LMFDB - Embedded newform 546.2.cg.a.241.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			241.5
Character	$\chi$	$=$	546.241
Dual form			546.2.cg.a.145.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-3.46134 - 0.927465i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.74330 - 1.99020i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-3.46134 - 0.927465i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.74330 - 1.99020i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.79172 - 3.10336i) q^{10} +(-3.84991 - 1.03158i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.05596 + 1.91340i) q^{13} +(0.174582 - 2.63999i) q^{14} +(-3.46134 + 0.927465i) q^{15} -1.00000 q^{16} -4.31782 q^{17} +(0.965926 - 0.258819i) q^{18} +(1.87046 + 6.98067i) q^{19} +(0.927465 - 3.46134i) q^{20} +(-2.50484 - 0.851912i) q^{21} +(-1.99286 - 3.45173i) q^{22} -0.712056i q^{23} +(-0.258819 + 0.965926i) q^{24} +(6.79059 + 3.92055i) q^{25} +(-3.51387 - 0.807915i) q^{26} -1.00000i q^{27} +(1.99020 - 1.74330i) q^{28} +(4.49789 - 7.79058i) q^{29} +(-3.10336 - 1.79172i) q^{30} +(-1.93392 - 7.21748i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.84991 + 1.03158i) q^{33} +(-3.05316 - 3.05316i) q^{34} +(4.18833 + 8.50562i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.627321 - 0.627321i) q^{37} +(-3.61346 + 6.25869i) q^{38} +(-1.68984 + 3.18503i) q^{39} +(3.10336 - 1.79172i) q^{40} +(-0.511837 - 1.91020i) q^{41} +(-1.16880 - 2.37359i) q^{42} +(10.1649 - 5.86869i) q^{43} +(1.03158 - 3.84991i) q^{44} +(-2.53388 + 2.53388i) q^{45} +(0.503500 - 0.503500i) q^{46} +(-0.430209 + 1.60556i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-0.921790 + 6.93904i) q^{49} +(2.02943 + 7.57392i) q^{50} +(-3.73934 + 2.15891i) q^{51} +(-1.91340 - 3.05596i) q^{52} +(-0.862951 + 1.49467i) q^{53} +(0.707107 - 0.707107i) q^{54} +(12.3691 + 7.14131i) q^{55} +(2.63999 + 0.174582i) q^{56} +(5.11020 + 5.11020i) q^{57} +(8.68926 - 2.32828i) q^{58} +(-2.86582 - 2.86582i) q^{59} +(-0.927465 - 3.46134i) q^{60} +(-7.04381 - 4.06674i) q^{61} +(3.73604 - 6.47102i) q^{62} +(-2.59521 + 0.514645i) q^{63} -1.00000i q^{64} +(12.3523 - 3.78863i) q^{65} +(-3.45173 - 1.99286i) q^{66} +(-3.29307 + 12.2899i) q^{67} -4.31782i q^{68} +(-0.356028 - 0.616658i) q^{69} +(-3.05278 + 8.97598i) q^{70} +(-0.167008 + 0.623283i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-3.77262 + 1.01087i) q^{73} +0.887166 q^{74} +7.84110 q^{75} +(-6.98067 + 1.87046i) q^{76} +(4.65851 + 9.46044i) q^{77} +(-3.44706 + 1.05726i) q^{78} +(-2.49494 - 4.32136i) q^{79} +(3.46134 + 0.927465i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.988794 - 1.71264i) q^{82} +(-7.15916 + 7.15916i) q^{83} +(0.851912 - 2.50484i) q^{84} +(14.9455 + 4.00462i) q^{85} +(11.3374 + 3.03786i) q^{86} -8.99579i q^{87} +(3.45173 - 1.99286i) q^{88} +(-11.8393 - 11.8393i) q^{89} -3.58345 q^{90} +(9.13551 + 2.74634i) q^{91} +0.712056 q^{92} +(-5.28357 - 5.28357i) q^{93} +(-1.43951 + 0.831100i) q^{94} -25.8973i q^{95} +(-0.965926 - 0.258819i) q^{96} +(8.33554 + 2.23350i) q^{97} +(-5.55845 + 4.25484i) q^{98} +(-2.81833 + 2.81833i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) $ 32 * q - 4 * q^7 + 16 * q^9	$ 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$			1.00000i			0.500000i
$5$	−3.46134	−	0.927465i	−1.54796	−	0.414775i	−0.619133	−	0.785286i	$-0.712516\pi$
$5$	−3.46134	−	0.927465i	−1.54796	−	0.414775i	−0.928828	+	0.370512i	$0.879182\pi$
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−1.74330	−	1.99020i	−0.658907	−	0.752225i
$7$	−1.74330	−	1.99020i	−0.658907	−	0.752225i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.79172	−	3.10336i	−0.566593	−	0.981368i
$11$	−3.84991	−	1.03158i	−1.16079	−	0.311033i	−0.373509	−	0.927626i	$-0.621846\pi$
$11$	−3.84991	−	1.03158i	−1.16079	−	0.311033i	−0.787282	+	0.616593i	$0.788512\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.05596	+	1.91340i	−0.847572	+	0.530681i
$13$	−3.05596	+	1.91340i	−0.847572	+	0.530681i
$14$	0.174582	−	2.63999i	0.0466591	−	0.705566i
$15$	−3.46134	+	0.927465i	−0.893715	+	0.239470i
$16$	−1.00000			−0.250000
$17$	−4.31782			−1.04722			−0.523612	−	0.851957i	$-0.675416\pi$
$17$	−4.31782			−1.04722			−0.523612	+	0.851957i	$0.675416\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	1.87046	+	6.98067i	0.429114	+	1.60147i	0.754772	+	0.655987i	$0.227747\pi$
$19$	1.87046	+	6.98067i	0.429114	+	1.60147i	−0.325658	+	0.945487i	$0.605586\pi$
$20$	0.927465	−	3.46134i	0.207387	−	0.773980i
$21$	−2.50484	−	0.851912i	−0.546602	−	0.185902i
$22$	−1.99286	−	3.45173i	−0.424879	−	0.735912i
$23$		−	0.712056i		−	0.148474i	−0.997241	−	0.0742370i	$-0.976348\pi$
$23$		−	0.712056i		−	0.148474i	0.997241	−	0.0742370i	$-0.0236521\pi$
$24$	−0.258819	+	0.965926i	−0.0528312	+	0.197169i
$25$	6.79059	+	3.92055i	1.35812	+	0.784110i
$26$	−3.51387	−	0.807915i	−0.689126	−	0.158445i
$27$		−	1.00000i		−	0.192450i
$28$	1.99020	−	1.74330i	0.376112	−	0.329453i
$29$	4.49789	−	7.79058i	0.835238	−	1.44667i	−0.0585987	−	0.998282i	$-0.518663\pi$
$29$	4.49789	−	7.79058i	0.835238	−	1.44667i	0.893837	−	0.448393i	$-0.148003\pi$
$30$	−3.10336	−	1.79172i	−0.566593	−	0.327123i
$31$	−1.93392	−	7.21748i	−0.347342	−	1.29630i	−0.889852	−	0.456249i	$-0.849193\pi$
$31$	−1.93392	−	7.21748i	−0.347342	−	1.29630i	0.542510	−	0.840049i	$-0.317474\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−3.84991	+	1.03158i	−0.670183	+	0.179575i
$34$	−3.05316	−	3.05316i	−0.523612	−	0.523612i
$35$	4.18833	+	8.50562i	0.707957	+	1.43771i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	0.627321	−	0.627321i	0.103131	−	0.103131i	−0.653659	−	0.756790i	$-0.726767\pi$
$37$	0.627321	−	0.627321i	0.103131	−	0.103131i	0.756790	+	0.653659i	$0.226767\pi$
$38$	−3.61346	+	6.25869i	−0.586180	+	1.01529i
$39$	−1.68984	+	3.18503i	−0.270591	+	0.510013i
$40$	3.10336	−	1.79172i	0.490684	−	0.283296i
$41$	−0.511837	−	1.91020i	−0.0799356	−	0.298324i	0.914371	−	0.404876i	$-0.132685\pi$
$41$	−0.511837	−	1.91020i	−0.0799356	−	0.298324i	−0.994307	+	0.106553i	$0.966019\pi$
$42$	−1.16880	−	2.37359i	−0.180350	−	0.366252i
$43$	10.1649	−	5.86869i	1.55013	−	0.894967i	0.551998	−	0.833846i	$-0.313866\pi$
$43$	10.1649	−	5.86869i	1.55013	−	0.894967i	0.998130	−	0.0611213i	$-0.0194676\pi$
$44$	1.03158	−	3.84991i	0.155517	−	0.580395i
$45$	−2.53388	+	2.53388i	−0.377729	+	0.377729i
$46$	0.503500	−	0.503500i	0.0742370	−	0.0742370i
$47$	−0.430209	+	1.60556i	−0.0627524	+	0.234195i	−0.990178	−	0.139813i	$-0.955350\pi$
$47$	−0.430209	+	1.60556i	−0.0627524	+	0.234195i	0.927426	+	0.374008i	$0.122017\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−0.921790	+	6.93904i	−0.131684	+	0.991292i
$50$	2.02943	+	7.57392i	0.287004	+	1.07111i
$51$	−3.73934	+	2.15891i	−0.523612	+	0.302308i
$52$	−1.91340	−	3.05596i	−0.265341	−	0.423786i
$53$	−0.862951	+	1.49467i	−0.118535	+	0.205309i	−0.919187	−	0.393820i	$-0.871153\pi$
$53$	−0.862951	+	1.49467i	−0.118535	+	0.205309i	0.800652	+	0.599130i	$0.204487\pi$
$54$	0.707107	−	0.707107i	0.0962250	−	0.0962250i
$55$	12.3691	+	7.14131i	1.66785	+	0.962934i
$56$	2.63999	+	0.174582i	0.352783	+	0.0233296i
$57$	5.11020	+	5.11020i	0.676863	+	0.676863i
$58$	8.68926	−	2.32828i	1.14096	−	0.305718i
$59$	−2.86582	−	2.86582i	−0.373098	−	0.373098i	0.495506	−	0.868605i	$-0.334983\pi$
$59$	−2.86582	−	2.86582i	−0.373098	−	0.373098i	−0.868605	+	0.495506i	$0.834983\pi$
$60$	−0.927465	−	3.46134i	−0.119735	−	0.446858i
$61$	−7.04381	−	4.06674i	−0.901867	−	0.520693i	−0.0240615	−	0.999710i	$-0.507660\pi$
$61$	−7.04381	−	4.06674i	−0.901867	−	0.520693i	−0.877805	+	0.479017i	$0.840993\pi$
$62$	3.73604	−	6.47102i	0.474478	−	0.821820i
$63$	−2.59521	+	0.514645i	−0.326966	+	0.0648391i
$64$		−	1.00000i		−	0.125000i
$65$	12.3523	−	3.78863i	1.53212	−	0.469922i
$66$	−3.45173	−	1.99286i	−0.424879	−	0.245304i
$67$	−3.29307	+	12.2899i	−0.402312	+	1.50145i	0.406647	+	0.913586i	$0.366698\pi$
$67$	−3.29307	+	12.2899i	−0.402312	+	1.50145i	−0.808959	+	0.587865i	$0.799969\pi$
$68$		−	4.31782i		−	0.523612i
$69$	−0.356028	−	0.616658i	−0.0428607	−	0.0742370i
$70$	−3.05278	+	8.97598i	−0.364877	+	1.07283i
$71$	−0.167008	+	0.623283i	−0.0198202	+	0.0739701i	−0.975128	−	0.221644i	$-0.928858\pi$
$71$	−0.167008	+	0.623283i	−0.0198202	+	0.0739701i	0.955307	+	0.295614i	$0.0955243\pi$
$72$	0.258819	+	0.965926i	0.0305021	+	0.113835i
$73$	−3.77262	+	1.01087i	−0.441551	+	0.118313i	−0.472743	−	0.881200i	$-0.656736\pi$
$73$	−3.77262	+	1.01087i	−0.441551	+	0.118313i	0.0311922	+	0.999513i	$0.490070\pi$
$74$	0.887166			0.103131
$75$	7.84110			0.905412
$76$	−6.98067	+	1.87046i	−0.800737	+	0.214557i
$77$	4.65851	+	9.46044i	0.530886	+	1.07812i
$78$	−3.44706	+	1.05726i	−0.390302	+	0.119711i
$79$	−2.49494	−	4.32136i	−0.280703	−	0.486191i	0.690855	−	0.722993i	$-0.257234\pi$
$79$	−2.49494	−	4.32136i	−0.280703	−	0.486191i	−0.971558	+	0.236802i	$0.923901\pi$
$80$	3.46134	+	0.927465i	0.386990	+	0.103694i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.988794	−	1.71264i	0.109194	−	0.189130i
$83$	−7.15916	+	7.15916i	−0.785820	+	0.785820i	−0.980806	−	0.194986i	$-0.937534\pi$
