LMFDB - Embedded newform 546.2.bz.b.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(31,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 2, 9]))

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

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

chi := DirichletCharacter("546.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bz (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	546.31
Dual form			546.2.bz.b.229.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.326078 + 1.21694i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.699081 - 2.55172i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.326078 + 1.21694i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.699081 - 2.55172i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.629934 - 1.09108i) q^{10} +(-0.452217 + 0.121171i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.447540 + 3.57767i) q^{13} +(-1.33569 + 2.28384i) q^{14} +(0.890861 - 0.890861i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.64373 - 2.84702i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(1.48539 - 5.54353i) q^{19} +(-0.890861 + 0.890861i) q^{20} +(-1.88128 + 1.86032i) q^{21} +0.468170 q^{22} +(-0.932940 + 0.538633i) q^{23} +(0.258819 + 0.965926i) q^{24} +(2.95551 + 1.70637i) q^{25} +(0.493678 - 3.57159i) q^{26} -1.00000i q^{27} +(1.88128 - 1.86032i) q^{28} -5.64101 q^{29} +(-1.09108 + 0.629934i) q^{30} +(9.37395 - 2.51174i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.452217 + 0.121171i) q^{33} +(-2.32458 + 2.32458i) q^{34} +(2.87734 + 1.68280i) q^{35} +1.00000i q^{36} +(2.39408 - 8.93481i) q^{37} +(-2.86954 + 4.97020i) q^{38} +(1.40125 - 3.32212i) q^{39} +(1.09108 - 0.629934i) q^{40} +(5.51172 + 5.51172i) q^{41} +(2.29866 - 1.31002i) q^{42} -9.81229i q^{43} +(-0.452217 - 0.121171i) q^{44} +(-1.21694 + 0.326078i) q^{45} +(1.04056 - 0.278817i) q^{46} +(5.97861 + 1.60196i) q^{47} -1.00000i q^{48} +(-6.02257 - 3.56772i) q^{49} +(-2.41317 - 2.41317i) q^{50} +(-2.84702 + 1.64373i) q^{51} +(-1.40125 + 3.32212i) q^{52} +(6.26166 - 10.8455i) q^{53} +(-0.258819 + 0.965926i) q^{54} -0.589832i q^{55} +(-2.29866 + 1.31002i) q^{56} +(-4.05815 + 4.05815i) q^{57} +(5.44879 + 1.46000i) q^{58} +(-2.94135 - 10.9773i) q^{59} +(1.21694 - 0.326078i) q^{60} +(-1.92642 + 1.11222i) q^{61} -9.70462 q^{62} +(2.55940 - 0.670440i) q^{63} +1.00000i q^{64} +(-4.49974 - 0.621970i) q^{65} +(-0.405447 - 0.234085i) q^{66} +(-1.46827 - 5.47965i) q^{67} +(2.84702 - 1.64373i) q^{68} +1.07727 q^{69} +(-2.34375 - 2.37017i) q^{70} +(-8.53822 + 8.53822i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-1.40244 - 5.23398i) q^{73} +(-4.62500 + 8.01074i) q^{74} +(-1.70637 - 2.95551i) q^{75} +(4.05815 - 4.05815i) q^{76} +(-0.00694096 + 1.23864i) q^{77} +(-2.21333 + 2.84625i) q^{78} +(4.70287 + 8.14561i) q^{79} +(-1.21694 + 0.326078i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.89737 - 6.75044i) q^{82} +(7.71996 + 7.71996i) q^{83} +(-2.55940 + 0.670440i) q^{84} +(2.92866 + 2.92866i) q^{85} +(-2.53961 + 9.47795i) q^{86} +(4.88525 + 2.82050i) q^{87} +(0.405447 + 0.234085i) q^{88} +(5.93301 + 1.58975i) q^{89} +1.25987 q^{90} +(9.44208 + 1.35908i) q^{91} -1.07727 q^{92} +(-9.37395 - 2.51174i) q^{93} +(-5.36028 - 3.09476i) q^{94} +(6.26179 + 3.61525i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(6.33885 + 6.33885i) q^{97} +(4.89396 + 5.00491i) q^{98} +(-0.331046 - 0.331046i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	−0.326078	+	1.21694i	−0.145826	+	0.544232i	0.853891	+	0.520452i	$0.174237\pi$
$5$	−0.326078	+	1.21694i	−0.145826	+	0.544232i	−0.999717	+	0.0237794i	$0.992430\pi$
$6$	0.707107	+	0.707107i	0.288675	+	0.288675i
$7$	0.699081	−	2.55172i	0.264228	−	0.964460i
$7$	0.699081	−	2.55172i	0.264228	−	0.964460i
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.629934	−	1.09108i	0.199203	−	0.345029i
$11$	−0.452217	+	0.121171i	−0.136349	+	0.0365345i	−0.326348	−	0.945250i	$-0.605818\pi$
$11$	−0.452217	+	0.121171i	−0.136349	+	0.0365345i	0.189999	+	0.981784i	$0.439151\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	0.447540	+	3.57767i	0.124125	+	0.992267i
$13$	0.447540	+	3.57767i	0.124125	+	0.992267i
$14$	−1.33569	+	2.28384i	−0.356979	+	0.610382i
$15$	0.890861	−	0.890861i	0.230019	−	0.230019i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	1.64373	−	2.84702i	0.398662	−	0.690503i	−0.594899	−	0.803801i	$-0.702808\pi$
$17$	1.64373	−	2.84702i	0.398662	−	0.690503i	0.993561	+	0.113297i	$0.0361412\pi$
$18$	−0.258819	−	0.965926i	−0.0610042	−	0.227671i
$19$	1.48539	−	5.54353i	0.340771	−	1.27177i	−0.556705	−	0.830710i	$-0.687935\pi$
$19$	1.48539	−	5.54353i	0.340771	−	1.27177i	0.897476	−	0.441064i	$-0.145399\pi$
$20$	−0.890861	+	0.890861i	−0.199203	+	0.199203i
$21$	−1.88128	+	1.86032i	−0.410530	+	0.405954i
$22$	0.468170			0.0998142
$23$	−0.932940	+	0.538633i	−0.194531	+	0.112313i	−0.594102	−	0.804390i	$-0.702493\pi$
$23$	−0.932940	+	0.538633i	−0.194531	+	0.112313i	0.399571	+	0.916702i	$0.369159\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	2.95551	+	1.70637i	0.591103	+	0.341273i
$26$	0.493678	−	3.57159i	0.0968183	−	0.700447i
$27$		−	1.00000i		−	0.192450i
$28$	1.88128	−	1.86032i	0.355529	−	0.351567i
$29$	−5.64101			−1.04751			−0.523754	−	0.851869i	$-0.675469\pi$
$29$	−5.64101			−1.04751			−0.523754	+	0.851869i	$0.675469\pi$
$30$	−1.09108	+	0.629934i	−0.199203	+	0.115010i
$31$	9.37395	−	2.51174i	1.68361	−	0.451122i	0.714882	−	0.699245i	$-0.246480\pi$
$31$	9.37395	−	2.51174i	1.68361	−	0.451122i	0.968729	+	0.248123i	$0.0798137\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	0.452217	+	0.121171i	0.0787209	+	0.0210932i
$34$	−2.32458	+	2.32458i	−0.398662	+	0.398662i
$35$	2.87734	+	1.68280i	0.486358	+	0.284445i
$36$			1.00000i			0.166667i
$37$	2.39408	−	8.93481i	0.393584	−	1.46887i	−0.430595	−	0.902545i	$-0.641696\pi$
$37$	2.39408	−	8.93481i	0.393584	−	1.46887i	0.824179	−	0.566329i	$-0.191637\pi$
$38$	−2.86954	+	4.97020i	−0.465501	+	0.806272i
$39$	1.40125	−	3.32212i	0.224380	−	0.531965i
$40$	1.09108	−	0.629934i	0.172514	−	0.0996013i
$41$	5.51172	+	5.51172i	0.860785	+	0.860785i	0.991429	−	0.130644i	$-0.0417045\pi$
$41$	5.51172	+	5.51172i	0.860785	+	0.860785i	−0.130644	+	0.991429i	$0.541705\pi$
$42$	2.29866	−	1.31002i	0.354692	−	0.202140i
$43$		−	9.81229i		−	1.49636i	−0.663495	−	0.748180i	$-0.730928\pi$
$43$		−	9.81229i		−	1.49636i	0.663495	−	0.748180i	$-0.269072\pi$
$44$	−0.452217	−	0.121171i	−0.0681743	−	0.0182673i
$45$	−1.21694	+	0.326078i	−0.181411	+	0.0486088i
$46$	1.04056	−	0.278817i	0.153422	−	0.0411093i
$47$	5.97861	+	1.60196i	0.872070	+	0.233670i	0.666983	−	0.745073i	$-0.267585\pi$
$47$	5.97861	+	1.60196i	0.872070	+	0.233670i	0.205087	+	0.978744i	$0.434252\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−6.02257	−	3.56772i	−0.860368	−	0.509674i
$50$	−2.41317	−	2.41317i	−0.341273	−	0.341273i
$51$	−2.84702	+	1.64373i	−0.398662	+	0.230168i
$52$	−1.40125	+	3.32212i	−0.194319	+	0.460695i
$53$	6.26166	−	10.8455i	0.860105	−	1.48975i	−0.0117217	−	0.999931i	$-0.503731\pi$
$53$	6.26166	−	10.8455i	0.860105	−	1.48975i	0.871827	−	0.489814i	$-0.162935\pi$
$54$	−0.258819	+	0.965926i	−0.0352208	+	0.131446i
$55$		−	0.589832i		−	0.0795329i
$56$	−2.29866	+	1.31002i	−0.307172	+	0.175058i
$57$	−4.05815	+	4.05815i	−0.537515	+	0.537515i
$58$	5.44879	+	1.46000i	0.715461	+	0.191707i
$59$	−2.94135	−	10.9773i	−0.382931	−	1.42912i	−0.841402	−	0.540409i	$-0.818269\pi$
$59$	−2.94135	−	10.9773i	−0.382931	−	1.42912i	0.458471	−	0.888709i	$-0.348397\pi$
$60$	1.21694	−	0.326078i	0.157106	−	0.0420965i
$61$	−1.92642	+	1.11222i	−0.246652	+	0.142405i	−0.618230	−	0.785997i	$-0.712150\pi$
$61$	−1.92642	+	1.11222i	−0.246652	+	0.142405i	0.371578	+	0.928402i	$0.378817\pi$
$62$	−9.70462			−1.23249
$63$	2.55940	−	0.670440i	0.322454	−	0.0844674i
$64$			1.00000i			0.125000i
$65$	−4.49974	−	0.621970i	−0.558124	−	0.0771458i
$66$	−0.405447	−	0.234085i	−0.0499071	−	0.0288139i
$67$	−1.46827	−	5.47965i	−0.179377	−	0.669446i	−0.995764	−	0.0919406i	$-0.970693\pi$
$67$	−1.46827	−	5.47965i	−0.179377	−	0.669446i	0.816387	−	0.577505i	$-0.195974\pi$
$68$	2.84702	−	1.64373i	0.345252	−	0.199331i
$69$	1.07727			0.129688
$70$	−2.34375	−	2.37017i	−0.280132	−	0.283289i
$71$	−8.53822	+	8.53822i	−1.01330	+	1.01330i	−0.0133903	+	0.999910i	$0.504262\pi$
$71$	−8.53822	+	8.53822i	−1.01330	+	1.01330i	−0.999910	+	0.0133903i	$0.995738\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	−1.40244	−	5.23398i	−0.164143	−	0.612591i	−0.998148	−	0.0608338i	$-0.980624\pi$
$73$	−1.40244	−	5.23398i	−0.164143	−	0.612591i	0.834005	−	0.551758i	$-0.186043\pi$
$74$	−4.62500	+	8.01074i	−0.537645	+	0.931229i
$75$	−1.70637	−	2.95551i	−0.197034	−	0.341273i
$76$	4.05815	−	4.05815i	0.465501	−	0.465501i
$77$	−0.00694096	+	1.23864i	−0.000790996	+	0.141156i
$78$	−2.21333	+	2.84625i	−0.250611	+	0.322275i
$79$	4.70287	+	8.14561i	0.529114	+	0.916453i	0.999423	+	0.0339512i	$0.0108091\pi$
$79$	4.70287	+	8.14561i	0.529114	+	0.916453i	−0.470309	+	0.882502i	$0.655858\pi$
$80$	−1.21694	+	0.326078i	−0.136058	+	0.0364566i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.89737	−	6.75044i	−0.430393	−	0.745462i
