587084i
$329$			1.38027i			0.0760968i
$330$	0.721042	+	2.07332i	0.0396921	+	0.114133i
$331$			3.72215i			0.204588i	0.994754	+	0.102294i	$0.0326182\pi$
$331$			3.72215i			0.204588i	−0.994754	+	0.102294i	$0.967382\pi$
$332$	−29.4519	−	2.95060i	−1.61638	−	0.161935i
$333$	−3.13537	+	2.27798i	−0.171817	+	0.124832i
$334$	−5.82452	−	21.5276i	−0.318703	−	1.17794i
$335$	−26.4265	+	8.58650i	−1.44383	+	0.469130i
$336$	0.269259	−	0.247232i	0.0146893	−	0.0134876i
$337$	12.8616	−	17.7024i	0.700614	−	0.964312i	−0.299335	−	0.954148i	$-0.596765\pi$
$337$	12.8616	−	17.7024i	0.700614	−	0.964312i	0.999948	−	0.0101639i	$-0.00323532\pi$
$338$	−1.41245	−	0.0705756i	−0.0768272	−	0.00383881i
$339$	−0.809333	−	0.262968i	−0.0439569	−	0.0142825i
$340$	2.64578	−	0.575857i	0.143488	−	0.0312302i
$341$	16.4078	−	1.15791i	0.888530	−	0.0627046i
$342$	18.7119	+	15.0773i	1.01182	+	0.815289i
$343$	−3.42467	+	10.5401i	−0.184915	+	0.569110i
$344$	2.59598	+	15.6497i	0.139966	+	0.843774i
$345$	−3.27658	−	2.38058i	−0.176405	−	0.128166i
$346$	13.6011	+	5.18300i	0.731197	+	0.278640i
$347$	8.35488	+	25.7137i	0.448514	+	1.38038i	0.878584	+	0.477588i	$0.158489\pi$
$347$	8.35488	+	25.7137i	0.448514	+	1.38038i	−0.430070	+	0.902795i	$0.641511\pi$
$348$	0.737803	−	1.67909i	0.0395504	−	0.0900086i
$349$	4.65842	+	6.41176i	0.249359	+	0.343214i	0.915287	−	0.402803i	$-0.131964\pi$
$349$	4.65842	+	6.41176i	0.249359	+	0.343214i	−0.665927	+	0.746016i	$0.731964\pi$
$350$	−13.0112	+	8.49470i	−0.695480	+	0.454061i
$351$	0.657025			0.0350694
$352$	−18.5910	+	2.52490i	−0.990903	+	0.134578i
$353$	18.2794			0.972915			0.486458	−	0.873704i	$-0.338289\pi$
$353$	18.2794			0.972915			0.486458	+	0.873704i	$0.338289\pi$
$354$	0.427498	−	0.279103i	0.0227213	−	0.0148341i
$355$	29.2644	+	40.2790i	1.55319	+	2.13779i
$356$	−0.559625	+	1.27359i	−0.0296601	+	0.0675002i
$357$	−0.00896384	−	0.0275879i	−0.000474417	−	0.00146010i
$358$	16.2088	+	6.17676i	0.856664	+	0.326452i
$359$	−11.2244	−	8.15503i	−0.592403	−	0.430406i	0.250771	−	0.968046i	$-0.419316\pi$
$359$	−11.2244	−	8.15503i	−0.592403	−	0.430406i	−0.843174	+	0.537641i	$0.819316\pi$
$360$	−5.89882	−	35.5607i	−0.310895	−	1.87421i
$361$	4.12237	−	12.6873i	0.216967	−	0.667755i
$362$	20.0278	+	16.1377i	1.05264	+	0.848176i
$363$	−1.18890	−	0.208063i	−0.0624010	−	0.0109205i
$364$	1.62764	−	0.354258i	0.0853115	−	0.0185682i
$365$	−1.47159	−	0.478148i	−0.0770265	−	0.0250274i
$366$	1.68659	+	0.0842736i	0.0881596	+	0.00440505i
$367$	20.2556	−	27.8794i	1.05733	−	1.45530i	0.175060	−	0.984558i	$-0.443988\pi$
$367$	20.2556	−	27.8794i	1.05733	−	1.45530i	0.882273	−	0.470737i	$-0.156012\pi$
$368$	25.4979	−	23.4120i	1.32917	−	1.22043i
$369$	−14.9982	+	4.87321i	−0.780775	+	0.253689i
$370$	−2.04333	−	7.55221i	−0.106228	−	0.392621i
$371$	−2.49317	+	1.81139i	−0.129439	+	0.0940428i
$372$	1.08292	+	0.108491i	0.0561468	+	0.00562499i
$373$		−	21.1404i		−	1.09461i	−0.836935	−	0.547303i	$-0.815655\pi$
$373$		−	21.1404i		−	1.09461i	0.836935	−	0.547303i	$-0.184345\pi$
$374$	−0.430907	+	1.42509i	−0.0222817	+	0.0736899i
$375$		−	3.83403i		−	0.197988i
$376$	3.29018	−	3.33860i	0.169678	−	0.172175i
$377$	6.76134	−	4.91240i	0.348227	−	0.253002i
$378$	−0.747024	+	0.202115i	−0.0384228	+	0.0103957i
$379$	−32.1080	+	10.4325i	−1.64928	+	0.535882i	−0.978583	−	0.205853i	$-0.934003\pi$
$379$	−32.1080	+	10.4325i	−1.64928	+	0.535882i	−0.670693	+	0.741735i	$0.734003\pi$
$380$	−41.8937	+	24.4601i	−2.14910	+	1.25478i
$381$	0.935087	−	1.28704i	0.0479060	−	0.0659369i
$382$	0.291204	−	5.82796i	0.0148993	−	0.298185i
$383$	−18.6863	−	6.07156i	−0.954827	−	0.310242i	−0.210151	−	0.977669i	$-0.567396\pi$
$383$	−18.6863	−	6.07156i	−0.954827	−	0.310242i	−0.744675	+	0.667427i	$0.767396\pi$
$384$	−1.24061	−	0.0438335i	−0.0633099	−	0.00223687i
$385$	−0.829407	−	11.7528i	−0.0422705	−	0.598977i
$386$	4.13606	−	5.13312i	0.210520	−	0.261269i
$387$	5.17860	−	15.9381i	0.263243	−	0.810178i
$388$	7.61517	+	6.78988i	0.386602	+	0.344704i
$389$	−6.51273	−	4.73178i	−0.330209	−	0.239911i	0.410310	−	0.911946i	$-0.365420\pi$
$389$	−6.51273	−	4.73178i	−0.330209	−	0.239911i	−0.740519	+	0.672035i	$0.765420\pi$
$390$	−0.235682	+	0.618470i	−0.0119342	+	0.0313174i
$391$	−0.848845	−	2.61248i	−0.0429279	−	0.132119i
$392$	15.8333	−	8.21368i	0.799702	−	0.414853i
$393$	−0.379732	−	0.522656i	−0.0191549	−	0.0263645i
$394$	9.04307	+	13.8512i	0.455583	+	0.697811i
$395$	24.0868			1.21194
$396$	18.6617	+	6.67607i	0.937784	+	0.335485i
$397$	17.2611			0.866310			0.433155	−	0.901319i	$-0.357400\pi$
$397$	17.2611			0.866310			0.433155	+	0.901319i	$0.357400\pi$
$398$	12.2647	+	18.7857i	0.614775	+	0.941643i
$399$	0.305473	+	0.420447i	0.0152928	+	0.0210487i
$400$	51.7206	+	10.4682i	2.58603	+	0.523409i
$401$	4.31276	+	13.2733i	0.215369	+	0.662837i	0.999127	+	0.0417713i	$0.0133001\pi$
$401$	4.31276	+	13.2733i	0.215369	+	0.662837i	−0.783758	+	0.621066i	$0.786700\pi$
$402$	0.359975	−	0.944634i	0.0179539	−	0.0471140i
$403$	4.01226	+	2.91508i	0.199865	+	0.145211i
$404$	−3.82662	+	4.29173i	−0.190381	+	0.213522i
$405$	−11.7197	+	36.0695i	−0.582356	+	1.79231i
$406$	−6.17635	+	7.66524i	−0.306527	+	0.380419i
$407$	4.17470	+	1.03803i	0.206932	+	0.0514531i
$408$	−0.0440801	+	0.0880969i	−0.00218229	+	0.00436144i
$409$	−7.95797	−	2.58570i	−0.393496	−	0.127855i	0.105584	−	0.994410i	$-0.466329\pi$
$409$	−7.95797	−	2.58570i	−0.393496	−	0.127855i	−0.499080	+	0.866556i	$0.666329\pi$
$410$	1.58876	−	31.7962i	0.0784630	−	1.57030i
$411$	−0.958344	+	1.31905i	−0.0472716	+	0.0650638i
$412$	7.71064	+	13.2063i	0.379876	+	0.650628i
$413$	−2.60614	+	0.846788i	−0.128240	+	0.0416677i
$414$	−35.2992	+	9.55057i	−1.73486	+	0.469385i
$415$	−51.0686	+	37.1035i	−2.50686	+	1.82134i
$416$	−4.78139	−	3.02296i	−0.234427	−	0.148213i
$417$			1.65607i			0.0810983i
$418$	−0.547548	−	26.6681i	−0.0267814	−	1.30438i
$419$			1.48226i			0.0724130i	0.999344	+	0.0362065i	$0.0115274\pi$
$419$			1.48226i			0.0724130i	−0.999344	+	0.0362065i	$0.988473\pi$
$420$	0.0777113	−	0.775689i	0.00379192	−	0.0378497i
$421$	−7.31670	+	5.31589i	−0.356594	+	0.259081i	−0.751630	−	0.659585i	$-0.770732\pi$