$83$	−7.15916	+	7.15916i	−0.785820	+	0.785820i	0.194986	+	0.980806i	$0.437534\pi$
$84$	0.851912	−	2.50484i	0.0929512	−	0.273301i
$85$	14.9455	+	4.00462i	1.62106	+	0.434362i
$86$	11.3374	+	3.03786i	1.22255	+	0.327581i
$87$		−	8.99579i		−	0.964450i
$88$	3.45173	−	1.99286i	0.367956	−	0.212439i
$89$	−11.8393	−	11.8393i	−1.25497	−	1.25497i	−0.953465	−	0.301503i	$-0.902512\pi$
$89$	−11.8393	−	11.8393i	−1.25497	−	1.25497i	−0.301503	−	0.953465i	$-0.597488\pi$
$90$	−3.58345			−0.377729
$91$	9.13551	+	2.74634i	0.957662	+	0.287895i
$92$	0.712056			0.0742370
$93$	−5.28357	−	5.28357i	−0.547880	−	0.547880i
$94$	−1.43951	+	0.831100i	−0.148474	+	0.0857214i
$95$		−	25.8973i		−	2.65700i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	8.33554	+	2.23350i	0.846346	+	0.226778i	0.655832	−	0.754907i	$-0.272318\pi$
$97$	8.33554	+	2.23350i	0.846346	+	0.226778i	0.190514	+	0.981684i	$0.438985\pi$
$98$	−5.55845	+	4.25484i	−0.561488	+	0.429804i
$99$	−2.81833	+	2.81833i	−0.283253	+	0.283253i
$100$	−3.92055	+	6.79059i	−0.392055	+	0.679059i
$101$	2.68348	+	4.64792i	0.267016	+	0.462486i	0.968090	−	0.250603i	$-0.0806290\pi$
$101$	2.68348	+	4.64792i	0.267016	+	0.462486i	−0.701074	+	0.713089i	$0.747296\pi$
$102$	−4.17069	−	1.11753i	−0.412960	−	0.110652i
$103$	−1.95134	−	3.37982i	−0.192271	−	0.333024i	0.753731	−	0.657183i	$-0.228252\pi$
$103$	−1.95134	−	3.37982i	−0.192271	−	0.333024i	−0.946003	+	0.324159i	$0.894919\pi$
$104$	0.807915	−	3.51387i	0.0792226	−	0.344563i
$105$	7.88001	+	5.27192i	0.769010	+	0.514486i
$106$	−1.66709	+	0.446696i	−0.161922	+	0.0433870i
$107$	−19.4175			−1.87716			−0.938582	−	0.345056i	$-0.887860\pi$
$107$	−19.4175			−1.87716			−0.938582	+	0.345056i	$0.887860\pi$
$108$	1.00000			0.0962250
$109$	−12.9072	+	3.45849i	−1.23629	+	0.331263i	−0.817026	−	0.576601i	$-0.804379\pi$
$109$	−12.9072	+	3.45849i	−1.23629	+	0.331263i	−0.419264	+	0.907864i	$0.637712\pi$
$110$	3.69661	+	13.7959i	0.352458	+	1.31539i
$111$	0.229615	−	0.856937i	0.0217941	−	0.0813368i
$112$	1.74330	+	1.99020i	0.164727	+	0.188056i
$113$	−0.175668	−	0.304265i	−0.0165254	−	0.0286229i	0.857644	−	0.514243i	$-0.171927\pi$
$113$	−0.175668	−	0.304265i	−0.0165254	−	0.0286229i	−0.874170	+	0.485620i	$0.838594\pi$
$114$			7.22692i			0.676863i
$115$	−0.660407	+	2.46467i	−0.0615832	+	0.229832i
$116$	7.79058	+	4.49789i	0.723337	+	0.417619i
$117$	0.129070	+	3.60324i	0.0119325	+	0.333120i
$118$		−	4.05289i		−	0.373098i
$119$	7.52726	+	8.59332i	0.690023	+	0.787748i
$120$	1.79172	−	3.10336i	0.163561	−	0.283296i
$121$	4.23136	+	2.44297i	0.384669	+	0.222089i
$122$	−2.10510	−	7.85634i	−0.190587	−	0.711280i
$123$	−1.39837	−	1.39837i	−0.126086	−	0.126086i
$124$	7.21748	−	1.93392i	0.648149	−	0.173671i
$125$	−7.19900	−	7.19900i	−0.643898	−	0.643898i
$126$	−2.19900	−	1.47119i	−0.195903	−	0.131064i
$127$	2.86847	+	1.65611i	0.254535	+	0.146956i	0.621839	−	0.783145i	$-0.286386\pi$
$127$	2.86847	+	1.65611i	0.254535	+	0.146956i	−0.367304	+	0.930101i	$0.619719\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	5.86869	−	10.1649i	0.516709	−	0.894967i
$130$	11.4134	+	6.05546i	1.00102	+	0.531099i
$131$	−1.14746	+	0.662484i	−0.100254	+	0.0578815i	−0.549289	−	0.835633i	$-0.685101\pi$
$131$	−1.14746	+	0.662484i	−0.100254	+	0.0578815i	0.449035	+	0.893514i	$0.351768\pi$
$132$	−1.03158	−	3.84991i	−0.0897875	−	0.335091i
$133$	10.6321	−	15.8920i	0.921923	−	1.37801i
$134$	−11.0188	+	6.36172i	−0.951881	+	0.549569i
$135$	−0.927465	+	3.46134i	−0.0798234	+	0.297905i
$136$	3.05316	−	3.05316i	0.261806	−	0.261806i
$137$	1.52374	−	1.52374i	0.130182	−	0.130182i	−0.639014	−	0.769195i	$-0.720657\pi$
$137$	1.52374	−	1.52374i	0.130182	−	0.130182i	0.769195	+	0.639014i	$0.220657\pi$
$138$	0.184294	−	0.687793i	0.0156881	−	0.0585488i
$139$	4.27921	−	2.47060i	0.362958	−	0.209554i	−0.307420	−	0.951574i	$-0.599466\pi$
$139$	4.27921	−	2.47060i	0.362958	−	0.209554i	0.670377	+	0.742020i	$0.266132\pi$
$140$	−8.50562	+	4.18833i	−0.718856	+	0.353979i
$141$	0.430209	+	1.60556i	0.0362301	+	0.135213i
$142$	−0.558821	+	0.322635i	−0.0468952	+	0.0270749i
$143$	13.7390	−	4.21394i	1.14891	−	0.352387i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−22.7942	+	22.7942i	−1.89296	+	1.89296i
$146$	−3.38243	−	1.95285i	−0.279932	−	0.161619i
$147$	2.67123	+	6.47028i	0.220319	+	0.533660i
$148$	0.627321	+	0.627321i	0.0515655	+	0.0515655i
$149$	7.16290	−	1.91929i	0.586808	−	0.157235i	0.0468138	−	0.998904i	$-0.485093\pi$
$149$	7.16290	−	1.91929i	0.586808	−	0.157235i	0.539994	+	0.841669i	$0.318427\pi$
$150$	5.54449	+	5.54449i	0.452706	+	0.452706i
$151$	−2.94021	−	10.9730i	−0.239271	−	0.892970i	−0.976177	−	0.216976i	$-0.930381\pi$
$151$	−2.94021	−	10.9730i	−0.239271	−	0.892970i	0.736906	−	0.675995i	$-0.236286\pi$
$152$	−6.25869	−	3.61346i	−0.507647	−	0.293090i
$153$	−2.15891	+	3.73934i	−0.174537	+	0.302308i
$154$	−3.39548	+	9.98360i	−0.273616	+	0.804502i
$155$			26.7758i			2.15069i
$156$	−3.18503	−	1.68984i	−0.255007	−	0.135296i
$157$	18.0270	+	10.4079i	1.43871	+	0.830641i	0.997760	−	0.0668898i	$-0.0213076\pi$
$157$	18.0270	+	10.4079i	1.43871	+	0.830641i	0.440952	+	0.897531i	$0.354641\pi$
$158$	1.29148	−	4.81985i	0.102744	−	0.383447i
$159$			1.72590i			0.136873i
$160$	1.79172	+	3.10336i	0.141648	+	0.245342i
$161$	−1.41713	+	1.24133i	−0.111686	+	0.0978304i
$162$	0.258819	−	0.965926i	0.0203347	−	0.0758903i
$163$	−2.21749	−	8.27580i	−0.173688	−	0.648211i	−0.996771	−	0.0802909i	$-0.974415\pi$
$163$	−2.21749	−	8.27580i	−0.173688	−	0.648211i	0.823084	−	0.567920i	$-0.192252\pi$
$164$	1.91020	−	0.511837i	0.149162	−	0.0399678i
$165$	14.2826			1.11190
$166$	−10.1246			−0.785820
$167$	−10.7973	+	2.89312i	−0.835519	+	0.223877i	−0.651120	−	0.758975i	$-0.725701\pi$
$167$	−10.7973	+	2.89312i	−0.835519	+	0.223877i	−0.184399	+	0.982851i	$0.559034\pi$
$168$	2.37359	−	1.16880i	0.183126	−	0.0901749i
$169$	5.67782	−	11.6945i	0.436755	−	0.899580i
$170$	7.73634	+	13.3997i	0.593350	+	1.02771i
$171$	6.98067	+	1.87046i	0.533825	+	0.143038i
$172$	5.86869	+	10.1649i	0.447483	+	0.775064i
$173$	−3.47656	+	6.02158i	−0.264318	+	0.457812i	−0.967385	−	0.253312i	$-0.918480\pi$
$173$	−3.47656	+	6.02158i	−0.264318	+	0.457812i	0.703067	+	0.711124i	$0.251814\pi$
$174$	6.36098	−	6.36098i	0.482225	−	0.482225i
$175$	−4.03538	−	20.3493i	−0.305046	−	1.53827i
$176$	3.84991	+	1.03158i	0.290198	+	0.0777583i
$177$	−3.91479	−	1.04896i	−0.294253	−	0.0788450i
$178$		−	16.7434i		−	1.25497i
$179$	−15.3799	+	8.87956i	−1.14954	+	0.663690i	−0.948776	−	0.315949i	$-0.897677\pi$
$179$	−15.3799	+	8.87956i	−1.14954	+	0.663690i	−0.200768	+	0.979639i	$0.564344\pi$
$180$	−2.53388	−	2.53388i	−0.188864	−	0.188864i
$181$	13.6380			1.01371			0.506853	−	0.862032i	$-0.330809\pi$
$181$	13.6380			1.01371			0.506853	+	0.862032i	$0.330809\pi$
$182$	4.51783	+	8.40174i	0.334883	+	0.622778i
$183$	−8.13349			−0.601245
$184$	0.503500	+	0.503500i	0.0371185	+	0.0371185i
$185$	−2.75319	+	1.58956i	−0.202419	+	0.116867i
$186$		−	7.47209i		−	0.547880i
$187$	16.6232	+	4.45417i	1.21561	+	0.325721i
$188$	−1.60556	−	0.430209i	−0.117098	−	0.0313762i
$189$	−1.99020	+	1.74330i	−0.144766	+	0.126807i
$190$	18.3121	−	18.3121i	1.32850	−	1.32850i
$191$	−5.06856	+	8.77900i	−0.366748	+	0.635226i	−0.989055	−	0.147547i	$-0.952862\pi$
$191$	−5.06856	+	8.77900i	−0.366748	+	0.635226i	0.622307	+	0.782773i	$0.286196\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	12.4154	+	3.32669i	0.893678	+	0.239460i	0.676299	−	0.736627i	$-0.263583\pi$
$193$	12.4154	+	3.32669i	0.893678	+	0.239460i	0.217379	+	0.976087i	$0.430249\pi$
$194$	4.31479	+	7.47344i	0.309784	+	0.536562i
$195$	8.80313	−	9.45723i	0.630405	−	0.677246i
$196$	−6.93904	−	0.921790i	−0.495646	−	0.0658421i
$197$	14.3021	−	3.83225i	1.01899	−	0.273036i	0.289606	−	0.957146i	$-0.406476\pi$
$197$	14.3021	−	3.83225i	1.01899	−	0.273036i	0.729379	+	0.684110i	$0.239809\pi$
$198$	−3.98572			−0.283253
$199$	−21.6106			−1.53194			−0.765969	−	0.642877i	$-0.777740\pi$
$199$	−21.6106			−1.53194			−0.765969	+	0.642877i	$0.777740\pi$
$200$	−7.57392	+	2.02943i	−0.535557	+	0.143502i
$201$	3.29307	+	12.2899i	0.232275	+	0.866863i
$202$	−1.38907	+	5.18408i	−0.0977347	+	0.364751i
$203$	−23.3460	+	4.62963i	−1.63857	+	0.324937i
$204$	−2.15891	−	3.73934i	−0.151154	−	0.261806i
$205$			7.08658i			0.494948i
$206$	1.01009	−	3.76970i	0.0703762	−	0.262648i
$207$	−0.616658	−	0.356028i	−0.0428607	−	0.0247457i
$208$	3.05596	−	1.91340i	0.211893	−	0.132670i
$209$		−	28.8045i		−	1.99245i
$210$	1.84420	+	9.29982i	0.127262	+	0.641748i
$211$	−11.9473	+	20.6934i	−0.822487	+	1.42459i	0.0813372	+	0.996687i	$0.474081\pi$
$211$	−11.9473	+	20.6934i	−0.822487	+	1.42459i	−0.903825	+	0.427903i	$0.859252\pi$
$212$	−1.49467	−	0.862951i	−0.102655	−	0.0592677i
$213$	0.167008	+	0.623283i	0.0114432	+	0.0427067i
$214$	−13.7303	−	13.7303i	−0.938582	−	0.938582i
$215$	−40.6271	+	10.8860i	−2.77075	+	0.742419i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−10.9928	+	16.4311i	−0.746242	+	1.11542i
$218$	−11.5723	−	6.68128i	−0.783776	−	0.452514i
$219$	−2.76175	+	2.76175i	−0.186621	+	0.186621i
$220$	−7.14131	+	12.3691i	−0.481467	+	0.833925i
$221$	13.1951	−	8.26170i	0.887598	−	0.555742i
$222$	0.768308	−	0.443583i	0.0515655	−	0.0297713i