$83$	7.71996	+	7.71996i	0.847376	+	0.847376i	0.989805	−	0.142429i	$-0.0454913\pi$
$83$	7.71996	+	7.71996i	0.847376	+	0.847376i	−0.142429	+	0.989805i	$0.545491\pi$
$84$	−2.55940	+	0.670440i	−0.279253	+	0.0731509i
$85$	2.92866	+	2.92866i	0.317658	+	0.317658i
$86$	−2.53961	+	9.47795i	−0.273853	+	1.02203i
$87$	4.88525	+	2.82050i	0.523754	+	0.302390i
$88$	0.405447	+	0.234085i	0.0432208	+	0.0249535i
$89$	5.93301	+	1.58975i	0.628898	+	0.168513i	0.559170	−	0.829053i	$-0.311120\pi$
$89$	5.93301	+	1.58975i	0.628898	+	0.168513i	0.0697285	+	0.997566i	$0.477787\pi$
$90$	1.25987			0.132802
$91$	9.44208	+	1.35908i	0.989799	+	0.142470i
$92$	−1.07727			−0.112313
$93$	−9.37395	−	2.51174i	−0.972033	−	0.260455i
$94$	−5.36028	−	3.09476i	−0.552870	−	0.319200i
$95$	6.26179	+	3.61525i	0.642446	+	0.370916i
$96$	−0.258819	+	0.965926i	−0.0264156	+	0.0985844i
$97$	6.33885	+	6.33885i	0.643613	+	0.643613i	0.951442	−	0.307829i	$-0.0996023\pi$
$97$	6.33885	+	6.33885i	0.643613	+	0.643613i	−0.307829	+	0.951442i	$0.599602\pi$
$98$	4.89396	+	5.00491i	0.494365	+	0.505572i
$99$	−0.331046	−	0.331046i	−0.0332714	−	0.0332714i
$100$	1.70637	+	2.95551i	0.170637	+	0.295551i
$101$	−1.72140	+	2.98154i	−0.171285	+	0.296675i	−0.938869	−	0.344273i	$-0.888125\pi$
$101$	−1.72140	+	2.98154i	−0.171285	+	0.296675i	0.767584	+	0.640948i	$0.221459\pi$
$102$	3.17544	−	0.850856i	0.314415	−	0.0842473i
$103$	2.60757	+	4.51645i	0.256932	+	0.445019i	0.965418	−	0.260705i	$-0.0839551\pi$
$103$	2.60757	+	4.51645i	0.256932	+	0.445019i	−0.708487	+	0.705724i	$0.750622\pi$
$104$	2.21333	−	2.84625i	0.217035	−	0.279098i
$105$	−1.65045	−	2.89601i	−0.161067	−	0.282622i
$106$	−8.85532	+	8.85532i	−0.860105	+	0.860105i
$107$	−3.38886	−	5.86967i	−0.327613	−	0.567442i	0.654425	−	0.756127i	$-0.272911\pi$
$107$	−3.38886	−	5.86967i	−0.327613	−	0.567442i	−0.982038	+	0.188685i	$0.939578\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	3.64370	+	13.5985i	0.349003	+	1.30250i	0.887865	+	0.460103i	$0.152188\pi$
$109$	3.64370	+	13.5985i	0.349003	+	1.30250i	−0.538862	+	0.842394i	$0.681146\pi$
$110$	−0.152660	+	0.569734i	−0.0145555	+	0.0543220i
$111$	−6.54074	+	6.54074i	−0.620819	+	0.620819i
$112$	2.55940	−	0.670440i	0.241840	−	0.0633506i
$113$	−12.5822			−1.18364			−0.591819	−	0.806071i	$-0.701590\pi$
$113$	−12.5822			−1.18364			−0.591819	+	0.806071i	$0.701590\pi$
$114$	4.97020	−	2.86954i	0.465501	−	0.268757i
$115$	−0.351273	−	1.31097i	−0.0327563	−	0.122248i
$116$	−4.88525	−	2.82050i	−0.453584	−	0.261877i
$117$	−2.87458	+	2.17641i	−0.265755	+	0.201210i
$118$			11.3645i			1.04619i
$119$	−6.11570	−	6.18463i	−0.560626	−	0.566944i
$120$	−1.25987			−0.115010
$121$	−9.33646	+	5.39041i	−0.848769	+	0.490037i
$122$	2.14864	−	0.575726i	0.194529	−	0.0521238i
$123$	−2.01743	−	7.52914i	−0.181905	−	0.678880i
$124$	9.37395	+	2.51174i	0.841805	+	0.225561i
$125$	−7.49458	+	7.49458i	−0.670335	+	0.670335i
$126$	−2.64571	−	0.0148257i	−0.235699	−	0.00132078i
$127$			8.46041i			0.750740i	0.926875	+	0.375370i	$0.122484\pi$
$127$			8.46041i			0.750740i	−0.926875	+	0.375370i	$0.877516\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−4.90615	+	8.49770i	−0.431962	+	0.748180i
$130$	4.18543	+	1.76539i	0.367087	+	0.154835i
$131$	11.0365	−	6.37192i	0.964263	−	0.556718i	0.0667807	−	0.997768i	$-0.478727\pi$
$131$	11.0365	−	6.37192i	0.964263	−	0.556718i	0.897483	+	0.441050i	$0.145394\pi$
$132$	0.331046	+	0.331046i	0.0288139	+	0.0288139i
$133$	−13.1072	−	7.66567i	−1.13653	−	0.664698i
$134$			5.67295i			0.490068i
$135$	1.21694	+	0.326078i	0.104737	+	0.0280643i
$136$	−3.17544	+	0.850856i	−0.272291	+	0.0729603i
$137$	−1.82370	+	0.488660i	−0.155809	+	0.0417490i	−0.335881	−	0.941905i	$-0.609034\pi$
$137$	−1.82370	+	0.488660i	−0.155809	+	0.0417490i	0.180071	+	0.983654i	$0.442367\pi$
$138$	−1.04056	−	0.278817i	−0.0885783	−	0.0237345i
$139$			22.5693i			1.91430i	0.289590	+	0.957151i	$0.406481\pi$
$139$			22.5693i			1.91430i	−0.289590	+	0.957151i	$0.593519\pi$
$140$	1.65045	+	2.89601i	0.139488	+	0.244758i
$141$	−4.37665	−	4.37665i	−0.368580	−	0.368580i
$142$	10.4571	−	6.03744i	0.877544	−	0.506650i
$143$	−0.635896	−	1.56365i	−0.0531763	−	0.130759i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.83941	−	6.86476i	0.152754	−	0.570087i
$146$			5.41862i			0.448448i
$147$	3.43184	+	6.10102i	0.283053	+	0.503204i
$148$	6.54074	−	6.54074i	0.537645	−	0.537645i
$149$	3.84137	+	1.02929i	0.314697	+	0.0843228i	0.412710	−	0.910862i	$-0.364582\pi$
$149$	3.84137	+	1.02929i	0.314697	+	0.0843228i	−0.0980134	+	0.995185i	$0.531249\pi$
$150$	0.883280	+	3.29645i	0.0721195	+	0.269154i
$151$	−3.44445	+	0.922938i	−0.280306	+	0.0751076i	−0.396233	−	0.918150i	$-0.629683\pi$
$151$	−3.44445	+	0.922938i	−0.280306	+	0.0751076i	0.115927	+	0.993258i	$0.463016\pi$
$152$	−4.97020	+	2.86954i	−0.403136	+	0.232751i
$153$	3.28745			0.265775
$154$	0.327289	−	1.19464i	0.0263737	−	0.0962668i
$155$			12.2265i			0.982060i
$156$	2.87458	−	2.17641i	0.230151	−	0.174253i
$157$	−9.11496	−	5.26252i	−0.727453	−	0.419995i	0.0900369	−	0.995938i	$-0.471302\pi$
$157$	−9.11496	−	5.26252i	−0.727453	−	0.419995i	−0.817490	+	0.575943i	$0.804635\pi$
$158$	−2.43439	−	9.08525i	−0.193669	−	0.722784i
$159$	−10.8455	+	6.26166i	−0.860105	+	0.496582i
$160$	1.25987			0.0996013
$161$	0.722242	+	2.75715i	0.0569206	+	0.217294i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	−1.84974	+	6.90334i	−0.144883	+	0.540711i	0.854877	+	0.518830i	$0.173632\pi$
$163$	−1.84974	+	6.90334i	−0.144883	+	0.540711i	−0.999761	+	0.0218812i	$0.993034\pi$
$164$	2.01743	+	7.52914i	0.157535	+	0.587927i
$165$	−0.294916	+	0.510810i	−0.0229592	+	0.0397665i
$166$	−5.45884	−	9.45498i	−0.423688	−	0.733849i
$167$	17.3653	−	17.3653i	1.34377	−	1.34377i	0.451500	−	0.892271i	$-0.350889\pi$
$167$	17.3653	−	17.3653i	1.34377	−	1.34377i	0.892271	−	0.451500i	$-0.149111\pi$
$168$	2.64571	+	0.0148257i	0.204121	+	0.00114383i
$169$	−12.5994	+	3.20230i	−0.969186	+	0.246331i
$170$	−2.07088	−	3.58687i	−0.158829	−	0.275100i
$171$	5.54353	−	1.48539i	0.423925	−	0.113590i
$172$	4.90615	−	8.49770i	0.374090	−	0.647943i
$173$	−5.20194	−	9.01003i	−0.395496	−	0.685020i	0.597668	−	0.801744i	$-0.296094\pi$
$173$	−5.20194	−	9.01003i	−0.395496	−	0.685020i	−0.993164	+	0.116724i	$0.962761\pi$
$174$	−3.98879	−	3.98879i	−0.302390	−	0.302390i
$175$	6.42032	−	6.34876i	0.485330	−	0.479921i
$176$	−0.331046	−	0.331046i	−0.0249535	−	0.0249535i
$177$	−2.94135	+	10.9773i	−0.221085	+	0.825102i
$178$	−5.31939	−	3.07115i	−0.398705	−	0.230193i
$179$	−17.6864	−	10.2113i	−1.32195	−	0.763226i	−0.337907	−	0.941180i	$-0.609719\pi$
$179$	−17.6864	−	10.2113i	−1.32195	−	0.763226i	−0.984039	+	0.177954i	$0.943052\pi$
$180$	−1.21694	−	0.326078i	−0.0907053	−	0.0243044i
$181$	−11.6753			−0.867815			−0.433908	−	0.900957i	$-0.642866\pi$
$181$	−11.6753			−0.867815			−0.433908	+	0.900957i	$0.642866\pi$
$182$	−8.76859	−	3.75656i	−0.649971	−	0.278455i
$183$	2.22443			0.164435
$184$	1.04056	+	0.278817i	0.0767110	+	0.0205547i
$185$	10.0925	+	5.82689i	0.742013	+	0.428401i
$186$	8.40445	+	4.85231i	0.616244	+	0.355789i
$187$	−0.398345	+	1.48664i	−0.0291299	+	0.108714i
$188$	4.37665	+	4.37665i	0.319200	+	0.319200i
$189$	−2.55172	−	0.699081i	−0.185610	−	0.0508506i
$190$	−5.11273	−	5.11273i	−0.370916	−	0.370916i
$191$	−1.87084	−	3.24039i	−0.135369	−	0.234466i	0.790369	−	0.612631i	$-0.209889\pi$
$191$	−1.87084	−	3.24039i	−0.135369	−	0.234466i	−0.925738	+	0.378164i	$0.876555\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	5.93176	−	1.58941i	0.426978	−	0.114408i	−0.0389294	−	0.999242i	$-0.512395\pi$
$193$	5.93176	−	1.58941i	0.426978	−	0.114408i	0.465907	+	0.884834i	$0.345728\pi$
$194$	−4.48225	−	7.76348i	−0.321807	−	0.557385i
$195$	3.58590	+	2.78851i	0.256792	+	0.199689i
$196$	−3.43184	−	6.10102i	−0.245132	−	0.435787i
$197$	−0.722366	+	0.722366i	−0.0514665	+	0.0514665i	−0.732372	−	0.680905i	$-0.761587\pi$
$197$	−0.722366	+	0.722366i	−0.0514665	+	0.0514665i	0.680905	+	0.732372i	$0.261587\pi$
$198$	0.234085	+	0.405447i	0.0166357	+	0.0288139i
$199$	−1.65464	+	2.86592i	−0.117294	+	0.203159i	−0.918694	−	0.394969i	$-0.870755\pi$
$199$	−1.65464	+	2.86592i	−0.117294	+	0.203159i	0.801400	+	0.598128i	$0.204089\pi$
$200$	−0.883280	−	3.29645i	−0.0624574	−	0.233094i
$201$	−1.46827	+	5.47965i	−0.103564	+	0.386505i
$202$	2.43442	−	2.43442i	0.171285	−	0.171285i
$203$	−3.94352	+	14.3943i	−0.276781	+	1.01028i
$204$	−3.28745			−0.230168
$205$	−8.50467	+	4.91017i	−0.593992	+	0.342941i
$206$	−1.34978	−	5.03744i	−0.0940435	−	0.350975i
$207$	−0.932940	−	0.538633i	−0.0648438	−	0.0374376i
$208$	−2.87458	+	2.17641i	−0.199316	+	0.150907i
$209$			2.68687i			0.185855i
$210$	0.844665	+	3.22450i	0.0582874	+	0.222512i
$211$	10.7129			0.737509			0.368755	−	0.929527i	$-0.379784\pi$
$211$	10.7129			0.737509			0.368755	+	0.929527i	$0.379784\pi$
$212$	10.8455	−	6.26166i	0.744873	−	0.430053i
$213$	11.6634	−	3.12521i	0.799165	−	0.214136i
$214$	1.75420	+	6.54677i	0.119915	+	0.447528i
$215$	11.9410	+	3.19957i	0.814367	+	0.218209i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	0.143878	−	25.6756i	0.00976709	−	1.74297i
$218$		−	14.0782i		−	0.953494i
