LMFDB - Embedded newform 353.2.d.a.70.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [353,2,Mod(70,353)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(353, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("353.70");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	353.d (of order $8$, 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:	$2.81871919135$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			70.11
Character	$\chi$	$=$	353.70
Dual form			353.2.d.a.116.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.999206i q^{2} +(0.722463 - 1.74418i) q^{3} +1.00159 q^{4} +(-2.60544 - 1.07921i) q^{5} +(-1.74279 - 0.721889i) q^{6} +(3.34997 - 1.38760i) q^{7} -2.99920i q^{8} +(-0.398887 - 0.398887i) q^{9} +O(q^{10})$	\(q-0.999206i q^{2} +(0.722463 - 1.74418i) q^{3} +1.00159 q^{4} +(-2.60544 - 1.07921i) q^{5} +(-1.74279 - 0.721889i) q^{6} +(3.34997 - 1.38760i) q^{7} -2.99920i q^{8} +(-0.398887 - 0.398887i) q^{9} +(-1.07835 + 2.60337i) q^{10} +0.301577i q^{11} +(0.723610 - 1.74695i) q^{12} +(-1.98615 + 4.79499i) q^{13} +(-1.38650 - 3.34731i) q^{14} +(-3.76467 + 3.76467i) q^{15} -0.993646 q^{16} -3.19772i q^{17} +(-0.398570 + 0.398570i) q^{18} +(1.08533 - 1.08533i) q^{19} +(-2.60958 - 1.08092i) q^{20} -6.84544i q^{21} +0.301338 q^{22} +(-6.26561 + 6.26561i) q^{23} +(-5.23115 - 2.16681i) q^{24} +(2.08811 + 2.08811i) q^{25} +(4.79118 + 1.98457i) q^{26} +(4.24862 - 1.75984i) q^{27} +(3.35529 - 1.38981i) q^{28} +0.750794i q^{29} +(3.76168 + 3.76168i) q^{30} +(5.37165 + 2.22501i) q^{31} -5.00555i q^{32} +(0.526005 + 0.217878i) q^{33} -3.19518 q^{34} -10.2257 q^{35} +(-0.399520 - 0.399520i) q^{36} +(-8.20726 + 3.39956i) q^{37} +(-1.08447 - 1.08447i) q^{38} +(6.92841 + 6.92841i) q^{39} +(-3.23677 + 7.81426i) q^{40} +(5.34704 - 5.34704i) q^{41} -6.84001 q^{42} +(-0.536106 + 0.536106i) q^{43} +0.302056i q^{44} +(0.608795 + 1.46976i) q^{45} +(6.26063 + 6.26063i) q^{46} +(8.37227 + 8.37227i) q^{47} +(-0.717872 + 1.73310i) q^{48} +(4.34713 - 4.34713i) q^{49} +(2.08645 - 2.08645i) q^{50} +(-5.57740 - 2.31024i) q^{51} +(-1.98930 + 4.80261i) q^{52} +(0.0700567 - 0.0290184i) q^{53} +(-1.75844 - 4.24525i) q^{54} +(0.325465 - 0.785743i) q^{55} +(-4.16171 - 10.0473i) q^{56} +(-1.10890 - 2.67712i) q^{57} +0.750198 q^{58} +(3.77351 - 1.56304i) q^{59} +(-3.77065 + 3.77065i) q^{60} -9.69814i q^{61} +(2.22324 - 5.36738i) q^{62} +(-1.88976 - 0.782764i) q^{63} -6.98887 q^{64} +(10.3496 - 10.3496i) q^{65} +(0.217705 - 0.525587i) q^{66} +(-0.784430 + 1.89378i) q^{67} -3.20280i q^{68} +(6.40167 + 15.4550i) q^{69} +10.2176i q^{70} +(-0.541680 - 1.30773i) q^{71} +(-1.19634 + 1.19634i) q^{72} +3.79603i q^{73} +(3.39686 + 8.20074i) q^{74} +(5.15061 - 2.13345i) q^{75} +(1.08705 - 1.08705i) q^{76} +(0.418470 + 1.01028i) q^{77} +(6.92290 - 6.92290i) q^{78} +(12.6702 - 5.24818i) q^{79} +(2.58889 + 1.07235i) q^{80} -10.3741i q^{81} +(-5.34280 - 5.34280i) q^{82} +11.0434i q^{83} -6.85631i q^{84} +(-3.45102 + 8.33149i) q^{85} +(0.535680 + 0.535680i) q^{86} +(1.30952 + 0.542421i) q^{87} +0.904492 q^{88} +(0.755075 - 1.82291i) q^{89} +(1.46859 - 0.608311i) q^{90} +18.8191i q^{91} +(-6.27555 + 6.27555i) q^{92} +(7.76163 - 7.76163i) q^{93} +(8.36562 - 8.36562i) q^{94} +(-3.99906 + 1.65647i) q^{95} +(-8.73057 - 3.61632i) q^{96} -1.70612 q^{97} +(-4.34367 - 4.34367i) q^{98} +(0.120295 - 0.120295i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 112 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 112 * q - 112 * q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 + 4 * q^9	$ 112 q - 112 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} + 4 q^{9} - 4 q^{10} - 16 q^{12} + 16 q^{13} + 24 q^{14} + 96 q^{16} - 12 q^{18} - 4 q^{19} - 24 q^{22} - 24 q^{23} - 20 q^{24} - 44 q^{25} + 8 q^{26} + 24 q^{27} - 44 q^{28} + 44 q^{30} + 4 q^{31} - 36 q^{33} + 24 q^{35} + 20 q^{36} - 4 q^{37} + 32 q^{38} + 8 q^{39} - 32 q^{40} - 32 q^{41} + 56 q^{42} - 48 q^{43} - 104 q^{45} + 76 q^{46} - 44 q^{47} + 4 q^{48} + 8 q^{49} + 20 q^{50} - 32 q^{51} - 72 q^{52} + 20 q^{53} + 64 q^{54} + 16 q^{55} - 24 q^{56} - 20 q^{57} - 64 q^{58} + 60 q^{59} - 176 q^{60} - 12 q^{62} + 28 q^{63} - 104 q^{64} + 4 q^{65} + 64 q^{66} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 56 q^{72} + 4 q^{74} + 92 q^{75} - 20 q^{77} + 72 q^{78} + 24 q^{79} - 36 q^{80} - 72 q^{82} - 4 q^{85} - 44 q^{86} + 24 q^{87} + 344 q^{88} + 16 q^{89} - 44 q^{90} + 44 q^{92} + 76 q^{93} + 148 q^{94} - 20 q^{95} + 4 q^{96} + 72 q^{97} - 64 q^{98} + 56 q^{99}+O(q^{100}) $ 112 * q - 112 * q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 + 4 * q^9 - 4 * q^10 - 16 * q^12 + 16 * q^13 + 24 * q^14 + 96 * q^16 - 12 * q^18 - 4 * q^19 - 24 * q^22 - 24 * q^23 - 20 * q^24 - 44 * q^25 + 8 * q^26 + 24 * q^27 - 44 * q^28 + 44 * q^30 + 4 * q^31 - 36 * q^33 + 24 * q^35 + 20 * q^36 - 4 * q^37 + 32 * q^38 + 8 * q^39 - 32 * q^40 - 32 * q^41 + 56 * q^42 - 48 * q^43 - 104 * q^45 + 76 * q^46 - 44 * q^47 + 4 * q^48 + 8 * q^49 + 20 * q^50 - 32 * q^51 - 72 * q^52 + 20 * q^53 + 64 * q^54 + 16 * q^55 - 24 * q^56 - 20 * q^57 - 64 * q^58 + 60 * q^59 - 176 * q^60 - 12 * q^62 + 28 * q^63 - 104 * q^64 + 4 * q^65 + 64 * q^66 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 56 * q^72 + 4 * q^74 + 92 * q^75 - 20 * q^77 + 72 * q^78 + 24 * q^79 - 36 * q^80 - 72 * q^82 - 4 * q^85 - 44 * q^86 + 24 * q^87 + 344 * q^88 + 16 * q^89 - 44 * q^90 + 44 * q^92 + 76 * q^93 + 148 * q^94 - 20 * q^95 + 4 * q^96 + 72 * q^97 - 64 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/353\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{8}\right)$

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 $

$2$		−	0.999206i		−	0.706545i	−0.935520	−	0.353273i	$-0.885069\pi$
$2$		−	0.999206i		−	0.706545i	0.935520	−	0.353273i	$-0.114931\pi$
$3$	0.722463	−	1.74418i	0.417114	−	1.00700i	−0.566066	−	0.824360i	$-0.691535\pi$
$3$	0.722463	−	1.74418i	0.417114	−	1.00700i	0.983180	−	0.182642i	$-0.0584649\pi$
$4$	1.00159			0.500794
$5$	−2.60544	−	1.07921i	−1.16519	−	0.482637i	−0.285590	−	0.958352i	$-0.592190\pi$
$5$	−2.60544	−	1.07921i	−1.16519	−	0.482637i	−0.879600	+	0.475714i	$0.842190\pi$
$6$	−1.74279	−	0.721889i	−0.711492	−	0.294710i
$7$	3.34997	−	1.38760i	1.26617	−	0.524465i	0.354373	−	0.935104i	$-0.384694\pi$
$7$	3.34997	−	1.38760i	1.26617	−	0.524465i	0.911798	+	0.410639i	$0.134694\pi$
$8$		−	2.99920i		−	1.06038i
$9$	−0.398887	−	0.398887i	−0.132962	−	0.132962i
$10$	−1.07835	+	2.60337i	−0.341005	+	0.823259i
$11$			0.301577i			0.0909290i	0.998966	+	0.0454645i	$0.0144768\pi$
$11$			0.301577i			0.0909290i	−0.998966	+	0.0454645i	$0.985523\pi$
$12$	0.723610	−	1.74695i	0.208888	−	0.504300i
$13$	−1.98615	+	4.79499i	−0.550859	+	1.32989i	0.365975	+	0.930625i	$0.380735\pi$