$223$	−5.54886	−	20.7086i	−0.371579	−	1.38675i	−0.858279	−	0.513183i	$-0.828466\pi$
$223$	−5.54886	−	20.7086i	−0.371579	−	1.38675i	0.486700	−	0.873569i	$-0.338200\pi$
$224$	−0.174582	+	2.63999i	−0.0116648	+	0.176391i
$225$	6.79059	−	3.92055i	0.452706	−	0.261370i
$226$	0.0909323	−	0.339364i	0.00604873	−	0.0225742i
$227$	−1.86102	+	1.86102i	−0.123520	+	0.123520i	−0.766165	−	0.642644i	$-0.777837\pi$
$227$	−1.86102	+	1.86102i	−0.123520	+	0.123520i	0.642644	+	0.766165i	$0.277837\pi$
$228$	−5.11020	+	5.11020i	−0.338431	+	0.338431i
$229$	5.43526	−	20.2847i	0.359172	−	1.34045i	−0.515980	−	0.856601i	$-0.672572\pi$
$229$	5.43526	−	20.2847i	0.359172	−	1.34045i	0.875152	−	0.483848i	$-0.160761\pi$
$230$	−2.20976	+	1.27581i	−0.145707	+	0.0841243i
$231$	8.76461	+	5.86373i	0.576669	+	0.385805i
$232$	2.32828	+	8.68926i	0.152859	+	0.570478i
$233$	16.1588	−	9.32927i	1.05860	−	0.611181i	0.133553	−	0.991042i	$-0.457362\pi$
$233$	16.1588	−	9.32927i	1.05860	−	0.611181i	0.925044	+	0.379861i	$0.124028\pi$
$234$	−2.45661	+	2.63914i	−0.160594	+	0.172526i
$235$	2.97820	−	5.15840i	0.194277	−	0.336497i
$236$	2.86582	−	2.86582i	0.186549	−	0.186549i
$237$	−4.32136	−	2.49494i	−0.280703	−	0.162064i
$238$	−0.753815	+	11.3990i	−0.0488626	+	0.738886i
$239$	8.43037	+	8.43037i	0.545315	+	0.545315i	0.925082	−	0.379767i	$-0.123996\pi$
$239$	8.43037	+	8.43037i	0.545315	+	0.545315i	−0.379767	+	0.925082i	$0.623996\pi$
$240$	3.46134	−	0.927465i	0.223429	−	0.0598676i
$241$	−10.6320	−	10.6320i	−0.684866	−	0.684866i	0.276227	−	0.961092i	$-0.410916\pi$
$241$	−10.6320	−	10.6320i	−0.684866	−	0.684866i	−0.961092	+	0.276227i	$0.910916\pi$
$242$	1.26458	+	4.71946i	0.0812901	+	0.303379i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	4.06674	−	7.04381i	0.260347	−	0.450933i
$245$	9.62635	−	23.1635i	0.615005	−	1.47986i
$246$		−	1.97759i		−	0.126086i
$247$	−19.0729	−	17.7537i	−1.21358	−	1.12964i
$248$	6.47102	+	3.73604i	0.410910	+	0.237239i
$249$	−2.62043	+	9.77959i	−0.166063	+	0.619756i
$250$		−	10.1809i		−	0.643898i
$251$	5.32365	+	9.22082i	0.336026	+	0.582013i	0.983681	−	0.179920i	$-0.0575838\pi$
$251$	5.32365	+	9.22082i	0.336026	+	0.582013i	−0.647656	+	0.761933i	$0.724250\pi$
$252$	−0.514645	−	2.59521i	−0.0324196	−	0.163483i
$253$	−0.734542	+	2.74135i	−0.0461803	+	0.172347i
$254$	0.857266	+	3.19936i	0.0537896	+	0.200746i
$255$	14.9455	−	4.00462i	0.935921	−	0.250779i
$256$	1.00000			0.0625000
$257$	12.6998			0.792194			0.396097	−	0.918209i	$-0.370364\pi$
$257$	12.6998			0.792194			0.396097	+	0.918209i	$0.370364\pi$
$258$	11.3374	−	3.03786i	0.705838	−	0.189129i
$259$	−2.34211	−	0.154884i	−0.145531	−	0.00962400i
$260$	3.78863	+	12.3523i	0.234961	+	0.766060i
$261$	−4.49789	−	7.79058i	−0.278413	−	0.482225i
$262$	−1.27982	−	0.342927i	−0.0790676	−	0.0211861i
$263$	−9.33453	−	16.1679i	−0.575592	−	0.996954i	−0.995977	−	0.0896086i	$-0.971438\pi$
$263$	−9.33453	−	16.1679i	−0.575592	−	0.996954i	0.420385	−	0.907346i	$-0.361895\pi$
$264$	1.99286	−	3.45173i	0.122652	−	0.212439i
$265$	4.37323	−	4.37323i	0.268645	−	0.268645i
$266$	18.7554	−	3.71929i	1.14997	−	0.228045i
$267$	−16.1728	−	4.33350i	−0.989762	−	0.265206i
$268$	−12.2899	−	3.29307i	−0.750725	−	0.201156i
$269$		−	15.5528i		−	0.948269i	−0.880452	−	0.474135i	$-0.842761\pi$
$269$		−	15.5528i		−	0.948269i	0.880452	−	0.474135i	$-0.157239\pi$
$270$	−3.10336	+	1.79172i	−0.188864	+	0.109041i
$271$	−9.71103	−	9.71103i	−0.589903	−	0.589903i	0.347702	−	0.937605i	$-0.386962\pi$
$271$	−9.71103	−	9.71103i	−0.589903	−	0.589903i	−0.937605	+	0.347702i	$0.886962\pi$
$272$	4.31782			0.261806
$273$	9.28476	−	2.18935i	0.561939	−	0.132506i
$274$	2.15489			0.130182
$275$	−22.0988	−	22.0988i	−1.33261	−	1.33261i
$276$	0.616658	−	0.356028i	0.0371185	−	0.0214304i
$277$		−	1.85671i		−	0.111559i	−0.998443	−	0.0557794i	$-0.982236\pi$
$277$		−	1.85671i		−	0.111559i	0.998443	−	0.0557794i	$-0.0177643\pi$
$278$	4.77283	+	1.27888i	0.286256	+	0.0767020i
$279$	−7.21748	−	1.93392i	−0.432099	−	0.115781i
$280$	−8.97598	−	3.05278i	−0.536417	−	0.182439i
$281$	12.6667	−	12.6667i	0.755630	−	0.755630i	−0.219894	−	0.975524i	$-0.570571\pi$
$281$	12.6667	−	12.6667i	0.755630	−	0.755630i	0.975524	+	0.219894i	$0.0705710\pi$
$282$	−0.831100	+	1.43951i	−0.0494913	+	0.0857214i
$283$	3.73778	+	6.47402i	0.222188	+	0.384841i	0.955472	−	0.295082i	$-0.0953468\pi$
$283$	3.73778	+	6.47402i	0.222188	+	0.384841i	−0.733284	+	0.679922i	$0.762014\pi$
$284$	−0.623283	−	0.167008i	−0.0369851	−	0.00991012i
$285$	−12.9486	−	22.4277i	−0.767011	−	1.32850i
$286$	12.6946	+	6.73523i	0.750650	+	0.398263i
$287$	−2.90940	+	4.34872i	−0.171736	+	0.256697i
$288$	−0.965926	+	0.258819i	−0.0569177	+	0.0152511i
$289$	1.64354			0.0966791
$290$	−32.2359			−1.89296
$291$	8.33554	−	2.23350i	0.488638	−	0.130930i
$292$	−1.01087	−	3.77262i	−0.0591566	−	0.220776i
$293$	0.984079	−	3.67263i	0.0574905	−	0.214557i	−0.931205	−	0.364497i	$-0.881241\pi$
$293$	0.984079	−	3.67263i	0.0574905	−	0.214557i	0.988695	+	0.149939i	$0.0479078\pi$
$294$	−2.68634	+	6.46402i	−0.156670	+	0.376989i
$295$	7.26165	+	12.5776i	0.422790	+	0.732294i
$296$			0.887166i			0.0515655i
$297$	−1.03158	+	3.84991i	−0.0598583	+	0.223394i
$298$	6.42208	+	3.70779i	0.372021	+	0.214786i
$299$	1.36245	+	2.17602i	0.0787923	+	0.125842i
$300$			7.84110i			0.452706i
$301$	−29.4003	−	9.99922i	−1.69461	−	0.576345i
$302$	5.68004	−	9.83813i	0.326850	−	0.566121i
$303$	4.64792	+	2.68348i	0.267016	+	0.154162i
$304$	−1.87046	−	6.98067i	−0.107278	−	0.400369i
$305$	20.6093	+	20.6093i	1.18008	+	1.18008i
$306$	−4.17069	+	1.11753i	−0.238423	+	0.0638851i
$307$	−11.3549	−	11.3549i	−0.648060	−	0.648060i	0.304464	−	0.952524i	$-0.401523\pi$
$307$	−11.3549	−	11.3549i	−0.648060	−	0.648060i	−0.952524	+	0.304464i	$0.901523\pi$
$308$	−9.46044	+	4.65851i	−0.539059	+	0.265443i
$309$	−3.37982	−	1.95134i	−0.192271	−	0.111008i
$310$	−18.9334	+	18.9334i	−1.07534	+	1.07534i
$311$	5.29988	−	9.17966i	0.300529	−	0.520531i	−0.675727	−	0.737152i	$-0.736170\pi$
$311$	5.29988	−	9.17966i	0.300529	−	0.520531i	0.976256	+	0.216621i	$0.0695036\pi$
$312$	−1.05726	−	3.44706i	−0.0598555	−	0.195151i
$313$	17.3619	−	10.0239i	0.981352	−	0.566584i	0.0786742	−	0.996900i	$-0.474931\pi$
$313$	17.3619	−	10.0239i	0.981352	−	0.566584i	0.902678	+	0.430316i	$0.141598\pi$
$314$	5.38753	+	20.1065i	0.304036	+	1.13468i
$315$	9.46025	+	0.625607i	0.533025	+	0.0352490i
$316$	4.32136	−	2.49494i	0.243096	−	0.140351i
$317$	−1.66934	+	6.23006i	−0.0937594	+	0.349915i	−0.996828	−	0.0795806i	$-0.974642\pi$
$317$	−1.66934	+	6.23006i	−0.0937594	+	0.349915i	0.903069	+	0.429495i	$0.141309\pi$
$318$	−1.22040	+	1.22040i	−0.0684364	+	0.0684364i
$319$	−25.3531	+	25.3531i	−1.41950	+	1.41950i
$320$	−0.927465	+	3.46134i	−0.0518468	+	0.193495i
$321$	−16.8161	+	9.70877i	−0.938582	+	0.541891i
$322$	−1.87982	−	0.124312i	−0.104758	−	0.00692766i
$323$	−8.07632	−	30.1412i	−0.449378	−	1.67710i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−28.2534	+	1.01205i	−1.56721	+	0.0561385i
$326$	4.28387	−	7.41988i	0.237262	−	0.410949i
$327$	−9.44876	+	9.44876i	−0.522518	+	0.522518i
$328$	1.71264	+	0.988794i	0.0945648	+	0.0545970i
$329$	3.94537	−	1.94278i	0.217515	−	0.107109i
$330$	10.0993	+	10.0993i	0.555950	+	0.555950i
$331$	19.4177	−	5.20295i	1.06729	−	0.285980i	0.317912	−	0.948120i	$-0.397018\pi$
$331$	19.4177	−	5.20295i	1.06729	−	0.285980i	0.749380	+	0.662140i	$0.230352\pi$
$332$	−7.15916	−	7.15916i	−0.392910	−	0.392910i
$333$	−0.229615	−	0.856937i	−0.0125828	−	0.0469598i
$334$	−9.68058	−	5.58909i	−0.529698	−	0.305821i
$335$	22.7969	−	39.4854i	1.24553	−	2.15732i
$336$	2.50484	+	0.851912i	0.136650	+	0.0464756i
$337$			2.51782i			0.137154i	0.997646	+	0.0685772i	$0.0218460\pi$
$337$			2.51782i			0.137154i	−0.997646	+	0.0685772i	$0.978154\pi$
$338$	12.2841	−	4.25447i	0.668168	−	0.231413i
$339$	−0.304265	−	0.175668i	−0.0165254	−	0.00954096i
$340$	−4.00462	+	14.9455i	−0.217181	+	0.810531i
$341$			29.7816i			1.61277i
$342$	3.61346	+	6.25869i	0.195393	+	0.338431i
$343$	15.4170	−	10.2623i	0.832442	−	0.554112i
$344$	−3.03786	+	11.3374i	−0.163790	+	0.611274i
$345$	0.660407	+	2.46467i	0.0355551	+	0.132693i
$346$	−6.71620	+	1.79960i	−0.361065	+	0.0967472i
$347$	17.7585			0.953328			0.476664	−	0.879086i	$-0.341846\pi$
$347$	17.7585			0.953328			0.476664	+	0.879086i	$0.341846\pi$
$348$	8.99579			0.482225
$349$	4.09488	−	1.09722i	0.219194	−	0.0587329i	−0.147551	−	0.989055i	$-0.547139\pi$
$349$	4.09488	−	1.09722i	0.219194	−	0.0587329i	0.366745	+	0.930322i	$0.380472\pi$
$350$	11.5357	−	17.2426i	0.616610	−	0.921656i
$351$	1.91340	+	3.05596i	0.102130	+	0.163115i
$352$	1.99286	+	3.45173i	0.106220	+	0.183978i
$353$	28.6691	+	7.68186i	1.52590	+	0.408864i	0.921680	−	0.387952i	$-0.126817\pi$
$353$	28.6691	+	7.68186i	1.52590	+	0.408864i	0.604222	+	0.796816i	$0.293484\pi$
$354$	−2.02644	−	3.50990i	−0.107704	−	0.186549i
$355$	1.15615	−	2.00250i	0.0613619	−	0.106282i
$356$	11.8393	−	11.8393i	0.627484	−	0.627484i
$357$	10.8155	+	3.67840i	0.572415	+	0.194682i
$358$	−17.1540	−	4.59640i	−0.906617	−	0.242927i
$359$	0.500851	+	0.134203i	0.0264339	+	0.00708294i	0.272012	−	0.962294i	$-0.412311\pi$