$219$	−1.40244	+	5.23398i	−0.0947682	+	0.353680i
$220$	0.294916	−	0.510810i	0.0198832	−	0.0344388i
$221$	10.9213	+	4.60656i	0.734647	+	0.309870i
$222$	8.01074	−	4.62500i	0.537645	−	0.310410i
$223$	−6.88438	−	6.88438i	−0.461012	−	0.461012i	0.437975	−	0.898987i	$-0.355696\pi$
$223$	−6.88438	−	6.88438i	−0.461012	−	0.461012i	−0.898987	+	0.437975i	$0.855696\pi$
$224$	−2.64571	−	0.0148257i	−0.176774	−	0.000990586i
$225$			3.41273i			0.227516i
$226$	12.1535	+	3.25653i	0.808440	+	0.216621i
$227$	26.2834	−	7.04262i	1.74449	−	0.467435i	0.761056	−	0.648687i	$-0.224681\pi$
$227$	26.2834	−	7.04262i	1.74449	−	0.467435i	0.983437	+	0.181251i	$0.0580147\pi$
$228$	−5.54353	+	1.48539i	−0.367129	+	0.0983720i
$229$	−5.72759	−	1.53470i	−0.378490	−	0.101416i	0.0645582	−	0.997914i	$-0.479436\pi$
$229$	−5.72759	−	1.53470i	−0.378490	−	0.101416i	−0.443048	+	0.896498i	$0.646103\pi$
$230$			1.35721i			0.0894920i
$231$	0.625332	−	1.06922i	0.0411438	−	0.0703498i
$232$	3.98879	+	3.98879i	0.261877	+	0.261877i
$233$	5.15172	−	2.97434i	0.337500	−	0.194856i	−0.321666	−	0.946853i	$-0.604243\pi$
$233$	5.15172	−	2.97434i	0.337500	−	0.194856i	0.659166	+	0.751997i	$0.270909\pi$
$234$	3.33993	−	1.35826i	0.218338	−	0.0887922i
$235$	−3.89898	+	6.75324i	−0.254342	+	0.440533i
$236$	2.94135	−	10.9773i	0.191466	−	0.714559i
$237$		−	9.40574i		−	0.610969i
$238$	4.30661	+	7.55675i	0.279156	+	0.489832i
$239$	3.85435	−	3.85435i	0.249317	−	0.249317i	−0.571373	−	0.820690i	$-0.693589\pi$
$239$	3.85435	−	3.85435i	0.249317	−	0.249317i	0.820690	+	0.571373i	$0.193589\pi$
$240$	1.21694	+	0.326078i	0.0785531	+	0.0210482i
$241$	0.549364	+	2.05025i	0.0353876	+	0.132068i	0.981360	−	0.192179i	$-0.0615555\pi$
$241$	0.549364	+	2.05025i	0.0353876	+	0.132068i	−0.945972	+	0.324248i	$0.894889\pi$
$242$	10.4135	−	2.79028i	0.669403	−	0.179366i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−2.22443			−0.142405
$245$	6.30552	−	6.16575i	0.402845	−	0.393915i
$246$			7.79474i			0.496975i
$247$	20.4977	+	2.83326i	1.30424	+	0.180276i
$248$	−8.40445	−	4.85231i	−0.533683	−	0.308122i
$249$	−2.82570	−	10.5457i	−0.179072	−	0.668304i
$250$	9.17894	−	5.29947i	0.580527	−	0.335168i
$251$	−24.4683			−1.54443			−0.772213	−	0.635364i	$-0.780850\pi$
$251$	−24.4683			−1.54443			−0.772213	+	0.635364i	$0.780850\pi$
$252$	2.55172	+	0.699081i	0.160743	+	0.0440379i
$253$	0.356625	−	0.356625i	0.0224208	−	0.0224208i
$254$	2.18972	−	8.17213i	0.137395	−	0.512765i
$255$	−1.07197	−	4.00063i	−0.0671291	−	0.250529i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	11.5545	+	20.0129i	0.720748	+	1.24837i	0.960700	+	0.277588i	$0.0895349\pi$
$257$	11.5545	+	20.0129i	0.720748	+	1.24837i	−0.239952	+	0.970785i	$0.577132\pi$
$258$	6.93834	−	6.93834i	0.431962	−	0.431962i
$259$	−21.1255	−	12.3552i	−1.31268	−	0.767713i
$260$	−3.58590	−	2.78851i	−0.222388	−	0.172936i
$261$	−2.82050	−	4.88525i	−0.174585	−	0.302390i
$262$	−12.3096	+	3.29835i	−0.760490	+	0.203773i
$263$	−0.0390839	+	0.0676953i	−0.00241002	+	0.00417427i	−0.867228	−	0.497911i	$-0.834100\pi$
$263$	−0.0390839	+	0.0676953i	−0.00241002	+	0.00417427i	0.864818	+	0.502086i	$0.167434\pi$
$264$	−0.234085	−	0.405447i	−0.0144069	−	0.0249535i
$265$	11.1565	+	11.1565i	0.685341	+	0.685341i
$266$	10.6765	+	10.7968i	0.654619	+	0.661997i
$267$	−4.34327	−	4.34327i	−0.265804	−	0.265804i
$268$	1.46827	−	5.47965i	0.0896887	−	0.334723i
$269$	14.7061	+	8.49059i	0.896649	+	0.517680i	0.876111	−	0.482109i	$-0.160129\pi$
$269$	14.7061	+	8.49059i	0.896649	+	0.517680i	0.0205373	+	0.999789i	$0.493462\pi$
$270$	−1.09108	−	0.629934i	−0.0664009	−	0.0383366i
$271$	6.56211	+	1.75831i	0.398620	+	0.106810i	0.452559	−	0.891734i	$-0.350511\pi$
$271$	6.56211	+	1.75831i	0.398620	+	0.106810i	−0.0539395	+	0.998544i	$0.517178\pi$
$272$	3.28745			0.199331
$273$	−7.49754	−	5.89804i	−0.453772	−	0.356966i
$274$	1.88804			0.114060
$275$	−1.54330	−	0.413525i	−0.0930643	−	0.0249365i
$276$	0.932940	+	0.538633i	0.0561564	+	0.0324219i
$277$	−16.2126	−	9.36032i	−0.974118	−	0.562407i	−0.0736287	−	0.997286i	$-0.523458\pi$
$277$	−16.2126	−	9.36032i	−0.974118	−	0.562407i	−0.900489	+	0.434879i	$0.856791\pi$
$278$	5.84136	−	21.8003i	0.350342	−	1.30749i
$279$	6.86221	+	6.86221i	0.410829	+	0.410829i
$280$	−0.844665	−	3.22450i	−0.0504784	−	0.192701i
$281$	−11.9711	−	11.9711i	−0.714135	−	0.714135i	0.253263	−	0.967398i	$-0.418496\pi$
$281$	−11.9711	−	11.9711i	−0.714135	−	0.714135i	−0.967398	+	0.253263i	$0.918496\pi$
$282$	3.09476	+	5.36028i	0.184290	+	0.319200i
$283$	−3.08097	+	5.33639i	−0.183145	+	0.317216i	−0.942950	−	0.332935i	$-0.891961\pi$
$283$	−3.08097	+	5.33639i	−0.183145	+	0.317216i	0.759805	+	0.650151i	$0.225294\pi$
$284$	−11.6634	+	3.12521i	−0.692097	+	0.185447i
$285$	−3.61525	−	6.26179i	−0.214149	−	0.370916i
$286$	0.209525	+	1.67496i	0.0123894	+	0.0990422i
$287$	17.9175	−	10.2112i	1.05764	−	0.602750i
$288$	0.707107	−	0.707107i	0.0416667	−	0.0416667i
$289$	3.09632	+	5.36299i	0.182137	+	0.315470i
$290$	−3.55346	+	6.15477i	−0.208666	+	0.361421i
$291$	−2.32018	−	8.65904i	−0.136011	−	0.507602i
$292$	1.40244	−	5.23398i	0.0820717	−	0.306296i
$293$	−13.1790	+	13.1790i	−0.769927	+	0.769927i	−0.978093	−	0.208167i	$-0.933250\pi$
$293$	−13.1790	+	13.1790i	−0.769927	+	0.769927i	0.208167	+	0.978093i	$0.433250\pi$
$294$	−1.73584	−	6.78136i	−0.101236	−	0.395497i
$295$	14.3178			0.833613
$296$	−8.01074	+	4.62500i	−0.465615	+	0.268823i
$297$	0.121171	+	0.452217i	0.00703107	+	0.0262403i
$298$	−3.44408	−	1.98844i	−0.199510	−	0.115187i
$299$	−2.34458	−	3.09669i	−0.135590	−	0.179086i
$300$		−	3.41273i		−	0.197034i
$301$	−25.0382	−	6.85958i	−1.44318	−	0.395380i
$302$	3.56596			0.205198
$303$	2.98154	−	1.72140i	0.171285	−	0.0988916i
$304$	5.54353	−	1.48539i	0.317943	−	0.0851927i
$305$	−0.725338	−	2.70700i	−0.0415327	−	0.155002i
$306$	−3.17544	−	0.850856i	−0.181528	−	0.0486402i
$307$	7.87487	−	7.87487i	0.449443	−	0.449443i	−0.445727	−	0.895169i	$-0.647055\pi$
$307$	7.87487	−	7.87487i	0.449443	−	0.449443i	0.895169	+	0.445727i	$0.147055\pi$
$308$	−0.625332	+	1.06922i	−0.0356316	+	0.0609247i
$309$		−	5.21514i		−	0.296679i
$310$	3.16446	−	11.8099i	0.179729	−	0.670759i
$311$	4.66499	−	8.07999i	0.264527	−	0.458174i	−0.702913	−	0.711276i	$-0.748117\pi$
$311$	4.66499	−	8.07999i	0.264527	−	0.458174i	0.967440	+	0.253102i	$0.0814508\pi$
$312$	−3.33993	+	1.35826i	−0.189086	+	0.0768963i
$313$	−10.7413	+	6.20151i	−0.607136	+	0.350530i	−0.771844	−	0.635812i	$-0.780665\pi$
$313$	−10.7413	+	6.20151i	−0.607136	+	0.350530i	0.164708	+	0.986342i	$0.447332\pi$
$314$	7.44233	+	7.44233i	0.419995	+	0.419995i
$315$	−0.0186785	+	3.33324i	−0.00105241	+	0.187807i
$316$			9.40574i			0.529114i
$317$	9.88384	+	2.64837i	0.555132	+	0.148747i	0.525469	−	0.850813i	$-0.323890\pi$
$317$	9.88384	+	2.64837i	0.555132	+	0.148747i	0.0296629	+	0.999560i	$0.490557\pi$
$318$	12.0966	−	3.24127i	0.678343	−	0.181762i
$319$	2.55096	−	0.683528i	0.142826	−	0.0382702i
$320$	−1.21694	−	0.326078i	−0.0680289	−	0.0182283i
$321$			6.77771i			0.378295i
$322$	0.0159713	−	2.85013i	0.000890043	−	0.158832i
$323$	−13.3410	−	13.3410i	−0.742312	−	0.742312i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−4.78210	+	11.3375i	−0.265263	+	0.628892i
$326$	3.57343	−	6.18936i	0.197914	−	0.342797i
$327$	3.64370	−	13.5985i	0.201497	−	0.751997i
$328$		−	7.79474i		−	0.430393i
$329$	8.26730	−	14.1359i	0.455791	−	0.779335i
$330$	0.417074	−	0.417074i	0.0229592	−	0.0229592i
$331$	−31.1232	−	8.33944i	−1.71069	−	0.458377i	−0.735094	−	0.677965i	$-0.762862\pi$
$331$	−31.1232	−	8.33944i	−1.71069	−	0.458377i	−0.975593	+	0.219588i	$0.929529\pi$
$332$	2.82570	+	10.5457i	0.155081	+	0.578768i
$333$	8.93481	−	2.39408i	0.489625	−	0.131195i
$334$	−21.2681	+	12.2792i	−1.16374	+	0.671885i
$335$	7.14717			0.390491
$336$	−2.55172	−	0.699081i	−0.139208	−	0.0381380i
$337$			11.3341i			0.617406i	0.951159	+	0.308703i	$0.0998949\pi$
$337$			11.3341i			0.617406i	−0.951159	+	0.308703i	$0.900105\pi$
$338$	12.9989	+	0.167788i	0.707048	+	0.00912646i
$339$	10.8965	+	6.29112i	0.591819	+	0.341687i
$340$	1.07197	+	4.00063i	0.0581355	+	0.216965i
$341$	−3.93471	+	2.27171i	−0.213077	+	0.123020i
$342$	−5.73909			−0.310334
$343$	−13.3141	+	12.8738i	−0.718893	+	0.695120i
$344$	−6.93834	+	6.93834i	−0.374090	+	0.374090i
$345$	−0.351273	+	1.31097i	−0.0189119	+	0.0705801i
$346$	2.69272	+	10.0494i	0.144762	+	0.540258i
$347$	−12.4142	+	21.5020i	−0.666429	+	1.15429i	0.312466	+	0.949929i	$0.398845\pi$
$347$	−12.4142	+	21.5020i	−0.666429	+	1.15429i	−0.978896	+	0.204361i	$0.934488\pi$
$348$	2.82050	+	4.88525i	0.151195	+	0.261877i
$349$	9.64215	−	9.64215i	0.516132	−	0.516132i	−0.400266	−	0.916399i	$-0.631082\pi$
$349$	9.64215	−	9.64215i	0.516132	−	0.516132i	0.916399	+	0.400266i	$0.131082\pi$
$350$	−7.84473	+	4.47073i	−0.419318	+	0.238971i
$351$	3.57767	−	0.447540i	0.190962	−	0.0238879i
$352$	0.234085	+	0.405447i	0.0124768	+	0.0216104i
$353$	16.5210	−	4.42680i	0.879327	−	0.235615i	0.209210	−	0.977871i	$-0.432911\pi$
$353$	16.5210	−	4.42680i	0.879327	−	0.235615i	0.670117	+	0.742256i	$0.266244\pi$
$354$	5.68225	−	9.84195i	0.302008	−	0.523094i
$355$	−7.60637	−	13.1746i	−0.403704	−	0.699236i
$356$	4.34327	+	4.34327i	0.230193	+	0.230193i