$421$	−7.31670	+	5.31589i	−0.356594	+	0.259081i	0.395036	+	0.918666i	$0.370732\pi$
$422$	6.15438	+	22.7468i	0.299590	+	1.10730i
$423$	−4.70941	+	1.53018i	−0.228979	+	0.0743999i
$424$	10.3483	+	1.56162i	0.502559	+	0.0758391i
$425$	2.46133	−	3.38773i	0.119392	−	0.164329i
$426$	−1.80906	−	0.0903930i	−0.0876493	−	0.00437955i
$427$	−8.62023	−	2.80088i	−0.417162	−	0.135544i
$428$	3.90653	+	17.9486i	0.188829	+	0.867577i
$429$	−0.234098	−	0.278625i	−0.0113024	−	0.0134521i
$430$	26.3433	+	21.2264i	1.27039	+	1.02363i
$431$	6.10044	−	18.7752i	0.293848	−	0.904370i	−0.689758	−	0.724040i	$-0.742283\pi$
$431$	6.10044	−	18.7752i	0.293848	−	0.904370i	0.983606	−	0.180331i	$-0.0577168\pi$
$432$	2.28869	+	1.29182i	0.110115	+	0.0621529i
$433$	−12.3335	−	8.96082i	−0.592711	−	0.430630i	0.250573	−	0.968098i	$-0.419381\pi$
$433$	−12.3335	−	8.96082i	−0.592711	−	0.430630i	−0.843284	+	0.537468i	$0.819381\pi$
$434$	−5.45861	−	2.08013i	−0.262022	−	0.0998494i
$435$	−1.20866	−	3.71988i	−0.0579509	−	0.178354i
$436$	1.88493	+	0.828250i	0.0902716	+	0.0396660i
$437$	28.9272	+	39.8149i	1.38378	+	1.90460i
$438$	0.0471365	−	0.0307742i	0.00225227	−	0.00147045i
$439$	−7.76868			−0.370779			−0.185389	−	0.982665i	$-0.559355\pi$
$439$	−7.76868			−0.370779			−0.185389	+	0.982665i	$0.559355\pi$
$440$	−26.0092	+	30.4047i	−1.23994	+	1.44949i
$441$	−18.8430			−0.897288
$442$	−0.375879	+	0.245402i	−0.0178787	+	0.0116726i
$443$	−14.4040	−	19.8254i	−0.684355	−	0.941934i	0.315621	−	0.948885i	$-0.397787\pi$
$443$	−14.4040	−	19.8254i	−0.684355	−	0.941934i	−0.999976	+	0.00695162i	$0.997787\pi$
$444$	0.260588	+	0.114504i	0.0123669	+	0.00543412i
$445$	0.916772	+	2.82153i	0.0434592	+	0.133754i
$446$	−10.9906	−	4.18823i	−0.520421	−	0.198319i
$447$	0.461906	+	0.335594i	0.0218474	+	0.0158731i
$448$	6.36628	+	1.96619i	0.300778	+	0.0928938i
$449$	2.76670	−	8.51502i	0.130569	−	0.401849i	−0.864306	−	0.502967i	$-0.832242\pi$
$449$	2.76670	−	8.51502i	0.130569	−	0.401849i	0.994874	+	0.101118i	$0.0322419\pi$
$450$	−43.4079	−	34.9763i	−2.04627	−	1.64880i
$451$	14.8508	+	9.26655i	0.699295	+	0.436345i
$452$	−3.29882	−	15.1564i	−0.155163	−	0.712899i
$453$	0.838586	+	0.272473i	0.0394002	+	0.0128019i
$454$	17.8298	+	0.890895i	0.836792	+	0.0418118i
$455$	2.08805	−	2.87396i	0.0978895	−	0.134733i
$456$	0.263352	−	1.74514i	0.0123326	−	0.0817236i
$457$	−15.9127	+	5.17036i	−0.744366	+	0.241859i	−0.656555	−	0.754278i	$-0.727987\pi$
$457$	−15.9127	+	5.17036i	−0.744366	+	0.241859i	−0.0878109	+	0.996137i	$0.527987\pi$
$458$	2.87806	+	10.6374i	0.134483	+	0.497052i
$459$	0.168721	−	0.122583i	0.00787523	−	0.00572169i
$460$	7.35899	−	73.4551i	0.343115	−	3.42486i
$461$		−	1.53052i		−	0.0712833i	−0.999365	−	0.0356416i	$-0.988653\pi$
$461$		−	1.53052i		−	0.0712833i	0.999365	−	0.0356416i	$-0.0113475\pi$
$462$	0.351876	+	0.244777i	0.0163708	+	0.0113881i
$463$		−	4.36101i		−	0.202673i	−0.994852	−	0.101337i	$-0.967688\pi$
$463$		−	4.36101i		−	0.202673i	0.994852	−	0.101337i	$-0.0323119\pi$
$464$	33.2112	−	3.81798i	1.54179	−	0.177245i
$465$	1.87775	−	1.36426i	0.0870784	−	0.0632661i
$466$	−34.7241	+	9.39497i	−1.60856	+	0.435213i
$467$	22.9619	−	7.46078i	1.06255	−	0.345244i	0.274969	−	0.961453i	$-0.411333\pi$
$467$	22.9619	−	7.46078i	1.06255	−	0.345244i	0.787582	+	0.616210i	$0.211333\pi$
$468$	3.01313	+	5.16069i	0.139282	+	0.238553i
$469$	−3.18924	+	4.38961i	−0.147265	+	0.202693i
$470$	0.498867	−	9.98397i	0.0230110	−	0.460526i
$471$	−1.74470	−	0.566887i	−0.0803914	−	0.0261208i
$472$	8.32225	+	4.16412i	0.383063	+	0.191669i
$473$	−17.2427	+	6.97935i	−0.792819	+	0.320911i
$474$	−0.549814	+	0.682353i	−0.0252538	+	0.0313415i
$475$	−23.1833	+	71.3510i	−1.06372	+	3.27381i
$476$	0.351876	−	0.394645i	0.0161282	−	0.0180885i
$477$	−8.94432	−	6.49843i	−0.409532	−	0.297543i
$478$	−4.05322	+	10.6363i	−0.185390	+	0.486494i
$479$	1.48433	+	4.56831i	0.0678209	+	0.208731i	0.979223	−	0.202785i	$-0.0649993\pi$
$479$	1.48433	+	4.56831i	0.0678209	+	0.208731i	−0.911402	+	0.411516i	$0.864999\pi$
$480$	−2.03700	+	1.69099i	−0.0929757	+	0.0771830i
$481$	0.762385	+	1.04933i	0.0347618	+	0.0478455i
$482$	−10.1073	−	15.4812i	−0.460374	−	0.705150i
$483$	−0.790857			−0.0359852
$484$	−7.65147	−	20.6266i	−0.347794	−	0.937571i
$485$	21.7583			0.987995
$486$	−2.27817	−	3.48945i	−0.103340	−	0.158285i
$487$	13.9336	+	19.1780i	0.631394	+	0.869039i	0.998120	−	0.0612898i	$-0.0195214\pi$
$487$	13.9336	+	19.1780i	0.631394	+	0.869039i	−0.366726	+	0.930329i	$0.619521\pi$
$488$	14.1741	+	27.3230i	0.641631	+	1.23685i
$489$	−0.121659	−	0.374427i	−0.00550160	−	0.0169322i
$490$	13.5457	−	35.5461i	0.611930	−	1.60581i
$491$	29.2102	+	21.2224i	1.31824	+	0.957754i	0.999952	+	0.00975860i	$0.00310631\pi$
$491$	29.2102	+	21.2224i	1.31824	+	0.957754i	0.318283	+	0.947996i	$0.396894\pi$
$492$	0.864488	+	0.770800i	0.0389741	+	0.0347503i
$493$	0.819761	−	2.52297i	0.0369202	−	0.113629i
$494$	5.04603	−	6.26244i	0.227031	−	0.281760i
$495$	39.1804	−	15.8591i	1.76103	−	0.712815i
$496$	8.24483	+	18.0432i	0.370204	+	0.810165i
$497$	9.24618	+	3.00427i	0.414748	+	0.134760i
$498$	0.114607	−	2.29366i	0.00513565	−	0.102781i
$499$	12.0369	−	16.5674i	0.538846	−	0.741658i	−0.449600	−	0.893230i	$-0.648434\pi$
$499$	12.0369	−	16.5674i	0.538846	−	0.741658i	0.988446	+	0.151572i	$0.0484335\pi$
$500$	60.3511	−	35.2366i	2.69898	−	1.57583i
$501$	1.64563	−	0.534696i	0.0735211	−	0.0238885i
$502$	−19.7091	+	5.33249i	−0.879659	+	0.238001i
$503$	−4.88408	+	3.54849i	−0.217770	+	0.158219i	−0.691322	−	0.722546i	$-0.742972\pi$
$503$	−4.88408	+	3.54849i	−0.217770	+	0.158219i	0.473552	+	0.880766i	$0.342972\pi$
$504$	−5.01340	−	4.94070i	−0.223315	−	0.220076i
$505$			12.2625i			0.545674i
$506$	33.3215	+	23.1795i	1.48132	+	1.03046i
$507$		−	0.109724i		−	0.00487303i
$508$	28.8531	+	2.89060i	1.28015	+	0.128250i
$509$	10.5403	−	7.65799i	0.467191	−	0.339434i	−0.329154	−	0.944276i	$-0.606764\pi$
$509$	10.5403	−	7.65799i	0.467191	−	0.339434i	0.796346	+	0.604842i	$0.206764\pi$
$510$	0.0548675	+	0.202792i	0.00242957	+	0.00897979i