$359$	0.500851	+	0.134203i	0.0264339	+	0.00708294i	−0.245578	+	0.969377i	$0.578978\pi$
$360$		−	3.58345i		−	0.188864i
$361$	−28.7766	+	16.6142i	−1.51456	+	0.874429i
$362$	9.64354	+	9.64354i	0.506853	+	0.506853i
$363$	4.88595			0.256446
$364$	−2.74634	+	9.13551i	−0.143948	+	0.478831i
$365$	13.9959			0.732577
$366$	−5.75124	−	5.75124i	−0.300622	−	0.300622i
$367$	−29.0561	+	16.7755i	−1.51671	+	0.875675i	−0.516907	+	0.856042i	$0.672917\pi$
$367$	−29.0561	+	16.7755i	−1.51671	+	0.875675i	−0.999807	+	0.0196332i	$0.993750\pi$
$368$			0.712056i			0.0371185i
$369$	−1.91020	−	0.511837i	−0.0994412	−	0.0266452i
$370$	−3.07079	−	0.822815i	−0.159643	−	0.0427761i
$371$	4.47908	−	0.888226i	0.232542	−	0.0461144i
$372$	5.28357	−	5.28357i	0.273940	−	0.273940i
$373$	−15.3407	+	26.5709i	−0.794314	+	1.37579i	0.128960	+	0.991650i	$0.458836\pi$
$373$	−15.3407	+	26.5709i	−0.794314	+	1.37579i	−0.923274	+	0.384142i	$0.874497\pi$
$374$	8.60480	+	14.9040i	0.444944	+	0.770665i
$375$	−9.83402	−	2.63502i	−0.507827	−	0.136072i
$376$	−0.831100	−	1.43951i	−0.0428607	−	0.0742369i
$377$	1.16109	+	32.4140i	0.0597990	+	1.66941i
$378$	−2.63999	−	0.174582i	−0.135786	−	0.00897955i
$379$	2.21846	−	0.594436i	0.113955	−	0.0305341i	−0.201391	−	0.979511i	$-0.564546\pi$
$379$	2.21846	−	0.594436i	0.113955	−	0.0305341i	0.315346	+	0.948977i	$0.397879\pi$
$380$	25.8973			1.32850
$381$	3.31222			0.169690
$382$	−9.79170	+	2.62368i	−0.500987	+	0.134239i
$383$	−3.80442	−	14.1983i	−0.194397	−	0.725498i	−0.992422	−	0.122875i	$-0.960789\pi$
$383$	−3.80442	−	14.1983i	−0.194397	−	0.725498i	0.798026	−	0.602624i	$-0.205878\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	−7.35047	−	37.0665i	−0.374615	−	1.88908i
$386$	6.42667	+	11.1313i	0.327109	+	0.566569i
$387$		−	11.7374i		−	0.596645i
$388$	−2.23350	+	8.33554i	−0.113389	+	0.423173i
$389$	−28.5510	−	16.4839i	−1.44759	−	0.835767i	−0.449254	−	0.893404i	$-0.648310\pi$
$389$	−28.5510	−	16.4839i	−1.44759	−	0.835767i	−0.998338	+	0.0576369i	$0.981643\pi$
$390$	12.9120	−	0.462516i	0.653826	−	0.0234204i
$391$			3.07453i			0.155486i
$392$	−4.25484	−	5.55845i	−0.214902	−	0.280744i
$393$	−0.662484	+	1.14746i	−0.0334179	+	0.0578815i
$394$	12.8230	+	7.40333i	0.646011	+	0.372975i
$395$	4.62794	+	17.2717i	0.232857	+	0.869033i
$396$	−2.81833	−	2.81833i	−0.141626	−	0.141626i
$397$	12.7620	−	3.41956i	0.640506	−	0.171623i	0.0760733	−	0.997102i	$-0.475762\pi$
$397$	12.7620	−	3.41956i	0.640506	−	0.171623i	0.564433	+	0.825479i	$0.309095\pi$
$398$	−15.2810	−	15.2810i	−0.765969	−	0.765969i
$399$	1.26169	−	19.0790i	0.0631636	−	0.955142i
$400$	−6.79059	−	3.92055i	−0.339530	−	0.196027i
$401$	−10.4686	+	10.4686i	−0.522777	+	0.522777i	−0.918409	−	0.395632i	$-0.870526\pi$
$401$	−10.4686	+	10.4686i	−0.522777	+	0.522777i	0.395632	+	0.918409i	$0.370526\pi$
$402$	−6.36172	+	11.0188i	−0.317294	+	0.549569i
$403$	19.7199	+	18.3560i	0.982318	+	0.914378i
$404$	−4.64792	+	2.68348i	−0.231243	+	0.133508i
$405$	0.927465	+	3.46134i	0.0460861	+	0.171996i
$406$	−19.7818	−	13.2345i	−0.981752	−	0.656816i
$407$	−3.06226	+	1.76800i	−0.151791	+	0.0876364i
$408$	1.11753	−	4.17069i	0.0553261	−	0.206480i
$409$	−14.9768	+	14.9768i	−0.740556	+	0.740556i	−0.972685	−	0.232129i	$-0.925431\pi$
$409$	−14.9768	+	14.9768i	−0.740556	+	0.740556i	0.232129	+	0.972685i	$0.425431\pi$
$410$	−5.01097	+	5.01097i	−0.247474	+	0.247474i
$411$	0.557727	−	2.08146i	0.0275106	−	0.102671i
$412$	3.37982	−	1.95134i	0.166512	−	0.0961357i
$413$	−0.707563	+	10.6996i	−0.0348169	+	0.526491i
$414$	−0.184294	−	0.687793i	−0.00905754	−	0.0338032i
$415$	31.4202	−	18.1405i	1.54236	−	0.890480i
$416$	3.51387	+	0.807915i	0.172282	+	0.0396113i
$417$	2.47060	−	4.27921i	0.120986	−	0.209554i
$418$	20.3678	−	20.3678i	0.996223	−	0.996223i
$419$	7.81110	+	4.50974i	0.381597	+	0.220315i	0.678513	−	0.734588i	$-0.262625\pi$
$419$	7.81110	+	4.50974i	0.381597	+	0.220315i	−0.296916	+	0.954904i	$0.595958\pi$
$420$	−5.27192	+	7.88001i	−0.257243	+	0.384505i
$421$	−5.07143	−	5.07143i	−0.247166	−	0.247166i	0.572640	−	0.819807i	$-0.305919\pi$
$421$	−5.07143	−	5.07143i	−0.247166	−	0.247166i	−0.819807	+	0.572640i	$0.805919\pi$
$422$	−23.0804	+	6.18439i	−1.12354	+	0.301051i
$423$	1.17535	+	1.17535i	0.0571476	+	0.0571476i
$424$	−0.446696	−	1.66709i	−0.0216935	−	0.0809612i
$425$	−29.3205	−	16.9282i	−1.42225	−	0.821139i
$426$	−0.322635	+	0.558821i	−0.0156317	+	0.0270749i
$427$	4.18586	+	21.1081i	0.202568	+	1.02149i
$428$		−	19.4175i		−	0.938582i
$429$	9.79135	−	10.5189i	0.472731	−	0.507856i
$430$	−36.4253	−	21.0301i	−1.75658	−	1.01416i
$431$	−3.90772	+	14.5838i	−0.188228	+	0.702477i	0.805688	+	0.592340i	$0.201796\pi$
$431$	−3.90772	+	14.5838i	−0.188228	+	0.702477i	−0.993916	+	0.110137i	$0.964871\pi$
$432$			1.00000i			0.0481125i
$433$	−18.3240	−	31.7381i	−0.880596	−	1.52524i	−0.850679	−	0.525685i	$-0.823809\pi$
$433$	−18.3240	−	31.7381i	−0.880596	−	1.52524i	−0.0299168	−	0.999552i	$-0.509524\pi$
$434$	−19.3917	+	3.84547i	−0.930830	+	0.184589i
$435$	−8.34327	+	31.1375i	−0.400029	+	1.49293i
$436$	−3.45849	−	12.9072i	−0.165631	−	0.618145i
$437$	4.97062	−	1.33187i	0.237777	−	0.0637122i
$438$	−3.90570			−0.186621
$439$	−27.7745			−1.32561			−0.662803	−	0.748794i	$-0.730633\pi$
$439$	−27.7745			−1.32561			−0.662803	+	0.748794i	$0.730633\pi$
$440$	−13.7959	+	3.69661i	−0.657696	+	0.176229i
$441$	5.54849	+	4.26781i	0.264214	+	0.203229i
$442$	15.1722	+	3.48843i	0.721670	+	0.165928i
$443$	7.82321	+	13.5502i	0.371692	+	0.643789i	0.989826	−	0.142283i	$-0.0454445\pi$
$443$	7.82321	+	13.5502i	0.371692	+	0.643789i	−0.618134	+	0.786073i	$0.712111\pi$
$444$	0.856937	+	0.229615i	0.0406684	+	0.0108971i
$445$	29.9995	+	51.9606i	1.42211	+	2.46317i
$446$	10.7196	−	18.5668i	0.507587	−	0.879166i
$447$	5.24361	−	5.24361i	0.248014	−	0.248014i
$448$	−1.99020	+	1.74330i	−0.0940281	+	0.0823633i
$449$	9.64984	+	2.58567i	0.455404	+	0.122025i	0.479227	−	0.877691i	$-0.340917\pi$
$449$	9.64984	+	2.58567i	0.455404	+	0.122025i	−0.0238228	+	0.999716i	$0.507584\pi$
$450$	7.57392	+	2.02943i	0.357038	+	0.0956680i
$451$			7.88211i			0.371154i
$452$	0.304265	−	0.175668i	0.0143114	−	0.00826271i
$453$	−8.03280	−	8.03280i	−0.377414	−	0.377414i
$454$	−2.63188			−0.123520
$455$	−29.0740	−	17.9789i	−1.36301	−	0.842864i
$456$	−7.22692			−0.338431
$457$	−10.0672	−	10.0672i	−0.470924	−	0.470924i	0.431289	−	0.902214i	$-0.358059\pi$
$457$	−10.0672	−	10.0672i	−0.470924	−	0.470924i	−0.902214	+	0.431289i	$0.858059\pi$
$458$	18.1867	−	10.5001i	0.849811	−	0.490638i
$459$			4.31782i			0.201538i
$460$	−2.46467	−	0.660407i	−0.114916	−	0.0307916i
$461$	27.4644	+	7.35907i	1.27915	+	0.342746i	0.833528	−	0.552478i	$-0.186318\pi$
$461$	27.4644	+	7.35907i	1.27915	+	0.342746i	0.445617	+	0.895223i	$0.352984\pi$
$462$	2.05123	+	10.3438i	0.0954318	+	0.481237i
$463$	9.63165	−	9.63165i	0.447621	−	0.447621i	−0.446942	−	0.894563i	$-0.647487\pi$
$463$	9.63165	−	9.63165i	0.447621	−	0.447621i	0.894563	+	0.446942i	$0.147487\pi$
$464$	−4.49789	+	7.79058i	−0.208809	+	0.361669i
$465$	13.3879	+	23.1886i	0.620850	+	1.07534i
$466$	18.0228	+	4.82918i	0.834888	+	0.223708i
$467$	15.3719	+	26.6250i	0.711329	+	1.23206i	0.964359	+	0.264599i	$0.0852396\pi$
$467$	15.3719	+	26.6250i	0.711329	+	1.23206i	−0.253030	+	0.967458i	$0.581427\pi$
$468$	−3.60324	+	0.129070i	−0.166560	+	0.00596627i
$469$	30.2002	−	14.8712i	1.39451	−	0.686686i
$470$	5.75345	−	1.54163i	0.265387	−	0.0711101i
$471$	20.8158			0.959142
$472$	4.05289			0.186549
$473$	−45.1878	+	12.1080i	−2.07774	+	0.556728i
$474$	−1.29148	−	4.81985i	−0.0593195	−	0.221383i
$475$	−14.6665	+	54.7361i	−0.672945	+	2.51146i
$476$	−8.59332	+	7.52726i	−0.393874	+	0.345012i
$477$	0.862951	+	1.49467i	0.0395118	+	0.0684364i
$478$			11.9223i			0.545315i
$479$	4.08006	−	15.2270i	0.186423	−	0.695739i	−0.807899	−	0.589321i	$-0.799395\pi$
$479$	4.08006	−	15.2270i	0.186423	−	0.695739i	0.994322	−	0.106418i	$-0.0339380\pi$
$480$	3.10336	+	1.79172i	0.141648	+	0.0817806i
$481$	−0.716755	+	3.11738i	−0.0326812	+	0.142141i
$482$		−	15.0359i		−	0.684866i
$483$	−0.606609	+	1.78359i	−0.0276017	+	0.0811561i
$484$	−2.44297	+	4.23136i	−0.111044	+	0.192334i
$485$	−26.7807	−	15.4618i	−1.21605	−	0.702086i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	−13.1445	−	13.1445i	−0.595635	−	0.595635i	0.343513	−	0.939148i	$-0.388383\pi$
$487$	−13.1445	−	13.1445i	−0.595635	−	0.595635i	−0.939148	+	0.343513i	$0.888383\pi$
$488$	7.85634	−	2.10510i	0.355640	−	0.0952935i
$489$	−6.05831	−	6.05831i	−0.273966	−	0.273966i
$490$	23.1859	−	9.57220i	1.04743	−	0.432428i
$491$	−11.0514	−	6.38052i	−0.498742	−	0.287949i	0.229452	−	0.973320i	$-0.426307\pi$
$491$	−11.0514	−	6.38052i	−0.498742	−	0.287949i	−0.728194	+	0.685371i	$0.759640\pi$
$492$	1.39837	−	1.39837i	0.0630432	−	0.0630432i
$493$	−19.4211	+	33.6383i	−0.874682	+	1.51499i
$494$	−0.932779	−	26.0403i	−0.0419677	−	1.17161i
$495$	12.3691	−	7.14131i	0.555950	−	0.320978i
$496$	1.93392	+	7.21748i	0.0868355	+	0.324075i
$497$	1.53160	−	0.754192i	0.0687018	−	0.0338301i
$498$	−8.76814	+	5.06229i	−0.392910	+	0.226847i
$499$	8.34647	−	31.1495i	0.373639	−	1.39444i	−0.481683	−	0.876345i	$-0.659974\pi$