$357$	2.20404	+	8.41390i	0.116650	+	0.445311i
$358$	14.4409	+	14.4409i	0.763226	+	0.763226i
$359$	−0.201345	+	0.751428i	−0.0106266	+	0.0396589i	−0.971036	−	0.238935i	$-0.923202\pi$
$359$	−0.201345	+	0.751428i	−0.0106266	+	0.0396589i	0.960409	+	0.278594i	$0.0898684\pi$
$360$	1.09108	+	0.629934i	0.0575048	+	0.0332004i
$361$	−12.0699	−	6.96856i	−0.635258	−	0.366767i
$362$	11.2774	+	3.02178i	0.592729	+	0.158821i
$363$	10.7808			0.565846
$364$	7.49754	+	5.89804i	0.392978	+	0.309141i
$365$	6.82674			0.357328
$366$	−2.14864	−	0.575726i	−0.112311	−	0.0300937i
$367$	−11.0096	−	6.35641i	−0.574698	−	0.331802i	0.184325	−	0.982865i	$-0.440990\pi$
$367$	−11.0096	−	6.35641i	−0.574698	−	0.331802i	−0.759024	+	0.651063i	$0.774323\pi$
$368$	−0.932940	−	0.538633i	−0.0486328	−	0.0280782i
$369$	−2.01743	+	7.52914i	−0.105023	+	0.391952i
$370$	−8.24046	−	8.24046i	−0.428401	−	0.428401i
$371$	−23.2973	−	23.5599i	−1.20954	−	1.22317i
$372$	−6.86221	−	6.86221i	−0.355789	−	0.355789i
$373$	11.4809	+	19.8855i	0.594459	+	1.02963i	0.993623	+	0.112754i	$0.0359672\pi$
$373$	11.4809	+	19.8855i	0.594459	+	1.02963i	−0.399164	+	0.916880i	$0.630700\pi$
$374$	0.769543	−	1.33289i	0.0397921	−	0.0689220i
$375$	10.2378	−	2.74321i	0.528677	−	0.141659i
$376$	−3.09476	−	5.36028i	−0.159600	−	0.276435i
$377$	−2.52457	−	20.1816i	−0.130022	−	1.03941i
$378$	2.28384	+	1.33569i	0.117468	+	0.0687007i
$379$	21.3202	−	21.3202i	1.09515	−	1.09515i	0.100178	−	0.994970i	$-0.468059\pi$
$379$	21.3202	−	21.3202i	1.09515	−	1.09515i	0.994970	−	0.100178i	$-0.0319412\pi$
$380$	3.61525	+	6.26179i	0.185458	+	0.321223i
$381$	4.23021	−	7.32693i	0.216720	−	0.375370i
$382$	0.968418	+	3.61418i	0.0495486	+	0.184918i
$383$	−6.78800	+	25.3332i	−0.346851	+	1.29446i	0.543585	+	0.839354i	$0.317067\pi$
$383$	−6.78800	+	25.3332i	−0.346851	+	1.29446i	−0.890435	+	0.455110i	$0.849600\pi$
$384$	−0.707107	+	0.707107i	−0.0360844	+	0.0360844i
$385$	−1.50509	−	0.412340i	−0.0767064	−	0.0210148i
$386$	−6.14101			−0.312569
$387$	8.49770	−	4.90615i	0.431962	−	0.249393i
$388$	2.32018	+	8.65904i	0.117789	+	0.439596i
$389$	12.7127	+	7.33965i	0.644557	+	0.372135i	0.786368	−	0.617759i	$-0.211959\pi$
$389$	12.7127	+	7.33965i	0.644557	+	0.372135i	−0.141811	+	0.989894i	$0.545292\pi$
$390$	−2.74199	−	3.62159i	−0.138846	−	0.183386i
$391$			3.54146i			0.179099i
$392$	1.73584	+	6.78136i	0.0876733	+	0.342510i
$393$	−12.7438			−0.642842
$394$	0.884714	−	0.510790i	0.0445713	−	0.0257332i
$395$	−11.4462	+	3.06700i	−0.575921	+	0.154318i
$396$	−0.121171	−	0.452217i	−0.00608909	−	0.0227248i
$397$	14.1029	+	3.77887i	0.707806	+	0.189656i	0.594724	−	0.803930i	$-0.297261\pi$
$397$	14.1029	+	3.77887i	0.707806	+	0.189656i	0.113082	+	0.993586i	$0.463928\pi$
$398$	2.34001	−	2.34001i	0.117294	−	0.117294i
$399$	7.51829	+	13.1922i	0.376385	+	0.660438i
$400$			3.41273i			0.170637i
$401$	6.28288	−	23.4480i	0.313752	−	1.17094i	−0.611394	−	0.791326i	$-0.709391\pi$
$401$	6.28288	−	23.4480i	0.313752	−	1.17094i	0.925146	−	0.379612i	$-0.123942\pi$
$402$	2.83648	−	4.91292i	0.141471	−	0.245034i
$403$	13.1814	+	32.4128i	0.656612	+	1.61459i
$404$	−2.98154	+	1.72140i	−0.148337	+	0.0856426i
$405$	−0.890861	−	0.890861i	−0.0442672	−	0.0442672i
$406$	7.53466	−	12.8831i	0.373939	−	0.639380i
$407$			4.33057i			0.214658i
$408$	3.17544	+	0.850856i	0.157208	+	0.0421236i
$409$	1.77554	−	0.475754i	0.0877947	−	0.0235245i	−0.214654	−	0.976690i	$-0.568862\pi$
$409$	1.77554	−	0.475754i	0.0877947	−	0.0235245i	0.302449	+	0.953166i	$0.402196\pi$
$410$	9.48572	−	2.54169i	0.468467	−	0.125525i
$411$	1.82370	+	0.488660i	0.0899566	+	0.0241038i
$412$			5.21514i			0.256932i
$413$	−30.0672	−	0.168487i	−1.47951	−	0.00829071i
$414$	0.761742	+	0.761742i	0.0374376	+	0.0374376i
$415$	−11.9120	+	6.87741i	−0.584738	+	0.337599i
$416$	3.33993	−	1.35826i	0.163754	−	0.0665941i
$417$	11.2846	−	19.5456i	0.552611	−	0.957151i
$418$	0.695413	−	2.59532i	0.0340137	−	0.126941i
$419$			6.05412i			0.295763i	0.989005	+	0.147882i	$0.0472455\pi$
$419$			6.05412i			0.295763i	−0.989005	+	0.147882i	$0.952755\pi$
$420$	0.0186785	−	3.33324i	0.000911416	−	0.162646i
$421$	−2.64725	+	2.64725i	−0.129019	+	0.129019i	−0.768668	−	0.639648i	$-0.779080\pi$
$421$	−2.64725	+	2.64725i	−0.129019	+	0.129019i	0.639648	+	0.768668i	$0.279080\pi$
$422$	−10.3479	−	2.77271i	−0.503728	−	0.134974i
$423$	1.60196	+	5.97861i	0.0778902	+	0.290690i
$424$	−12.0966	+	3.24127i	−0.587463	+	0.157410i
$425$	9.71611	−	5.60960i	0.471301	−	0.272106i
$426$	−12.0749			−0.585029
$427$	1.49135	+	5.69321i	0.0721714	+	0.275514i
$428$		−	6.77771i		−	0.327613i
$429$	−0.231125	+	1.67211i	−0.0111588	+	0.0807304i
$430$	−10.7060	−	6.18110i	−0.516288	−	0.298079i
$431$	−2.93529	−	10.9547i	−0.141388	−	0.527667i	−0.999890	−	0.0148565i	$-0.995271\pi$
$431$	−2.93529	−	10.9547i	−0.141388	−	0.527667i	0.858502	−	0.512811i	$-0.171396\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−0.446726			−0.0214683			−0.0107341	−	0.999942i	$-0.503417\pi$
$433$	−0.446726			−0.0214683			−0.0107341	+	0.999942i	$0.503417\pi$
$434$	−6.78431	+	24.7635i	−0.325658	+	1.18869i
$435$	−5.02535	+	5.02535i	−0.240947	+	0.240947i
$436$	−3.64370	+	13.5985i	−0.174502	+	0.651249i
$437$	1.60016	+	5.97186i	0.0765458	+	0.285673i
$438$	2.70931	−	4.69266i	0.129456	−	0.224224i
$439$	6.55200	+	11.3484i	0.312710	+	0.541630i	0.978948	−	0.204109i	$-0.0654299\pi$
$439$	6.55200	+	11.3484i	0.312710	+	0.541630i	−0.666238	+	0.745739i	$0.732097\pi$
$440$	−0.417074	+	0.417074i	−0.0198832	+	0.0198832i
$441$	0.0784492	−	6.99956i	0.00373567	−	0.333312i
$442$	−9.35692	−	7.27624i	−0.445063	−	0.346095i
$443$	−14.2567	−	24.6933i	−0.677356	−	1.17321i	−0.975774	−	0.218779i	$-0.929793\pi$
$443$	−14.2567	−	24.6933i	−0.677356	−	1.17321i	0.298419	−	0.954435i	$-0.403541\pi$
$444$	−8.93481	+	2.39408i	−0.424028	+	0.113618i
$445$	−3.86925	+	6.70173i	−0.183420	+	0.317693i
$446$	4.86799	+	8.43160i	0.230506	+	0.399248i
$447$	−2.81208	−	2.81208i	−0.133007	−	0.133007i
$448$	2.55172	+	0.699081i	0.120558	+	0.0330285i
$449$	−4.74753	−	4.74753i	−0.224050	−	0.224050i	0.586152	−	0.810201i	$-0.300642\pi$
$449$	−4.74753	−	4.74753i	−0.224050	−	0.224050i	−0.810201	+	0.586152i	$0.800642\pi$
$450$	0.883280	−	3.29645i	0.0416382	−	0.155396i
$451$	−3.16036	−	1.82463i	−0.148815	−	0.0859186i
$452$	−10.8965	−	6.29112i	−0.512530	−	0.295910i
$453$	3.44445	+	0.922938i	0.161834	+	0.0433634i
$454$	−27.2106			−1.27706
$455$	−4.73277	+	11.0473i	−0.221876	+	0.517904i
$456$	5.73909			0.268757
$457$	−7.47514	−	2.00296i	−0.349673	−	0.0936945i	0.0797077	−	0.996818i	$-0.474601\pi$
$457$	−7.47514	−	2.00296i	−0.349673	−	0.0936945i	−0.429380	+	0.903124i	$0.641268\pi$
$458$	5.13522	+	2.96482i	0.239953	+	0.138537i
$459$	−2.84702	−	1.64373i	−0.132887	−	0.0767226i
$460$	0.351273	−	1.31097i	0.0163782	−	0.0611241i
$461$	29.9051	+	29.9051i	1.39282	+	1.39282i	0.818937	+	0.573884i	$0.194564\pi$
$461$	29.9051	+	29.9051i	1.39282	+	1.39282i	0.573884	+	0.818937i	$0.305436\pi$
$462$	−0.880760	+	0.870944i	−0.0409767	+	0.0405200i
$463$	−7.92000	−	7.92000i	−0.368074	−	0.368074i	0.498701	−	0.866774i	$-0.333811\pi$
$463$	−7.92000	−	7.92000i	−0.368074	−	0.368074i	−0.866774	+	0.498701i	$0.833811\pi$
$464$	−2.82050	−	4.88525i	−0.130939	−	0.226792i
$465$	6.11327	−	10.5885i	0.283496	−	0.491030i
$466$	−5.74599	+	1.53963i	−0.266178	+	0.0713222i
$467$	−5.64991	−	9.78594i	−0.261447	−	0.452839i	0.705180	−	0.709029i	$-0.250866\pi$
$467$	−5.64991	−	9.78594i	−0.261447	−	0.452839i	−0.966627	+	0.256189i	$0.917533\pi$
$468$	−3.57767	+	0.447540i	−0.165378	+	0.0206875i
$469$	−15.0090	−	0.0841056i	−0.693050	−	0.00388364i
$470$	5.51400	−	5.51400i	0.254342	−	0.254342i
$471$	5.26252	+	9.11496i	0.242484	+	0.419995i
$472$	−5.68225	+	9.84195i	−0.261547	+	0.453013i
$473$	1.18897	+	4.43729i	0.0546688	+	0.204027i
$474$	−2.43439	+	9.08525i	−0.111815	+	0.417299i
$475$	13.8494	−	13.8494i	0.635453	−	0.635453i
$476$	−2.20404	−	8.41390i	−0.101022	−	0.385650i
$477$	12.5233			0.573403
$478$	−4.72059	+	2.72544i	−0.215915	+	0.124659i
$479$	2.48456	+	9.27249i	0.113522	+	0.423671i	0.999172	−	0.0406828i	$-0.0129533\pi$
$479$	2.48456	+	9.27249i	0.113522	+	0.423671i	−0.885650	+	0.464354i	$0.846287\pi$
$480$	−1.09108	−	0.629934i	−0.0498006	−	0.0287524i
$481$	33.0372	+	4.56653i	1.50637	+	0.208216i
$482$		−	2.12258i		−	0.0966808i
$483$	0.753096	−	2.74888i	0.0342670	−	0.125079i
$484$	−10.7808			−0.490037
$485$	−9.78096	+	5.64704i	−0.444130	+	0.256419i
$486$	−0.965926	+	0.258819i	−0.0438153	+	0.0117403i
$487$	2.24656	+	8.38427i	0.101801	+	0.379928i	0.997963	−	0.0638006i	$-0.0203222\pi$
$487$	2.24656	+	8.38427i	0.101801	+	0.379928i	−0.896161	+	0.443728i	$0.853656\pi$
$488$	2.14864	+	0.575726i	0.0972643	+	0.0260619i
$489$	5.05359	−	5.05359i	0.228531	−	0.228531i
$490$	−7.68648	+	4.32367i	−0.347240	+	0.195323i
$491$			39.2967i			1.77343i	0.462313	+	0.886717i	$0.347020\pi$
$491$			39.2967i			1.77343i	−0.462313	+	0.886717i	$0.652980\pi$
$492$	2.01743	−	7.52914i	0.0909527	−	0.339440i
$493$	−9.27227	+	16.0600i	−0.417602	+	0.723308i
$494$	−19.0659	−	8.04192i	−0.857817	−	0.361823i
$495$	0.510810	−	0.294916i	0.0229592	−	0.0132555i
$496$	6.86221	+	6.86221i	0.308122	+	0.308122i