$13$	−1.98615	+	4.79499i	−0.550859	+	1.32989i	−0.916835	+	0.399267i	$0.869265\pi$
$14$	−1.38650	−	3.34731i	−0.370558	−	0.894607i
$15$	−3.76467	+	3.76467i	−0.972034	+	0.972034i
$16$	−0.993646			−0.248412
$17$		−	3.19772i		−	0.775562i	−0.921752	−	0.387781i	$-0.873242\pi$
$17$		−	3.19772i		−	0.775562i	0.921752	−	0.387781i	$-0.126758\pi$
$18$	−0.398570	+	0.398570i	−0.0939439	+	0.0939439i
$19$	1.08533	−	1.08533i	0.248992	−	0.248992i	−0.571565	−	0.820557i	$-0.693664\pi$
$19$	1.08533	−	1.08533i	0.248992	−	0.248992i	0.820557	+	0.571565i	$0.193664\pi$
$20$	−2.60958	−	1.08092i	−0.583520	−	0.241702i
$21$		−	6.84544i		−	1.49380i
$22$	0.301338			0.0642454
$23$	−6.26561	+	6.26561i	−1.30647	+	1.30647i	−0.382523	+	0.923946i	$0.624945\pi$
$23$	−6.26561	+	6.26561i	−1.30647	+	1.30647i	−0.923946	+	0.382523i	$0.875055\pi$
$24$	−5.23115	−	2.16681i	−1.06780	−	0.442299i
$25$	2.08811	+	2.08811i	0.417622	+	0.417622i
$26$	4.79118	+	1.98457i	0.939629	+	0.389207i
$27$	4.24862	−	1.75984i	0.817648	−	0.338681i
$28$	3.35529	−	1.38981i	0.634091	−	0.262649i
$29$			0.750794i			0.139419i	0.997567	+	0.0697095i	$0.0222072\pi$
$29$			0.750794i			0.139419i	−0.997567	+	0.0697095i	$0.977793\pi$
$30$	3.76168	+	3.76168i	0.686786	+	0.686786i
$31$	5.37165	+	2.22501i	0.964777	+	0.399624i	0.808765	−	0.588132i	$-0.200136\pi$
$31$	5.37165	+	2.22501i	0.964777	+	0.399624i	0.156012	+	0.987755i	$0.450136\pi$
$32$		−	5.00555i		−	0.884865i
$33$	0.526005	+	0.217878i	0.0915657	+	0.0379277i
$34$	−3.19518			−0.547970
$35$	−10.2257			−1.72846
$36$	−0.399520	−	0.399520i	−0.0665867	−	0.0665867i
$37$	−8.20726	+	3.39956i	−1.34927	+	0.558884i	−0.936088	−	0.351767i	$-0.885581\pi$
$37$	−8.20726	+	3.39956i	−1.34927	+	0.558884i	−0.413178	+	0.910651i	$0.635581\pi$
$38$	−1.08447	−	1.08447i	−0.175924	−	0.175924i
$39$	6.92841	+	6.92841i	1.10943	+	1.10943i
$40$	−3.23677	+	7.81426i	−0.511778	+	1.23554i
$41$	5.34704	−	5.34704i	0.835068	−	0.835068i	−0.153137	−	0.988205i	$-0.548938\pi$
$41$	5.34704	−	5.34704i	0.835068	−	0.835068i	0.988205	+	0.153137i	$0.0489377\pi$
$42$	−6.84001			−1.05544
$43$	−0.536106	+	0.536106i	−0.0817553	+	0.0817553i	−0.746802	−	0.665047i	$-0.768412\pi$
$43$	−0.536106	+	0.536106i	−0.0817553	+	0.0817553i	0.665047	+	0.746802i	$0.268412\pi$
$44$			0.302056i			0.0455367i
$45$	0.608795	+	1.46976i	0.0907538	+	0.219099i
$46$	6.26063	+	6.26063i	0.923080	+	0.923080i
$47$	8.37227	+	8.37227i	1.22122	+	1.22122i	0.967198	+	0.254024i	$0.0817541\pi$
$47$	8.37227	+	8.37227i	1.22122	+	1.22122i	0.254024	+	0.967198i	$0.418246\pi$
$48$	−0.717872	+	1.73310i	−0.103616	+	0.250151i
$49$	4.34713	−	4.34713i	0.621018	−	0.621018i
$50$	2.08645	−	2.08645i	0.295069	−	0.295069i
$51$	−5.57740	−	2.31024i	−0.780993	−	0.323498i
$52$	−1.98930	+	4.80261i	−0.275867	+	0.666002i
$53$	0.0700567	−	0.0290184i	0.00962302	−	0.00398599i	−0.377867	−	0.925860i	$-0.623342\pi$
$53$	0.0700567	−	0.0290184i	0.00962302	−	0.00398599i	0.387490	+	0.921874i	$0.373342\pi$
$54$	−1.75844	−	4.24525i	−0.239293	−	0.577705i
$55$	0.325465	−	0.785743i	0.0438857	−	0.105950i
$56$	−4.16171	−	10.0473i	−0.556132	−	1.34262i
$57$	−1.10890	−	2.67712i	−0.146877	−	0.354593i
$58$	0.750198			0.0985058
$59$	3.77351	−	1.56304i	0.491270	−	0.203491i	−0.123275	−	0.992373i	$-0.539340\pi$
$59$	3.77351	−	1.56304i	0.491270	−	0.203491i	0.614545	+	0.788882i	$0.289340\pi$
$60$	−3.77065	+	3.77065i	−0.486789	+	0.486789i
$61$		−	9.69814i		−	1.24172i	−0.783921	−	0.620860i	$-0.786784\pi$
$61$		−	9.69814i		−	1.24172i	0.783921	−	0.620860i	$-0.213216\pi$
$62$	2.22324	−	5.36738i	0.282352	−	0.681658i
$63$	−1.88976	−	0.782764i	−0.238087	−	0.0986190i
$64$	−6.98887			−0.873609
$65$	10.3496	−	10.3496i	1.28371	−	1.28371i
$66$	0.217705	−	0.525587i	0.0267977	−	0.0646953i
$67$	−0.784430	+	1.89378i	−0.0958333	+	0.231362i	−0.964525	−	0.263991i	$-0.914961\pi$
$67$	−0.784430	+	1.89378i	−0.0958333	+	0.231362i	0.868692	+	0.495353i	$0.164961\pi$
$68$		−	3.20280i		−	0.388397i
$69$	6.40167	+	15.4550i	0.770671	+	1.86056i
$70$			10.2176i			1.22123i
$71$	−0.541680	−	1.30773i	−0.0642856	−	0.155199i	0.888472	−	0.458931i	$-0.151767\pi$
$71$	−0.541680	−	1.30773i	−0.0642856	−	0.155199i	−0.952758	+	0.303732i	$0.901767\pi$
$72$	−1.19634	+	1.19634i	−0.140990	+	0.140990i
$73$			3.79603i			0.444291i	0.975013	+	0.222146i	$0.0713061\pi$
$73$			3.79603i			0.444291i	−0.975013	+	0.222146i	$0.928694\pi$
$74$	3.39686	+	8.20074i	0.394877	+	0.953317i
$75$	5.15061	−	2.13345i	0.594742	−	0.246350i
$76$	1.08705	−	1.08705i	0.124693	−	0.124693i
$77$	0.418470	+	1.01028i	0.0476891	+	0.115132i
$78$	6.92290	−	6.92290i	0.783864	−	0.783864i
$79$	12.6702	−	5.24818i	1.42551	−	0.590467i	0.469273	−	0.883053i	$-0.344516\pi$
$79$	12.6702	−	5.24818i	1.42551	−	0.590467i	0.956239	+	0.292586i	$0.0945158\pi$
$80$	2.58889	+	1.07235i	0.289447	+	0.119893i
$81$		−	10.3741i		−	1.15268i
$82$	−5.34280	−	5.34280i	−0.590013	−	0.590013i
$83$			11.0434i			1.21217i	0.795400	+	0.606085i	$0.207261\pi$
$83$			11.0434i			1.21217i	−0.795400	+	0.606085i	$0.792739\pi$
$84$		−	6.85631i		−	0.748085i
$85$	−3.45102	+	8.33149i	−0.374315	+	0.903677i
$86$	0.535680	+	0.535680i	0.0577638	+	0.0577638i
$87$	1.30952	+	0.542421i	0.140395	+	0.0581536i
$88$	0.904492			0.0964192
$89$	0.755075	−	1.82291i	0.0800378	−	0.193228i	−0.878795	−	0.477199i	$-0.841652\pi$
$89$	0.755075	−	1.82291i	0.0800378	−	0.193228i	0.958833	+	0.283971i	$0.0916520\pi$
$90$	1.46859	−	0.608311i	0.154803	−	0.0641217i
$91$			18.8191i			1.97278i
$92$	−6.27555	+	6.27555i	−0.654272	+	0.654272i
$93$	7.76163	−	7.76163i	0.804844	−	0.804844i
$94$	8.36562	−	8.36562i	0.862848	−	0.862848i
$95$	−3.99906	+	1.65647i	−0.410295	+	0.169950i
$96$	−8.73057	−	3.61632i	−0.891061	−	0.369089i
$97$	−1.70612			−0.173230			−0.0866151	−	0.996242i	$-0.527605\pi$
$97$	−1.70612			−0.173230			−0.0866151	+	0.996242i	$0.527605\pi$
$98$	−4.34367	−	4.34367i	−0.438777	−	0.438777i
$99$	0.120295	−	0.120295i	0.0120901	−	0.0120901i
$100$	2.09142	+	2.09142i	0.209142	+	0.209142i
$101$	15.5281	+	6.43193i	1.54510	+	0.640001i	0.982422	−	0.186675i	$-0.0597712\pi$
$101$	15.5281	+	6.43193i	1.54510	+	0.640001i	0.562678	+	0.826676i	$0.309771\pi$
$102$	−2.30840	+	5.57297i	−0.228566	+	0.551807i
$103$	2.99293	−	1.23971i	0.294902	−	0.122152i	−0.230327	−	0.973113i	$-0.573980\pi$
$103$	2.99293	−	1.23971i	0.294902	−	0.122152i	0.525229	+	0.850961i	$0.323980\pi$
$104$	14.3812	+	5.95687i	1.41019	+	0.584119i
$105$	−7.38767	+	17.8354i	−0.720963	+	1.74056i
$106$	−0.0289954	−	0.0700010i	−0.00281628	−	0.00679910i
$107$	−7.07505	+	2.93058i	−0.683971	+	0.283310i	−0.697486	−	0.716599i	$-0.745698\pi$
$107$	−7.07505	+	2.93058i	−0.683971	+	0.283310i	0.0135149	+	0.999909i	$0.495698\pi$
$108$	4.25537	−	1.76263i	0.409473	−	0.169609i