$499$	8.34647	−	31.1495i	0.373639	−	1.39444i	0.855323	−	0.518096i	$-0.173359\pi$
$500$	7.19900	−	7.19900i	0.321949	−	0.321949i
$501$	−7.90416	+	7.90416i	−0.353132	+	0.353132i
$502$	−2.75572	+	10.2845i	−0.122994	+	0.459019i
$503$	−27.5872	+	15.9275i	−1.23005	+	0.710170i	−0.967040	−	0.254623i	$-0.918049\pi$
$503$	−27.5872	+	15.9275i	−1.23005	+	0.710170i	−0.263010	+	0.964793i	$0.584715\pi$
$504$	1.47119	−	2.19900i	0.0655318	−	0.0979514i
$505$	−4.97766	−	18.5769i	−0.221503	−	0.826661i
$506$	−2.45783	+	1.41903i	−0.109264	+	0.0630834i
$507$	−0.930141	−	12.9667i	−0.0413090	−	0.575871i
$508$	−1.65611	+	2.86847i	−0.0734780	+	0.127268i
$509$	−5.42481	+	5.42481i	−0.240451	+	0.240451i	−0.817037	−	0.576586i	$-0.804385\pi$
$509$	−5.42481	+	5.42481i	−0.240451	+	0.240451i	0.576586	+	0.817037i	$0.304385\pi$
$510$	13.3997	+	7.73634i	0.593350	+	0.342571i
$511$	8.58864	+	5.74601i	0.379939	+	0.254188i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	6.98067	−	1.87046i	0.308204	−	0.0825830i
$514$	8.98014	+	8.98014i	0.396097	+	0.396097i
$515$	3.61960	+	13.5085i	0.159499	+	0.595257i
$516$	10.1649	+	5.86869i	0.447483	+	0.258355i
$517$	3.31253	−	5.73747i	0.145685	−	0.252334i
$518$	−1.54660	−	1.76564i	−0.0679537	−	0.0775777i
$519$			6.95312i			0.305208i
$520$	−6.05546	+	11.4134i	−0.265550	+	0.500511i
$521$	17.2643	+	9.96755i	0.756363	+	0.436686i	0.827988	−	0.560745i	$-0.189485\pi$
$521$	17.2643	+	9.96755i	0.756363	+	0.436686i	−0.0716253	+	0.997432i	$0.522819\pi$
$522$	2.32828	−	8.68926i	0.101906	−	0.380319i
$523$			5.77080i			0.252340i	0.992009	+	0.126170i	$0.0402684\pi$
$523$			5.77080i			0.252340i	−0.992009	+	0.126170i	$0.959732\pi$
$524$	−0.662484	−	1.14746i	−0.0289407	−	0.0501268i
$525$	−13.6694	−	15.6054i	−0.596582	−	0.681073i
$526$	4.83191	−	18.0329i	0.210681	−	0.786273i
$527$	8.35031	+	31.1638i	0.363745	+	1.35752i
$528$	3.84991	−	1.03158i	0.167546	−	0.0448937i
$529$	22.4930			0.977955
$530$	6.18468			0.268645
$531$	−3.91479	+	1.04896i	−0.169887	+	0.0455212i
$532$	15.8920	+	10.6321i	0.689006	+	0.460961i
$533$	5.21914	+	4.85816i	0.226066	+	0.210430i
$534$	−8.37168	−	14.5002i	−0.362278	−	0.627484i
$535$	67.2108	+	18.0091i	2.90578	+	0.778600i
$536$	−6.36172	−	11.0188i	−0.274785	−	0.475941i
$537$	−8.87956	+	15.3799i	−0.383181	+	0.663690i
$538$	10.9975	−	10.9975i	0.474135	−	0.474135i
$539$	10.7070	−	25.7638i	0.461182	−	1.10972i
$540$	−3.46134	−	0.927465i	−0.148953	−	0.0399117i
$541$	28.0638	+	7.51967i	1.20656	+	0.323296i	0.805410	−	0.592718i	$-0.201945\pi$
$541$	28.0638	+	7.51967i	1.20656	+	0.323296i	0.401147	+	0.916014i	$0.368612\pi$
$542$		−	13.7335i		−	0.589903i
$543$	11.8109	−	6.81901i	0.506853	−	0.292632i
$544$	3.05316	+	3.05316i	0.130903	+	0.130903i
$545$	47.8841			2.05113
$546$	8.11342	+	5.01721i	0.347222	+	0.214717i
$547$	−7.46165			−0.319037			−0.159519	−	0.987195i	$-0.550994\pi$
$547$	−7.46165			−0.319037			−0.159519	+	0.987195i	$0.550994\pi$
$548$	1.52374	+	1.52374i	0.0650908	+	0.0650908i
$549$	−7.04381	+	4.06674i	−0.300622	+	0.173564i
$550$		−	31.2524i		−	1.33261i
$551$	62.7966	+	16.8263i	2.67522	+	0.716824i
$552$	0.687793	+	0.184294i	0.0292744	+	0.00784406i
$553$	−4.25094	+	12.4989i	−0.180768	+	0.531506i
$554$	1.31289	−	1.31289i	0.0557794	−	0.0557794i
$555$	−1.58956	+	2.75319i	−0.0674729	+	0.116867i
$556$	2.47060	+	4.27921i	0.104777	+	0.181479i
$557$	6.38717	+	1.71144i	0.270633	+	0.0725160i	0.391583	−	0.920143i	$-0.371927\pi$
$557$	6.38717	+	1.71144i	0.270633	+	0.0725160i	−0.120950	+	0.992659i	$0.538594\pi$
$558$	−3.73604	−	6.47102i	−0.158159	−	0.273940i
$559$	−19.8343	+	37.3839i	−0.838902	+	1.58117i
$560$	−4.18833	−	8.50562i	−0.176989	−	0.359428i
$561$	16.6232	−	4.45417i	0.701832	−	0.188055i
$562$	17.9134			0.755630
$563$	40.4902			1.70646			0.853230	−	0.521535i	$-0.174640\pi$
$563$	40.4902			1.70646			0.853230	+	0.521535i	$0.174640\pi$
$564$	−1.60556	+	0.430209i	−0.0676063	+	0.0181151i
$565$	0.325851	+	1.21609i	0.0137087	+	0.0511614i
$566$	−1.93482	+	7.22083i	−0.0813264	+	0.303514i
$567$	−0.851912	+	2.50484i	−0.0357769	+	0.105194i
$568$	−0.322635	−	0.558821i	−0.0135375	−	0.0234476i
$569$			3.73110i			0.156416i	0.996937	+	0.0782080i	$0.0249198\pi$
$569$			3.73110i			0.156416i	−0.996937	+	0.0782080i	$0.975080\pi$
$570$	6.70271	−	25.0148i	0.280746	−	1.04776i
$571$	−17.2895	−	9.98211i	−0.723544	−	0.417738i	0.0925116	−	0.995712i	$-0.470510\pi$
$571$	−17.2895	−	9.98211i	−0.723544	−	0.417738i	−0.816056	+	0.577973i	$0.803844\pi$
$572$	4.21394	+	13.7390i	0.176194	+	0.574456i
$573$			10.1371i			0.423484i
$574$	−5.13227	+	1.01776i	−0.214217	+	0.0424803i
$575$	2.79165	−	4.83528i	0.116420	−	0.201645i
$576$	−0.866025	−	0.500000i	−0.0360844	−	0.0208333i
$577$	−1.83883	−	6.86259i	−0.0765513	−	0.285693i	0.917029	−	0.398820i	$-0.130580\pi$
$577$	−1.83883	−	6.86259i	−0.0765513	−	0.285693i	−0.993581	+	0.113127i	$0.963913\pi$
$578$	1.16216	+	1.16216i	0.0483395	+	0.0483395i
$579$	12.4154	−	3.32669i	0.515965	−	0.138252i
$580$	−22.7942	−	22.7942i	−0.946480	−	0.946480i
$581$	26.7287	+	1.76757i	1.10889	+	0.0733313i
$582$	7.47344	+	4.31479i	0.309784	+	0.178854i
$583$	4.86416	−	4.86416i	0.201453	−	0.201453i
$584$	1.95285	−	3.38243i	0.0808095	−	0.139966i
$585$	2.89512	−	12.5918i	0.119699	−	0.520605i
$586$	3.29279	−	1.90109i	0.136024	−	0.0785335i
$587$	6.45668	+	24.0967i	0.266496	+	0.994576i	0.961328	+	0.275404i	$0.0888117\pi$
$587$	6.45668	+	24.0967i	0.266496	+	0.994576i	−0.694833	+	0.719171i	$0.744522\pi$
$588$	−6.47028	+	2.67123i	−0.266830	+	0.110160i
$589$	46.7655	−	27.0001i	1.92694	−	1.11252i
$590$	−3.75891	+	14.0284i	−0.154752	+	0.577542i
$591$	10.4699	−	10.4699i	0.430674	−	0.430674i
$592$	−0.627321	+	0.627321i	−0.0257827	+	0.0257827i
$593$	−8.49895	+	31.7185i	−0.349010	+	1.30252i	0.538847	+	0.842404i	$0.318860\pi$
$593$	−8.49895	+	31.7185i	−0.349010	+	1.30252i	−0.887857	+	0.460120i	$0.847806\pi$
$594$	−3.45173	+	1.99286i	−0.141626	+	0.0817680i
$595$	−18.0845	−	36.7257i	−0.741390	−	1.50561i
$596$	1.91929	+	7.16290i	0.0786173	+	0.293404i
$597$	−18.7154	+	10.8053i	−0.765969	+	0.442232i
$598$	−0.575281	+	2.50207i	−0.0235250	+	0.102317i
$599$	15.6586	−	27.1214i	0.639792	−	1.10815i	−0.345686	−	0.938350i	$-0.612354\pi$
$599$	15.6586	−	27.1214i	0.639792	−	1.10815i	0.985478	−	0.169802i	$-0.0543129\pi$
$600$	−5.54449	+	5.54449i	−0.226353	+	0.226353i
$601$	−24.7157	−	14.2696i	−1.00817	−	0.582069i	−0.0975167	−	0.995234i	$-0.531090\pi$
$601$	−24.7157	−	14.2696i	−1.00817	−	0.582069i	−0.910656	+	0.413165i	$0.864423\pi$
$602$	−13.7186	−	27.8597i	−0.559130	−	1.13548i
$603$	8.99683	+	8.99683i	0.366379	+	0.366379i
$604$	10.9730	−	2.94021i	0.446485	−	0.119635i
$605$	−12.3804	−	12.3804i	−0.503335	−	0.503335i
$606$	1.38907	+	5.18408i	0.0564272	+	0.210589i
$607$	−16.7950	−	9.69658i	−0.681687	−	0.393572i	0.118803	−	0.992918i	$-0.462094\pi$
$607$	−16.7950	−	9.69658i	−0.681687	−	0.393572i	−0.800490	+	0.599346i	$0.795427\pi$
$608$	3.61346	−	6.25869i	0.146545	−	0.253824i
$609$	−17.9034	+	15.6824i	−0.725483	+	0.635482i
$610$			29.1459i			1.18008i
$611$	−1.75738	−	5.72970i	−0.0710958	−	0.231799i
$612$	−3.73934	−	2.15891i	−0.151154	−	0.0872687i
$613$	−0.0218165	+	0.0814203i	−0.000881160	+	0.00328853i	−0.966365	−	0.257174i	$-0.917209\pi$
$613$	−0.0218165	+	0.0814203i	−0.000881160	+	0.00328853i	0.965484	+	0.260463i	$0.0838752\pi$
$614$		−	16.0583i		−	0.648060i
$615$	3.54329	+	6.13716i	0.142879	+	0.247474i
$616$	−9.98360	−	3.39548i	−0.402251	−	0.136808i
$617$	−7.58497	+	28.3075i	−0.305360	+	1.13962i	0.627276	+	0.778797i	$0.284170\pi$
$617$	−7.58497	+	28.3075i	−0.305360	+	1.13962i	−0.932635	+	0.360820i	$0.882497\pi$
$618$	−1.01009	−	3.76970i	−0.0406317	−	0.151640i
$619$	12.1835	−	3.26457i	0.489698	−	0.131214i	−0.00551671	−	0.999985i	$-0.501756\pi$
$619$	12.1835	−	3.26457i	0.489698	−	0.131214i	0.495215	+	0.868771i	$0.335089\pi$
$620$	−26.7758			−1.07534
$621$	−0.712056			−0.0285738
$622$	10.2386	−	2.74342i	0.410530	−	0.110001i
$623$	−2.92310	+	44.2022i	−0.117111	+	1.77092i
$624$	1.68984	−	3.18503i	0.0676478	−	0.127503i
$625$	−1.36134	−	2.35790i	−0.0544535	−	0.0943161i
$626$	19.3647	+	5.18875i	0.773968	+	0.207384i
$627$	−14.4022	−	24.9454i	−0.575170	−	0.996223i
$628$	−10.4079	+	18.0270i	−0.415320	+	0.719356i
$629$	−2.70866	+	2.70866i	−0.108001	+	0.108001i
$630$	6.24703	+	7.13178i	0.248888	+	0.284137i
$631$	18.9752	+	5.08439i	0.755392	+	0.202407i	0.615908	−	0.787818i	$-0.288789\pi$
$631$	18.9752	+	5.08439i	0.755392	+	0.202407i	0.139483	+	0.990224i	$0.455456\pi$
$632$	4.81985	+	1.29148i	0.191723	+	0.0513722i
$633$			23.8946i			0.949727i
$634$	−5.58571	+	3.22491i	−0.221837	+	0.128078i
$635$	−8.39277	−	8.39277i	−0.333057	−	0.333057i
$636$	−1.72590			−0.0684364
$637$	−10.4602	−	22.9692i	−0.414448	−	0.910073i
$638$	−35.8547			−1.41950
$639$	0.456275	+	0.456275i	0.0180500	+	0.0180500i
$640$	−3.10336	+	1.79172i	−0.122671	+	0.0708241i
$641$		−	29.8364i		−	1.17847i	−0.807962	−	0.589234i	$-0.799430\pi$
$641$		−	29.8364i		−	1.17847i	0.807962	−	0.589234i	$-0.200570\pi$
$642$	−18.7559	−	5.02563i	−0.740237	−	0.198346i
$643$	−24.2952	−	6.50987i	−0.958108	−	0.256724i	−0.254309	−	0.967123i	$-0.581848\pi$
$643$	−24.2952	−	6.50987i	−0.958108	−	0.256724i	−0.703799	+	0.710399i	$0.748515\pi$