$497$	15.8183	+	27.7561i	0.709546	+	1.24503i
$498$			10.9177i			0.489233i
$499$	−18.4356	−	4.93979i	−0.825289	−	0.221135i	−0.178631	−	0.983916i	$-0.557167\pi$
$499$	−18.4356	−	4.93979i	−0.825289	−	0.221135i	−0.646657	+	0.762781i	$0.723834\pi$
$500$	−10.2378	+	2.74321i	−0.457848	+	0.122680i
$501$	−23.7215	+	6.35616i	−1.05980	+	0.283972i
$502$	23.6346	+	6.33286i	1.05486	+	0.282649i
$503$		−	19.9322i		−	0.888732i	−0.895845	−	0.444366i	$-0.853429\pi$
$503$		−	19.9322i		−	0.888732i	0.895845	−	0.444366i	$-0.146571\pi$
$504$	−2.28384	−	1.33569i	−0.101730	−	0.0594966i
$505$	−3.06705	−	3.06705i	−0.136482	−	0.136482i
$506$	−0.436774	+	0.252172i	−0.0194170	+	0.0112104i
$507$	12.5126	+	3.52644i	0.555702	+	0.156615i
$508$	−4.23021	+	7.32693i	−0.187685	+	0.325080i
$509$	−5.97328	+	22.2926i	−0.264761	+	0.988102i	0.697635	+	0.716453i	$0.254236\pi$
$509$	−5.97328	+	22.2926i	−0.264761	+	0.988102i	−0.962396	+	0.271649i	$0.912431\pi$
$510$			4.14176i			0.183400i
$511$	−14.3361	−	0.0803350i	−0.634191	−	0.00355381i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−5.54353	−	1.48539i	−0.244753	−	0.0655814i
$514$	−5.98104	−	22.3215i	−0.263812	−	0.984560i
$515$	−6.34651	+	1.70054i	−0.279661	+	0.0749348i
$516$	−8.49770	+	4.90615i	−0.374090	+	0.215981i
$517$	−2.89774			−0.127443
$518$	17.2079	+	17.4019i	0.756073	+	0.764594i
$519$			10.4039i			0.456680i
$520$	2.74199	+	3.62159i	0.120244	+	0.158817i
$521$	−5.47371	−	3.16025i	−0.239807	−	0.138453i	0.375281	−	0.926911i	$-0.377546\pi$
$521$	−5.47371	−	3.16025i	−0.239807	−	0.138453i	−0.615088	+	0.788458i	$0.710880\pi$
$522$	1.46000	+	5.44879i	0.0639024	+	0.238487i
$523$	−9.88058	+	5.70456i	−0.432048	+	0.249443i	−0.700219	−	0.713928i	$-0.746914\pi$
$523$	−9.88058	+	5.70456i	−0.432048	+	0.249443i	0.268171	+	0.963371i	$0.413581\pi$
$524$	12.7438			0.556718
$525$	−8.73454	+	2.28803i	−0.381206	+	0.0998579i
$526$	0.0552730	−	0.0552730i	0.00241002	−	0.00241002i
$527$	8.25723	−	30.8164i	0.359691	−	1.34238i
$528$	0.121171	+	0.452217i	0.00527330	+	0.0196802i
$529$	−10.9197	+	18.9136i	−0.474772	+	0.822329i
$530$	−7.88886	−	13.6639i	−0.342670	−	0.593522i
$531$	8.03592	−	8.03592i	0.348729	−	0.348729i
$532$	−7.51829	−	13.1922i	−0.325959	−	0.571956i
$533$	−17.2524	+	22.1858i	−0.747283	+	0.960974i
$534$	3.07115	+	5.31939i	0.132902	+	0.230193i
$535$	8.24806	−	2.21006i	0.356595	−	0.0955493i
$536$	−2.83648	+	4.91292i	−0.122517	+	0.212206i
$537$	10.2113	+	17.6864i	0.440648	+	0.763226i
$538$	−12.0075	−	12.0075i	−0.517680	−	0.517680i
$539$	3.15582	+	0.883622i	0.135931	+	0.0380603i
$540$	0.890861	+	0.890861i	0.0383366	+	0.0383366i
$541$	−3.90070	+	14.5576i	−0.167704	+	0.625880i	0.829976	+	0.557799i	$0.188354\pi$
$541$	−3.90070	+	14.5576i	−0.167704	+	0.625880i	−0.997680	+	0.0680806i	$0.978313\pi$
$542$	−5.88342	−	3.39680i	−0.252715	−	0.145905i
$543$	10.1111	+	5.83763i	0.433908	+	0.250517i
$544$	−3.17544	−	0.850856i	−0.136146	−	0.0364801i
$545$	−17.7366			−0.759754
$546$	5.71554	+	7.63758i	0.244603	+	0.326858i
$547$	10.1855			0.435500			0.217750	−	0.976005i	$-0.430128\pi$
$547$	10.1855			0.435500			0.217750	+	0.976005i	$0.430128\pi$
$548$	−1.82370	−	0.488660i	−0.0779047	−	0.0208745i
$549$	−1.92642	−	1.11222i	−0.0822174	−	0.0474682i
$550$	1.38368	+	0.798869i	0.0590004	+	0.0340639i
$551$	−8.37907	+	31.2711i	−0.356960	+	1.33219i
$552$	−0.761742	−	0.761742i	−0.0324219	−	0.0324219i
$553$	24.0730	−	6.30598i	1.02369	−	0.268158i
$554$	13.2375	+	13.2375i	0.562407	+	0.562407i
$555$	−5.82689	−	10.0925i	−0.247338	−	0.428401i
$556$	−11.2846	+	19.5456i	−0.478575	+	0.828917i
$557$	30.5883	−	8.19611i	1.29607	−	0.347280i	0.456106	−	0.889926i	$-0.349244\pi$
$557$	30.5883	−	8.19611i	1.29607	−	0.347280i	0.839962	+	0.542645i	$0.182577\pi$
$558$	−4.85231	−	8.40445i	−0.205415	−	0.355789i
$559$	35.1051	−	4.39139i	1.48479	−	0.185736i
$560$	−0.0186785	+	3.33324i	−0.000789309	+	0.140855i
$561$	1.08830	−	1.08830i	0.0459480	−	0.0459480i
$562$	8.46483	+	14.6615i	0.357067	+	0.618459i
$563$	−6.59182	+	11.4174i	−0.277812	+	0.481184i	−0.970841	−	0.239726i	$-0.922943\pi$
$563$	−6.59182	+	11.4174i	−0.277812	+	0.481184i	0.693029	+	0.720910i	$0.256276\pi$
$564$	−1.60196	−	5.97861i	−0.0674549	−	0.251745i
$565$	4.10279	−	15.3118i	0.172606	−	0.644173i
$566$	4.35715	−	4.35715i	0.183145	−	0.183145i
$567$	1.86032	+	1.88128i	0.0781259	+	0.0790064i
$568$	12.0749			0.506650
$569$	−21.0866	+	12.1743i	−0.883994	+	0.510374i	−0.871973	−	0.489553i	$-0.837160\pi$
$569$	−21.0866	+	12.1743i	−0.883994	+	0.510374i	−0.0120210	+	0.999928i	$0.503826\pi$
$570$	1.87139	+	6.98412i	0.0783839	+	0.292533i
$571$	15.1955	+	8.77315i	0.635914	+	0.367145i	0.783039	−	0.621973i	$-0.213669\pi$
$571$	15.1955	+	8.77315i	0.635914	+	0.367145i	−0.147125	+	0.989118i	$0.547002\pi$
$572$	0.231125	−	1.67211i	0.00966384	−	0.0699145i
$573$			3.74168i			0.156311i
$574$	−19.9498	+	5.22590i	−0.832690	+	0.218125i
$575$	−3.67642			−0.153317
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−29.6768	+	7.95188i	−1.23546	+	0.331041i	−0.816704	−	0.577057i	$-0.804201\pi$
$577$	−29.6768	+	7.95188i	−1.23546	+	0.331041i	−0.418758	+	0.908098i	$0.637534\pi$
$578$	−1.60278	−	5.98164i	−0.0666667	−	0.248803i
$579$	−5.93176	−	1.58941i	−0.246516	−	0.0660537i
$580$	5.02535	−	5.02535i	0.208666	−	0.208666i
$581$	25.0961	−	14.3023i	1.04116	−	0.593360i
$582$			8.96449i			0.371590i
$583$	−1.51747	+	5.66326i	−0.0628470	+	0.234548i
$584$	−2.70931	+	4.69266i	−0.112112	+	0.194184i
$585$	−1.71123	−	4.20787i	−0.0707505	−	0.173974i
$586$	16.1409	−	9.31897i	0.666776	−	0.384963i
$587$	−30.1846	−	30.1846i	−1.24585	−	1.24585i	−0.957535	−	0.288318i	$-0.906904\pi$
$587$	−30.1846	−	30.1846i	−1.24585	−	1.24585i	−0.288318	−	0.957535i	$-0.593096\pi$
$588$	−0.0784492	+	6.99956i	−0.00323519	+	0.288657i
$589$		−	55.6957i		−	2.29490i
$590$	−13.8299	−	3.70571i	−0.569368	−	0.152562i
$591$	0.986771	−	0.264404i	0.0405903	−	0.0108761i
$592$	8.93481	−	2.39408i	0.367219	−	0.0983959i
$593$	−33.0766	−	8.86284i	−1.35829	−	0.363953i	−0.495103	−	0.868834i	$-0.664870\pi$
$593$	−33.0766	−	8.86284i	−1.35829	−	0.363953i	−0.863189	+	0.504881i	$0.831536\pi$
$594$		−	0.468170i		−	0.0192092i
$595$	9.52051	−	5.42577i	0.390303	−	0.222435i
$596$	2.81208	+	2.81208i	0.115187	+	0.115187i
$597$	2.86592	−	1.65464i	0.117294	−	0.0677198i
$598$	1.46321	+	3.59799i	0.0598349	+	0.147133i
$599$	−1.94166	+	3.36306i	−0.0793341	+	0.137411i	−0.902963	−	0.429719i	$-0.858613\pi$
$599$	−1.94166	+	3.36306i	−0.0793341	+	0.137411i	0.823629	+	0.567129i	$0.191946\pi$
$600$	−0.883280	+	3.29645i	−0.0360598	+	0.134577i
$601$		−	31.2983i		−	1.27668i	−0.769753	−	0.638342i	$-0.779621\pi$
$601$		−	31.2983i		−	1.27668i	0.769753	−	0.638342i	$-0.220379\pi$
$602$	22.4097	+	13.1062i	0.913351	+	0.534170i
$603$	4.01138	−	4.01138i	0.163356	−	0.163356i
$604$	−3.44445	−	0.922938i	−0.140153	−	0.0375538i
$605$	−3.51538	−	13.1196i	−0.142921	−	0.533387i
$606$	−3.32548	+	0.891060i	−0.135088	+	0.0361968i
$607$	4.91179	−	2.83582i	0.199363	−	0.115103i	−0.396995	−	0.917821i	$-0.629947\pi$
$607$	4.91179	−	2.83582i	0.199363	−	0.115103i	0.596359	+	0.802718i	$0.296614\pi$
$608$	−5.73909			−0.232751
$609$	10.6123	−	10.4941i	0.430033	−	0.425240i
$610$			2.80249i			0.113470i
$611$	−3.05563	+	22.1064i	−0.123618	+	0.894330i
$612$	2.84702	+	1.64373i	0.115084	+	0.0664437i
$613$	10.2285	+	38.1732i	0.413124	+	1.54180i	0.788564	+	0.614953i	$0.210825\pi$
$613$	10.2285	+	38.1732i	0.413124	+	1.54180i	−0.375440	+	0.926847i	$0.622508\pi$
$614$	−9.64471	+	5.56837i	−0.389229	+	0.224721i
$615$	9.82034			0.395995
$616$	0.880760	−	0.870944i	0.0354868	−	0.0350913i
$617$	15.9817	−	15.9817i	0.643398	−	0.643398i	−0.307991	−	0.951389i	$-0.599657\pi$
$617$	15.9817	−	15.9817i	0.643398	−	0.643398i	0.951389	+	0.307991i	$0.0996567\pi$
$618$	−1.34978	+	5.03744i	−0.0542960	+	0.202636i
$619$	−7.08566	−	26.4440i	−0.284797	−	1.06288i	−0.948988	−	0.315313i	$-0.897891\pi$
$619$	−7.08566	−	26.4440i	−0.284797	−	1.06288i	0.664191	−	0.747563i	$-0.268776\pi$
$620$	−6.11327	+	10.5885i	−0.245515	+	0.425244i
$621$	0.538633	+	0.932940i	0.0216146	+	0.0374376i
$622$	−6.59729	+	6.59729i	−0.264527	+	0.264527i
$623$	8.20425	−	14.0280i	0.328696	−	0.562022i
$624$	3.57767	−	0.447540i	0.143221	−	0.0179159i
$625$	1.85521	+	3.21331i	0.0742083	+	0.128533i
$626$	11.9804	−	3.21014i	0.478833	−	0.128303i
$627$	1.34343	−	2.32690i	0.0536516	−	0.0929273i
$628$	−5.26252	−	9.11496i	−0.209997	−	0.363726i
$629$	−21.5024	−	21.5024i	−0.857356	−	0.857356i
$630$	0.880749	−	3.21483i	0.0350899	−	0.128082i
$631$	29.6680	+	29.6680i	1.18107	+	1.18107i	0.979468	+	0.201598i	$0.0646133\pi$
$631$	29.6680	+	29.6680i	1.18107	+	1.18107i	0.201598	+	0.979468i	$0.435387\pi$
$632$	2.43439	−	9.08525i	0.0968346	−	0.361392i
$633$	−9.27768	−	5.35647i	−0.368755	−	0.212901i
$634$	−8.86161	−	5.11625i	−0.351939	−	0.203192i
$635$	−10.2958	−	2.75875i	−0.408576	−	0.109478i
$636$	−12.5233			−0.496582
$637$	10.0688	−	23.1435i	0.398939	−	0.916977i
$638$	−2.64095			−0.104556
$639$	−11.6634	−	3.12521i	−0.461398	−	0.123631i
$640$	1.09108	+	0.629934i	0.0431286	+	0.0249003i
$641$	−7.25534	−	4.18887i	−0.286569	−	0.165451i	0.349825	−	0.936815i	$-0.386241\pi$