$511$	−0.287357	+	0.0933678i	−0.0127119	+	0.00413035i
$512$	−10.7119	−	19.9313i	−0.473403	−	0.880846i
$513$	−2.19620	+	3.02281i	−0.0969647	+	0.133460i
$514$	36.9381	+	1.84568i	1.62927	+	0.0814094i
$515$	31.0169	+	10.0780i	1.36677	+	0.444090i
$516$	−1.20264	+	0.261757i	−0.0529435	+	0.0115232i
$517$	4.66312	+	2.90968i	0.205084	+	0.127968i
$518$	−1.18961	−	0.958545i	−0.0522687	−	0.0421160i
$519$	−0.348969	+	1.07402i	−0.0153180	+	0.0471441i
$520$	−11.9013	+	1.97419i	−0.521907	+	0.0865742i
$521$	10.6026	+	7.70321i	0.464507	+	0.337484i	0.795297	−	0.606221i	$-0.207315\pi$
$521$	10.6026	+	7.70321i	0.464507	+	0.337484i	−0.330790	+	0.943704i	$0.607315\pi$
$522$	−33.0005	−	12.5756i	−1.44439	−	0.550420i
$523$	6.57912	+	20.2484i	0.287685	+	0.885402i	0.985581	+	0.169204i	$0.0541196\pi$
$523$	6.57912	+	20.2484i	0.287685	+	0.885402i	−0.697896	+	0.716199i	$0.745880\pi$
$524$	4.73716	−	10.7808i	0.206944	−	0.470962i
$525$	−0.708634	−	0.975352i	−0.0309273	−	0.0425678i
$526$	−14.3289	+	9.35499i	−0.624771	+	0.407897i
$527$	1.57421			0.0685735
$528$	−0.267638	−	1.43084i	−0.0116475	−	0.0622694i
$529$	−51.8914			−2.25615
$530$	18.6886	−	12.2013i	0.811781	−	0.529991i
$531$	−5.77839	−	7.95327i	−0.250761	−	0.345143i
$532$	−3.81077	+	8.67254i	−0.165218	+	0.376002i
$533$	1.63095	+	5.01954i	0.0706442	+	0.217421i
$534$	−0.100858	−	0.0384342i	−0.00436454	−	0.00166321i
$535$	31.6922	+	23.0257i	1.37017	+	0.995489i
$536$	18.1777	−	3.01533i	0.785159	−	0.130242i
$537$	−0.415878	+	1.27994i	−0.0179465	+	0.0552335i
$538$	−12.2776	−	9.89277i	−0.529323	−	0.426508i
$539$	13.4546	+	16.0137i	0.579532	+	0.689760i
$540$	5.47653	−	1.19197i	0.235672	−	0.0512944i
$541$	−9.17399	−	2.98081i	−0.394420	−	0.128155i	0.105090	−	0.994463i	$-0.466487\pi$
$541$	−9.17399	−	2.98081i	−0.394420	−	0.128155i	−0.499511	+	0.866308i	$0.666487\pi$
$542$	39.0400	+	1.95070i	1.67691	+	0.0837898i
$543$	−1.17296	+	1.61444i	−0.0503366	+	0.0692824i
$544$	−1.79184	+	0.115794i	−0.0768246	+	0.00496462i
$545$	4.17590	−	1.35683i	0.178876	−	0.0581202i
$546$	0.0337536	+	0.124754i	0.00144452	+	0.00533900i
$547$	−25.4845	+	18.5155i	−1.08964	+	0.791668i	−0.979338	−	0.202231i	$-0.935181\pi$
$547$	−25.4845	+	18.5155i	−1.08964	+	0.791668i	−0.110299	+	0.993898i	$0.535181\pi$
$548$	−29.5707	−	2.96250i	−1.26320	−	0.126552i
$549$		−	32.5169i		−	1.38779i
$550$	1.27020	+	61.8645i	0.0541615	+	2.63791i
$551$			47.5277i			2.02475i
$552$	1.91292	+	1.88518i	0.0814195	+	0.0802387i
$553$	3.80515	−	2.76460i	0.161811	−	0.117563i
$554$	−1.12192	+	0.303548i	−0.0476659	+	0.0128965i
$555$	0.577310	−	0.187579i	0.0245054	−	0.00796230i
$556$	−26.0681	+	15.2201i	−1.10553	+	0.645478i
$557$	19.0461	−	26.2148i	0.807011	−	1.11076i	−0.184767	−	0.982782i	$-0.559153\pi$
$557$	19.0461	−	26.2148i	0.807011	−	1.11076i	0.991778	−	0.127973i	$-0.0408470\pi$
$558$	1.04583	−	20.9305i	0.0442735	−	0.886060i
$559$	−5.33410	−	1.73315i	−0.225608	−	0.0733046i
$560$	12.9243	−	5.90572i	0.546149	−	0.249562i
$561$	−0.112099	−	0.0278732i	−0.00473283	−	0.00117681i
$562$	−22.9995	+	28.5438i	−0.970174	+	1.20405i
$563$	−9.66803	+	29.7551i	−0.407459	+	1.25403i	0.511366	+	0.859363i	$0.329140\pi$
$563$	−9.66803	+	29.7551i	−0.407459	+	1.25403i	−0.918825	+	0.394666i	$0.870860\pi$
$564$	0.271448	+	0.242030i	0.0114300	+	0.0101913i
$565$	−26.7621	−	19.4438i	−1.12589	−	0.818006i
$566$	3.28667	−	8.62478i	0.138149	−	0.362526i
$567$	2.28850	+	7.04327i	0.0961079	+	0.295790i
$568$	−15.2033	−	29.3070i	−0.637917	−	1.22970i
$569$	8.24351	+	11.3462i	0.345586	+	0.475658i	0.946063	−	0.323984i	$-0.105022\pi$
$569$	8.24351	+	11.3462i	0.345586	+	0.475658i	−0.600476	+	0.799642i	$0.705022\pi$
$570$	−2.05763	−	3.15164i	−0.0861845	−	0.132008i
$571$	−10.6526			−0.445798			−0.222899	−	0.974842i	$-0.571552\pi$
$571$	−10.6526			−0.445798			−0.222899	+	0.974842i	$0.571552\pi$
$572$	2.23432	−	6.24562i	0.0934217	−	0.261143i
$573$	0.452737			0.0189134
$574$	−3.39848	−	5.20541i	−0.141850	−	0.217270i
$575$	−67.1052	−	92.3624i	−2.79848	−	3.85178i
$576$	0.349169	+	23.9011i	0.0145487	+	0.995881i
$577$	10.8036	+	33.2502i	0.449761	+	1.38422i	0.877177	+	0.480167i	$0.159424\pi$
$577$	10.8036	+	33.2502i	0.449761	+	1.38422i	−0.427416	+	0.904055i	$0.640576\pi$
$578$	8.51034	−	22.3326i	0.353984	−	0.928912i
$579$	0.413781	+	0.300629i	0.0171961	+	0.0124937i
$580$	47.4461	−	53.2130i	1.97009	−	2.20955i
$581$	−3.80902	+	11.7230i	−0.158025	+	0.486350i
$582$	−0.496663	+	0.616390i	−0.0205874	+	0.0255502i
$583$	0.863892	+	12.2414i	0.0357787	+	0.506988i
$584$	0.917622	+	0.459140i	0.0379715	+	0.0189994i
$585$	12.1206	+	3.93823i	0.501127	+	0.162826i
$586$	0.696770	−	13.9447i	0.0287833	−	0.576049i
$587$	7.24065	−	9.96590i	0.298854	−	0.411337i	−0.633011	−	0.774143i	$-0.718181\pi$
$587$	7.24065	−	9.96590i	0.298854	−	0.411337i	0.931865	+	0.362806i	$0.118181\pi$
$588$	0.697785	+	1.19512i	0.0287762	+	0.0492860i
$589$	−26.8232	+	8.71537i	−1.10523	+	0.359111i
$590$	19.1572	−	5.18317i	0.788689	−	0.213388i
$591$	−1.03831	+	0.754379i	−0.0427105	+	0.0310310i
$592$	0.592535	+	5.15424i	0.0243531	+	0.211838i
$593$			10.6600i			0.437752i	0.975753	+	0.218876i	$0.0702390\pi$
$593$			10.6600i			0.437752i	−0.975753	+	0.218876i	$0.929761\pi$
$594$	−0.891939	+	2.94982i	−0.0365967	+	0.121033i
$595$		−	1.12759i		−	0.0462269i
$596$	−1.03741	+	10.3551i	−0.0424941	+	0.424162i
$597$	−1.40822	+	1.02313i	−0.0576346	+	0.0418740i
$598$	3.19635	+	11.8138i	0.130708	+	0.483103i
$599$	−31.6717	+	10.2907i	−1.29407	+	0.420469i	−0.873514	−	0.486799i	$-0.838165\pi$
$599$	−31.6717	+	10.2907i	−1.29407	+	0.420469i	−0.420555	+	0.907267i	$0.638165\pi$
$600$	−0.610922	+	4.04837i	−0.0249408	+	0.165274i
$601$	12.9774	−	17.8618i	0.529358	−	0.728599i	−0.457675	−	0.889120i	$-0.651318\pi$
$601$	12.9774	−	17.8618i	0.529358	−	0.728599i	0.987032	+	0.160521i	$0.0513175\pi$
$602$	6.59792	+	0.329677i	0.268911	+	0.0134366i
$603$	−18.5127	−	6.01515i	−0.753897	−	0.244956i
$604$	3.41805	+	15.7043i	0.139079	+	0.638998i
$605$	−41.4541	−	21.9734i	−1.68535	−	0.893346i
$606$	−0.347383	−	0.279908i	−0.0141115	−	0.0113705i