$644$	−1.24133	−	1.41713i	−0.0489152	−	0.0558429i
$645$	−29.7411	+	29.7411i	−1.17106	+	1.17106i
$646$	15.6023	−	27.0239i	0.613862	−	1.06324i
$647$	10.1862	+	17.6431i	0.400462	+	0.693620i	0.993782	−	0.111347i	$-0.0355164\pi$
$647$	10.1862	+	17.6431i	0.400462	+	0.693620i	−0.593320	+	0.804967i	$0.702183\pi$
$648$	0.965926	+	0.258819i	0.0379452	+	0.0101674i
$649$	8.07683	+	13.9895i	0.317043	+	0.549135i
$650$	−20.6938	−	19.2625i	−0.811676	−	0.755538i
$651$	−1.30450	+	19.7262i	−0.0511272	+	0.773131i
$652$	8.27580	−	2.21749i	0.324105	−	0.0868438i
$653$	−37.3896			−1.46317			−0.731584	−	0.681752i	$-0.761219\pi$
$653$	−37.3896			−1.46317			−0.731584	+	0.681752i	$0.761219\pi$
$654$	−13.3626			−0.522518
$655$	4.58617	−	1.22886i	0.179196	−	0.0480155i
$656$	0.511837	+	1.91020i	0.0199839	+	0.0745809i
$657$	−1.01087	+	3.77262i	−0.0394378	+	0.147184i
$658$	4.16355	+	1.41605i	0.162312	+	0.0552033i
$659$	−14.5963	−	25.2816i	−0.568593	−	0.984832i	−0.996705	−	0.0811063i	$-0.974155\pi$
$659$	−14.5963	−	25.2816i	−0.568593	−	0.984832i	0.428113	−	0.903725i	$-0.359179\pi$
$660$			14.2826i			0.555950i
$661$	2.36366	−	8.82130i	0.0919357	−	0.343109i	−0.904601	−	0.426259i	$-0.859831\pi$
$661$	2.36366	−	8.82130i	0.0919357	−	0.343109i	0.996537	+	0.0831499i	$0.0264980\pi$
$662$	17.4094	+	10.0513i	0.676636	+	0.390656i
$663$	7.29643	−	13.7524i	0.283370	−	0.534099i
$664$		−	10.1246i		−	0.392910i
$665$	−51.5408	+	45.1468i	−1.99866	+	1.75072i
$666$	0.443583	−	0.768308i	0.0171885	−	0.0297713i
$667$	−5.54733	−	3.20275i	−0.214793	−	0.124011i
$668$	−2.89312	−	10.7973i	−0.111938	−	0.417760i
$669$	−15.1598	−	15.1598i	−0.586110	−	0.586110i
$670$	44.0402	−	11.8005i	1.70142	−	0.455895i
$671$	22.9228	+	22.9228i	0.884926	+	0.884926i
$672$	1.16880	+	2.37359i	0.0450874	+	0.0915630i
$673$	−31.7383	−	18.3241i	−1.22342	−	0.706342i	−0.257774	−	0.966205i	$-0.582989\pi$
$673$	−31.7383	−	18.3241i	−1.22342	−	0.706342i	−0.965645	+	0.259863i	$0.916322\pi$
$674$	−1.78037	+	1.78037i	−0.0685772	+	0.0685772i
$675$	3.92055	−	6.79059i	0.150902	−	0.261370i
$676$	11.6945	+	5.67782i	0.449790	+	0.218378i
$677$	−7.40989	+	4.27810i	−0.284785	+	0.164421i	−0.635588	−	0.772029i	$-0.719242\pi$
$677$	−7.40989	+	4.27810i	−0.284785	+	0.164421i	0.350803	+	0.936449i	$0.385909\pi$
$678$	−0.0909323	−	0.339364i	−0.00349223	−	0.0130332i
$679$	−10.0863	−	20.4831i	−0.387075	−	0.786068i
$680$	−13.3997	+	7.73634i	−0.513856	+	0.296675i
$681$	−0.681182	+	2.54220i	−0.0261029	+	0.0974175i
$682$	−21.0588	+	21.0588i	−0.806383	+	0.806383i
$683$	8.05282	−	8.05282i	0.308133	−	0.308133i	−0.536052	−	0.844185i	$-0.680085\pi$
$683$	8.05282	−	8.05282i	0.308133	−	0.308133i	0.844185	+	0.536052i	$0.180085\pi$
$684$	−1.87046	+	6.98067i	−0.0715190	+	0.266912i
$685$	−6.68739	+	3.86097i	−0.255512	+	0.147520i
$686$	18.1580	+	3.64495i	0.693277	+	0.139165i
$687$	−5.43526	−	20.2847i	−0.207368	−	0.773909i
$688$	−10.1649	+	5.86869i	−0.387532	+	0.223742i
$689$	−0.222762	−	6.21884i	−0.00848656	−	0.236919i
$690$	−1.27581	+	2.20976i	−0.0485692	+	0.0841243i
$691$	−5.36678	+	5.36678i	−0.204162	+	0.204162i	−0.801781	−	0.597619i	$-0.796114\pi$
$691$	−5.36678	+	5.36678i	−0.204162	+	0.204162i	0.597619	+	0.801781i	$0.296114\pi$
$692$	−6.02158	−	3.47656i	−0.228906	−	0.132159i
$693$	10.5222	+	0.695836i	0.399707	+	0.0264326i
$694$	12.5572	+	12.5572i	0.476664	+	0.476664i
$695$	−17.1032	+	4.58279i	−0.648761	+	0.173835i
$696$	6.36098	+	6.36098i	0.241112	+	0.241112i
$697$	2.21002	+	8.24791i	0.0837105	+	0.312412i
$698$	3.67137	+	2.11967i	0.138963	+	0.0802306i
$699$	9.32927	−	16.1588i	0.352865	−	0.611181i
$700$	20.3493	−	4.03538i	0.769133	−	0.152523i
$701$		−	7.89055i		−	0.298022i	−0.988836	−	0.149011i	$-0.952391\pi$
$701$		−	7.89055i		−	0.298022i	0.988836	−	0.149011i	$-0.0476090\pi$
$702$	−0.807915	+	3.51387i	−0.0304928	+	0.132622i
$703$	5.55250	+	3.20574i	0.209417	+	0.120907i
$704$	−1.03158	+	3.84991i	−0.0388791	+	0.145099i
$705$		−	5.95641i		−	0.224331i
$706$	14.8402	+	25.7040i	0.558519	+	0.967383i
$707$	4.57218	−	13.4434i	0.171954	−	0.505591i
$708$	1.04896	−	3.91479i	0.0394225	−	0.147127i
$709$	3.37772	+	12.6058i	0.126853	+	0.473422i	0.999899	−	0.0142160i	$-0.00452525\pi$
$709$	3.37772	+	12.6058i	0.126853	+	0.473422i	−0.873046	+	0.487638i	$0.837859\pi$
$710$	2.23350	−	0.598465i	0.0838219	−	0.0224600i
$711$	−4.98988			−0.187135
$712$	16.7434			0.627484
$713$	−5.13925	+	1.37706i	−0.192467	+	0.0515712i
$714$	5.04666	+	10.2487i	0.188867	+	0.383548i
$715$	−51.4637	+	1.84346i	−1.92463	+	0.0689414i
$716$	−8.87956	−	15.3799i	−0.331845	−	0.574772i
$717$	11.5161	+	3.08573i	0.430077	+	0.115239i
$718$	0.259260	+	0.449051i	0.00967548	+	0.0167584i
$719$	20.3699	−	35.2816i	0.759667	−	1.31578i	−0.183353	−	0.983047i	$-0.558695\pi$
$719$	20.3699	−	35.2816i	0.759667	−	1.31578i	0.943020	−	0.332735i	$-0.107972\pi$
$720$	2.53388	−	2.53388i	0.0944321	−	0.0944321i
$721$	−3.32474	+	9.77561i	−0.123820	+	0.364063i
$722$	−32.0961	−	8.60012i	−1.19449	−	0.320063i
$723$	−14.5235	−	3.89157i	−0.540136	−	0.144729i
$724$			13.6380i			0.506853i
$725$	61.0867	−	35.2684i	2.26870	−	1.30984i
$726$	3.45489	+	3.45489i	0.128223	+	0.128223i
$727$	24.1295			0.894913			0.447457	−	0.894306i	$-0.352330\pi$
$727$	24.1295			0.894913			0.447457	+	0.894306i	$0.352330\pi$
$728$	−8.40174	+	4.51783i	−0.311389	+	0.167442i
$729$	−1.00000			−0.0370370
$730$	9.89657	+	9.89657i	0.366289	+	0.366289i
$731$	−43.8900	+	25.3399i	−1.62333	+	0.937231i
$732$		−	8.13349i		−	0.300622i
$733$	−21.4643	−	5.75135i	−0.792804	−	0.212431i	−0.160382	−	0.987055i	$-0.551272\pi$
$733$	−21.4643	−	5.75135i	−0.792804	−	0.212431i	−0.632422	+	0.774624i	$0.717939\pi$
$734$	−32.4078	−	8.68365i	−1.19619	−	0.320519i
$735$	−3.24508	−	24.8733i	−0.119697	−	0.917467i
$736$	−0.503500	+	0.503500i	−0.0185592	+	0.0185592i
$737$	25.3560	−	43.9179i	0.934001	−	1.61774i
$738$	−0.988794	−	1.71264i	−0.0363980	−	0.0630432i
$739$	−14.8523	−	3.97967i	−0.546351	−	0.146394i	−0.0249227	−	0.999689i	$-0.507934\pi$
$739$	−14.8523	−	3.97967i	−0.546351	−	0.146394i	−0.521428	+	0.853295i	$0.674601\pi$
$740$	−1.58956	−	2.75319i	−0.0584333	−	0.101209i
$741$	−25.3944	−	5.83873i	−0.932888	−	0.214491i
$742$	3.79526	+	2.53912i	0.139328	+	0.0932140i
$743$	−49.3360	+	13.2195i	−1.80996	+	0.484978i	−0.995460	−	0.0951843i	$-0.969656\pi$
$743$	−49.3360	+	13.2195i	−1.80996	+	0.484978i	−0.814501	+	0.580162i	$0.802989\pi$
$744$	7.47209			0.273940
$745$	−26.5733			−0.973572
$746$	−29.6360	+	7.94095i	−1.08505	+	0.290739i
$747$	2.62043	+	9.77959i	0.0958767	+	0.357817i
$748$	−4.45417	+	16.6232i	−0.162861	+	0.607804i
$749$	33.8507	+	38.6448i	1.23688	+	1.41205i
$750$	−5.09046	−	8.81694i	−0.185877	−	0.321949i
$751$			18.6065i			0.678962i	0.940613	+	0.339481i	$0.110251\pi$
$751$			18.6065i			0.678962i	−0.940613	+	0.339481i	$0.889749\pi$
$752$	0.430209	−	1.60556i	0.0156881	−	0.0585488i
$753$	9.22082	+	5.32365i	0.336026	+	0.194004i
$754$	−22.0991	+	23.7412i	−0.804803	+	0.864602i
$755$			40.7083i			1.48153i
$756$	−1.74330	−	1.99020i	−0.0634033	−	0.0723829i
$757$	−9.09650	+	15.7556i	−0.330618	+	0.572647i	−0.982633	−	0.185559i	$-0.940590\pi$
$757$	−9.09650	+	15.7556i	−0.330618	+	0.572647i	0.652015	+	0.758206i	$0.273924\pi$
$758$	1.98902	+	1.14836i	0.0722445	+	0.0417104i
$759$	0.734542	+	2.74135i	0.0266622	+	0.0995047i
$760$	18.3121	+	18.3121i	0.664251	+	0.664251i
$761$	21.5729	−	5.78044i	0.782017	−	0.209541i	0.154343	−	0.988017i	$-0.450674\pi$
$761$	21.5729	−	5.78044i	0.782017	−	0.209541i	0.627674	+	0.778476i	$0.284007\pi$
$762$	2.34209	+	2.34209i	0.0848451	+	0.0848451i
$763$	29.3843	+	19.6588i	1.06378	+	0.711697i
$764$	−8.77900	−	5.06856i	−0.317613	−	0.183374i
$765$	10.9408	−	10.9408i	0.395567	−	0.395567i
$766$	7.34957	−	12.7298i	0.265551	−	0.459947i
$767$	14.2413	+	3.27439i	0.514224	+	0.118231i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−4.19052	−	15.6392i	−0.151114	−	0.563966i	−0.999407	−	0.0344380i	$-0.989036\pi$
$769$	−4.19052	−	15.6392i	−0.151114	−	0.563966i	0.848293	−	0.529528i	$-0.177631\pi$
$770$	21.0124	−	31.4075i	0.757233	−	1.13185i
$771$	10.9984	−	6.34992i	0.396097	−	0.228687i
$772$	−3.32669	+	12.4154i	−0.119730	+	0.446839i
$773$	−11.9898	+	11.9898i	−0.431241	+	0.431241i	−0.889050	−	0.457809i	$-0.848634\pi$
$773$	−11.9898	+	11.9898i	−0.431241	+	0.431241i	0.457809	+	0.889050i	$0.348634\pi$
$774$	8.29958	−	8.29958i	0.298322	−	0.298322i
$775$	15.1640	−	56.5930i	0.544709	−	2.03288i
$776$	−7.47344	+	4.31479i	−0.268281	+	0.154892i
$777$	−2.10576	+	1.03692i	−0.0755439	+	0.0371993i
$778$	−8.53270	−	31.8445i	−0.305912	−	1.14168i
$779$	12.3771	−	7.14593i	0.443456	−	0.256030i
$780$	9.45723	+	8.80313i	0.338623	+	0.315203i
$781$	1.28593	−	2.22730i	0.0460143	−	0.0796991i
$782$	−2.17402	+	2.17402i	−0.0777428	+	0.0777428i
$783$	−7.79058	−	4.49789i	−0.278413	−	0.160742i
$784$	0.921790	−	6.93904i	0.0329211	−	0.247823i
$785$	−52.7447	−	52.7447i	−1.88254	−	1.88254i
$786$	−1.27982	+	0.342927i	−0.0456497	+	0.0122318i
$787$	11.5739	+	11.5739i	0.412565	+	0.412565i	0.882631	−	0.470066i	$-0.155770\pi$
$787$	11.5739	+	11.5739i	0.412565	+	0.412565i	−0.470066	+	0.882631i	$0.655770\pi$
$788$	3.83225	+	14.3021i	0.136518	+	0.509493i