$641$	−7.25534	−	4.18887i	−0.286569	−	0.165451i	−0.636393	+	0.771365i	$0.719575\pi$
$642$	1.75420	−	6.54677i	0.0692328	−	0.258380i
$643$	−2.24848	−	2.24848i	−0.0886715	−	0.0886715i	0.661380	−	0.750051i	$-0.269971\pi$
$643$	−2.24848	−	2.24848i	−0.0886715	−	0.0886715i	−0.750051	+	0.661380i	$0.769971\pi$
$644$	−0.753096	+	2.74888i	−0.0296761	+	0.108321i
$645$	−8.74139	−	8.74139i	−0.344192	−	0.344192i
$646$	9.43349	+	16.3393i	0.371156	+	0.642861i
$647$	3.43253	−	5.94531i	0.134947	−	0.233734i	−0.790630	−	0.612294i	$-0.790247\pi$
$647$	3.43253	−	5.94531i	0.134947	−	0.233734i	0.925577	+	0.378559i	$0.123580\pi$
$648$	0.965926	−	0.258819i	0.0379452	−	0.0101674i
$649$	2.66026	+	4.60771i	0.104424	+	0.180868i
$650$	7.55352	−	9.71350i	0.296274	−	0.380995i
$651$	−12.9624	+	22.1638i	−0.508037	+	0.868668i
$652$	−5.05359	+	5.05359i	−0.197914	+	0.197914i
$653$	18.0862	+	31.3261i	0.707766	+	1.22589i	0.965684	+	0.259720i	$0.0836303\pi$
$653$	18.0862	+	31.3261i	0.707766	+	1.22589i	−0.257918	+	0.966167i	$0.583036\pi$
$654$	−7.03909	+	12.1921i	−0.275250	+	0.476747i
$655$	4.15549	+	15.5085i	0.162368	+	0.605967i
$656$	−2.01743	+	7.52914i	−0.0787673	+	0.293964i
$657$	3.83154	−	3.83154i	0.149483	−	0.149483i
$658$	−11.6442	+	11.5145i	−0.453939	+	0.448880i
$659$	18.5073			0.720944			0.360472	−	0.932770i	$-0.382616\pi$
$659$	18.5073			0.720944			0.360472	+	0.932770i	$0.382616\pi$
$660$	−0.510810	+	0.294916i	−0.0198832	+	0.0114796i
$661$	−0.357728	−	1.33506i	−0.0139140	−	0.0519278i	0.958620	−	0.284689i	$-0.0918905\pi$
$661$	−0.357728	−	1.33506i	−0.0139140	−	0.0519278i	−0.972534	+	0.232762i	$0.925224\pi$
$662$	27.9043	+	16.1106i	1.08453	+	0.626155i
$663$	−7.15486	−	9.45005i	−0.277872	−	0.367010i
$664$		−	10.9177i		−	0.423688i
$665$	13.6026	−	13.4510i	0.527486	−	0.521607i
$666$	−9.25000			−0.358430
$667$	5.26272	−	3.03843i	0.203773	−	0.117649i
$668$	23.7215	−	6.35616i	0.917813	−	0.245927i
$669$	2.51986	+	9.40423i	0.0974233	+	0.363589i
$670$	−6.90363	−	1.84982i	−0.266711	−	0.0714649i
$671$	0.736390	−	0.736390i	0.0284280	−	0.0284280i
$672$	2.28384	+	1.33569i	0.0881010	+	0.0515255i
$673$		−	37.0021i		−	1.42633i	−0.700998	−	0.713163i	$-0.747262\pi$
$673$		−	37.0021i		−	1.42633i	0.700998	−	0.713163i	$-0.252738\pi$
$674$	2.93347	−	10.9479i	0.112993	−	0.421696i
$675$	1.70637	−	2.95551i	0.0656781	−	0.113758i
$676$	−12.5126	−	3.52644i	−0.481252	−	0.135632i
$677$	34.5968	−	19.9745i	1.32966	−	0.767682i	0.344416	−	0.938817i	$-0.388077\pi$
$677$	34.5968	−	19.9745i	1.32966	−	0.767682i	0.985248	+	0.171135i	$0.0547435\pi$
$678$	−8.89699	−	8.89699i	−0.341687	−	0.341687i
$679$	20.6064	−	11.7436i	0.790800	−	0.450679i
$680$		−	4.14176i		−	0.158829i
$681$	−26.2834	−	7.04262i	−1.00718	−	0.269874i
$682$	4.38860	−	1.17592i	0.168048	−	0.0450284i
$683$	−42.6320	+	11.4232i	−1.63127	+	0.437097i	−0.954285	−	0.298900i	$-0.903380\pi$
$683$	−42.6320	+	11.4232i	−1.63127	+	0.437097i	−0.676985	+	0.735997i	$0.736714\pi$
$684$	5.54353	+	1.48539i	0.211962	+	0.0567951i
$685$		−	2.37868i		−	0.0908845i
$686$	16.1924	−	8.98920i	0.618229	−	0.343209i
$687$	4.19289	+	4.19289i	0.159969	+	0.159969i
$688$	8.49770	−	4.90615i	0.323972	−	0.187045i
$689$	41.6040	+	17.5483i	1.58499	+	0.668539i
$690$	0.678606	−	1.17538i	0.0258341	−	0.0447460i
$691$	3.22410	−	12.0325i	0.122650	−	0.457738i	−0.877095	−	0.480318i	$-0.840521\pi$
$691$	3.22410	−	12.0325i	0.122650	−	0.457738i	0.999745	+	0.0225799i	$0.00718802\pi$
$692$		−	10.4039i		−	0.395496i
$693$	−1.07617	+	0.613310i	−0.0408802	+	0.0232977i
$694$	17.5563	−	17.5563i	0.666429	−	0.666429i
$695$	−27.4654	−	7.35934i	−1.04182	−	0.279156i
$696$	−1.46000	−	5.44879i	−0.0553411	−	0.206536i
$697$	24.7517	−	6.63220i	0.937538	−	0.251212i
$698$	−11.8092	+	6.81803i	−0.446984	+	0.258066i
$699$	−5.94869			−0.225000
$700$	8.73454	−	2.28803i	0.330135	−	0.0864795i
$701$		−	1.92902i		−	0.0728580i	−0.999336	−	0.0364290i	$-0.988402\pi$
$701$		−	1.92902i		−	0.0728580i	0.999336	−	0.0364290i	$-0.0115983\pi$
$702$	−3.57159	−	0.493678i	−0.134801	−	0.0186327i
$703$	−45.9743	−	26.5433i	−1.73395	−	1.00110i
$704$	−0.121171	−	0.452217i	−0.00456681	−	0.0170436i
$705$	6.75324	−	3.89898i	0.254342	−	0.146844i
$706$	−17.1038			−0.643712
$707$	6.40468	+	6.47686i	0.240873	+	0.243587i
$708$	−8.03592	+	8.03592i	−0.302008	+	0.302008i
$709$	6.44025	−	24.0353i	0.241868	−	0.902665i	−0.733063	−	0.680161i	$-0.761910\pi$
$709$	6.44025	−	24.0353i	0.241868	−	0.902665i	0.974932	−	0.222505i	$-0.0714233\pi$
$710$	3.93735	+	14.6944i	0.147766	+	0.551470i
$711$	−4.70287	+	8.14561i	−0.176371	+	0.305484i
$712$	−3.07115	−	5.31939i	−0.115096	−	0.199353i
$713$	−7.39242	+	7.39242i	−0.276848	+	0.276848i
$714$	0.0487389	−	8.69765i	0.00182401	−	0.325501i
$715$	2.11022	−	0.263973i	0.0789179	−	0.00987204i
$716$	−10.2113	−	17.6864i	−0.381613	−	0.660973i
$717$	−5.26514	+	1.41079i	−0.196630	+	0.0526869i
$718$	0.388968	−	0.673712i	0.0145162	−	0.0251427i
$719$	−6.59723	−	11.4267i	−0.246035	−	0.426145i	0.716387	−	0.697703i	$-0.245795\pi$
$719$	−6.59723	−	11.4267i	−0.246035	−	0.426145i	−0.962422	+	0.271558i	$0.912461\pi$
$720$	−0.890861	−	0.890861i	−0.0332004	−	0.0332004i
$721$	13.3476	−	3.49644i	0.497091	−	0.130214i
$722$	9.85504	+	9.85504i	0.366767	+	0.366767i
$723$	0.549364	−	2.05025i	0.0204311	−	0.0762498i
$724$	−10.1111	−	5.83763i	−0.375775	−	0.216954i
$725$	−16.6721	−	9.62562i	−0.619185	−	0.357487i
$726$	−10.4135	−	2.79028i	−0.386480	−	0.103557i
$727$	−20.3223			−0.753713			−0.376856	−	0.926272i	$-0.622995\pi$
$727$	−20.3223			−0.753713			−0.376856	+	0.926272i	$0.622995\pi$
$728$	−5.71554	−	7.63758i	−0.211832	−	0.283067i
$729$	−1.00000			−0.0370370
$730$	−6.59413	−	1.76689i	−0.244060	−	0.0653956i
$731$	−27.9358	−	16.1287i	−1.03324	−	0.596543i
$732$	1.92642	+	1.11222i	0.0712024	+	0.0411087i
$733$	−10.0500	+	37.5070i	−0.371204	+	1.38535i	0.487608	+	0.873063i	$0.337870\pi$
$733$	−10.0500	+	37.5070i	−0.371204	+	1.38535i	−0.858812	+	0.512291i	$0.828797\pi$
$734$	8.98933	+	8.98933i	0.331802	+	0.331802i
$735$	−8.54362	+	2.18693i	−0.315136	+	0.0806662i
$736$	0.761742	+	0.761742i	0.0280782	+	0.0280782i
$737$	1.32795	+	2.30008i	0.0489158	+	0.0847246i
$738$	3.89737	−	6.75044i	0.143464	−	0.248487i
$739$	−47.3036	+	12.6750i	−1.74009	+	0.466256i	−0.982467	−	0.186437i	$-0.940306\pi$
$739$	−47.3036	+	12.6750i	−1.74009	+	0.466256i	−0.757623	+	0.652693i	$0.773639\pi$
$740$	5.82689	+	10.0925i	0.214201	+	0.371006i
$741$	−16.3349	−	12.7025i	−0.600077	−	0.466639i
$742$	16.4057	+	28.7869i	0.602274	+	1.05680i
$743$	−2.39985	+	2.39985i	−0.0880419	+	0.0880419i	−0.749756	−	0.661714i	$-0.769829\pi$
$743$	−2.39985	+	2.39985i	−0.0880419	+	0.0880419i	0.661714	+	0.749756i	$0.269829\pi$
$744$	4.85231	+	8.40445i	0.177894	+	0.308122i
$745$	−2.50517	+	4.33908i	−0.0917823	+	0.158972i
$746$	−5.94296	−	22.1794i	−0.217587	−	0.812046i
$747$	−2.82570	+	10.5457i	−0.103387	+	0.385846i
$748$	−1.08830	+	1.08830i	−0.0397921	+	0.0397921i
$749$	−17.3468	+	4.54404i	−0.633840	+	0.166036i
$750$	−10.5989			−0.387018
$751$	43.9021	−	25.3469i	1.60201	−	0.924921i	0.610926	−	0.791687i	$-0.290797\pi$
$751$	43.9021	−	25.3469i	1.60201	−	0.924921i	0.991085	−	0.133234i	$-0.0425362\pi$
$752$	1.60196	+	5.97861i	0.0584176	+	0.218018i
$753$	21.1902	+	12.2342i	0.772213	+	0.445837i
$754$	−2.78484	+	20.1474i	−0.101418	+	0.733724i
$755$		−	4.49264i		−	0.163504i
$756$	−1.86032	−	1.88128i	−0.0676590	−	0.0684216i
$757$	48.1029			1.74833			0.874164	−	0.485630i	$-0.161410\pi$
$757$	48.1029			1.74833			0.874164	+	0.485630i	$0.161410\pi$
$758$	−26.1119	+	15.0757i	−0.948426	+	0.547574i
$759$	−0.487158	+	0.130534i	−0.0176827	+	0.00473807i
$760$	−1.87139	−	6.98412i	−0.0678824	−	0.253341i
$761$	−7.87026	−	2.10883i	−0.285297	−	0.0764450i	0.113333	−	0.993557i	$-0.463847\pi$
$761$	−7.87026	−	2.10883i	−0.285297	−	0.0764450i	−0.398629	+	0.917112i	$0.630514\pi$
$762$	−5.98241	+	5.98241i	−0.216720	+	0.216720i
$763$	37.2468	+	0.208719i	1.34842	+	0.00755614i
$764$		−	3.74168i		−	0.135369i
$765$	−1.07197	+	4.00063i	−0.0387570	+	0.144643i
$766$	13.1134	−	22.7131i	0.473807	−	0.820658i
$767$	37.9567	−	15.4359i	1.37054	−	0.557359i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	30.5941	+	30.5941i	1.10325	+	1.10325i	0.994016	+	0.109235i	$0.0348401\pi$
$769$	30.5941	+	30.5941i	1.10325	+	1.10325i	0.109235	+	0.994016i	$0.465160\pi$
$770$	1.34708	+	0.787835i	0.0485455	+	0.0283916i
$771$		−	23.1089i		−	0.832248i
$772$	5.93176	+	1.58941i	0.213489	+	0.0572042i
$773$	21.8944	−	5.86660i	0.787488	−	0.211007i	0.157405	−	0.987534i	$-0.449687\pi$
$773$	21.8944	−	5.86660i	0.787488	−	0.211007i	0.630083	+	0.776527i	$0.283021\pi$
$774$	−9.47795	+	2.53961i	−0.340678	+	0.0912843i
$775$	31.9908	+	8.57190i	1.14914	+	0.307912i
$776$		−	8.96449i		−	0.321807i
$777$	12.1176	+	21.2626i	0.434718	+	0.762793i
$778$	−10.3798	−	10.3798i	−0.372135	−	0.372135i
$779$	38.7414	−	22.3674i	1.38805	−	0.801394i
$780$	1.71123	+	4.20787i	0.0612717	+	0.150666i
$781$	2.82655	−	4.89572i	0.101142	−	0.175183i
$782$	0.916598	−	3.42079i	0.0327775	−	0.122327i
$783$			5.64101i			0.201593i
$784$	0.0784492	−	6.99956i	0.00280176	−	0.249984i
$785$	9.37635	−	9.37635i	0.334656	−	0.334656i
$786$	12.3096	+	3.29835i	0.439069	+	0.117648i