$109$			6.47985i			0.620657i	0.950629	+	0.310328i	$0.100439\pi$
$109$			6.47985i			0.620657i	−0.950629	+	0.310328i	$0.899561\pi$
$110$	−0.785119	−	0.325207i	−0.0748581	−	0.0310073i
$111$			16.7710i			1.59183i
$112$	−3.32869	+	1.37879i	−0.314532	+	0.130283i
$113$	−11.5593	+	11.5593i	−1.08741	+	1.08741i	−0.0916178	+	0.995794i	$0.529204\pi$
$113$	−11.5593	+	11.5593i	−1.08741	+	1.08741i	−0.995794	+	0.0916178i	$0.970796\pi$
$114$	−2.67499	+	1.10802i	−0.250536	+	0.103775i
$115$	23.0866	−	9.56278i	2.15284	−	0.891734i
$116$			0.751986i			0.0698202i
$117$	2.70491	−	1.12041i	0.250069	−	0.103582i
$118$	−1.56180	−	3.77052i	−0.143775	−	0.347104i
$119$	−4.43718	−	10.7123i	−0.406755	−	0.981994i
$120$	11.2910	+	11.2910i	1.03072	+	1.03072i
$121$	10.9091			0.991732
$122$	−9.69044			−0.877331
$123$	−5.46316	−	13.1892i	−0.492597	−	1.18923i
$124$	5.38018	+	2.22854i	0.483154	+	0.200129i
$125$	2.20911	+	5.33326i	0.197589	+	0.477022i
$126$	−0.782142	+	1.88826i	−0.0696787	+	0.168219i
$127$	−12.2630	−	12.2630i	−1.08817	−	1.08817i	−0.995717	−	0.0924485i	$-0.970531\pi$
$127$	−12.2630	−	12.2630i	−1.08817	−	1.08817i	−0.0924485	−	0.995717i	$-0.529469\pi$
$128$		−	3.02778i		−	0.267621i
$129$	0.547748	+	1.32238i	0.0482265	+	0.116429i
$130$	−10.3414	−	10.3414i	−0.907000	−	0.907000i
$131$	−21.8881			−1.91238			−0.956188	−	0.292753i	$-0.905429\pi$
$131$	−21.8881			−1.91238			−0.956188	+	0.292753i	$0.905429\pi$
$132$	0.526840	+	0.218224i	0.0458555	+	0.0189940i
$133$	2.12982	−	5.14183i	0.184678	−	0.445853i
$134$	1.89228	+	0.783807i	0.163468	+	0.0677106i
$135$	−12.9688			−1.11618
$136$	−9.59063			−0.822390
$137$	−2.60751	−	6.29508i	−0.222774	−	0.537825i	0.772490	−	0.635027i	$-0.219011\pi$
$137$	−2.60751	−	6.29508i	−0.222774	−	0.537825i	−0.995265	+	0.0972016i	$0.969011\pi$
$138$	15.4427	−	6.39659i	1.31457	−	0.544514i
$139$	−1.72397	−	4.16203i	−0.146225	−	0.353019i	0.833749	−	0.552144i	$-0.186190\pi$
$139$	−1.72397	−	4.16203i	−0.146225	−	0.353019i	−0.979974	+	0.199125i	$0.936190\pi$
$140$	−10.2419			−0.865600
$141$	20.6514	−	8.55409i	1.73916	−	0.720384i
$142$	−1.30669	+	0.541250i	−0.109655	+	0.0454207i
$143$	−1.44606	−	0.598978i	−0.120926	−	0.0500891i
$144$	0.396353	+	0.396353i	0.0330294	+	0.0330294i
$145$	0.810265	−	1.95615i	0.0672888	−	0.162450i
$146$	3.79301			0.313912
$147$	−4.44153	−	10.7228i	−0.366331	−	0.884401i
$148$	−8.22029	+	3.40496i	−0.675704	+	0.279886i
$149$	−14.1656	−	5.86759i	−1.16049	−	0.480692i	−0.282453	−	0.959281i	$-0.591148\pi$
$149$	−14.1656	−	5.86759i	−1.16049	−	0.480692i	−0.878039	+	0.478589i	$0.841148\pi$
$150$	−2.13176	−	5.14652i	−0.174057	−	0.420212i
$151$	3.26096	−	7.87265i	0.265373	−	0.640667i	−0.733881	−	0.679278i	$-0.762293\pi$
$151$	3.26096	−	7.87265i	0.265373	−	0.640667i	0.999254	+	0.0386106i	$0.0122932\pi$
$152$	−3.25512	−	3.25512i	−0.264025	−	0.264025i
$153$	−1.27553	+	1.27553i	−0.103121	+	0.103121i
$154$	1.00947	−	0.418138i	0.0813457	−	0.0336945i
$155$	−11.5943	−	11.5943i	−0.931275	−	0.931275i
$156$	6.93941	+	6.93941i	0.555597	+	0.555597i
$157$	−0.919569	+	0.919569i	−0.0733896	+	0.0733896i	−0.742849	−	0.669459i	$-0.766526\pi$
$157$	−0.919569	+	0.919569i	−0.0733896	+	0.0733896i	0.669459	+	0.742849i	$0.266526\pi$
$158$	−5.24401	−	12.6602i	−0.417191	−	1.00719i
$159$		−	0.143156i		−	0.0113530i
$160$	−5.40204	+	13.0417i	−0.427069	+	1.03104i
$161$	−12.2954	+	29.6838i	−0.969016	+	2.33941i
$162$	−10.3659			−0.814420
$163$	−4.28744	−	10.3508i	−0.335818	−	0.810736i	−0.998108	−	0.0614885i	$-0.980415\pi$
$163$	−4.28744	−	10.3508i	−0.335818	−	0.810736i	0.662290	−	0.749248i	$-0.269585\pi$
$164$	5.35553	−	5.35553i	0.418197	−	0.418197i
$165$	−1.13534	−	1.13534i	−0.0883861	−	0.0883861i
$166$	11.0346			0.856453
$167$	5.65694	+	5.65694i	0.437747	+	0.437747i	0.891253	−	0.453506i	$-0.149827\pi$
$167$	5.65694	+	5.65694i	0.437747	+	0.437747i	−0.453506	+	0.891253i	$0.649827\pi$
$168$	−20.5309			−1.58399
$169$	−9.85477	−	9.85477i	−0.758059	−	0.758059i
$170$	8.32487	+	3.44828i	0.638489	+	0.264471i
$171$	−0.865848			−0.0662130
$172$	−0.536957	+	0.536957i	−0.0409426	+	0.0409426i
$173$	2.17738	+	5.25666i	0.165543	+	0.399656i	0.984782	−	0.173797i	$-0.0556035\pi$
$173$	2.17738	+	5.25666i	0.165543	+	0.399656i	−0.819238	+	0.573453i	$0.805604\pi$
$174$	0.541990	−	1.30848i	0.0410881	−	0.0991956i
$175$	9.89257	+	4.09764i	0.747808	+	0.309752i
$176$		−	0.299661i		−	0.0225878i
$177$		−	7.71092i		−	0.579588i
$178$	−1.82147	−	0.754476i	−0.136525	−	0.0565503i
$179$	8.20519	−	19.8091i	0.613284	−	1.48060i	−0.246087	−	0.969248i	$-0.579145\pi$
$179$	8.20519	−	19.8091i	0.613284	−	1.48060i	0.859371	−	0.511352i	$-0.170855\pi$
$180$	0.609762	+	1.47209i	0.0454489	+	0.109723i
$181$	−16.7684	+	16.7684i	−1.24639	+	1.24639i	−0.289082	+	0.957304i	$0.593350\pi$
$181$	−16.7684	+	16.7684i	−1.24639	+	1.24639i	−0.957304	+	0.289082i	$0.906650\pi$
$182$	18.8041			1.39386
$183$	−16.9153	−	7.00654i	−1.25041	−	0.517939i
$184$	18.7918	+	18.7918i	1.38535	+	1.38535i
$185$	25.0524			1.84189
$186$	−7.75547	−	7.75547i	−0.568658	−	0.568658i
$187$	0.964361			0.0705211
$188$	8.38557	+	8.38557i	0.611580	+	0.611580i
$189$	11.7908	−	11.7908i	0.857656	−	0.857656i
$190$	1.65515	+	3.99589i	0.120077	+	0.289892i
$191$	−2.07838			−0.150387			−0.0751933	−	0.997169i	$-0.523957\pi$
$191$	−2.07838			−0.150387			−0.0751933	+	0.997169i	$0.523957\pi$
$192$	−5.04920	+	12.1898i	−0.364394	+	0.879726i
$193$	−9.55542	+	23.0688i	−0.687814	+	1.66053i	0.0613242	+	0.998118i	$0.480468\pi$
$193$	−9.55542	+	23.0688i	−0.687814	+	1.66053i	−0.749139	+	0.662413i	$0.769532\pi$
$194$			1.70477i			0.122395i
$195$	−10.5744	−	25.5288i	−0.757246	−	1.82815i
$196$	4.35403	−	4.35403i	0.311002	−	0.311002i
$197$	−3.91264	−	3.91264i	−0.278764	−	0.278764i	0.553851	−	0.832616i	$-0.313158\pi$
$197$	−3.91264	−	3.91264i	−0.278764	−	0.278764i	−0.832616	+	0.553851i	$0.813158\pi$
$198$	−0.120200	−	0.120200i	−0.00854223	−	0.00854223i
$199$	−15.7959	+	6.54288i	−1.11974	+	0.463812i	−0.864282	−	0.503008i	$-0.832227\pi$
$199$	−15.7959	+	6.54288i	−1.11974	+	0.463812i	−0.255460	+	0.966820i	$0.582227\pi$
$200$	6.26266	−	6.26266i	0.442837	−	0.442837i
$201$	2.73637	+	2.73637i	0.193009	+	0.193009i
$202$	6.42682	−	15.5157i	0.452190	−	1.09168i
$203$	1.04181	+	2.51514i	0.0731204	+	0.176528i
$204$	−5.58626	−	2.31390i	−0.391116	−	0.162006i
$205$	−19.7020	+	8.16083i	−1.37605	+	0.569977i
$206$	−1.23873	−	2.99055i	−0.0863062	−	0.208362i
$207$	4.99854			0.347423
$208$	1.97353	−	4.76453i	0.136840	−	0.330361i
$209$	0.327311	+	0.327311i	0.0226406	+	0.0226406i
$210$	17.8213	+	7.38180i	1.22978	+	0.509393i
$211$	−21.1873	+	8.77607i	−1.45859	+	0.604170i	−0.964226	−	0.265083i	$-0.914601\pi$
$211$	−21.1873	+	8.77607i	−1.45859	+	0.604170i	−0.494369	+	0.869252i	$0.664601\pi$