$607$	2.03948	−	6.27687i	0.0827798	−	0.254770i	−0.901097	−	0.433618i	$-0.857237\pi$
$607$	2.03948	−	6.27687i	0.0827798	−	0.254770i	0.983877	+	0.178847i	$0.0572369\pi$
$608$	29.8904	−	11.8933i	1.21222	−	0.482338i
$609$	−0.617895	−	0.448927i	−0.0250384	−	0.0181914i
$610$	61.3407	+	23.3753i	2.48361	+	0.946439i
$611$	0.512115	+	1.57613i	0.0207180	+	0.0637634i
$612$	1.73660	+	0.763075i	0.0701980	+	0.0308455i
$613$	2.34232	+	3.22392i	0.0946053	+	0.130213i	0.853696	−	0.520772i	$-0.174356\pi$
$613$	2.34232	+	3.22392i	0.0946053	+	0.130213i	−0.759090	+	0.650985i	$0.774356\pi$
$614$	−19.7829	+	12.9158i	−0.798373	+	0.521237i
$615$	2.47005			0.0996019
$616$	−0.619092	+	7.78848i	−0.0249439	+	0.313807i
$617$	−7.76299			−0.312526			−0.156263	−	0.987715i	$-0.549945\pi$
$617$	−7.76299			−0.312526			−0.156263	+	0.987715i	$0.549945\pi$
$618$	−0.993503	+	0.648633i	−0.0399646	+	0.0260918i
$619$	−26.1306	−	35.9656i	−1.05028	−	1.44558i	−0.888570	−	0.458741i	$-0.848300\pi$
$619$	−26.1306	−	35.9656i	−1.05028	−	1.44558i	−0.161706	−	0.986839i	$-0.551700\pi$
$620$	38.7322	+	17.0192i	1.55552	+	0.683506i
$621$	−1.75703	−	5.40760i	−0.0705074	−	0.216999i
$622$	44.7253	+	17.0436i	1.79332	+	0.683386i
$623$	0.468675	+	0.340512i	0.0187771	+	0.0136423i
$624$	0.215737	−	0.382215i	0.00863638	−	0.0153009i
$625$	25.6719	−	79.0101i	1.02688	−	3.16040i
$626$	−12.2995	−	9.91042i	−0.491585	−	0.396100i
$627$	2.06439	−	0.145686i	0.0824439	−	0.00581816i
$628$	−7.11134	−	32.6731i	−0.283773	−	1.30380i
$629$	0.391554	+	0.127224i	0.0156123	+	0.00507274i
$630$	−14.9924	−	0.749122i	−0.597312	−	0.0298457i
$631$	22.3449	−	30.7551i	0.889537	−	1.22434i	−0.0841503	−	0.996453i	$-0.526818\pi$
$631$	22.3449	−	30.7551i	0.889537	−	1.22434i	0.973687	−	0.227889i	$-0.0731824\pi$
$632$	−15.7939	−	2.38340i	−0.628249	−	0.0948064i
$633$	−1.73882	+	0.564978i	−0.0691120	+	0.0224558i
$634$	9.08857	+	33.5917i	0.360953	+	1.33410i
$635$	50.0302	−	36.3491i	1.98539	−	1.44247i
$636$	−0.0809424	+	0.807940i	−0.00320957	+	0.0320369i
$637$			6.30632i			0.249866i
$638$	12.8762	+	37.0249i	0.509775	+	1.46583i
$639$			34.8780i			1.37975i
$640$	−45.3388	−	16.5231i	−1.79217	−	0.653132i
$641$	23.3897	−	16.9936i	0.923838	−	0.671207i	−0.0206386	−	0.999787i	$-0.506570\pi$
$641$	23.3897	−	16.9936i	0.923838	−	0.671207i	0.944476	+	0.328580i	$0.106570\pi$
$642$	−1.37571	+	0.372213i	−0.0542950	+	0.0146901i
$643$	−10.0341	+	3.26028i	−0.395707	+	0.128573i	−0.500110	−	0.865962i	$-0.666707\pi$
$643$	−10.0341	+	3.26028i	−0.395707	+	0.128573i	0.104403	+	0.994535i	$0.466707\pi$
$644$	−7.26837	−	12.4488i	−0.286414	−	0.490552i
$645$	−1.54284	+	2.12354i	−0.0607492	+	0.0836142i
$646$	0.127396	−	2.54962i	0.00501234	−	0.100313i
$647$	−29.8120	−	9.68650i	−1.17203	−	0.380816i	−0.342630	−	0.939470i	$-0.611318\pi$
$647$	−29.8120	−	9.68650i	−1.17203	−	0.380816i	−0.829400	+	0.558655i	$0.811318\pi$
$648$	11.2538	−	22.4914i	0.442091	−	0.883546i
$649$	−2.63309	+	10.5897i	−0.103358	+	0.415681i
$650$	−11.7058	+	14.5276i	−0.459138	+	0.569819i
$651$	0.140054	−	0.431042i	0.00548916	−	0.0168939i
$652$	4.77572	−	5.35620i	0.187032	−	0.209765i
$653$	1.82531	+	1.32616i	0.0714299	+	0.0518968i	0.622927	−	0.782280i	$-0.285943\pi$
$653$	1.82531	+	1.32616i	0.0714299	+	0.0518968i	−0.551497	+	0.834177i	$0.685943\pi$
$654$	−0.0568829	+	0.149270i	−0.00222430	+	0.00583693i
$655$	−7.76037	−	23.8840i	−0.303223	−	0.933223i
$656$	−4.18801	+	20.6919i	−0.163514	+	0.807882i
$657$	−0.637132	−	0.876937i	−0.0248569	−	0.0342126i
$658$	−1.06712	−	1.63449i	−0.0416006	−	0.0637191i
$659$	9.62701			0.375015			0.187508	−	0.982263i	$-0.439959\pi$
$659$	9.62701			0.375015			0.187508	+	0.982263i	$0.439959\pi$
$660$	−2.45677	−	1.89773i	−0.0956297	−	0.0738691i
$661$	34.4602			1.34035			0.670173	−	0.742205i	$-0.266220\pi$
$661$	34.4602			1.34035			0.670173	+	0.742205i	$0.266220\pi$
$662$	−2.87767	−	4.40770i	−0.111844	−	0.171310i
$663$	−0.0204716	−	0.0281767i	−0.000795051	−	0.00109429i
$664$	37.1576	−	19.2759i	1.44199	−	0.748048i
$665$	6.24277	+	19.2133i	0.242084	+	0.745059i
$666$	1.95169	−	5.12155i	0.0756263	−	0.198456i
$667$	−58.5125	−	42.5118i	−2.26561	−	1.64606i
$668$	23.5407	+	20.9895i	0.910818	+	0.812109i
$669$	0.281992	−	0.867882i	0.0109024	−	0.0335543i
$670$	24.6554	−	30.5989i	0.952520	−	1.18214i
$671$	−27.6344	+	23.2182i	−1.06681	+	0.896330i
$672$	−0.127711	+	0.500937i	−0.00492655	+	0.0193240i
$673$	−25.0698	−	8.14569i	−0.966372	−	0.313993i	−0.217021	−	0.976167i	$-0.569634\pi$
$673$	−25.0698	−	8.14569i	−0.966372	−	0.313993i	−0.749350	+	0.662174i	$0.769634\pi$
$674$	−1.54429	+	30.9064i	−0.0594839	+	1.19047i
$675$	5.09474	−	7.01231i	0.196097	−	0.269904i
$676$	1.72716	−	1.00842i	0.0664293	−	0.0387855i
$677$	−6.36829	+	2.06918i	−0.244753	+	0.0795251i	−0.428825	−	0.903388i	$-0.641072\pi$
$677$	−6.36829	+	2.06918i	−0.244753	+	0.0795251i	0.184072	+	0.982913i	$0.441072\pi$
$678$	1.16170	−	0.314311i	0.0446149	−	0.0120710i
$679$	3.43730	−	2.49735i	0.131912	−	0.0958394i
$680$	−2.68787	+	2.72743i	−0.103075	+	0.104592i
$681$			1.38508i			0.0530764i
$682$	−18.5345	+	14.0564i	−0.709725	+	0.538246i
$683$			9.31128i			0.356286i	0.984005	+	0.178143i	$0.0570090\pi$
$683$			9.31128i			0.356286i	−0.984005	+	0.178143i	$0.942991\pi$
$684$	−33.8149	−	3.38770i	−1.29294	−	0.129532i
$685$	−51.2745	+	37.2531i	−1.95910	+	1.42337i
$686$	−4.09331	−	15.1290i	−0.156283	−	0.577629i
$687$	−0.813149	+	0.264208i	−0.0310236	+	0.0100802i
$688$	−15.1732	−	16.5250i	−0.578473	−	0.630011i
$689$	−2.17487	+	2.99345i	−0.0828560	+	0.114041i
$690$	5.72054	+	0.285837i	0.217777	+	0.0108816i
$691$	24.9130	+	8.09472i	0.947734	+	0.307938i	0.741795	−	0.670627i	$-0.233975\pi$
$691$	24.9130	+	8.09472i	0.947734	+	0.307938i	0.205940	+	0.978565i	$0.433975\pi$
$692$	−20.1132	+	4.37766i	−0.764589	+	0.166414i
$693$	4.36932	−	7.00236i	0.165977	−	0.265998i
$694$	−29.7735	−	23.9903i	−1.13019	−	0.910660i
$695$	−19.8931	+	61.2248i	−0.754590	+	2.32239i
$696$	0.424447	+	2.55875i	0.0160886	+	0.0969893i
$697$	1.35533	+	0.984706i	0.0513368	+	0.0372984i
$698$	−10.4735	−	3.99116i	−0.396427	−	0.151068i
$699$	−0.862467	−	2.65440i	−0.0326215	−	0.100399i