$787$	−3.91009	−	14.5926i	−0.139380	−	0.520172i	−0.999941	−	0.0108257i	$-0.996554\pi$
$787$	−3.91009	−	14.5926i	−0.139380	−	0.520172i	0.860562	−	0.509346i	$-0.170113\pi$
$788$	−0.986771	+	0.264404i	−0.0351523	+	0.00941902i
$789$	0.0676953	−	0.0390839i	0.00241002	−	0.00139142i
$790$	11.8500			0.421604
$791$	−8.79601	+	32.1064i	−0.312750	+	1.14157i
$792$			0.468170i			0.0166357i
$793$	−4.84129	−	6.39431i	−0.171919	−	0.227069i
$794$	−12.6443	−	7.30022i	−0.448731	−	0.259075i
$795$	−4.08358	−	15.2401i	−0.144830	−	0.540511i
$796$	−2.86592	+	1.65464i	−0.101580	+	0.0586470i
$797$	21.7494			0.770405			0.385202	−	0.922832i	$-0.374132\pi$
$797$	21.7494			0.770405			0.385202	+	0.922832i	$0.374132\pi$
$798$	−3.84771	−	14.6886i	−0.136208	−	0.519971i
$799$	14.3880	−	14.3880i	0.509012	−	0.509012i
$800$	0.883280	−	3.29645i	0.0312287	−	0.116547i
$801$	1.58975	+	5.93301i	0.0561709	+	0.209633i
$802$	−12.1376	+	21.0229i	−0.428593	+	0.742345i
$803$	1.26842	+	2.19696i	0.0447615	+	0.0775291i
$804$	−4.01138	+	4.01138i	−0.141471	+	0.141471i
$805$	−3.59079	−	0.0201217i	−0.126559	−	0.000709196i
$806$	−4.34320	−	34.7199i	−0.152983	−	1.22296i
$807$	−8.49059	−	14.7061i	−0.298883	−	0.517680i
$808$	3.32548	−	0.891060i	0.116990	−	0.0313474i
$809$	−8.23382	+	14.2614i	−0.289486	+	0.501404i	−0.973687	−	0.227889i	$-0.926818\pi$
$809$	−8.23382	+	14.2614i	−0.289486	+	0.501404i	0.684201	+	0.729293i	$0.260151\pi$
$810$	0.629934	+	1.09108i	0.0221336	+	0.0383366i
$811$	18.2084	+	18.2084i	0.639384	+	0.639384i	0.950404	−	0.311019i	$-0.100670\pi$
$811$	18.2084	+	18.2084i	0.639384	+	0.639384i	−0.311019	+	0.950404i	$0.600670\pi$
$812$	−10.6123	+	10.4941i	−0.372420	+	0.368269i
$813$	−4.80380	−	4.80380i	−0.168476	−	0.168476i
$814$	1.12083	−	4.18301i	0.0392852	−	0.146614i
$815$	−7.79778	−	4.50205i	−0.273144	−	0.157700i
$816$	−2.84702	−	1.64373i	−0.0996656	−	0.0575419i
$817$	−54.3948	−	14.5750i	−1.90303	−	0.509916i
$818$	−1.83817			−0.0642702
$819$	3.54404	+	8.85662i	0.123839	+	0.309475i
$820$	−9.82034			−0.342941
$821$	25.5618	+	6.84927i	0.892114	+	0.239041i	0.675626	−	0.737244i	$-0.263873\pi$
$821$	25.5618	+	6.84927i	0.892114	+	0.239041i	0.216488	+	0.976285i	$0.430540\pi$
$822$	−1.63509	−	0.944018i	−0.0570302	−	0.0329264i
$823$	−5.69932	−	3.29051i	−0.198666	−	0.114700i	0.397367	−	0.917660i	$-0.369924\pi$
$823$	−5.69932	−	3.29051i	−0.198666	−	0.114700i	−0.596033	+	0.802960i	$0.703257\pi$
$824$	1.34978	−	5.03744i	0.0470218	−	0.175488i
$825$	1.12977	+	1.12977i	0.0393336	+	0.0393336i
$826$	28.9991	+	7.94471i	1.00901	+	0.276432i
$827$	3.49836	+	3.49836i	0.121650	+	0.121650i	0.765311	−	0.643661i	$-0.222585\pi$
$827$	3.49836	+	3.49836i	0.121650	+	0.121650i	−0.643661	+	0.765311i	$0.722585\pi$
$828$	−0.538633	−	0.932940i	−0.0187188	−	0.0324219i
$829$	−1.48443	+	2.57110i	−0.0515562	+	0.0892980i	−0.890652	−	0.454686i	$-0.849751\pi$
$829$	−1.48443	+	2.57110i	−0.0515562	+	0.0892980i	0.839096	+	0.543984i	$0.183085\pi$
$830$	13.2861	−	3.56001i	0.461169	−	0.123570i
$831$	9.36032	+	16.2126i	0.324706	+	0.562407i
$832$	−3.57767	+	0.447540i	−0.124033	+	0.0155156i
$833$	−20.0568	+	11.2820i	−0.694928	+	0.390899i
$834$	−15.9589	+	15.9589i	−0.552611	+	0.552611i
$835$	15.4701	+	26.7950i	0.535365	+	0.927280i
$836$	−1.34343	+	2.32690i	−0.0464636	+	0.0804774i
$837$	−2.51174	−	9.37395i	−0.0868185	−	0.324011i
$838$	1.56692	−	5.84783i	0.0541284	−	0.202010i
$839$	−20.3262	+	20.3262i	−0.701740	+	0.701740i	−0.964784	−	0.263044i	$-0.915274\pi$
$839$	−20.3262	+	20.3262i	−0.701740	+	0.701740i	0.263044	+	0.964784i	$0.415274\pi$
$840$	−0.880749	+	3.21483i	−0.0303887	+	0.110922i
$841$	2.82094			0.0972737
$842$	3.24221	−	1.87189i	0.111734	−	0.0645096i
$843$	4.38172	+	16.3528i	0.150914	+	0.563220i
$844$	9.27768	+	5.35647i	0.319351	+	0.184377i
$845$	0.211391	−	16.3769i	0.00727206	−	0.563383i
$846$		−	6.18951i		−	0.212800i
$847$	7.22789	+	27.5924i	0.248353	+	0.948086i
$848$	12.5233			0.430053
$849$	5.33639	−	3.08097i	0.183145	−	0.105739i
$850$	−10.8369	+	2.90374i	−0.371703	+	0.0995976i
$851$	2.57906	+	9.62517i	0.0884089	+	0.329947i
$852$	11.6634	+	3.12521i	0.399583	+	0.107068i
$853$	−20.5558	+	20.5558i	−0.703816	+	0.703816i	−0.965227	−	0.261412i	$-0.915812\pi$
$853$	−20.5558	+	20.5558i	−0.703816	+	0.703816i	0.261412	+	0.965227i	$0.415812\pi$
$854$	0.0329789	−	5.88520i	0.00112851	−	0.201388i
$855$			7.23049i			0.247278i
$856$	−1.75420	+	6.54677i	−0.0599573	+	0.223764i
$857$	1.11154	−	1.92524i	0.0379693	−	0.0657648i	−0.846416	−	0.532522i	$-0.821244\pi$
$857$	1.11154	−	1.92524i	0.0379693	−	0.0657648i	0.884386	+	0.466757i	$0.154578\pi$
$858$	0.656025	−	1.55532i	0.0223963	−	0.0530977i
$859$	−27.5537	+	15.9082i	−0.940121	+	0.542779i	−0.889998	−	0.455964i	$-0.849295\pi$
$859$	−27.5537	+	15.9082i	−0.940121	+	0.542779i	−0.0501229	+	0.998743i	$0.515961\pi$
$860$	8.74139	+	8.74139i	0.298079	+	0.298079i
$861$	−20.6226	−	0.115563i	−0.702817	−	0.00393837i
$862$			11.3411i			0.386279i
$863$	−39.8334	−	10.6733i	−1.35595	−	0.363325i	−0.493620	−	0.869678i	$-0.664326\pi$
$863$	−39.8334	−	10.6733i	−1.35595	−	0.363325i	−0.862326	+	0.506353i	$0.830993\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	12.6609	−	3.39248i	0.430483	−	0.115348i
$866$	0.431504	+	0.115621i	0.0146631	+	0.00392897i
$867$		−	6.19265i		−	0.210313i
$868$	12.9624	−	22.1638i	0.439973	−	0.752288i
$869$	−3.11373	−	3.11373i	−0.105626	−	0.105626i
$870$	6.15477	−	3.55346i	0.208666	−	0.120474i
$871$	18.9473	−	7.70533i	0.642003	−	0.261085i
$872$	7.03909	−	12.1921i	0.238374	−	0.412875i
$873$	−2.32018	+	8.65904i	−0.0785263	+	0.293064i
$874$		−	6.18252i		−	0.209127i
$875$	13.8848	+	24.3634i	0.469391	+	0.823633i
$876$	−3.83154	+	3.83154i	−0.129456	+	0.129456i
$877$	−26.3475	−	7.05980i	−0.889693	−	0.238392i	−0.215108	−	0.976590i	$-0.569010\pi$
$877$	−26.3475	−	7.05980i	−0.889693	−	0.238392i	−0.674584	+	0.738198i	$0.735677\pi$
$878$	−3.39157	−	12.6575i	−0.114460	−	0.427170i
$879$	18.0029	−	4.82386i	0.607222	−	0.162705i
$880$	0.510810	−	0.294916i	0.0172194	−	0.00994162i
$881$	−37.5870			−1.26634			−0.633169	−	0.774014i	$-0.718246\pi$
$881$	−37.5870			−1.26634			−0.633169	+	0.774014i	$0.718246\pi$
$882$	−1.88740	+	6.74075i	−0.0635519	+	0.226973i
$883$		−	40.8704i		−	1.37540i	−0.725995	−	0.687700i	$-0.758620\pi$
$883$		−	40.8704i		−	1.37540i	0.725995	−	0.687700i	$-0.241380\pi$
$884$	7.15486	+	9.45005i	0.240644	+	0.317840i
$885$	−12.3996	−	7.15889i	−0.416807	−	0.240643i
$886$	7.37980	+	27.5418i	0.247929	+	0.925285i
$887$	−7.09732	+	4.09764i	−0.238305	+	0.137585i	−0.614397	−	0.788997i	$-0.710601\pi$
$887$	−7.09732	+	4.09764i	−0.238305	+	0.137585i	0.376093	+	0.926582i	$0.377267\pi$
$888$	9.25000			0.310410
$889$	21.5886	+	5.91451i	0.724059	+	0.198366i
$890$	5.47194	−	5.47194i	0.183420	−	0.183420i
$891$	0.121171	−	0.452217i	0.00405939	−	0.0151499i
$892$	−2.51986	−	9.40423i	−0.0843710	−	0.314877i
$893$	17.7611	−	30.7631i	0.594352	−	1.02945i
$894$	1.98844	+	3.44408i	0.0665033	+	0.115187i
$895$	18.1936	−	18.1936i	0.608146	−	0.608146i
$896$	−2.28384	−	1.33569i	−0.0762977	−	0.0446224i
$897$	0.482119	+	3.85410i	0.0160975	+	0.128685i
$898$	3.35701	+	5.81451i	0.112025	+	0.194033i
$899$	−52.8785	+	14.1687i	−1.76360	+	0.472554i
$900$	−1.70637	+	2.95551i	−0.0568789	+	0.0985171i
$901$	−20.5849	−	35.6541i	−0.685783	−	1.18781i
$902$	2.58042	+	2.58042i	0.0859186	+	0.0859186i
$903$	18.2540	+	18.4597i	0.607454	+	0.614300i
$904$	8.89699	+	8.89699i	0.295910	+	0.295910i
$905$	3.80704	−	14.2081i	0.126550	−	0.472292i
$906$	−3.08821	−	1.78298i	−0.102599	−	0.0592355i
$907$	−34.1051	−	19.6906i	−1.13244	−	0.653815i	−0.187893	−	0.982190i	$-0.560166\pi$
$907$	−34.1051	−	19.6906i	−1.13244	−	0.653815i	−0.944547	+	0.328375i	$0.893499\pi$
$908$	26.2834	+	7.04262i	0.872246	+	0.233718i
$909$	−3.44279			−0.114190
$910$	7.43075	−	9.44591i	0.246327	−	0.313129i
$911$	52.0039			1.72297			0.861483	−	0.507786i	$-0.169536\pi$
$911$	52.0039			1.72297			0.861483	+	0.507786i	$0.169536\pi$
$912$	−5.54353	−	1.48539i	−0.183565	−	0.0491860i
$913$	−4.42654	−	2.55566i	−0.146497	−	0.0845801i
$914$	6.70203	+	3.86942i	0.221683	+	0.127989i
$915$	−0.725338	+	2.70700i	−0.0239789	+	0.0894906i
$916$	−4.19289	−	4.19289i	−0.138537	−	0.138537i
$917$	−8.54398	−	32.6166i	−0.282147	−	1.07709i
$918$	2.32458	+	2.32458i	0.0767226	+	0.0767226i
$919$	0.633227	+	1.09678i	0.0208882	+	0.0361795i	0.876281	−	0.481801i	$-0.160017\pi$
$919$	0.633227	+	1.09678i	0.0208882	+	0.0361795i	−0.855392	+	0.517981i	$0.826684\pi$
$920$	−0.678606	+	1.17538i	−0.0223730	+	0.0387512i
$921$	−10.7573	+	2.88240i	−0.354464	+	0.0949784i
$922$	−21.1461	−	36.6261i	−0.696410	−	1.20622i
$923$	−34.3681	−	26.7257i	−1.13124	−	0.879688i
$924$	1.07617	−	0.613310i	0.0354032	−	0.0201764i
$925$	22.3218	−	22.3218i	0.733936	−	0.733936i
$926$	5.60028	+	9.69998i	0.184037	+	0.318761i
$927$	−2.60757	+	4.51645i	−0.0856439	+	0.148340i
$928$	1.46000	+	5.44879i	0.0479268	+	0.178865i
$929$	−1.53521	+	5.72949i	−0.0503686	+	0.187978i	−0.986526	−	0.163602i	$-0.947689\pi$
$929$	−1.53521	+	5.72949i	−0.0503686	+	0.187978i	0.936158	+	0.351580i	$0.114355\pi$
$930$	−8.64547	+	8.64547i	−0.283496	+	0.283496i
$931$	−28.7236	+	28.0869i	−0.941378	+	0.920511i