$789$	−16.1679	−	9.33453i	−0.575592	−	0.332318i
$790$	−8.94049	+	15.4854i	−0.318088	+	0.550945i
$791$	−0.299307	+	0.880041i	−0.0106421	+	0.0312906i
$792$		−	3.98572i		−	0.141626i
$793$	29.3069	−	1.04979i	1.04072	−	0.0372791i
$794$	11.4421	+	6.60609i	0.406064	+	0.234441i
$795$	1.60071	−	5.97394i	0.0567714	−	0.211874i
$796$		−	21.6106i		−	0.765969i
$797$	12.8616	+	22.2770i	0.455581	+	0.789090i	0.998721	−	0.0505519i	$-0.0160980\pi$
$797$	12.8616	+	22.2770i	0.455581	+	0.789090i	−0.543140	+	0.839642i	$0.682765\pi$
$798$	14.3830	−	12.5987i	0.509153	−	0.445989i
$799$	1.85756	−	6.93252i	0.0657159	−	0.245255i
$800$	−2.02943	−	7.57392i	−0.0717510	−	0.267778i
$801$	−16.1728	+	4.33350i	−0.571439	+	0.153117i
$802$	−14.8048			−0.522777
$803$	15.5670			0.549348
$804$	−12.2899	+	3.29307i	−0.433431	+	0.116138i
$805$	6.05648	−	2.98233i	0.213463	−	0.105113i
$806$	0.964423	+	26.9237i	0.0339704	+	0.948348i
$807$	−7.77639	−	13.4691i	−0.273742	−	0.474135i
$808$	−5.18408	−	1.38907i	−0.182375	−	0.0488673i
$809$	−5.36185	−	9.28700i	−0.188513	−	0.326514i	0.756242	−	0.654292i	$-0.227033\pi$
$809$	−5.36185	−	9.28700i	−0.188513	−	0.326514i	−0.944755	+	0.327779i	$0.893700\pi$
$810$	−1.79172	+	3.10336i	−0.0629548	+	0.109041i
$811$	−28.0122	+	28.0122i	−0.983641	+	0.983641i	−0.999868	−	0.0162272i	$-0.994834\pi$
$811$	−28.0122	+	28.0122i	−0.983641	+	0.983641i	0.0162272	+	0.999868i	$0.494834\pi$
$812$	−4.62963	−	23.3460i	−0.162468	−	0.819284i
$813$	−13.2655	−	3.55448i	−0.465242	−	0.124661i
$814$	−3.41551	−	0.915183i	−0.119713	−	0.0320771i
$815$			30.7020i			1.07545i
$816$	3.73934	−	2.15891i	0.130903	−	0.0755769i
$817$	59.9804	+	59.9804i	2.09845	+	2.09845i
$818$	−21.1804			−0.740556
$819$	6.94616	−	6.53841i	0.242718	−	0.228471i
$820$	−7.08658			−0.247474
$821$	−26.2639	−	26.2639i	−0.916618	−	0.916618i	0.0801641	−	0.996782i	$-0.474456\pi$
$821$	−26.2639	−	26.2639i	−0.916618	−	0.916618i	−0.996782	+	0.0801641i	$0.974456\pi$
$822$	1.86619	−	1.07745i	0.0650908	−	0.0375802i
$823$			32.9801i			1.14961i	0.818289	+	0.574807i	$0.194923\pi$
$823$			32.9801i			1.14961i	−0.818289	+	0.574807i	$0.805077\pi$
$824$	3.76970	+	1.01009i	0.131324	+	0.0351881i
$825$	−30.1875	−	8.08872i	−1.05099	−	0.281613i
$826$	−8.06605	+	7.06541i	−0.280654	+	0.245837i
$827$	−5.18018	+	5.18018i	−0.180132	+	0.180132i	−0.791414	−	0.611281i	$-0.790654\pi$
$827$	−5.18018	+	5.18018i	−0.180132	+	0.180132i	0.611281	+	0.791414i	$0.290654\pi$
$828$	0.356028	−	0.616658i	0.0123728	−	0.0214304i
$829$	−24.0315	−	41.6237i	−0.834648	−	1.44565i	−0.894317	−	0.447434i	$-0.852338\pi$
$829$	−24.0315	−	41.6237i	−0.834648	−	1.44565i	0.0596693	−	0.998218i	$-0.480995\pi$
$830$	35.0447	+	9.39019i	1.21642	+	0.325938i
$831$	−0.928354	−	1.60796i	−0.0322042	−	0.0557794i
$832$	1.91340	+	3.05596i	0.0663351	+	0.105946i
$833$	3.98012	−	29.9615i	0.137903	−	1.03810i
$834$	4.77283	−	1.27888i	0.165270	−	0.0442839i
$835$	40.0564			1.38621
$836$	28.8045			0.996223
$837$	−7.21748	+	1.93392i	−0.249473	+	0.0668460i
$838$	2.33441	+	8.71215i	0.0806410	+	0.300956i
$839$	−3.47079	+	12.9532i	−0.119825	+	0.447193i	−0.999603	−	0.0281929i	$-0.991025\pi$
$839$	−3.47079	+	12.9532i	−0.119825	+	0.447193i	0.879778	+	0.475385i	$0.157691\pi$
$840$	−9.29982	+	1.84420i	−0.320874	+	0.0636310i
$841$	−25.9621	−	44.9677i	−0.895245	−	1.55061i
$842$		−	7.17208i		−	0.247166i
$843$	4.63632	−	17.3030i	0.159683	−	0.595947i
$844$	−20.6934	−	11.9473i	−0.712295	−	0.411244i
$845$	−30.4992	+	35.2129i	−1.04920	+	1.21136i
$846$			1.66220i			0.0571476i
$847$	−2.51453	−	12.6801i	−0.0864002	−	0.435693i
$848$	0.862951	−	1.49467i	0.0296338	−	0.0513273i
$849$	6.47402	+	3.73778i	0.222188	+	0.128280i
$850$	−8.76269	−	32.7028i	−0.300558	−	1.12170i
$851$	−0.446688	−	0.446688i	−0.0153123	−	0.0153123i
$852$	−0.623283	+	0.167008i	−0.0213533	+	0.00572161i
$853$	34.5255	+	34.5255i	1.18213	+	1.18213i	0.979191	+	0.202939i	$0.0650492\pi$
$853$	34.5255	+	34.5255i	1.18213	+	1.18213i	0.202939	+	0.979191i	$0.434951\pi$
$854$	−11.9659	+	17.8856i	−0.409464	+	0.612031i
$855$	−22.4277	−	12.9486i	−0.767011	−	0.442834i
$856$	13.7303	−	13.7303i	0.469291	−	0.469291i
$857$	20.6789	−	35.8169i	0.706377	−	1.22348i	−0.259815	−	0.965658i	$-0.583662\pi$
$857$	20.6789	−	35.8169i	0.706377	−	1.22348i	0.966192	−	0.257823i	$-0.0830051\pi$
$858$	14.3615	−	0.514437i	0.490294	−	0.0175626i
$859$	30.9750	−	17.8834i	1.05685	−	0.610175i	0.132293	−	0.991211i	$-0.457766\pi$
$859$	30.9750	−	17.8834i	1.05685	−	0.610175i	0.924560	+	0.381036i	$0.124433\pi$
$860$	−10.8860	−	40.6271i	−0.371210	−	1.38537i
$861$	−0.345252	+	5.22080i	−0.0117662	+	0.177924i
$862$	−13.0755	+	7.54913i	−0.445352	+	0.257124i
$863$	0.863708	−	3.22340i	0.0294010	−	0.109726i	−0.949666	−	0.313264i	$-0.898577\pi$
$863$	0.863708	−	3.22340i	0.0294010	−	0.109726i	0.979067	+	0.203538i	$0.0652441\pi$
$864$	−0.707107	+	0.707107i	−0.0240563	+	0.0240563i
$865$	17.6184	−	17.6184i	0.599043	−	0.599043i
$866$	9.48521	−	35.3993i	0.322321	−	1.20292i
$867$	1.42335	−	0.821772i	0.0483395	−	0.0279088i
$868$	−16.4311	−	10.9928i	−0.557709	−	0.373121i
$869$	5.14746	+	19.2106i	0.174616	+	0.651674i
$870$	−27.9171	+	16.1180i	−0.946480	+	0.546450i
$871$	−13.4520	−	43.8584i	−0.455803	−	1.48609i
$872$	6.68128	−	11.5723i	0.226257	−	0.391888i
$873$	6.10204	−	6.10204i	0.206523	−	0.206523i
$874$	4.45654	+	2.57298i	0.150745	+	0.0870325i
$875$	−1.77741	+	26.8775i	−0.0600874	+	0.908625i
$876$	−2.76175	−	2.76175i	−0.0933107	−	0.0933107i
$877$	−14.8962	+	3.99142i	−0.503008	+	0.134781i	−0.501396	−	0.865218i	$-0.667180\pi$
$877$	−14.8962	+	3.99142i	−0.503008	+	0.134781i	−0.00161249	+	0.999999i	$0.500513\pi$
$878$	−19.6396	−	19.6396i	−0.662803	−	0.662803i
$879$	−0.984079	−	3.67263i	−0.0331922	−	0.123875i
$880$	−12.3691	−	7.14131i	−0.416962	−	0.240733i
$881$	0.913525	−	1.58227i	0.0307774	−	0.0533081i	−0.850226	−	0.526417i	$-0.823535\pi$
$881$	0.913525	−	1.58227i	0.0307774	−	0.0533081i	0.881004	+	0.473109i	$0.156868\pi$
$882$	0.905576	+	6.94118i	0.0304923	+	0.233722i
$883$			2.82109i			0.0949371i	0.998873	+	0.0474686i	$0.0151154\pi$
$883$			2.82109i			0.0949371i	−0.998873	+	0.0474686i	$0.984885\pi$
$884$	8.26170	+	13.1951i	0.277871	+	0.443799i
$885$	12.5776	+	7.26165i	0.422790	+	0.244098i
$886$	−4.04959	+	15.1133i	−0.136049	+	0.507741i
$887$			5.81024i			0.195089i	0.995231	+	0.0975445i	$0.0310988\pi$
$887$			5.81024i			0.195089i	−0.995231	+	0.0975445i	$0.968901\pi$
$888$	0.443583	+	0.768308i	0.0148857	+	0.0257827i
$889$	−1.70462	−	8.59592i	−0.0571710	−	0.288298i
$890$	−15.5289	+	57.9545i	−0.520529	+	1.94264i
$891$	1.03158	+	3.84991i	0.0345592	+	0.128977i
$892$	20.7086	−	5.54886i	0.693376	−	0.185790i
$893$	−12.0126			−0.401986
$894$	7.41558			0.248014
$895$	61.4704	−	16.4710i	2.05473	−	0.550563i
$896$	−2.63999	−	0.174582i	−0.0881957	−	0.00583239i
$897$	2.26792	+	1.20326i	0.0757237	+	0.0401758i
$898$	4.99512	+	8.65181i	0.166689	+	0.288715i
$899$	−64.9270	−	17.3971i	−2.16544	−	0.580227i
$900$	3.92055	+	6.79059i	0.130685	+	0.226353i
$901$	3.72606	−	6.45373i	0.124133	−	0.215005i
$902$	−5.57349	+	5.57349i	−0.185577	+	0.185577i
$903$	−30.4610	+	6.04058i	−1.01368	+	0.201018i
$904$	0.339364	+	0.0909323i	0.0112871	+	0.00302436i
$905$	−47.2059	−	12.6488i	−1.56918	−	0.420460i
$906$		−	11.3601i		−	0.377414i
$907$	10.6409	−	6.14352i	0.353325	−	0.203992i	−0.312824	−	0.949811i	$-0.601275\pi$
$907$	10.6409	−	6.14352i	0.353325	−	0.203992i	0.666149	+	0.745819i	$0.267942\pi$
$908$	−1.86102	−	1.86102i	−0.0617602	−	0.0617602i
$909$	5.36696			0.178011
$910$	−7.84543	−	33.2714i	−0.260074	−	1.10294i
$911$	−55.2245			−1.82967			−0.914834	−	0.403830i	$-0.867679\pi$
$911$	−55.2245			−1.82967			−0.914834	+	0.403830i	$0.867679\pi$
$912$	−5.11020	−	5.11020i	−0.169216	−	0.169216i
$913$	34.9473	−	20.1769i	1.15659	−	0.667757i
$914$		−	14.2372i		−	0.470924i
$915$	28.1528	+	7.54352i	0.930703	+	0.249381i
$916$	20.2847	+	5.43526i	0.670225	+	0.179586i
$917$	3.31884	+	1.12876i	0.109598	+	0.0372748i
$918$	−3.05316	+	3.05316i	−0.100769	+	0.100769i
$919$	−10.9433	+	18.9543i	−0.360985	+	0.625245i	−0.988123	−	0.153664i	$-0.950893\pi$
$919$	−10.9433	+	18.9543i	−0.360985	+	0.625245i	0.627138	+	0.778908i	$0.284226\pi$
$920$	−1.27581	−	2.20976i	−0.0420621	−	0.0728537i
$921$	−15.5111	−	4.15619i	−0.511109	−	0.136951i
$922$	14.2166	+	24.6239i	0.468200	+	0.810946i
$923$	−0.682218	−	2.22428i	−0.0224555	−	0.0732132i
$924$	−5.86373	+	8.76461i	−0.192903	+	0.288334i
$925$	6.71932	−	1.80044i	0.220930	−	0.0591980i
$926$	13.6212			0.447621
$927$	−3.90268			−0.128181
$928$	−8.68926	+	2.32828i	−0.285239	+	0.0764296i
$929$	3.75511	+	14.0143i	0.123201	+	0.459793i	0.999769	−	0.0214851i	$-0.00683944\pi$
$929$	3.75511	+	14.0143i	0.123201	+	0.459793i	−0.876568	+	0.481278i	$0.840173\pi$
$930$	−6.93010	+	25.8635i	−0.227247	+	0.848097i
$931$	−50.1633	+	6.54452i	−1.64404	+	0.214488i
$932$	9.32927	+	16.1588i	0.305590	+	0.529298i
$933$		−	10.5998i		−	0.347020i
$934$	−7.95710	+	29.6963i	−0.260364	+	0.971693i
$935$	−53.4075	−	30.8349i	−1.74661	−	1.00841i
$936$	−2.63914	−	2.45661i	−0.0862631	−	0.0802968i
$937$		−	20.5964i		−	0.672856i	−0.941709	−	0.336428i	$-0.890781\pi$