$212$	0.0701679	−	0.0290645i	0.00481915	−	0.00199616i
$213$	−2.67226			−0.183100
$214$	2.92825	+	7.06943i	0.200171	+	0.483256i
$215$	1.97536	−	0.818222i	0.134719	−	0.0558023i
$216$	−5.27811	−	12.7425i	−0.359130	−	0.867017i
$217$	21.0823			1.43116
$218$	6.47470			0.438522
$219$	6.62095	+	2.74249i	0.447402	+	0.185320i
$220$	0.325982	−	0.786990i	0.0219777	−	0.0530589i
$221$	15.3331	+	6.35116i	1.03141	+	0.427226i
$222$	16.7577			1.12470
$223$	0.848296	+	0.848296i	0.0568061	+	0.0568061i	0.734939	−	0.678133i	$-0.237211\pi$
$223$	0.848296	+	0.848296i	0.0568061	+	0.0568061i	−0.678133	+	0.734939i	$0.737211\pi$
$224$	−6.94572	−	16.7685i	−0.464081	−	1.12039i
$225$		−	1.66584i		−	0.111056i
$226$	11.5502	+	11.5502i	0.768306	+	0.768306i
$227$	−5.43680	+	13.1256i	−0.360853	+	0.871176i	0.634323	+	0.773068i	$0.281279\pi$
$227$	−5.43680	+	13.1256i	−0.360853	+	0.871176i	−0.995176	+	0.0981078i	$0.968721\pi$
$228$	−1.11066	−	2.68137i	−0.0735552	−	0.177578i
$229$	−8.06513	−	3.34069i	−0.532959	−	0.220759i	0.0999397	−	0.994993i	$-0.468135\pi$
$229$	−8.06513	−	3.34069i	−0.532959	−	0.220759i	−0.632899	+	0.774235i	$0.718135\pi$
$230$	−9.55518	−	23.0683i	−0.630050	−	1.52108i
$231$	2.06443			0.135830
$232$	2.25178			0.147837
$233$	7.82339	+	7.82339i	0.512527	+	0.512527i	0.915300	−	0.402773i	$-0.131954\pi$
$233$	7.82339	+	7.82339i	0.512527	+	0.512527i	−0.402773	+	0.915300i	$0.631954\pi$
$234$	−1.11952	−	2.70276i	−0.0731854	−	0.176685i
$235$	−12.7780	−	30.8489i	−0.833548	−	2.01236i
$236$	3.77951	−	1.56552i	0.246025	−	0.101907i
$237$		−	25.8908i		−	1.68179i
$238$	−10.7038	+	4.43365i	−0.693823	+	0.287391i
$239$	−24.7139	+	10.2368i	−1.59861	+	0.662165i	−0.991218	−	0.132240i	$-0.957783\pi$
$239$	−24.7139	+	10.2368i	−1.59861	+	0.662165i	−0.607389	+	0.794404i	$0.707783\pi$
$240$	3.74075	−	3.74075i	0.241464	−	0.241464i
$241$	8.33257	−	3.45146i	0.536748	−	0.222328i	−0.0978080	−	0.995205i	$-0.531183\pi$
$241$	8.33257	−	3.45146i	0.536748	−	0.222328i	0.634556	+	0.772877i	$0.281183\pi$
$242$		−	10.9004i		−	0.700703i
$243$	−5.34843	−	2.21539i	−0.343102	−	0.142118i
$244$		−	9.71354i		−	0.621846i
$245$	−16.0177	+	6.63473i	−1.02333	+	0.423877i
$246$	−13.1788	+	5.45882i	−0.840247	+	0.348042i
$247$	3.04852	+	7.35977i	0.193973	+	0.468291i
$248$	6.67326	−	16.1107i	0.423752	−	1.02303i
$249$	19.2617	+	7.97844i	1.22066	+	0.505613i
$250$	5.32903	−	2.20736i	0.337037	−	0.139605i
$251$	−7.86649	+	18.9914i	−0.496528	+	1.19873i	0.454813	+	0.890587i	$0.349706\pi$
$251$	−7.86649	+	18.9914i	−0.496528	+	1.19873i	−0.951342	+	0.308138i	$0.900294\pi$
$252$	−1.89276	−	0.784007i	−0.119233	−	0.0493878i
$253$	−1.88956	−	1.88956i	−0.118796	−	0.118796i
$254$	−12.2533	+	12.2533i	−0.768838	+	0.768838i
$255$	12.0384	+	12.0384i	0.753873	+	0.753873i
$256$	−17.0031			−1.06269
$257$	−16.0862	−	6.66314i	−1.00343	−	0.415635i	−0.180378	−	0.983597i	$-0.557732\pi$
$257$	−16.0862	−	6.66314i	−1.00343	−	0.415635i	−0.823055	+	0.567962i	$0.807732\pi$
$258$	1.32133	−	0.547313i	0.0822624	−	0.0340742i
$259$	−22.7769	+	22.7769i	−1.41529	+	1.41529i
$260$	10.3660	−	10.3660i	0.642875	−	0.642875i
$261$	0.299482	−	0.299482i	0.0185375	−	0.0185375i
$262$			21.8708i			1.35118i
$263$	5.47695	−	2.26862i	0.337723	−	0.139889i	−0.207376	−	0.978261i	$-0.566492\pi$
$263$	5.47695	−	2.26862i	0.337723	−	0.139889i	0.545099	+	0.838372i	$0.316492\pi$
$264$	0.653462	−	1.57760i	0.0402178	−	0.0970943i
$265$	−0.213846			−0.0131364
$266$	−5.13775	−	2.12812i	−0.315016	−	0.130484i
$267$	−2.63397	−	2.63397i	−0.161196	−	0.161196i
$268$	−0.785675	+	1.89679i	−0.0479927	+	0.115865i
$269$		−	1.43053i		−	0.0872208i	−0.999049	−	0.0436104i	$-0.986114\pi$
$269$		−	1.43053i		−	0.0872208i	0.999049	−	0.0436104i	$-0.0138860\pi$
$270$			12.9585i			0.788628i
$271$	10.6549	+	10.6549i	0.647240	+	0.647240i	0.952325	−	0.305085i	$-0.0986848\pi$
$271$	10.6549	+	10.6549i	0.647240	+	0.647240i	−0.305085	+	0.952325i	$0.598685\pi$
$272$			3.17741i			0.192659i
$273$	32.8239	+	13.5961i	1.98659	+	0.822872i
$274$	−6.29008	+	2.60544i	−0.379998	+	0.157400i
$275$	−0.629726	+	0.629726i	−0.0379739	+	0.0379739i
$276$	6.41184	+	15.4795i	0.385947	+	0.931759i
$277$	1.48453	−	1.48453i	0.0891969	−	0.0891969i	−0.661100	−	0.750297i	$-0.729910\pi$
$277$	1.48453	−	1.48453i	0.0891969	−	0.0891969i	0.750297	+	0.661100i	$0.229910\pi$
$278$	−4.15872	+	1.72260i	−0.249424	+	0.103315i
$279$	−1.25515	−	3.03021i	−0.0751441	−	0.181414i
$280$			30.6689i			1.83282i
$281$	14.0337	−	14.0337i	0.837179	−	0.837179i	−0.151307	−	0.988487i	$-0.548348\pi$
$281$	14.0337	−	14.0337i	0.837179	−	0.837179i	0.988487	+	0.151307i	$0.0483483\pi$
$282$	−8.54729	−	20.6350i	−0.508984	−	1.22880i
$283$		−	25.9324i		−	1.54152i	−0.637124	−	0.770762i	$-0.719876\pi$
$283$		−	25.9324i		−	1.54152i	0.637124	−	0.770762i	$-0.280124\pi$
$284$	−0.542541	−	1.30981i	−0.0321939	−	0.0777229i
$285$			8.17181i			0.484057i
$286$	−0.598502	+	1.44491i	−0.0353902	+	0.0854395i
$287$	10.4929	−	25.3320i	0.619374	−	1.49530i
$288$	−1.99665	+	1.99665i	−0.117654	+	0.117654i
$289$	6.77456			0.398503
$290$	−1.95460	−	0.809621i	−0.114778	−	0.0475426i
$291$	−1.23261	+	2.97578i	−0.0722568	+	0.174443i
$292$			3.80205i			0.222498i
$293$	5.86367	−	5.86367i	0.342559	−	0.342559i	−0.514770	−	0.857329i	$-0.672123\pi$
$293$	5.86367	−	5.86367i	0.342559	−	0.342559i	0.857329	+	0.514770i	$0.172123\pi$
$294$	−10.7143	+	4.43800i	−0.624870	+	0.258829i
$295$	−11.5185			−0.670635
$296$	10.1960	+	24.6152i	0.592629	+	1.43073i
$297$	0.530727	+	1.28129i	0.0307959	+	0.0743479i
$298$	−5.86293	+	14.1544i	−0.339630	+	0.819940i
$299$	−17.5991	−	42.4880i	−1.01778	−	2.45714i
$300$	5.15879	−	2.13684i	0.297843	−	0.123371i
$301$	−1.05204	+	2.53984i	−0.0606384	+	0.146394i
$302$	−7.86640	−	3.25837i	−0.452660	−	0.187498i
$303$	22.4369	−	22.4369i	1.28896	−	1.28896i
$304$	−1.07843	+	1.07843i	−0.0618524	+	0.0618524i
$305$	−10.4663	+	25.2680i	−0.599301	+	1.44684i
$306$	1.27452	+	1.27452i	0.0728594	+	0.0728594i
$307$	15.9549	+	15.9549i	0.910596	+	0.910596i	0.996319	−	0.0857226i	$-0.0273199\pi$
$307$	15.9549	+	15.9549i	0.910596	+	0.910596i	−0.0857226	+	0.996319i	$0.527320\pi$
$308$	0.419134	+	1.01188i	0.0238824	+	0.0576572i
$309$		−	6.11585i		−	0.347918i
$310$	−11.5851	+	11.5851i	−0.657988	+	0.657988i
$311$	14.0024			0.794003			0.397001	−	0.917818i	$-0.370051\pi$
$311$	14.0024			0.794003			0.397001	+	0.917818i	$0.370051\pi$
$312$	20.7797	−	20.7797i	1.17642	−	1.17642i
$313$	6.36011	−	15.3547i	0.359495	−	0.867897i	−0.635876	−	0.771791i	$-0.719361\pi$
$313$	6.36011	−	15.3547i	0.359495	−	0.867897i	0.995371	−	0.0961061i	$-0.0306388\pi$
$314$	0.918839	+	0.918839i	0.0518531	+	0.0518531i
$315$	4.07889	+	4.07889i	0.229820	+	0.229820i
$316$	12.6904	−	5.25652i	0.713888	−	0.295702i