$700$	8.84022	−	20.1185i	0.334129	−	0.760409i
$701$	−5.96809	−	8.21436i	−0.225411	−	0.310252i	0.681300	−	0.732005i	$-0.261415\pi$
$701$	−5.96809	−	8.21436i	−0.225411	−	0.310252i	−0.906711	+	0.421752i	$0.861415\pi$
$702$	−0.778036	+	0.507960i	−0.0293651	+	0.0191717i
$703$	−7.37611			−0.278195
$704$	20.0630	−	17.3630i	0.756154	−	0.654394i
$705$	0.775591			0.0292104
$706$	−21.6461	+	14.1322i	−0.814663	+	0.531873i
$707$	1.40745	+	1.93718i	0.0529325	+	0.0728553i
$708$	−0.290455	+	0.661016i	−0.0109160	+	0.0248425i
$709$	7.70391	+	23.7102i	0.289326	+	0.890455i	0.985068	+	0.172163i	$0.0550757\pi$
$709$	7.70391	+	23.7102i	0.289326	+	0.890455i	−0.695742	+	0.718292i	$0.744924\pi$
$710$	−65.7949	−	25.0727i	−2.46924	−	0.940961i
$711$	13.6511	+	9.91809i	0.511956	+	0.371958i
$712$	−0.321944	−	1.94082i	−0.0120654	−	0.0727353i
$713$	13.2626	−	40.8182i	0.496690	−	1.52865i
$714$	0.0319436	+	0.0257389i	0.00119546	+	0.000963253i
$715$	−5.30768	−	13.1128i	−0.198496	−	0.490389i
$716$	−23.9696	+	5.21701i	−0.895785	+	0.194969i
$717$	−0.839904	−	0.272901i	−0.0313668	−	0.0101917i
$718$	19.5966	+	0.979177i	0.731338	+	0.0365426i
$719$	−3.43070	+	4.72195i	−0.127943	+	0.176099i	−0.868183	−	0.496244i	$-0.834712\pi$
$719$	−3.43070	+	4.72195i	−0.127943	+	0.176099i	0.740240	+	0.672343i	$0.234712\pi$
$720$	34.4780	+	37.5497i	1.28492	+	1.39940i
$721$	6.05667	−	1.96793i	0.225562	−	0.0732895i
$722$	4.92722	+	18.2112i	0.183372	+	0.677750i
$723$	1.16051	−	0.843157i	0.0431597	−	0.0313573i
$724$	−36.1929	−	3.62594i	−1.34510	−	0.134757i
$725$		−	110.255i		−	4.09475i
$726$	1.56873	−	0.672778i	0.0582210	−	0.0249691i
$727$		−	23.3279i		−	0.865183i	−0.901590	−	0.432592i	$-0.857599\pi$
$727$		−	23.3279i		−	0.865183i	0.901590	−	0.432592i	$-0.142401\pi$
$728$	−1.65354	+	1.67787i	−0.0612841	+	0.0621859i
$729$	−21.3193	+	15.4893i	−0.789602	+	0.573679i
$730$	2.11229	−	0.571503i	0.0781795	−	0.0211523i
$731$	−1.69313	+	0.550132i	−0.0626228	+	0.0203474i
$732$	−2.06238	+	1.20415i	−0.0762279	+	0.0445065i
$733$	−23.0234	+	31.6890i	−0.850389	+	1.17046i	0.133388	+	0.991064i	$0.457414\pi$
$733$	−23.0234	+	31.6890i	−0.850389	+	1.17046i	−0.983777	+	0.179396i	$0.942586\pi$
$734$	−2.43210	+	48.6743i	−0.0897704	+	1.79660i
$735$	2.80692	+	0.912023i	0.103535	+	0.0336405i
$736$	−12.0938	+	47.4370i	−0.445782	+	1.74855i
$737$	8.10680	+	20.0281i	0.298618	+	0.737743i
$738$	13.9930	−	17.3662i	0.515089	−	0.639258i
$739$	6.18826	−	19.0455i	0.227639	−	0.700600i	−0.770374	−	0.637592i	$-0.779931\pi$
$739$	6.18826	−	19.0455i	0.227639	−	0.700600i	0.998013	−	0.0630081i	$-0.0200694\pi$
$740$	8.25844	+	7.36344i	0.303586	+	0.270685i
$741$	0.504815	+	0.366770i	0.0185448	+	0.0134736i
$742$	1.55193	−	4.07253i	0.0569733	−	0.149507i
$743$	10.7473	+	33.0767i	0.394280	+	1.21347i	0.929521	+	0.368769i	$0.120221\pi$
$743$	10.7473	+	33.0767i	0.394280	+	1.21347i	−0.535242	+	0.844699i	$0.679779\pi$
$744$	−1.36625	+	0.708755i	−0.0500891	+	0.0259842i
$745$	13.0454	+	17.9554i	0.477945	+	0.657835i
$746$	16.3441	+	25.0340i	0.598398	+	0.916560i
$747$	−44.2208			−1.61796
$748$	−0.591500	−	2.02071i	−0.0216274	−	0.0738846i
$749$	7.64943			0.279504
$750$	2.96417	+	4.54018i	0.108236	+	0.165784i
$751$	−0.418833	−	0.576475i	−0.0152834	−	0.0210359i	0.801307	−	0.598254i	$-0.204138\pi$
$751$	−0.418833	−	0.576475i	−0.0152834	−	0.0210359i	−0.816590	+	0.577218i	$0.804138\pi$
$752$	−1.31503	+	6.49722i	−0.0479542	+	0.236929i
$753$	−0.489528	−	1.50661i	−0.0178394	−	0.0549040i
$754$	−4.20877	+	11.0445i	−0.153274	+	0.402217i
$755$	27.7294	+	20.1466i	1.00918	+	0.733209i
$756$	0.728352	−	0.816881i	0.0264899	−	0.0297097i
$757$	−12.5584	+	38.6509i	−0.456444	+	1.40479i	0.412987	+	0.910737i	$0.364486\pi$
$757$	−12.5584	+	38.6509i	−0.456444	+	1.40479i	−0.869431	+	0.494054i	$0.835514\pi$
$758$	29.9560	−	37.1773i	1.08805	−	1.35034i
$759$	−1.66717	+	2.67183i	−0.0605143	+	0.0969815i
$760$	30.6991	−	61.3541i	1.11357	−	2.22555i
$761$	25.5026	+	8.28629i	0.924467	+	0.300378i	0.732298	−	0.680984i	$-0.238448\pi$
$761$	25.5026	+	8.28629i	0.924467	+	0.300378i	0.192169	+	0.981362i	$0.438448\pi$
$762$	−0.112276	+	2.24702i	−0.00406734	+	0.0814009i
$763$	0.503961	−	0.693642i	0.0182446	−	0.0251115i
$764$	4.16088	+	7.12650i	0.150536	+	0.257828i
$765$	3.84729	−	1.25006i	0.139099	−	0.0451961i
$766$	26.8220	−	7.25698i	0.969120	−	0.262205i
$767$	−2.66177	+	1.93389i	−0.0961110	+	0.0698287i
$768$	1.50300	−	0.907239i	0.0542349	−	0.0327372i
$769$			46.9938i			1.69464i	0.531082	+	0.847320i	$0.321785\pi$
$769$			46.9938i			1.69464i	−0.531082	+	0.847320i	$0.678215\pi$
$770$	10.0685	+	13.2762i	0.362843	+	0.478441i
$771$			2.86949i			0.103342i
$772$	−0.929325	+	9.27622i	−0.0334471	+	0.333858i
$773$	−33.8711	+	24.6088i	−1.21826	+	0.885116i	−0.995954	−	0.0898614i	$-0.971358\pi$
$773$	−33.8711	+	24.6088i	−1.21826	+	0.885116i	−0.222304	+	0.974978i	$0.571358\pi$
$774$	6.18968	+	22.8772i	0.222483	+	0.822306i
$775$	62.2243	−	20.2179i	2.23516	−	0.726248i
$776$	−14.2671	−	2.15299i	−0.512160	−	0.0772880i
$777$	0.0696717	−	0.0958948i	0.00249946	−	0.00344021i
$778$	11.3705	+	0.568147i	0.407652	+	0.0203690i
$779$	−28.5454	−	9.27496i	−1.02274	−	0.332310i
$780$	−0.199062	−	0.914590i	−0.00712755	−	0.0327476i
$781$	29.6410	−	24.9042i	1.06064	−	0.891142i
$782$	3.02495	+	2.43738i	0.108172	+	0.0871606i
$783$	1.69683	−	5.22232i	0.0606399	−	0.186630i
$784$	−12.3993	+	21.9675i	−0.442832	+	0.784555i
$785$	−57.6916	−	41.9154i	−2.05910	−	1.49603i
$786$	0.853748	+	0.325341i	0.0304522	+	0.0116045i
$787$	10.9846	+	33.8071i	0.391558	+	1.20509i	0.931610	+	0.363460i	$0.118405\pi$
$787$	10.9846	+	33.8071i	0.391558	+	1.20509i	−0.540051	+	0.841632i	$0.681595\pi$
$788$	−21.4173	−	9.41088i	−0.762958	−	0.335249i
$789$	−0.780400	−	1.07413i	−0.0277830	−	0.0382400i
$790$	−28.5231	+	18.6220i	−1.01481	+	0.662541i
$791$	−6.45947			−0.229672
$792$	−27.2602	+	6.52207i	−0.968649	+	0.231752i
$793$	−10.8826			−0.386453
$794$	−20.4403	+	13.3449i	−0.725398	+	0.473594i
$795$	1.01784	+	1.40094i	0.0360992	+	0.0496862i
$796$	−29.0473	−	12.7636i	−1.02955	−	0.452393i