$937$		−	20.5964i		−	0.672856i	0.941709	−	0.336428i	$-0.109219\pi$
$938$	31.8702	+	10.8393i	1.04060	+	0.353914i
$939$	10.0239	−	17.3619i	0.327117	−	0.566584i
$940$	5.15840	+	2.97820i	0.168248	+	0.0971383i
$941$	8.56080	+	31.9494i	0.279074	+	1.04152i	0.953062	+	0.302776i	$0.0979135\pi$
$941$	8.56080	+	31.9494i	0.279074	+	1.04152i	−0.673987	+	0.738743i	$0.735420\pi$
$942$	14.7190	+	14.7190i	0.479571	+	0.479571i
$943$	−1.36017	+	0.364457i	−0.0442933	+	0.0118683i
$944$	2.86582	+	2.86582i	0.0932746	+	0.0932746i
$945$	8.50562	−	4.18833i	0.276688	−	0.136246i
$946$	−40.5143	−	23.3909i	−1.31723	−	0.760505i
$947$	−22.6911	+	22.6911i	−0.737360	+	0.737360i	−0.972066	−	0.234706i	$-0.924587\pi$
$947$	−22.6911	+	22.6911i	−0.737360	+	0.737360i	0.234706	+	0.972066i	$0.424587\pi$
$948$	2.49494	−	4.32136i	0.0810319	−	0.140351i
$949$	9.59478	−	10.3077i	0.311460	−	0.334602i
$950$	−49.0750	+	28.3335i	−1.59220	+	0.919259i
$951$	1.66934	+	6.23006i	0.0541320	+	0.202023i
$952$	−11.3990	−	0.753815i	−0.369443	−	0.0244313i
$953$	33.5501	−	19.3702i	1.08679	−	0.627461i	0.154073	−	0.988059i	$-0.450761\pi$
$953$	33.5501	−	19.3702i	1.08679	−	0.627461i	0.932721	+	0.360598i	$0.117427\pi$
$954$	−0.446696	+	1.66709i	−0.0144623	+	0.0539741i
$955$	25.6862	−	25.6862i	0.831187	−	0.831187i
$956$	−8.43037	+	8.43037i	−0.272658	+	0.272658i
$957$	−9.27987	+	34.6330i	−0.299976	+	1.11952i
$958$	13.6521	−	7.88207i	0.441081	−	0.254658i
$959$	−5.68888	−	0.376206i	−0.183703	−	0.0121483i
$960$	0.927465	+	3.46134i	0.0299338	+	0.111714i
$961$	−21.5052	+	12.4161i	−0.693718	+	0.400518i
$962$	−2.71115	+	1.69750i	−0.0874109	+	0.0547297i
$963$	−9.70877	+	16.8161i	−0.312861	+	0.541891i
$964$	10.6320	−	10.6320i	0.342433	−	0.342433i
$965$	−39.8885	−	23.0296i	−1.28406	−	0.741350i
$966$	−1.69013	+	0.832251i	−0.0543789	+	0.0267772i
$967$	13.3179	+	13.3179i	0.428274	+	0.428274i	0.888040	−	0.459766i	$-0.152067\pi$
$967$	13.3179	+	13.3179i	0.428274	+	0.428274i	−0.459766	+	0.888040i	$0.652067\pi$
$968$	−4.71946	+	1.26458i	−0.151689	+	0.0406450i
$969$	−22.0649	−	22.0649i	−0.708827	−	0.708827i
$970$	−8.00364	−	29.8700i	−0.256981	−	0.959067i
$971$	−15.6269	−	9.02220i	−0.501491	−	0.289536i	0.227838	−	0.973699i	$-0.426834\pi$
$971$	−15.6269	−	9.02220i	−0.501491	−	0.289536i	−0.729329	+	0.684163i	$0.760168\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−12.3769	−	4.20947i	−0.396787	−	0.134949i
$974$		−	18.5892i		−	0.595635i
$975$	−23.9621	+	15.0031i	−0.767401	+	0.480485i
$976$	7.04381	+	4.06674i	0.225467	+	0.130173i
$977$	2.63296	−	9.82635i	0.0842360	−	0.314373i	−0.910932	−	0.412556i	$-0.864636\pi$
$977$	2.63296	−	9.82635i	0.0842360	−	0.314373i	0.995168	+	0.0981827i	$0.0313029\pi$
$978$		−	8.56774i		−	0.273966i
$979$	33.3672	+	57.7936i	1.06642	+	1.84709i
$980$	23.1635	+	9.62635i	0.739931	+	0.307502i
$981$	−3.45849	+	12.9072i	−0.110421	+	0.412097i
$982$	−3.30280	−	12.3262i	−0.105397	−	0.393345i
$983$	−2.10554	+	0.564179i	−0.0671564	+	0.0179945i	−0.292241	−	0.956345i	$-0.594401\pi$
$983$	−2.10554	+	0.564179i	−0.0671564	+	0.0179945i	0.225084	+	0.974339i	$0.427734\pi$
$984$	1.97759			0.0630432
$985$	−53.0589			−1.69060
$986$	−37.5186	+	10.0531i	−1.19484	+	0.320156i
$987$	2.44540	−	3.65518i	0.0778381	−	0.116346i
$988$	17.7537	−	19.0729i	0.564821	−	0.606788i
$989$	−4.17884	−	7.23796i	−0.132879	−	0.230154i
$990$	13.7959	+	3.69661i	0.438464	+	0.117486i
$991$	17.3203	+	29.9997i	0.550198	+	0.952971i	0.998260	+	0.0589682i	$0.0187811\pi$
$991$	17.3203	+	29.9997i	0.550198	+	0.952971i	−0.448062	+	0.894003i	$0.647886\pi$
$992$	−3.73604	+	6.47102i	−0.118620	+	0.205455i
$993$	14.2147	−	14.2147i	0.451091	−	0.451091i
$994$	1.61630	+	0.549714i	0.0512660	+	0.0174359i
$995$	74.8019	+	20.0431i	2.37138	+	0.635409i
$996$	−9.77959	−	2.62043i	−0.309878	−	0.0830316i
$997$			4.80515i			0.152181i	0.997101	+	0.0760903i	$0.0242437\pi$
$997$			4.80515i			0.152181i	−0.997101	+	0.0760903i	$0.975756\pi$
$998$	27.9278	−	16.1241i	0.884040	−	0.510401i
$999$	−0.627321	−	0.627321i	−0.0198476	−	0.0198476i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.a.241.5	yes	32
7.5	odd	6		546.2.by.a.397.5	✓	32
13.2	odd	12		546.2.by.a.535.5	yes	32
91.54	even	12	inner	546.2.cg.a.145.5	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.a.397.5	✓	32	7.5	odd	6
546.2.by.a.535.5	yes	32	13.2	odd	12
546.2.cg.a.145.5	yes	32	91.54	even	12	inner
546.2.cg.a.241.5	yes	32	1.1	even	1	trivial

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.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-3.46134 - 0.927465i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.74330 - 1.99020i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 - 0.500000i) q^{3} +1.00000i q^{4} +(-3.46134 - 0.927465i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.74330 - 1.99020i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.79172 - 3.10336i) q^{10} +(-3.84991 - 1.03158i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.05596 + 1.91340i) q^{13} +(0.174582 - 2.63999i) q^{14} +(-3.46134 + 0.927465i) q^{15} -1.00000 q^{16} -4.31782 q^{17} +(0.965926 - 0.258819i) q^{18} +(1.87046 + 6.98067i) q^{19} +(0.927465 - 3.46134i) q^{20} +(-2.50484 - 0.851912i) q^{21} +(-1.99286 - 3.45173i) q^{22} -0.712056i q^{23} +(-0.258819 + 0.965926i) q^{24} +(6.79059 + 3.92055i) q^{25} +(-3.51387 - 0.807915i) q^{26} -1.00000i q^{27} +(1.99020 - 1.74330i) q^{28} +(4.49789 - 7.79058i) q^{29} +(-3.10336 - 1.79172i) q^{30} +(-1.93392 - 7.21748i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-3.84991 + 1.03158i) q^{33} +(-3.05316 - 3.05316i) q^{34} +(4.18833 + 8.50562i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.627321 - 0.627321i) q^{37} +(-3.61346 + 6.25869i) q^{38} +(-1.68984 + 3.18503i) q^{39} +(3.10336 - 1.79172i) q^{40} +(-0.511837 - 1.91020i) q^{41} +(-1.16880 - 2.37359i) q^{42} +(10.1649 - 5.86869i) q^{43} +(1.03158 - 3.84991i) q^{44} +(-2.53388 + 2.53388i) q^{45} +(0.503500 - 0.503500i) q^{46} +(-0.430209 + 1.60556i) q^{47} +(-0.866025 + 0.500000i) q^{48} +(-0.921790 + 6.93904i) q^{49} +(2.02943 + 7.57392i) q^{50} +(-3.73934 + 2.15891i) q^{51} +(-1.91340 - 3.05596i) q^{52} +(-0.862951 + 1.49467i) q^{53} +(0.707107 - 0.707107i) q^{54} +(12.3691 + 7.14131i) q^{55} +(2.63999 + 0.174582i) q^{56} +(5.11020 + 5.11020i) q^{57} +(8.68926 - 2.32828i) q^{58} +(-2.86582 - 2.86582i) q^{59} +(-0.927465 - 3.46134i) q^{60} +(-7.04381 - 4.06674i) q^{61} +(3.73604 - 6.47102i) q^{62} +(-2.59521 + 0.514645i) q^{63} -1.00000i q^{64} +(12.3523 - 3.78863i) q^{65} +(-3.45173 - 1.99286i) q^{66} +(-3.29307 + 12.2899i) q^{67} -4.31782i q^{68} +(-0.356028 - 0.616658i) q^{69} +(-3.05278 + 8.97598i) q^{70} +(-0.167008 + 0.623283i) q^{71} +(0.258819 + 0.965926i) q^{72} +(-3.77262 + 1.01087i) q^{73} +0.887166 q^{74} +7.84110 q^{75} +(-6.98067 + 1.87046i) q^{76} +(4.65851 + 9.46044i) q^{77} +(-3.44706 + 1.05726i) q^{78} +(-2.49494 - 4.32136i) q^{79} +(3.46134 + 0.927465i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.988794 - 1.71264i) q^{82} +(-7.15916 + 7.15916i) q^{83} +(0.851912 - 2.50484i) q^{84} +(14.9455 + 4.00462i) q^{85} +(11.3374 + 3.03786i) q^{86} -8.99579i q^{87} +(3.45173 - 1.99286i) q^{88} +(-11.8393 - 11.8393i) q^{89} -3.58345 q^{90} +(9.13551 + 2.74634i) q^{91} +0.712056 q^{92} +(-5.28357 - 5.28357i) q^{93} +(-1.43951 + 0.831100i) q^{94} -25.8973i q^{95} +(-0.965926 - 0.258819i) q^{96} +(8.33554 + 2.23350i) q^{97} +(-5.55845 + 4.25484i) q^{98} +(-2.81833 + 2.81833i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{7} + 16 q^{9}+O(q^{10}) \) 32 * q - 4 * q^7 + 16 * q^9	\( 32 q - 4 q^{7} + 16 q^{9} + 8 q^{11} + 16 q^{12} + 4 q^{14} - 32 q^{16} - 16 q^{17} + 24 q^{19} + 8 q^{21} - 4 q^{22} + 24 q^{25} - 8 q^{26} + 8 q^{28} - 12 q^{29} + 4 q^{31} + 8 q^{33} + 8 q^{34} + 40 q^{35} - 12 q^{37} - 8 q^{38} + 28 q^{39} + 28 q^{41} - 12 q^{42} + 84 q^{43} - 4 q^{44} - 40 q^{46} - 4 q^{47} - 36 q^{49} - 16 q^{50} - 20 q^{52} - 4 q^{53} - 48 q^{55} + 12 q^{56} + 12 q^{57} + 12 q^{58} - 24 q^{59} - 36 q^{61} + 40 q^{62} + 4 q^{63} + 44 q^{65} - 16 q^{67} + 8 q^{69} + 40 q^{70} + 20 q^{71} - 16 q^{73} - 40 q^{74} + 16 q^{75} - 36 q^{76} + 12 q^{77} - 20 q^{78} - 16 q^{81} - 24 q^{82} - 12 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 60 q^{89} - 48 q^{91} - 16 q^{92} - 32 q^{93} - 76 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 32 * q - 4 * q^7 + 16 * q^9 + 8 * q^11 + 16 * q^12 + 4 * q^14 - 32 * q^16 - 16 * q^17 + 24 * q^19 + 8 * q^21 - 4 * q^22 + 24 * q^25 - 8 * q^26 + 8 * q^28 - 12 * q^29 + 4 * q^31 + 8 * q^33 + 8 * q^34 + 40 * q^35 - 12 * q^37 - 8 * q^38 + 28 * q^39 + 28 * q^41 - 12 * q^42 + 84 * q^43 - 4 * q^44 - 40 * q^46 - 4 * q^47 - 36 * q^49 - 16 * q^50 - 20 * q^52 - 4 * q^53 - 48 * q^55 + 12 * q^56 + 12 * q^57 + 12 * q^58 - 24 * q^59 - 36 * q^61 + 40 * q^62 + 4 * q^63 + 44 * q^65 - 16 * q^67 + 8 * q^69 + 40 * q^70 + 20 * q^71 - 16 * q^73 - 40 * q^74 + 16 * q^75 - 36 * q^76 + 12 * q^77 - 20 * q^78 - 16 * q^81 - 24 * q^82 - 12 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 60 * q^89 - 48 * q^91 - 16 * q^92 - 32 * q^93 - 76 * q^97 - 8 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more