$317$	15.1213	+	15.1213i	0.849296	+	0.849296i	0.990045	−	0.140749i	$-0.0449511\pi$
$317$	15.1213	+	15.1213i	0.849296	+	0.849296i	−0.140749	+	0.990045i	$0.544951\pi$
$318$	−0.143042			−0.00802142
$319$	−0.226423			−0.0126772
$320$	18.2091	+	7.54246i	1.01792	+	0.421636i
$321$			14.4574i			0.806933i
$322$	29.6602	+	12.2857i	1.65290	+	0.684653i
$323$	−3.47058	−	3.47058i	−0.193108	−	0.193108i
$324$		−	10.3906i		−	0.577255i
$325$	−14.1598	+	5.86517i	−0.785442	+	0.325341i
$326$	−10.3426	+	4.28403i	−0.572822	+	0.237271i
$327$	11.3020	+	4.68145i	0.625003	+	0.258885i
$328$	−16.0369	−	16.0369i	−0.885488	−	0.885488i
$329$	39.6643	+	16.4295i	2.18676	+	0.905787i
$330$	−1.13444	+	1.13444i	−0.0624487	+	0.0624487i
$331$	8.03484			0.441635			0.220817	−	0.975315i	$-0.429128\pi$
$331$	8.03484			0.441635			0.220817	+	0.975315i	$0.429128\pi$
$332$			11.0609i			0.607047i
$333$	4.62981	+	1.91773i	0.253712	+	0.105091i
$334$	5.65244	−	5.65244i	0.309288	−	0.309288i
$335$	4.08757	−	4.08757i	0.223328	−	0.223328i
$336$			6.80195i			0.371077i
$337$	−8.69863			−0.473844			−0.236922	−	0.971529i	$-0.576139\pi$
$337$	−8.69863			−0.473844			−0.236922	+	0.971529i	$0.576139\pi$
$338$	−9.84695	+	9.84695i	−0.535603	+	0.535603i
$339$	11.8104	+	28.5128i	0.641452	+	1.54860i
$340$	−3.45650	+	8.34472i	−0.187455	+	0.452556i
$341$	−0.671013	+	1.61997i	−0.0363374	+	0.0877262i
$342$			0.865160i			0.0467825i
$343$	−1.18257	+	2.85497i	−0.0638526	+	0.154154i
$344$	1.60789	+	1.60789i	0.0866916	+	0.0866916i
$345$		−	47.1759i		−	2.53986i
$346$	5.25248	−	2.17565i	0.282375	−	0.116964i
$347$	−15.5655	−	6.44745i	−0.835601	−	0.346117i	−0.0764837	−	0.997071i	$-0.524369\pi$
$347$	−15.5655	−	6.44745i	−0.835601	−	0.346117i	−0.759118	+	0.650953i	$0.774369\pi$
$348$	1.31160	+	0.543282i	0.0703091	+	0.0291230i
$349$	17.6575			0.945183			0.472592	−	0.881282i	$-0.343319\pi$
$349$	17.6575			0.945183			0.472592	+	0.881282i	$0.343319\pi$
$350$	4.09438	−	9.88472i	0.218854	−	0.528360i
$351$			23.8674i			1.27395i
$352$	1.50956			0.0804599
$353$	−18.4361	−	3.62058i	−0.981257	−	0.192704i
$353$	−18.4361	−	3.62058i	−0.981257	−	0.192704i
$354$	−7.70480			−0.409505
$355$			3.99181i			0.211863i
$356$	0.756274	−	1.82581i	0.0400824	−	0.0967676i
$357$	−21.8898			−1.15853
$358$	−19.7933	−	8.19867i	−1.04611	−	0.433313i
$359$	−4.09041	−	1.69430i	−0.215883	−	0.0894218i	0.272121	−	0.962263i	$-0.412275\pi$
$359$	−4.09041	−	1.69430i	−0.215883	−	0.0894218i	−0.488004	+	0.872841i	$0.662275\pi$
$360$	4.40811	−	1.82590i	0.232328	−	0.0962334i
$361$			16.6441i			0.876006i
$362$	16.7551	+	16.7551i	0.880628	+	0.880628i
$363$	7.88138	−	19.0273i	0.413665	−	0.998676i
$364$			18.8490i			0.987954i
$365$	4.09671	−	9.89033i	0.214432	−	0.517684i
$366$	−7.00098	+	16.9019i	−0.365947	+	0.883474i
$367$	−7.39577	−	17.8550i	−0.386056	−	0.932022i	−0.990767	−	0.135577i	$-0.956711\pi$
$367$	−7.39577	−	17.8550i	−0.386056	−	0.932022i	0.604711	−	0.796445i	$-0.293289\pi$
$368$	6.22580	−	6.22580i	0.324542	−	0.324542i
$369$	−4.26573			−0.222065
$370$		−	25.0325i		−	1.30138i
$371$	0.194422	−	0.194422i	0.0100939	−	0.0100939i
$372$	7.77396	−	7.77396i	0.403061	−	0.403061i
$373$	10.1013	+	4.18411i	0.523028	+	0.216645i	0.628546	−	0.777772i	$-0.283650\pi$
$373$	10.1013	+	4.18411i	0.523028	+	0.216645i	−0.105519	+	0.994417i	$0.533650\pi$
$374$		−	0.963595i		−	0.0498263i
$375$	10.8982			0.562779
$376$	25.1102	−	25.1102i	1.29496	−	1.29496i
$377$	−3.60005	−	1.49119i	−0.185412	−	0.0768002i
$378$	−11.7815	−	11.7815i	−0.605973	−	0.605973i
$379$	7.38338	+	3.05830i	0.379259	+	0.157094i	0.564165	−	0.825662i	$-0.309198\pi$
$379$	7.38338	+	3.05830i	0.379259	+	0.157094i	−0.184906	+	0.982756i	$0.559198\pi$
$380$	−4.00541	+	1.65910i	−0.205473	+	0.0851098i
$381$	−30.2484	+	12.5293i	−1.54967	+	0.641896i
$382$			2.07673i			0.106255i
$383$	7.44462	+	7.44462i	0.380402	+	0.380402i	0.871247	−	0.490845i	$-0.163312\pi$
$383$	7.44462	+	7.44462i	0.380402	+	0.380402i	−0.490845	+	0.871247i	$0.663312\pi$
$384$	−5.28100	−	2.18746i	−0.269495	−	0.111628i
$385$		−	3.08383i		−	0.157167i
$386$	23.0505	+	9.54784i	1.17324	+	0.485972i
$387$	0.427691			0.0217408
$388$	−1.70883			−0.0867527
$389$	−3.88133	−	3.88133i	−0.196791	−	0.196791i	0.601832	−	0.798623i	$-0.294438\pi$
$389$	−3.88133	−	3.88133i	−0.196791	−	0.196791i	−0.798623	+	0.601832i	$0.794438\pi$
$390$	−25.5085	+	10.5660i	−1.29167	+	0.535028i
$391$	20.0357	+	20.0357i	1.01325	+	1.01325i
$392$	−13.0379	−	13.0379i	−0.658514	−	0.658514i
$393$	−15.8134	+	38.1768i	−0.797679	+	1.92577i
$394$	−3.90953	+	3.90953i	−0.196959	+	0.196959i
$395$	−38.6755			−1.94597
$396$	0.120486	−	0.120486i	0.00605467	−	0.00605467i
$397$		−	30.1977i		−	1.51558i	−0.652500	−	0.757788i	$-0.726280\pi$
$397$		−	30.1977i		−	1.51558i	0.652500	−	0.757788i	$-0.273720\pi$
$398$	6.53768	+	15.7834i	0.327704	+	0.791148i
$399$	−7.42956	−	7.42956i	−0.371943	−	0.371943i
$400$	−2.07484	−	2.07484i	−0.103742	−	0.103742i
$401$	−2.83225	+	6.83765i	−0.141436	+	0.341456i	−0.978686	−	0.205365i	$-0.934162\pi$
$401$	−2.83225	+	6.83765i	−0.141436	+	0.341456i	0.837250	+	0.546820i	$0.184162\pi$
$402$	2.73420	−	2.73420i	0.136369	−	0.136369i
$403$	−21.3378	+	21.3378i	−1.06291	+	1.06291i
$404$	15.5527	+	6.44214i	0.773776	+	0.320509i
$405$	−11.1958	+	27.0292i	−0.556326	+	1.34309i
$406$	2.51314	−	1.04098i	0.124725	−	0.0516629i
$407$	−1.02523	−	2.47512i	−0.0508188	−	0.122687i
$408$	−6.92887	+	16.7278i	−0.343030	+	0.828148i
$409$	−8.36337	−	20.1910i	−0.413542	−	0.998378i	−0.984179	−	0.177176i	$-0.943304\pi$
$409$	−8.36337	−	20.1910i	−0.413542	−	0.998378i	0.570637	−	0.821202i	$-0.306696\pi$
$410$	8.15435	+	19.6864i	0.402715	+	0.972240i
$411$	−12.8636			−0.634513
$412$	2.99768	−	1.24168i	0.147685	−	0.0611732i
$413$	10.4723	−	10.4723i	0.515308	−	0.515308i
$414$		−	4.99457i		−	0.245470i
$415$	11.9181	−	28.7729i	0.585039	−	1.41241i
$416$	24.0016	+	9.94178i	1.17677	+	0.487436i
$417$	−8.50482			−0.416483
$418$	0.327051	−	0.327051i	0.0159966	−	0.0159966i
$419$	14.9489	−	36.0899i	0.730303	−	1.76311i	0.0887153	−	0.996057i	$-0.471724\pi$
$419$	14.9489	−	36.0899i	0.730303	−	1.76311i	0.641588	−	0.767050i	$-0.278276\pi$
$420$	−7.39940	+	17.8637i	−0.361054	+	0.871661i
$421$			28.9183i			1.40939i	0.709510	+	0.704695i	$0.248916\pi$
$421$			28.9183i			1.40939i	−0.709510	+	0.704695i	$0.751084\pi$
$422$	8.76910	+	21.1705i	0.426873	+	1.03056i
$423$		−	6.67919i		−	0.324753i
$424$	−0.0870322	−	0.210114i	−0.00422666	−	0.0102040i
$425$	6.67719	−	6.67719i	0.323891	−	0.323891i
$426$			2.67014i			0.129369i
$427$	−13.4572	−	32.4885i	−0.651239	−	1.57223i
$428$	−7.08628	+	2.93523i	−0.342528	+	0.141880i
$429$	−2.08945	+	2.08945i	−0.100880	+	0.100880i
$430$	−0.817572	−	1.97379i	−0.0394268	−	0.0951848i
$431$	3.96566	−	3.96566i	0.191019	−	0.191019i	−0.605117	−	0.796136i	$-0.706874\pi$