$797$	3.23025	+	9.94169i	0.114421	+	0.352153i	0.991826	−	0.127599i	$-0.0407269\pi$
$797$	3.23025	+	9.94169i	0.114421	+	0.352153i	−0.877405	+	0.479751i	$0.840727\pi$
$798$	−0.686791	−	0.261718i	−0.0243121	−	0.00926471i
$799$	0.425572	+	0.309196i	0.0150557	+	0.0109386i
$800$	−69.3397	+	27.5901i	−2.45153	+	0.975457i
$801$	−0.642232	+	1.97659i	−0.0226922	+	0.0698393i
$802$	−15.3690	−	12.3837i	−0.542697	−	0.437284i
$803$	−0.290328	+	1.16763i	−0.0102455	+	0.0412048i
$804$	0.304041	+	1.39692i	0.0107227	+	0.0492656i
$805$	−29.2379	−	9.49996i	−1.03050	−	0.334829i
$806$	−7.00496	−	0.350015i	−0.246739	−	0.0123288i
$807$	0.719055	−	0.989694i	0.0253119	−	0.0348389i
$808$	1.21338	−	8.04063i	0.0426865	−	0.282868i
$809$	19.9897	−	6.49505i	0.702801	−	0.228354i	0.0642502	−	0.997934i	$-0.479534\pi$
$809$	19.9897	−	6.49505i	0.702801	−	0.228354i	0.638550	+	0.769580i	$0.279534\pi$
$810$	−14.0079	−	51.7735i	−0.492186	−	1.81914i
$811$	10.4007	−	7.55656i	0.365219	−	0.265347i	−0.390007	−	0.920812i	$-0.627527\pi$
$811$	10.4007	−	7.55656i	0.365219	−	0.265347i	0.755225	+	0.655465i	$0.227527\pi$
$812$	1.38775	−	13.8521i	0.0487006	−	0.486113i
$813$			3.03277i			0.106364i
$814$	−5.74612	+	1.99834i	−0.201401	+	0.0700417i
$815$		−	15.3039i		−	0.536073i
$816$	−0.0159108	−	0.138402i	−0.000556989	−	0.00484503i
$817$	25.8038	−	18.7476i	0.902762	−	0.655895i
$818$	11.4227	−	3.09054i	0.399386	−	0.108058i
$819$	2.36679	−	0.769017i	0.0827024	−	0.0268716i
$820$	22.7010	+	38.8808i	0.792752	+	1.35778i
$821$	−10.5539	+	14.5263i	−0.368335	+	0.506970i	−0.952447	−	0.304703i	$-0.901443\pi$
$821$	−10.5539	+	14.5263i	−0.368335	+	0.506970i	0.584112	+	0.811673i	$0.301443\pi$
$822$	0.115069	−	2.30291i	0.00401348	−	0.0803231i
$823$	16.4856	+	5.35648i	0.574650	+	0.186715i	0.581903	−	0.813258i	$-0.302308\pi$
$823$	16.4856	+	5.35648i	0.574650	+	0.186715i	−0.00725227	+	0.999974i	$0.502308\pi$
$824$	−19.3409	−	9.67738i	−0.673771	−	0.337128i
$825$	−4.78897	+	0.337963i	−0.166731	+	0.0117664i
$826$	2.43148	−	3.01762i	0.0846019	−	0.104996i
$827$	8.93235	−	27.4909i	0.310608	−	0.955954i	−0.666916	−	0.745132i	$-0.732386\pi$
$827$	8.93235	−	27.4909i	0.310608	−	0.955954i	0.977525	−	0.210821i	$-0.0676138\pi$
$828$	34.4169	−	38.6002i	1.19607	−	1.34145i
$829$	12.3236	+	8.95363i	0.428017	+	0.310972i	0.780855	−	0.624712i	$-0.214784\pi$
$829$	12.3236	+	8.95363i	0.428017	+	0.310972i	−0.352839	+	0.935684i	$0.614784\pi$
$830$	31.7889	−	83.4195i	1.10341	−	2.89553i
$831$	−0.0278660	−	0.0857626i	−0.000966660	−	0.00297507i
$832$	7.99915	−	0.116859i	0.277321	−	0.00405134i
$833$	1.17659	+	1.61944i	0.0407664	+	0.0561101i
$834$	−1.28035	−	1.96109i	−0.0443347	−	0.0679070i
$835$	67.2614			2.32768
$836$	21.2660	+	31.1565i	0.735502	+	1.07757i
$837$	3.25847			0.112629
$838$	−1.14596	−	1.75526i	−0.0395867	−	0.0606345i
$839$	21.8925	+	30.1324i	0.755812	+	1.04029i	0.997551	+	0.0699444i	$0.0222822\pi$
$839$	21.8925	+	30.1324i	0.755812	+	1.04029i	−0.241739	+	0.970341i	$0.577718\pi$
$840$	0.507677	+	0.978636i	0.0175165	+	0.0337661i
$841$	−12.6225	−	38.8482i	−0.435260	−	1.33959i
$842$	4.55446	−	11.9517i	0.156957	−	0.411882i
$843$	−2.30092	−	1.67171i	−0.0792477	−	0.0575769i
$844$	−24.8739	−	22.1782i	−0.856195	−	0.763406i
$845$	1.31803	−	4.05649i	0.0453417	−	0.139548i
$846$	4.39378	−	5.45296i	0.151061	−	0.187477i
$847$	−9.07080	+	1.28668i	−0.311676	+	0.0442109i
$848$	−13.4616	+	6.15127i	−0.462274	+	0.211235i
$849$	0.681061	+	0.221290i	0.0233739	+	0.00759466i
$850$	−0.295533	+	5.91460i	−0.0101367	+	0.202869i
$851$	6.59767	−	9.08091i	0.226165	−	0.311290i
$852$	2.21214	−	1.29158i	0.0757867	−	0.0442489i
$853$	−2.15621	+	0.700597i	−0.0738274	+	0.0239880i	−0.345698	−	0.938346i	$-0.612358\pi$
$853$	−2.15621	+	0.700597i	−0.0738274	+	0.0239880i	0.271870	+	0.962334i	$0.412358\pi$
$854$	12.3733	−	3.34773i	0.423407	−	0.114557i
$855$	−58.6339	+	42.6000i	−2.00524	+	1.45689i
$856$	−18.5025	−	18.2341i	−0.632401	−	0.623230i
$857$		−	16.1535i		−	0.551792i	−0.961187	−	0.275896i	$-0.911025\pi$
$857$		−	16.1535i		−	0.551792i	0.961187	−	0.275896i	$-0.0889745\pi$
$858$	0.492625	+	0.148955i	0.0168180	+	0.00508525i
$859$		−	3.91888i		−	0.133711i	−0.997763	−	0.0668553i	$-0.978703\pi$
$859$		−	3.91888i		−	0.133711i	0.997763	−	0.0668553i	$-0.0212966\pi$
$860$	−47.6059	−	4.76933i	−1.62335	−	0.162633i
$861$	0.390209	−	0.283504i	0.0132983	−	0.00966177i
$862$	7.29150	+	26.9496i	0.248349	+	0.917908i
$863$	−13.8782	+	4.50929i	−0.472418	+	0.153498i	−0.535544	−	0.844508i	$-0.679893\pi$
$863$	−13.8782	+	4.50929i	−0.472418	+	0.153498i	0.0631252	+	0.998006i	$0.479893\pi$
$864$	−3.70896	+	0.239683i	−0.126181	+	0.00815419i
$865$	−25.8027	+	35.5143i	−0.877317	+	1.20752i
$866$	21.5329	+	1.07593i	0.731718	+	0.0365616i
$867$	1.76350	+	0.572997i	0.0598918	+	0.0194600i
$868$	8.07217	−	1.75692i	0.273987	−	0.0596337i
$869$	−1.31850	−	18.6832i	−0.0447270	−	0.633786i
$870$	4.30719	+	3.47056i	0.146027	+	0.117663i
$871$	−2.01313	+	6.19578i	−0.0682123	+	0.209936i
$872$	−2.87243	+	0.476480i	−0.0972728	+	0.0161356i
$873$	12.3314	+	8.95931i	0.417356	+	0.303227i
$874$	−65.0368	−	24.7838i	−2.19990	−	0.838323i
$875$	−8.99318	−	27.6782i	−0.304025	−	0.935693i
$876$	−0.0320259	+	0.0728844i	−0.00108205	+	0.00246254i
$877$	9.77616	+	13.4557i	0.330118	+	0.454368i	0.941523	−	0.336950i	$-0.109395\pi$
$877$	9.77616	+	13.4557i	0.330118	+	0.454368i	−0.611405	+	0.791318i	$0.709395\pi$
$878$	9.19952	−	6.00613i	0.310469	−	0.202697i
$879$	1.08327			0.0365379
$880$	7.29306	−	56.1129i	0.245849	−	1.89157i
$881$	20.4818			0.690048			0.345024	−	0.938594i	$-0.387871\pi$
$881$	20.4818			0.690048			0.345024	+	0.938594i	$0.387871\pi$
$882$	22.3136	−	14.5680i	0.751337	−	0.490529i
$883$	15.8280	+	21.7853i	0.532653	+	0.733135i	0.987532	−	0.157419i	$-0.0503173\pi$
$883$	15.8280	+	21.7853i	0.532653	+	0.733135i	−0.454878	+	0.890554i	$0.650317\pi$
$884$	0.255383	−	0.581200i	0.00858946	−	0.0195479i
$885$	0.475820	+	1.46442i	0.0159945	+	0.0492261i
$886$	32.3844	+	12.3408i	1.08797	+	0.414598i
$887$	−2.48706	−	1.80695i	−0.0835072	−	0.0606715i	0.545248	−	0.838275i	$-0.316435\pi$