$932$	5.94869			0.194856
$933$	−8.07999	+	4.66499i	−0.264527	+	0.152725i
$934$	2.92461	+	10.9148i	0.0956962	+	0.357143i
$935$	−1.67926	−	0.969523i	−0.0549178	−	0.0317068i
$936$	3.57159	+	0.493678i	0.116741	+	0.0161364i
$937$			36.7331i			1.20002i	0.799993	+	0.600010i	$0.204837\pi$
$937$			36.7331i			1.20002i	−0.799993	+	0.600010i	$0.795163\pi$
$938$	14.4758	+	3.96585i	0.472651	+	0.129490i
$939$	12.4030			0.404757
$940$	−6.75324	+	3.89898i	−0.220266	+	0.127171i
$941$	25.1089	−	6.72792i	0.818528	−	0.219324i	0.174825	−	0.984600i	$-0.444064\pi$
$941$	25.1089	−	6.72792i	0.818528	−	0.219324i	0.643703	+	0.765276i	$0.277397\pi$
$942$	−2.72408	−	10.1664i	−0.0887554	−	0.331240i
$943$	−8.11089	−	2.17331i	−0.264127	−	0.0707726i
$944$	8.03592	−	8.03592i	0.261547	−	0.261547i
$945$	1.68280	−	2.87734i	0.0547414	−	0.0935997i
$946$		−	4.59382i		−	0.149358i
$947$	−11.5531	+	43.1169i	−0.375426	+	1.40111i	0.477295	+	0.878743i	$0.341617\pi$
$947$	−11.5531	+	43.1169i	−0.375426	+	1.40111i	−0.852721	+	0.522367i	$0.825049\pi$
$948$	4.70287	−	8.14561i	0.152742	−	0.264557i
$949$	18.0978	−	7.35989i	0.587480	−	0.238912i
$950$	−16.9620	+	9.79299i	−0.550318	+	0.317726i
$951$	−7.23547	−	7.23547i	−0.234626	−	0.234626i
$952$	−0.0487389	+	8.69765i	−0.00157964	+	0.281892i
$953$			47.6968i			1.54505i	0.634984	+	0.772526i	$0.281007\pi$
$953$			47.6968i			1.54505i	−0.634984	+	0.772526i	$0.718993\pi$
$954$	−12.0966	−	3.24127i	−0.391642	−	0.104940i
$955$	4.55339	−	1.22008i	0.147344	−	0.0394808i
$956$	5.26514	−	1.41079i	0.170287	−	0.0456282i
$957$	−2.55096	−	0.683528i	−0.0824608	−	0.0220953i
$958$		−	9.59959i		−	0.310149i
$959$	−0.0279915	+	4.99520i	−0.000903893	+	0.161303i
$960$	0.890861	+	0.890861i	0.0287524	+	0.0287524i
$961$	54.7152	−	31.5899i	1.76501	−	1.01903i
$962$	−30.7296	−	12.9616i	−0.990763	−	0.417899i
$963$	3.38886	−	5.86967i	0.109204	−	0.189147i
$964$	−0.549364	+	2.05025i	−0.0176938	+	0.0660342i
$965$			7.73686i			0.249058i
$966$	−1.43890	+	2.46030i	−0.0462958	+	0.0791589i
$967$	13.3775	−	13.3775i	0.430193	−	0.430193i	−0.458501	−	0.888694i	$-0.651613\pi$
$967$	13.3775	−	13.3775i	0.430193	−	0.430193i	0.888694	+	0.458501i	$0.151613\pi$
$968$	10.4135	+	2.79028i	0.334702	+	0.0896830i
$969$	4.88313	+	18.2241i	0.156869	+	0.585443i
$970$	10.9092	−	2.92312i	0.350275	−	0.0938558i
$971$	−42.1214	+	24.3188i	−1.35174	+	0.780427i	−0.988493	−	0.151267i	$-0.951665\pi$
$971$	−42.1214	+	24.3188i	−1.35174	+	0.780427i	−0.363246	+	0.931693i	$0.618331\pi$
$972$	1.00000			0.0320750
$973$	57.5905	+	15.7777i	1.84627	+	0.505811i
$974$		−	8.68004i		−	0.278126i
$975$	9.81018	−	7.42752i	0.314177	−	0.237871i
$976$	−1.92642	−	1.11222i	−0.0616631	−	0.0356012i
$977$	−1.77945	−	6.64101i	−0.0569297	−	0.212465i	0.931601	−	0.363481i	$-0.118412\pi$
$977$	−1.77945	−	6.64101i	−0.0569297	−	0.212465i	−0.988531	+	0.151017i	$0.951745\pi$
$978$	−6.18936	+	3.57343i	−0.197914	+	0.114266i
$979$	−2.87564			−0.0919060
$980$	8.54362	−	2.18693i	0.272916	−	0.0698590i
$981$	−9.95477	+	9.95477i	−0.317831	+	0.317831i
$982$	10.1707	−	37.9577i	0.324561	−	1.21128i
$983$	−8.56761	−	31.9747i	−0.273264	−	1.01984i	−0.956996	−	0.290102i	$-0.906311\pi$
$983$	−8.56761	−	31.9747i	−0.273264	−	1.01984i	0.683731	−	0.729734i	$-0.260356\pi$
$984$	−3.89737	+	6.75044i	−0.124244	+	0.215196i
$985$	−0.643528	−	1.11462i	−0.0205045	−	0.0355148i
$986$	13.1130	−	13.1130i	0.417602	−	0.417602i
$987$	−14.2276	+	8.10836i	−0.452870	+	0.258092i
$988$	16.3349	+	12.7025i	0.519682	+	0.404121i
$989$	5.28523	+	9.15428i	0.168060	+	0.291089i
$990$	−0.569734	+	0.152660i	−0.0181073	+	0.00485185i
$991$	1.28742	−	2.22988i	0.0408963	−	0.0708345i	−0.844853	−	0.534999i	$-0.820312\pi$
$991$	1.28742	−	2.22988i	0.0408963	−	0.0708345i	0.885749	+	0.464164i	$0.153645\pi$
$992$	−4.85231	−	8.40445i	−0.154061	−	0.266842i
$993$	22.7838	+	22.7838i	0.723021	+	0.723021i
$994$	−8.09547	−	30.9044i	−0.256773	−	0.980227i
$995$	−2.94810	−	2.94810i	−0.0934611	−	0.0934611i
$996$	2.82570	−	10.5457i	0.0895358	−	0.334152i
$997$	−16.6005	−	9.58430i	−0.525743	−	0.303538i	0.213538	−	0.976935i	$-0.431501\pi$
$997$	−16.6005	−	9.58430i	−0.525743	−	0.303538i	−0.739281	+	0.673397i	$0.764835\pi$
$998$	16.5289	+	9.54294i	0.523212	+	0.302077i
$999$	−8.93481	−	2.39408i	−0.282685	−	0.0757452i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bz.b.31.2	yes	40
7.5	odd	6		546.2.bz.a.187.7	yes	40
13.8	odd	4		546.2.bz.a.73.7	✓	40
91.47	even	12	inner	546.2.bz.b.229.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bz.a.73.7	✓	40	13.8	odd	4
546.2.bz.a.187.7	yes	40	7.5	odd	6
546.2.bz.b.31.2	yes	40	1.1	even	1	trivial
546.2.bz.b.229.2	yes	40	91.47	even	12	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.326078 + 1.21694i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.699081 - 2.55172i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.965926 - 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-0.326078 + 1.21694i) q^{5} +(0.707107 + 0.707107i) q^{6} +(0.699081 - 2.55172i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.629934 - 1.09108i) q^{10} +(-0.452217 + 0.121171i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(0.447540 + 3.57767i) q^{13} +(-1.33569 + 2.28384i) q^{14} +(0.890861 - 0.890861i) q^{15} +(0.500000 + 0.866025i) q^{16} +(1.64373 - 2.84702i) q^{17} +(-0.258819 - 0.965926i) q^{18} +(1.48539 - 5.54353i) q^{19} +(-0.890861 + 0.890861i) q^{20} +(-1.88128 + 1.86032i) q^{21} +0.468170 q^{22} +(-0.932940 + 0.538633i) q^{23} +(0.258819 + 0.965926i) q^{24} +(2.95551 + 1.70637i) q^{25} +(0.493678 - 3.57159i) q^{26} -1.00000i q^{27} +(1.88128 - 1.86032i) q^{28} -5.64101 q^{29} +(-1.09108 + 0.629934i) q^{30} +(9.37395 - 2.51174i) q^{31} +(-0.258819 - 0.965926i) q^{32} +(0.452217 + 0.121171i) q^{33} +(-2.32458 + 2.32458i) q^{34} +(2.87734 + 1.68280i) q^{35} +1.00000i q^{36} +(2.39408 - 8.93481i) q^{37} +(-2.86954 + 4.97020i) q^{38} +(1.40125 - 3.32212i) q^{39} +(1.09108 - 0.629934i) q^{40} +(5.51172 + 5.51172i) q^{41} +(2.29866 - 1.31002i) q^{42} -9.81229i q^{43} +(-0.452217 - 0.121171i) q^{44} +(-1.21694 + 0.326078i) q^{45} +(1.04056 - 0.278817i) q^{46} +(5.97861 + 1.60196i) q^{47} -1.00000i q^{48} +(-6.02257 - 3.56772i) q^{49} +(-2.41317 - 2.41317i) q^{50} +(-2.84702 + 1.64373i) q^{51} +(-1.40125 + 3.32212i) q^{52} +(6.26166 - 10.8455i) q^{53} +(-0.258819 + 0.965926i) q^{54} -0.589832i q^{55} +(-2.29866 + 1.31002i) q^{56} +(-4.05815 + 4.05815i) q^{57} +(5.44879 + 1.46000i) q^{58} +(-2.94135 - 10.9773i) q^{59} +(1.21694 - 0.326078i) q^{60} +(-1.92642 + 1.11222i) q^{61} -9.70462 q^{62} +(2.55940 - 0.670440i) q^{63} +1.00000i q^{64} +(-4.49974 - 0.621970i) q^{65} +(-0.405447 - 0.234085i) q^{66} +(-1.46827 - 5.47965i) q^{67} +(2.84702 - 1.64373i) q^{68} +1.07727 q^{69} +(-2.34375 - 2.37017i) q^{70} +(-8.53822 + 8.53822i) q^{71} +(0.258819 - 0.965926i) q^{72} +(-1.40244 - 5.23398i) q^{73} +(-4.62500 + 8.01074i) q^{74} +(-1.70637 - 2.95551i) q^{75} +(4.05815 - 4.05815i) q^{76} +(-0.00694096 + 1.23864i) q^{77} +(-2.21333 + 2.84625i) q^{78} +(4.70287 + 8.14561i) q^{79} +(-1.21694 + 0.326078i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.89737 - 6.75044i) q^{82} +(7.71996 + 7.71996i) q^{83} +(-2.55940 + 0.670440i) q^{84} +(2.92866 + 2.92866i) q^{85} +(-2.53961 + 9.47795i) q^{86} +(4.88525 + 2.82050i) q^{87} +(0.405447 + 0.234085i) q^{88} +(5.93301 + 1.58975i) q^{89} +1.25987 q^{90} +(9.44208 + 1.35908i) q^{91} -1.07727 q^{92} +(-9.37395 - 2.51174i) q^{93} +(-5.36028 - 3.09476i) q^{94} +(6.26179 + 3.61525i) q^{95} +(-0.258819 + 0.965926i) q^{96} +(6.33885 + 6.33885i) q^{97} +(4.89396 + 5.00491i) q^{98} +(-0.331046 - 0.331046i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} - 4 q^{11} - 20 q^{12} + 4 q^{14} + 20 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{21} + 8 q^{22} + 24 q^{23} + 48 q^{25} + 8 q^{26} - 4 q^{28} + 24 q^{29} + 4 q^{33} + 16 q^{34} - 8 q^{35} - 32 q^{37} - 16 q^{38} - 4 q^{39} + 8 q^{41} - 4 q^{44} - 28 q^{46} - 20 q^{47} - 16 q^{49} + 32 q^{50} + 12 q^{51} + 4 q^{52} - 4 q^{53} - 16 q^{57} + 12 q^{58} + 24 q^{59} - 12 q^{61} - 16 q^{62} + 8 q^{63} + 8 q^{65} - 24 q^{67} - 12 q^{68} + 16 q^{69} + 12 q^{70} + 8 q^{71} - 36 q^{73} - 40 q^{74} + 36 q^{75} + 16 q^{76} - 48 q^{77} - 8 q^{78} - 20 q^{81} - 24 q^{83} - 8 q^{84} - 40 q^{85} - 56 q^{86} - 72 q^{87} - 72 q^{89} - 24 q^{91} - 16 q^{92} - 36 q^{94} + 32 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 - 4 * q^11 - 20 * q^12 + 4 * q^14 + 20 * q^16 - 8 * q^17 + 16 * q^19 + 4 * q^21 + 8 * q^22 + 24 * q^23 + 48 * q^25 + 8 * q^26 - 4 * q^28 + 24 * q^29 + 4 * q^33 + 16 * q^34 - 8 * q^35 - 32 * q^37 - 16 * q^38 - 4 * q^39 + 8 * q^41 - 4 * q^44 - 28 * q^46 - 20 * q^47 - 16 * q^49 + 32 * q^50 + 12 * q^51 + 4 * q^52 - 4 * q^53 - 16 * q^57 + 12 * q^58 + 24 * q^59 - 12 * q^61 - 16 * q^62 + 8 * q^63 + 8 * q^65 - 24 * q^67 - 12 * q^68 + 16 * q^69 + 12 * q^70 + 8 * q^71 - 36 * q^73 - 40 * q^74 + 36 * q^75 + 16 * q^76 - 48 * q^77 - 8 * q^78 - 20 * q^81 - 24 * q^83 - 8 * q^84 - 40 * q^85 - 56 * q^86 - 72 * q^87 - 72 * q^89 - 24 * q^91 - 16 * q^92 - 36 * q^94 + 32 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more