$431$	3.96566	−	3.96566i	0.191019	−	0.191019i	0.796136	+	0.605117i	$0.206874\pi$
$432$	−4.22163	+	1.74866i	−0.203113	+	0.0841323i
$433$	0.0973494	+	0.0403235i	0.00467831	+	0.00193782i	0.385021	−	0.922908i	$-0.374194\pi$
$433$	0.0973494	+	0.0403235i	0.00467831	+	0.00193782i	−0.380343	+	0.924845i	$0.624194\pi$
$434$		−	21.0656i		−	1.01118i
$435$	−2.82649	−	2.82649i	−0.135520	−	0.135520i
$436$			6.49013i			0.310821i
$437$			13.6005i			0.650600i
$438$	2.74031	−	6.61569i	0.130937	−	0.316110i
$439$	−18.4317	−	18.4317i	−0.879698	−	0.879698i	0.113805	−	0.993503i	$-0.463696\pi$
$439$	−18.4317	−	18.4317i	−0.879698	−	0.879698i	−0.993503	+	0.113805i	$0.963696\pi$
$440$	−2.35660	−	0.976137i	−0.112347	−	0.0465355i
$441$	−3.46802			−0.165144
$442$	6.34612	−	15.3209i	0.301854	−	0.728740i
$443$	15.1432	−	6.27251i	0.719474	−	0.298016i	0.00725553	−	0.999974i	$-0.497690\pi$
$443$	15.1432	−	6.27251i	0.719474	−	0.298016i	0.712219	+	0.701958i	$0.247690\pi$
$444$			16.7976i			0.797179i
$445$	−3.93461	+	3.93461i	−0.186518	+	0.186518i
$446$	0.847623	−	0.847623i	0.0401361	−	0.0401361i
$447$	−20.4682	+	20.4682i	−0.968115	+	0.968115i
$448$	−23.4125	+	9.69778i	−1.10614	+	0.458177i
$449$	0.389438	+	0.161310i	0.0183787	+	0.00761271i	0.391854	−	0.920027i	$-0.371834\pi$
$449$	0.389438	+	0.161310i	0.0183787	+	0.00761271i	−0.373475	+	0.927640i	$0.621834\pi$
$450$	−1.66452			−0.0784660
$451$	1.61255	+	1.61255i	0.0759319	+	0.0759319i
$452$	−11.5777	+	11.5777i	−0.544569	+	0.544569i
$453$	−11.3754	−	11.3754i	−0.534462	−	0.534462i
$454$	13.1152	+	5.43248i	0.615525	+	0.254959i
$455$	20.3097	−	49.0321i	0.952136	−	2.29866i
$456$	−8.02922	+	3.32581i	−0.376003	+	0.155745i
$457$	20.2263	+	8.37802i	0.946147	+	0.391907i	0.801782	−	0.597617i	$-0.203886\pi$
$457$	20.2263	+	8.37802i	0.946147	+	0.391907i	0.144366	+	0.989524i	$0.453886\pi$
$458$	−3.33803	+	8.05873i	−0.155976	+	0.376560i
$459$	−5.62748	−	13.5859i	−0.262668	−	0.634137i
$460$	23.1232	−	9.57796i	1.07813	−	0.446575i
$461$	−14.4308	+	5.97742i	−0.672108	+	0.278396i	−0.692523	−	0.721395i	$-0.743501\pi$
$461$	−14.4308	+	5.97742i	−0.672108	+	0.278396i	0.0204155	+	0.999792i	$0.493501\pi$
$462$		−	2.06279i		−	0.0959697i
$463$	7.50062	+	3.10686i	0.348583	+	0.144388i	0.550104	−	0.835096i	$-0.314588\pi$
$463$	7.50062	+	3.10686i	0.348583	+	0.144388i	−0.201520	+	0.979484i	$0.564588\pi$
$464$		−	0.746024i		−	0.0346333i
$465$	−28.5989	+	11.8461i	−1.32624	+	0.549348i
$466$	7.81717	−	7.81717i	0.362124	−	0.362124i
$467$	23.4701	−	9.72164i	1.08607	−	0.449864i	0.233434	−	0.972373i	$-0.425004\pi$
$467$	23.4701	−	9.72164i	1.08607	−	0.449864i	0.852634	+	0.522509i	$0.175004\pi$
$468$	2.70921	−	1.12219i	0.125233	−	0.0518732i
$469$			7.43259i			0.343205i
$470$	−30.8244	+	12.7679i	−1.42182	+	0.588939i
$471$	0.939539	+	2.26825i	0.0432917	+	0.104515i
$472$	−4.68788	−	11.3175i	−0.215777	−	0.520932i
$473$	−0.161677	−	0.161677i	−0.00743393	−	0.00743393i
$474$	−25.8702			−1.18826
$475$	4.53257			0.207969
$476$	−4.44422	−	10.7293i	−0.203701	−	0.491777i
$477$	−0.0395198	−	0.0163696i	−0.00180949	−	0.000749514i
$478$	10.2287	+	24.6942i	0.467849	+	1.12949i
$479$	3.70674	−	8.94885i	0.169365	−	0.408884i	−0.816293	−	0.577638i	$-0.803975\pi$
$479$	3.70674	−	8.94885i	0.169365	−	0.408884i	0.985658	+	0.168755i	$0.0539745\pi$
$480$	18.8442	+	18.8442i	0.860118	+	0.860118i
$481$		−	46.1058i		−	2.10224i
$482$	−3.44872	−	8.32595i	−0.157085	−	0.379237i
$483$	42.8909	+	42.8909i	1.95160	+	1.95160i
$484$	10.9264			0.496653
$485$	4.44520	+	1.84126i	0.201846	+	0.0836074i
$486$	−2.21363	+	5.34419i	−0.100412	+	0.242417i
$487$	18.9149	+	7.83480i	0.857115	+	0.355029i	0.767579	−	0.640955i	$-0.221461\pi$
$487$	18.9149	+	7.83480i	0.857115	+	0.355029i	0.0895364	+	0.995984i	$0.471461\pi$
$488$	−29.0867			−1.31669
$489$	−21.1511			−0.956487
$490$	6.62946	+	16.0049i	0.299488	+	0.723029i
$491$	5.15654	−	2.13591i	0.232711	−	0.0963922i	−0.263281	−	0.964719i	$-0.584805\pi$
$491$	5.15654	−	2.13591i	0.232711	−	0.0963922i	0.495992	+	0.868327i	$0.334805\pi$
$492$	−5.47183	−	13.2102i	−0.246689	−	0.595561i
$493$	2.40083			0.108128
$494$	7.35393	−	3.04610i	0.330869	−	0.137050i
$495$	−0.443247	+	0.183599i	−0.0199225	+	0.00825215i
$496$	−5.33752	−	2.21087i	−0.239662	−	0.0992712i
$497$	−3.62923	−	3.62923i	−0.162793	−	0.162793i
$498$	7.97210	−	19.2464i	0.357238	−	0.862450i
$499$	−41.4879			−1.85726			−0.928628	−	0.371013i	$-0.879011\pi$
$499$	−41.4879			−1.85726			−0.928628	+	0.371013i	$0.879011\pi$
$500$	2.21262	+	5.34173i	0.0989513	+	0.238889i
$501$	13.9536	−	5.77978i	0.623402	−	0.258222i
$502$	18.9763	+	7.86024i	0.846954	+	0.350820i
$503$	7.58883	+	18.3211i	0.338369	+	0.816895i	0.997873	+	0.0651938i	$0.0207666\pi$
$503$	7.58883	+	18.3211i	0.338369	+	0.816895i	−0.659503	+	0.751701i	$0.729233\pi$
$504$	−2.34767	+	5.66777i	−0.104573	+	0.252463i
$505$	−33.5161	−	33.5161i	−1.49145	−	1.49145i
$506$	−1.88806	+	1.88806i	−0.0839347	+	0.0839347i
$507$	−24.3082	+	10.0688i	−1.07956	+	0.447170i
$508$	−12.2825	−	12.2825i	−0.544947	−	0.544947i
$509$	4.66294	+	4.66294i	0.206681	+	0.206681i	0.802855	−	0.596174i	$-0.203313\pi$
$509$	4.66294	+	4.66294i	0.206681	+	0.206681i	−0.596174	+	0.802855i	$0.703313\pi$
$510$	12.0288	−	12.0288i	0.532645	−	0.532645i
$511$	5.26738	+	12.7166i	0.233015	+	0.562549i
$512$			10.9340i			0.483221i
$513$	2.70115	−	6.52116i	0.119259	−	0.287916i
$514$	−6.65785	+	16.0735i	−0.293665	+	0.708970i
$515$	−9.13582			−0.402572
$516$	0.548617	+	1.32448i	0.0241515	+	0.0583070i
$517$	−2.52489	+	2.52489i	−0.111044	+	0.111044i
$518$	22.7588	+	22.7588i	0.999963	+	0.999963i
$519$	10.7416			0.471505
$520$	−31.0406	−	31.0406i	−1.36122	−	1.36122i
$521$	−31.6023			−1.38452			−0.692262	−	0.721647i	$-0.743386\pi$
$521$	−31.6023			−1.38452			−0.692262	+	0.721647i	$0.743386\pi$
$522$	−0.299244	−	0.299244i	−0.0130976	−	0.0130976i
$523$	−35.9449	−	14.8889i	−1.57176	−	0.651045i	−0.584680	−	0.811264i	$-0.698780\pi$
$523$	−35.9449	−	14.8889i	−1.57176	−	0.651045i	−0.987081	+	0.160219i	$0.948780\pi$
$524$	−21.9229			−0.957706
$525$	14.2940	−	14.2940i	0.623842	−	0.623842i
$526$	−2.26682	−	5.47260i	−0.0988382	−	0.238616i
$527$	7.11497	−	17.1771i	0.309933	−	0.748244i
$528$	−0.522663	−	0.216494i	−0.0227460	−	0.00942169i
$529$		−	55.5156i		−	2.41372i
$530$			0.213676i			0.00928149i
$531$	−2.12868	−	0.881729i	−0.0923770	−	0.0382638i
$532$	2.13320	−	5.15000i	0.0924859	−	0.223281i
$533$	15.0190	+	36.2591i	0.650545	+	1.57055i
$534$	−2.63188	+	2.63188i	−0.113893	+	0.113893i
$535$	21.5964			0.933692
$536$	5.67983	+	2.35266i	0.245331	+	0.101620i
$537$	−28.6226	−	28.6226i	−1.23516	−	1.23516i
$538$	−1.42939			−0.0616254
$539$	1.31099	+	1.31099i	0.0564685	+	0.0564685i
$540$	−12.9894			−0.558974