$887$	−2.48706	−	1.80695i	−0.0835072	−	0.0606715i	−0.628756	+	0.777603i	$0.716435\pi$
$888$	−0.397109	+	0.0658725i	−0.0133261	+	0.00221054i
$889$	3.73157	−	11.4846i	0.125153	−	0.385181i
$890$	−3.26701	−	2.63243i	−0.109511	−	0.0882393i
$891$	28.6193	+	7.11611i	0.958783	+	0.238399i
$892$	16.2529	−	3.53746i	0.544187	−	0.118443i
$893$	−8.96321	−	2.91232i	−0.299942	−	0.0974572i
$894$	−0.806435	−	0.0402950i	−0.0269712	−	0.00134767i
$895$	−30.7499	+	42.3236i	−1.02786	+	1.41472i
$896$	−9.05892	+	2.59358i	−0.302637	+	0.0866454i
$897$	−0.903078	+	0.293428i	−0.0301529	+	0.00979727i
$898$	3.30687	+	12.2223i	0.110352	+	0.407864i
$899$	33.5324	−	24.3627i	1.11837	−	0.812542i
$900$	78.4437	+	7.85878i	2.61479	+	0.261959i
$901$			1.17448i			0.0391275i
$902$	−24.7501	+	0.508169i	−0.824090	+	0.0169202i
$903$			0.512550i			0.0170566i
$904$	15.6242	+	15.3976i	0.519652	+	0.512116i
$905$	−62.7573	+	45.5959i	−2.08612	+	1.51566i
$906$	−1.20369	+	0.325671i	−0.0399900	+	0.0108197i
$907$	−2.69229	+	0.874778i	−0.0893960	+	0.0290465i	−0.353374	−	0.935482i	$-0.614966\pi$
$907$	−2.69229	+	0.874778i	−0.0893960	+	0.0290465i	0.263978	+	0.964529i	$0.414966\pi$
$908$	−21.8024	+	12.7296i	−0.723539	+	0.422446i
$909$	−5.04926	+	6.94971i	−0.167473	+	0.230507i
$910$	−0.250714	+	5.01761i	−0.00831107	+	0.166332i
$911$	30.4506	+	9.89401i	1.00887	+	0.327803i	0.766406	−	0.642356i	$-0.222043\pi$
$911$	30.4506	+	9.89401i	1.00887	+	0.327803i	0.242468	+	0.970159i	$0.422043\pi$
$912$	1.03735	+	2.27016i	0.0343500	+	0.0751726i
$913$	31.5753	+	37.5810i	1.04499	+	1.24375i
$914$	14.8462	−	18.4251i	0.491070	−	0.609448i
$915$	−1.57385	+	4.84381i	−0.0520299	+	0.160131i
$916$	−11.6321	−	10.3715i	−0.384336	−	0.342684i
$917$	−3.96727	−	2.88239i	−0.131011	−	0.0951850i
$918$	−0.105025	+	0.275602i	−0.00346633	+	0.00909623i
$919$	8.21731	+	25.2903i	0.271064	+	0.834250i	0.990234	+	0.139415i	$0.0445223\pi$
$919$	8.21731	+	25.2903i	0.271064	+	0.834250i	−0.719170	+	0.694834i	$0.755478\pi$
$920$	48.0753	+	92.6734i	1.58500	+	3.05535i
$921$	−1.07744	−	1.48297i	−0.0355029	−	0.0488656i
$922$	1.18328	+	1.81241i	0.0389691	+	0.0596885i
$923$	11.6729			0.384217
$924$	−0.605927	−	0.0178171i	−0.0199335	−	0.000586138i
$925$	17.1111			0.562609
$926$	3.37159	+	5.16422i	0.110797	+	0.169707i
$927$	13.4289	+	18.4834i	0.441064	+	0.607073i
$928$	−36.3762	+	30.1974i	−1.19411	+	0.991279i
$929$	−15.1415	−	46.6007i	−0.496776	−	1.52892i	−0.814171	−	0.580625i	$-0.802808\pi$
$929$	−15.1415	−	46.6007i	−0.496776	−	1.52892i	0.317395	−	0.948293i	$-0.397192\pi$
$930$	−1.16885	+	3.06726i	−0.0383281	+	0.100579i
$931$	−29.0139	−	21.0798i	−0.950891	−	0.690863i
$932$	33.8562	−	37.9713i	1.10900	−	1.24379i
$933$	−1.14754	+	3.53176i	−0.0375687	+	0.115625i
$934$	−21.4230	+	26.5873i	−0.700981	+	0.869962i
$935$	−3.80947	−	2.37703i	−0.124583	−	0.0777371i
$936$	−7.55792	−	3.78168i	−0.247038	−	0.123608i
$937$	−12.4092	−	4.03201i	−0.405392	−	0.131720i	0.0992209	−	0.995065i	$-0.468365\pi$
$937$	−12.4092	−	4.03201i	−0.405392	−	0.131720i	−0.504613	+	0.863345i	$0.668365\pi$
$938$	0.382933	−	7.66376i	0.0125032	−	0.250231i
$939$	0.720337	−	0.991459i	0.0235073	−	0.0323550i
$940$	7.12807	+	12.2085i	0.232492	+	0.398198i
$941$	−8.39051	+	2.72624i	−0.273523	+	0.0888729i	−0.442567	−	0.896736i	$-0.645932\pi$
$941$	−8.39051	+	2.72624i	−0.273523	+	0.0888729i	0.169044	+	0.985609i	$0.445932\pi$
$942$	2.50431	−	0.677567i	0.0815948	−	0.0220763i
$943$	36.9515	−	26.8468i	1.20331	−	0.874252i
$944$	−13.0744	+	1.50304i	−0.425536	+	0.0489199i
$945$		−	2.33402i		−	0.0759258i
$946$	15.0225	−	21.5955i	0.488425	−	0.702130i
$947$		−	35.9330i		−	1.16766i	−0.811874	−	0.583832i	$-0.801553\pi$
$947$		−	35.9330i		−	1.16766i	0.811874	−	0.583832i	$-0.198447\pi$
$948$	0.123537	−	1.23310i	0.00401228	−	0.0400493i
$949$	−0.293490	+	0.213233i	−0.00952710	+	0.00692184i
$950$	−27.7097	−	102.416i	−0.899021	−	3.32281i
$951$	−2.56783	+	0.834340i	−0.0832677	+	0.0270553i
$952$	−0.111576	+	0.739374i	−0.00361619	+	0.0239633i
$953$	21.4852	−	29.5718i	0.695974	−	0.957926i	−0.304013	−	0.952668i	$-0.598326\pi$
$953$	21.4852	−	29.5718i	0.695974	−	0.957926i	0.999986	−	0.00525754i	$-0.00167353\pi$
$954$	15.6158	+	0.780269i	0.505579	+	0.0252621i
$955$	16.7376	+	5.43839i	0.541617	+	0.175982i
$956$	−3.42343	−	15.7290i	−0.110721	−	0.508711i
$957$	−2.81921	+	1.14114i	−0.0911322	+	0.0368878i
$958$	−5.28957	−	4.26213i	−0.170898	−	0.137703i
$959$	−3.82438	+	11.7702i	−0.123496	+	0.380081i
$960$	1.10483	−	3.57729i	0.0356581	−	0.115456i
$961$	−5.18098	−	3.76420i	−0.167128	−	0.121426i
$962$	−1.71406	−	0.653184i	−0.0552636	−	0.0210595i
$963$	8.48023	+	26.0995i	0.273272	+	0.841044i
$964$	23.9377	+	10.5184i	0.770981	+	0.338774i
$965$	11.6862	+	16.0846i	0.376191	+	0.517783i
$966$	0.936517	−	0.611428i	0.0301319	−	0.0196724i
$967$	3.21941			0.103529			0.0517647	−	0.998659i	$-0.483515\pi$
$967$	3.21941			0.103529			0.0517647	+	0.998659i	$0.483515\pi$
$968$	25.0076	+	18.5101i	0.803773	+	0.594936i
$969$	0.198064			0.00636272
$970$	−25.7658	+	16.8218i	−0.827290	+	0.540116i
$971$	−28.6738	−	39.4661i	−0.920187	−	1.26653i	−0.963566	−	0.267470i	$-0.913812\pi$
$971$	−28.6738	−	39.4661i	−0.920187	−	1.26653i	0.0433793	−	0.999059i	$-0.486188\pi$
$972$	5.39553	+	2.37083i	0.173062	+	0.0760445i
$973$	3.88452	+	11.9553i	0.124532	+	0.383271i
$974$	−31.3269	−	11.9378i	−1.00378	−	0.382513i
$975$	−1.17107	−	0.850831i	−0.0375042	−	0.0272484i
$976$	−37.9087	−	21.3971i	−1.21343	−	0.684904i
$977$	10.9434	−	33.6804i	0.350112	−	1.07753i	−0.608679	−	0.793417i	$-0.708300\pi$
$977$	10.9434	−	33.6804i	0.350112	−	1.07753i	0.958790	−	0.284116i	$-0.0916999\pi$
$978$	0.433544	+	0.349333i	0.0138632	+	0.0111704i
$979$	2.13838	−	0.865556i	0.0683429	−	0.0276633i
$980$	11.4409	+	52.5654i	0.365467	+	1.67914i
$981$	2.92537	+	0.950509i	0.0933997	+	0.0303474i
$982$	−50.9976	−	2.54818i	−1.62740	−	0.0813158i
$983$	−10.6975	+	14.7238i	−0.341196	+	0.469616i	−0.944790	−	0.327676i	$-0.893735\pi$
$983$	−10.6975	+	14.7238i	−0.341196	+	0.469616i	0.603595	+	0.797291i	$0.293735\pi$