$541$	24.0281	+	24.0281i	1.03305	+	1.03305i	0.999435	+	0.0336146i	$0.0107019\pi$
$541$	24.0281	+	24.0281i	1.03305	+	1.03305i	0.0336146	+	0.999435i	$0.489298\pi$
$542$	10.6465	−	10.6465i	0.457305	−	0.457305i
$543$	17.1326	+	41.3617i	0.735228	+	1.77500i
$544$	−16.0064			−0.686268
$545$	6.99311	−	16.8829i	0.299552	−	0.723183i
$546$	13.5853	−	32.7978i	0.581397	−	1.40362i
$547$			1.03547i			0.0442734i	0.999755	+	0.0221367i	$0.00704691\pi$
$547$			1.03547i			0.0442734i	−0.999755	+	0.0221367i	$0.992953\pi$
$548$	−2.61165	−	6.30507i	−0.111564	−	0.269339i
$549$	−3.86846	+	3.86846i	−0.165102	+	0.165102i
$550$	0.629226	+	0.629226i	0.0268303	+	0.0268303i
$551$	0.814859	+	0.814859i	0.0347142	+	0.0347142i
$552$	46.3527	−	19.1999i	1.97290	−	0.817203i
$553$	35.1625	−	35.1625i	1.49526	−	1.49526i
$554$	−1.48335	−	1.48335i	−0.0630216	−	0.0630216i
$555$	18.0994	−	43.6958i	0.768277	−	1.85479i
$556$	−1.72671	−	4.16864i	−0.0732286	−	0.176790i
$557$	−25.9145	−	10.7342i	−1.09803	−	0.454821i	−0.241233	−	0.970467i	$-0.577552\pi$
$557$	−25.9145	−	10.7342i	−1.09803	−	0.454821i	−0.856801	+	0.515646i	$0.827552\pi$
$558$	−3.02780	+	1.25416i	−0.128177	+	0.0530927i
$559$	−1.50584	−	3.63541i	−0.0636901	−	0.153761i
$560$	10.1607			0.429368
$561$	0.696715	−	1.68202i	0.0294153	−	0.0710149i
$562$	−14.0225	−	14.0225i	−0.591505	−	0.591505i
$563$	14.8979	+	6.17093i	0.627874	+	0.260074i	0.673849	−	0.738869i	$-0.264640\pi$
$563$	14.8979	+	6.17093i	0.627874	+	0.260074i	−0.0459757	+	0.998943i	$0.514640\pi$
$564$	20.6842	−	8.56767i	0.870961	−	0.360764i
$565$	42.5922	−	17.6423i	1.79187	−	0.742216i
$566$	−25.9118			−1.08916
$567$	−14.3952	−	34.7530i	−0.604540	−	1.45949i
$568$	−3.92216	+	1.62461i	−0.164570	+	0.0681671i
$569$	12.2154	+	29.4905i	0.512096	+	1.23631i	0.942662	+	0.333749i	$0.108314\pi$
$569$	12.2154	+	29.4905i	0.512096	+	1.23631i	−0.430566	+	0.902559i	$0.641686\pi$
$570$	8.16532			0.342008
$571$	4.25441			0.178042			0.0890208	−	0.996030i	$-0.471626\pi$
$571$	4.25441			0.178042			0.0890208	+	0.996030i	$0.471626\pi$
$572$	−1.44836	−	0.599929i	−0.0605589	−	0.0250843i
$573$	−1.50155	+	3.62507i	−0.0627283	+	0.151440i
$574$	−25.3119	−	10.4845i	−1.05650	−	0.437616i
$575$	−26.1665			−1.09122
$576$	2.78777	+	2.78777i	0.116157	+	0.116157i
$577$	0.661522	+	1.59706i	0.0275395	+	0.0664863i	0.937051	−	0.349192i	$-0.113544\pi$
$577$	0.661522	+	1.59706i	0.0275395	+	0.0664863i	−0.909511	+	0.415679i	$0.863544\pi$
$578$		−	6.76918i		−	0.281561i
$579$	33.3327	+	33.3327i	1.38526	+	1.38526i
$580$	0.811551	−	1.95926i	0.0336978	−	0.0813538i
$581$	15.3239	+	36.9951i	0.635741	+	1.53481i
$582$	2.97342	+	1.23163i	0.123252	+	0.0510527i
$583$	0.00875130	+	0.0211275i	0.000362442	+	0.000875012i
$584$	11.3851			0.471117
$585$	−8.25665			−0.341371
$586$	−5.85901	−	5.85901i	−0.242033	−	0.242033i
$587$	1.57376	+	3.79938i	0.0649559	+	0.156817i	0.953024	−	0.302894i	$-0.0979528\pi$
$587$	1.57376	+	3.79938i	0.0649559	+	0.156817i	−0.888068	+	0.459711i	$0.847953\pi$
$588$	−4.44858	−	10.7398i	−0.183456	−	0.442903i
$589$	8.24488	−	3.41514i	0.339724	−	0.140718i
$590$			11.5094i			0.473834i
$591$	−9.65108	+	3.99761i	−0.396992	+	0.164440i
$592$	8.15512	−	3.37796i	0.335173	−	0.138833i
$593$	24.8565	−	24.8565i	1.02073	−	1.02073i	0.0209539	−	0.999780i	$-0.493330\pi$
$593$	24.8565	−	24.8565i	1.02073	−	1.02073i	0.999780	−	0.0209539i	$-0.00667032\pi$
$594$	1.28027	−	0.530306i	0.0525302	−	0.0217587i
$595$			32.6989i			1.34052i
$596$	−14.1881	−	5.87691i	−0.581167	−	0.240727i
$597$			32.2779i			1.32104i
$598$	−42.4542	+	17.5851i	−1.73608	+	0.719109i
$599$	−0.673649	+	0.279035i	−0.0275246	+	0.0114010i	−0.396403	−	0.918077i	$-0.629742\pi$
$599$	−0.673649	+	0.279035i	−0.0275246	+	0.0114010i	0.368879	+	0.929478i	$0.379742\pi$
$600$	−6.39866	−	15.4477i	−0.261224	−	0.630651i
$601$	2.12958	−	5.14127i	0.0868675	−	0.209717i	−0.874476	−	0.485069i	$-0.838794\pi$
$601$	2.12958	−	5.14127i	0.0868675	−	0.209717i	0.961343	+	0.275352i	$0.0887945\pi$
$602$	2.53782	+	1.05120i	0.103434	+	0.0428438i
$603$	1.06830	−	0.442506i	0.0435047	−	0.0180202i
$604$	3.26614	−	7.88515i	0.132897	−	0.320842i
$605$	−28.4229	−	11.7732i	−1.15556	−	0.478647i
$606$	−22.4191	−	22.4191i	−0.910712	−	0.910712i
$607$	32.2564	−	32.2564i	1.30925	−	1.30925i	0.387286	−	0.921960i	$-0.373413\pi$
$607$	32.2564	−	32.2564i	1.30925	−	1.30925i	0.921960	−	0.387286i	$-0.126587\pi$
$608$	−5.43267	−	5.43267i	−0.220324	−	0.220324i
$609$	5.13952			0.208264
$610$	25.2479	+	10.4580i	1.02226	+	0.423433i
$611$	−56.7736	+	23.5164i	−2.29681	+	0.951371i
$612$	−1.27756	+	1.27756i	−0.0516422	+	0.0516422i
$613$	−28.7913	+	28.7913i	−1.16287	+	1.16287i	−0.179023	+	0.983845i	$0.557294\pi$
$613$	−28.7913	+	28.7913i	−1.16287	+	1.16287i	−0.983845	+	0.179023i	$0.942706\pi$
$614$	15.9423	−	15.9423i	0.643378	−	0.643378i
$615$			40.2597i			1.62343i
$616$	3.03002	−	1.25508i	0.122083	−	0.0505685i
$617$	−3.85611	+	9.30948i	−0.155241	+	0.374785i	−0.982296	−	0.187336i	$-0.940015\pi$
$617$	−3.85611	+	9.30948i	−0.155241	+	0.374785i	0.827055	+	0.562121i	$0.190015\pi$
$618$	−6.11099			−0.245820
$619$	4.79248	+	1.98511i	0.192626	+	0.0797884i	0.476911	−	0.878951i	$-0.341756\pi$
$619$	4.79248	+	1.98511i	0.192626	+	0.0797884i	−0.284285	+	0.958740i	$0.591756\pi$
$620$	−11.6127	−	11.6127i	−0.466377	−	0.466377i
$621$	−15.5938	+	37.6467i	−0.625756	+	1.51071i
$622$		−	13.9913i		−	0.560999i
$623$		−	7.15445i		−	0.286637i
$624$	−6.88439	−	6.88439i	−0.275596	−	0.275596i
$625$		−	31.0448i		−	1.24179i
$626$	−15.3425	−	6.35506i	−0.613208	−	0.253999i
$627$	0.807358	−	0.334419i	0.0322428	−	0.0133554i
$628$	−0.921029	+	0.921029i	−0.0367531	+	0.0367531i
$629$	10.8709	+	26.2446i	0.433449	+	1.04644i
$630$	4.07565	−	4.07565i	0.162378	−	0.162378i
$631$	−35.6458	+	14.7650i	−1.41904	+	0.587785i	−0.954619	−	0.297830i	$-0.903737\pi$
$631$	−35.6458	+	14.7650i	−1.41904	+	0.587785i	−0.464420	+	0.885615i	$0.653737\pi$
$632$	−15.7404	−	38.0006i	−0.626118	−	1.51158i
$633$			43.2948i			1.72082i
$634$	15.1093	−	15.1093i	0.600066	−	0.600066i
$635$	18.7162	+	45.1849i	0.742730	+	1.79311i
$636$		−	0.143383i		−	0.00568552i
$637$	12.2104	+	29.4785i	0.483793	+	1.16798i
$638$			0.226243i			0.00895703i
$639$	−0.305568	+	0.737707i	−0.0120881	+	0.0291832i
$640$	−3.26761	+	7.88872i	−0.129164	+	0.311829i
$641$	21.9009	−	21.9009i	0.865033	−	0.865033i	−0.126885	−	0.991917i	$-0.540498\pi$
$641$	21.9009	−	21.9009i	0.865033	−	0.865033i	0.991917	+	0.126885i	$0.0404978\pi$
$642$	14.4459			0.570134
$643$	−30.4873	−	12.6283i	−1.20230	−	0.498011i	−0.310561	−	0.950553i	$-0.600517\pi$
$643$	−30.4873	−	12.6283i	−1.20230	−	0.498011i	−0.891743	+	0.452543i	$0.850517\pi$
$644$	−12.3150	+	29.7309i	−0.485277	+	1.17156i
$645$		−	4.03652i		−	0.158938i