$984$	−1.61963	−	0.244412i	−0.0516320	−	0.00779157i
$985$	−47.4481	+	15.4168i	−1.51182	+	0.491221i
$986$	0.979813	+	3.62142i	0.0312036	+	0.115330i
$987$	0.122525	−	0.0890197i	0.00390002	−	0.00283353i
$988$	−1.13378	+	11.3170i	−0.0360704	+	0.360043i
$989$			48.5368i			1.54338i
$990$	−34.1356	+	49.0713i	−1.08490	+	1.55959i
$991$		−	40.7398i		−	1.29414i	−0.762429	−	0.647072i	$-0.775993\pi$
$991$		−	40.7398i		−	1.29414i	0.762429	−	0.647072i	$-0.224007\pi$
$992$	−23.7130	−	14.9922i	−0.752888	−	0.476002i
$993$	0.330411	−	0.240058i	0.0104853	−	0.00761800i
$994$	−13.2718	+	3.59082i	−0.420956	+	0.113894i
$995$	−64.3518	+	20.9092i	−2.04009	+	0.662865i
$996$	1.63756	+	2.80471i	0.0518881	+	0.0888706i
$997$	2.13995	−	2.94538i	0.0677728	−	0.0932813i	−0.773785	−	0.633448i	$-0.781639\pi$
$997$	2.13995	−	2.94538i	0.0677728	−	0.0932813i	0.841558	+	0.540167i	$0.181639\pi$
$998$	−1.44528	+	28.9248i	−0.0457494	+	0.915597i
$999$	0.810483	+	0.263342i	0.0256425	+	0.00833177i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.y.a.79.14	✓	288
4.3	odd	2	inner	572.2.y.a.79.28	yes	288
11.6	odd	10	inner	572.2.y.a.391.28	yes	288
44.39	even	10	inner	572.2.y.a.391.14	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.y.a.79.14	✓	288	1.1	even	1	trivial
572.2.y.a.79.28	yes	288	4.3	odd	2	inner
572.2.y.a.391.14	yes	288	44.39	even	10	inner
572.2.y.a.391.28	yes	288	11.6	odd	10	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18418 + 0.773121i) q^{2} +(-0.0644943 - 0.0887688i) q^{3} +(0.804567 - 1.83103i) q^{4} +(-1.31803 - 4.05649i) q^{5} +(0.145002 + 0.0552564i) q^{6} +(-0.673809 - 0.489551i) q^{7} +(0.462856 + 2.79030i) q^{8} +(0.923331 - 2.84172i) q^{9} +O(q^{10})\)	\(q+(-1.18418 + 0.773121i) q^{2} +(-0.0644943 - 0.0887688i) q^{3} +(0.804567 - 1.83103i) q^{4} +(-1.31803 - 4.05649i) q^{5} +(0.145002 + 0.0552564i) q^{6} +(-0.673809 - 0.489551i) q^{7} +(0.462856 + 2.79030i) q^{8} +(0.923331 - 2.84172i) q^{9} +(4.69695 + 3.78462i) q^{10} +(-3.07432 + 1.24440i) q^{11} +(-0.214428 + 0.0466706i) q^{12} +(-0.951057 - 0.309017i) q^{13} +(1.17639 + 0.0587805i) q^{14} +(-0.275084 + 0.378621i) q^{15} +(-2.70534 - 2.94637i) q^{16} +(-0.301881 + 0.0980872i) q^{17} +(1.10360 + 4.07896i) q^{18} +(4.60076 - 3.34265i) q^{19} +(-8.48801 - 0.850359i) q^{20} +0.0913865i q^{21} +(2.67848 - 3.85042i) q^{22} +8.65398i q^{23} +(0.217840 - 0.221046i) q^{24} +(-10.6728 + 7.75426i) q^{25} +(1.36513 - 0.369350i) q^{26} +(-0.624868 + 0.203032i) q^{27} +(-1.43851 + 0.839888i) q^{28} +(-4.91240 + 6.76134i) q^{29} +(0.0330295 - 0.661029i) q^{30} +(-4.71670 - 1.53255i) q^{31} +(5.48152 + 1.39748i) q^{32} +(0.308741 + 0.192647i) q^{33} +(0.281649 - 0.349544i) q^{34} +(-1.09776 + 3.37854i) q^{35} +(-4.46039 - 3.97700i) q^{36} +(-1.04933 - 0.762385i) q^{37} +(-2.86386 + 7.51524i) q^{38} +(0.0339067 + 0.104354i) q^{39} +(10.7088 - 5.55528i) q^{40} +(-3.10225 - 4.26988i) q^{41} +(-0.0706528 - 0.108218i) q^{42} +5.60860 q^{43} +(-0.194964 + 6.63038i) q^{44} -12.7444 q^{45} +(-6.69058 - 10.2479i) q^{46} +(-0.974102 - 1.34074i) q^{47} +(-0.0870668 + 0.430175i) q^{48} +(-1.94876 - 5.99767i) q^{49} +(6.64357 - 17.4338i) q^{50} +(0.0281767 + 0.0204716i) q^{51} +(-1.33101 + 1.49279i) q^{52} +(1.14340 - 3.51901i) q^{53} +(0.582988 - 0.723525i) q^{54} +(9.09997 + 10.8308i) q^{55} +(1.05412 - 2.10672i) q^{56} +(-0.593446 - 0.192822i) q^{57} +(0.589834 - 11.8045i) q^{58} +(1.93389 - 2.66177i) q^{59} +(0.471943 + 0.808314i) q^{60} +(10.3500 - 3.36292i) q^{61} +(6.77027 - 1.83177i) q^{62} +(-2.01331 + 1.46276i) q^{63} +(-7.57153 + 2.58301i) q^{64} +4.26525i q^{65} +(-0.514544 + 0.0105646i) q^{66} -6.51462i q^{67} +(-0.0632832 + 0.631672i) q^{68} +(0.768204 - 0.558133i) q^{69} +(-1.31208 - 4.84950i) q^{70} +(-11.1015 + 3.60711i) q^{71} +(8.35661 + 1.26106i) q^{72} +(0.213233 - 0.293490i) q^{73} +(1.83202 + 0.0915399i) q^{74} +(1.37667 + 0.447308i) q^{75} +(-2.41887 - 11.1135i) q^{76} +(2.68070 + 0.666549i) q^{77} +(-0.120830 - 0.0973600i) q^{78} +(-1.74509 + 5.37083i) q^{79} +(-8.38620 + 14.8576i) q^{80} +(-7.19361 - 5.22646i) q^{81} +(6.97476 + 2.65789i) q^{82} +(-4.57335 - 14.0753i) q^{83} +(0.167331 + 0.0735265i) q^{84} +(0.795780 + 1.09530i) q^{85} +(-6.64160 + 4.33613i) q^{86} +0.917018 q^{87} +(-4.89522 - 8.00230i) q^{88} -0.695560 q^{89} +(15.0917 - 9.85296i) q^{90} +(0.489551 + 0.673809i) q^{91} +(15.8457 + 6.96271i) q^{92} +(0.168158 + 0.517537i) q^{93} +(2.19006 + 0.834575i) q^{94} +(-19.6234 - 14.2572i) q^{95} +(-0.229474 - 0.576718i) q^{96} +(-1.57639 + 4.85163i) q^{97} +(6.94461 + 5.59569i) q^{98} +(0.697621 + 9.88536i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 4 q^{4} + 80 q^{9}+O(q^{10}) \) 288 * q - 4 * q^4 + 80 * q^9	\( 288 q - 4 q^{4} + 80 q^{9} + 8 q^{12} - 6 q^{14} - 32 q^{16} - 50 q^{18} + 16 q^{22} - 88 q^{25} - 50 q^{28} - 20 q^{30} - 4 q^{33} + 30 q^{36} - 48 q^{37} + 38 q^{38} + 70 q^{40} + 56 q^{42} + 66 q^{44} - 96 q^{45} + 70 q^{46} + 76 q^{48} - 56 q^{49} + 70 q^{50} - 20 q^{52} - 80 q^{53} + 44 q^{56} - 20 q^{57} - 2 q^{58} - 144 q^{60} - 150 q^{62} - 100 q^{64} + 30 q^{66} + 24 q^{69} - 28 q^{70} - 100 q^{72} + 40 q^{73} - 140 q^{74} - 24 q^{77} - 40 q^{78} + 118 q^{80} - 76 q^{81} + 56 q^{82} + 120 q^{84} + 80 q^{85} + 44 q^{88} - 8 q^{89} + 80 q^{90} - 14 q^{92} + 72 q^{93} + 50 q^{94} - 140 q^{96} + 116 q^{97}+O(q^{100}) \) 288 * q - 4 * q^4 + 80 * q^9 + 8 * q^12 - 6 * q^14 - 32 * q^16 - 50 * q^18 + 16 * q^22 - 88 * q^25 - 50 * q^28 - 20 * q^30 - 4 * q^33 + 30 * q^36 - 48 * q^37 + 38 * q^38 + 70 * q^40 + 56 * q^42 + 66 * q^44 - 96 * q^45 + 70 * q^46 + 76 * q^48 - 56 * q^49 + 70 * q^50 - 20 * q^52 - 80 * q^53 + 44 * q^56 - 20 * q^57 - 2 * q^58 - 144 * q^60 - 150 * q^62 - 100 * q^64 + 30 * q^66 + 24 * q^69 - 28 * q^70 - 100 * q^72 + 40 * q^73 - 140 * q^74 - 24 * q^77 - 40 * q^78 + 118 * q^80 - 76 * q^81 + 56 * q^82 + 120 * q^84 + 80 * q^85 + 44 * q^88 - 8 * q^89 + 80 * q^90 - 14 * q^92 + 72 * q^93 + 50 * q^94 - 140 * q^96 + 116 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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