$646$	−3.46783	+	3.46783i	−0.136440	+	0.136440i
$647$	−24.8440	+	10.2907i	−0.976720	+	0.404571i	−0.813210	−	0.581971i	$-0.802282\pi$
$647$	−24.8440	+	10.2907i	−0.976720	+	0.404571i	−0.163511	+	0.986542i	$0.552282\pi$
$648$	−31.1141			−1.22228
$649$	0.471378	+	1.13801i	0.0185032	+	0.0446707i
$650$	5.86051	+	14.1485i	0.229868	+	0.554950i
$651$	15.2312	−	36.7713i	0.596957	−	1.44118i
$652$	−4.29424	−	10.3672i	−0.168176	−	0.406012i
$653$	26.1784	−	10.8434i	1.02444	−	0.424337i	0.193737	−	0.981053i	$-0.437939\pi$
$653$	26.1784	−	10.8434i	1.02444	−	0.424337i	0.830702	+	0.556717i	$0.187939\pi$
$654$	4.67773	−	11.2930i	0.182914	−	0.441593i
$655$	57.0283	+	23.6219i	2.22828	+	0.922984i
$656$	−5.31307	+	5.31307i	−0.207441	+	0.207441i
$657$	1.51419	−	1.51419i	0.0590740	−	0.0590740i
$658$	16.4164	−	39.6328i	0.639979	−	1.54505i
$659$	−10.4968	−	10.4968i	−0.408898	−	0.408898i	0.472456	−	0.881354i	$-0.343368\pi$
$659$	−10.4968	−	10.4968i	−0.408898	−	0.408898i	−0.881354	+	0.472456i	$0.843368\pi$
$660$	−1.13714	−	1.13714i	−0.0442632	−	0.0442632i
$661$	−12.1972	−	29.4467i	−0.474417	−	1.14534i	−0.962191	−	0.272375i	$-0.912191\pi$
$661$	−12.1972	−	29.4467i	−0.474417	−	1.14534i	0.487774	−	0.872970i	$-0.337809\pi$
$662$		−	8.02846i		−	0.312035i
$663$	22.1551	−	22.1551i	0.860434	−	0.860434i
$664$	33.1214			1.28536
$665$	−11.0982	+	11.0982i	−0.430371	+	0.430371i
$666$	1.91621	−	4.62613i	0.0742515	−	0.179259i
$667$	−4.70418	−	4.70418i	−0.182147	−	0.182147i
$668$	5.66592	+	5.66592i	0.219221	+	0.219221i
$669$	2.09244	−	0.866718i	0.0808985	−	0.0335093i
$670$	−4.08433	−	4.08433i	−0.157791	−	0.157791i
$671$	2.92474			0.112908
$672$	−34.2652			−1.32181
$673$	−17.3331	−	7.17962i	−0.668143	−	0.276754i	0.0227174	−	0.999742i	$-0.492768\pi$
$673$	−17.3331	−	7.17962i	−0.668143	−	0.276754i	−0.690861	+	0.722988i	$0.742768\pi$
$674$			8.69172i			0.334792i
$675$	12.5463	+	5.19686i	0.482908	+	0.200027i
$676$	−9.87042	−	9.87042i	−0.379632	−	0.379632i
$677$			17.9683i			0.690578i	0.938496	+	0.345289i	$0.112219\pi$
$677$			17.9683i			0.690578i	−0.938496	+	0.345289i	$0.887781\pi$
$678$	28.4901	−	11.8010i	1.09416	−	0.453214i
$679$	−5.71546	+	2.36742i	−0.219339	+	0.0908532i
$680$	24.9878	+	10.3503i	0.958240	+	0.396916i
$681$	18.9655	+	18.9655i	0.726759	+	0.726759i
$682$	1.61868	+	0.670480i	0.0619825	+	0.0256740i
$683$	−12.3537	+	12.3537i	−0.472702	+	0.472702i	−0.902788	−	0.430086i	$-0.858483\pi$
$683$	−12.3537	+	12.3537i	−0.472702	+	0.472702i	0.430086	+	0.902788i	$0.358483\pi$
$684$	−0.867223			−0.0331591
$685$			19.2155i			0.734187i
$686$	2.85270	+	1.18163i	0.108917	+	0.0451148i
$687$	−11.6535	+	11.6535i	−0.444609	+	0.444609i
$688$	0.532699	−	0.532699i	0.0203090	−	0.0203090i
$689$			0.393556i			0.0149933i
$690$	−47.1384			−1.79453
$691$	−27.3944	+	27.3944i	−1.04213	+	1.04213i	−0.0430599	+	0.999072i	$0.513711\pi$
$691$	−27.3944	+	27.3944i	−1.04213	+	1.04213i	−0.999072	+	0.0430599i	$0.986289\pi$
$692$	2.18084	+	5.26501i	0.0829030	+	0.200145i
$693$	0.236064	−	0.569908i	0.00896732	−	0.0216490i
$694$	−6.44233	+	15.5532i	−0.244548	+	0.590390i
$695$			12.7045i			0.481907i
$696$	1.62683	−	3.92752i	0.0616648	−	0.148872i
$697$	−17.0984	−	17.0984i	−0.647647	−	0.647647i
$698$		−	17.6435i		−	0.667815i
$699$	19.2975	−	7.99328i	0.729898	−	0.302334i
$700$	9.90828	+	4.10414i	0.374498	+	0.155122i
$701$	−20.1414	−	8.34284i	−0.760730	−	0.315105i	−0.0316188	−	0.999500i	$-0.510066\pi$
$701$	−20.1414	−	8.34284i	−0.760730	−	0.315105i	−0.729111	+	0.684395i	$0.760066\pi$
$702$	23.8485			0.900103
$703$	−5.21794	+	12.5972i	−0.196798	+	0.475113i
$704$		−	2.10768i		−	0.0794363i
$705$	−63.0377			−2.37414
$706$	−3.61771	+	18.4215i	−0.136154	+	0.693302i
$707$	60.9435			2.29202
$708$		−	7.72316i		−	0.290254i
$709$	7.78088	−	18.7847i	0.292217	−	0.705474i	−0.707783	−	0.706430i	$-0.750304\pi$
$709$	7.78088	−	18.7847i	0.292217	−	0.705474i	1.00000		0.000956167i	$0.000304358\pi$
$710$	3.98864			0.149691
$711$	−7.14743	−	2.96056i	−0.268049	−	0.111030i
$712$	−5.46729	−	2.26462i	−0.204895	−	0.0848704i
$713$	−47.5977	+	19.7156i	−1.78255	+	0.738355i
$714$			21.8725i			0.818556i
$715$	3.12121	+	3.12121i	0.116727	+	0.116727i
$716$	8.21821	−	19.8405i	0.307129	−	0.741475i
$717$			50.5011i			1.88600i
$718$	−1.69296	+	4.08716i	−0.0631806	+	0.152531i
$719$	−13.1373	+	31.7161i	−0.489937	+	1.18281i	0.464815	+	0.885408i	$0.346121\pi$
$719$	−13.1373	+	31.7161i	−0.489937	+	1.18281i	−0.954752	+	0.297404i	$0.903879\pi$
$720$	−0.604927	−	1.46042i	−0.0225443	−	0.0544267i
$721$	8.30600	−	8.30600i	0.309332	−	0.309332i
$722$	16.6309			0.618938
$723$		−	17.0270i		−	0.633242i
$724$	−16.7950	+	16.7950i	−0.624183	+	0.624183i
$725$	−1.56774	+	1.56774i	−0.0582244	+	0.0582244i
$726$	−19.0122	−	7.87512i	−0.705610	−	0.292273i
$727$			12.1921i			0.452179i	0.974107	+	0.226089i	$0.0725942\pi$
$727$			12.1921i			0.452179i	−0.974107	+	0.226089i	$0.927406\pi$
$728$	56.4423			2.09189
$729$	14.2787	−	14.2787i	0.528842	−	0.528842i
$730$	−9.88248	−	4.09346i	−0.365767	−	0.151506i
$731$	1.71432	+	1.71432i	0.0634063	+	0.0634063i
$732$	−16.9422	−	7.01767i	−0.626200	−	0.259381i
$733$	−29.3641	+	12.1630i	−1.08459	+	0.449250i	−0.852116	−	0.523353i	$-0.824681\pi$
$733$	−29.3641	+	12.1630i	−1.08459	+	0.449250i	−0.232470	+	0.972604i	$0.574681\pi$
$734$	−17.8408	+	7.38990i	−0.658516	+	0.272766i
$735$			32.7310i			1.20730i
$736$	31.3628	+	31.3628i	1.15605	+	1.15605i
$737$	−0.571121	−	0.236566i	−0.0210375	−	0.00871403i
$738$			4.26234i			0.156899i
$739$	28.0339	+	11.6120i	1.03124	+	0.427154i	0.833161	−	0.553031i	$-0.186529\pi$
$739$	28.0339	+	11.6120i	1.03124	+	0.427154i	0.198081	+	0.980186i	$0.436529\pi$
$740$	25.0922			0.922406
$741$	15.0392			0.552479
$742$	−0.194267	−	0.194267i	−0.00713178	−	0.00713178i
$743$	18.9307	−	7.84136i	0.694501	−	0.287672i	−0.00737317	−	0.999973i	$-0.502347\pi$
$743$	18.9307	−	7.84136i	0.694501	−	0.287672i	0.701874	+	0.712301i	$0.252347\pi$
$744$	−23.2787	−	23.2787i	−0.853439	−	0.853439i
$745$	30.5753	+	30.5753i	1.12019	+	1.12019i
$746$	4.18079	−	10.0933i	0.153070	−	0.369543i
$747$	4.40507	−	4.40507i	0.161173	−	0.161173i
$748$	0.965892			0.0353165
$749$	−19.6347	+	19.6347i	−0.717438	+	0.717438i
$750$		−	10.8895i		−	0.397629i
$751$	−15.7124	−	37.9331i	−0.573353	−	1.38420i	−0.898684	−	0.438597i	$-0.855475\pi$
$751$	−15.7124	−	37.9331i	−0.573353	−	1.38420i	0.325330	−	0.945600i	$-0.394525\pi$
$752$	−8.31908	−	8.31908i	−0.303366	−	0.303366i
$753$	27.4411	+	27.4411i	1.00001	+	1.00001i
$754$	−1.49001	+	3.59719i	−0.0542628	+	0.131002i
$755$	−16.9925	+	16.9925i	−0.618420	+	0.618420i
$756$	11.8095	−	11.8095i	0.429509	−	0.429509i
$757$	−23.2090	−	9.61349i	−0.843546	−	0.349408i	−0.0812955	−	0.996690i	$-0.525906\pi$
$757$	−23.2090	−	9.61349i	−0.843546	−	0.349408i	−0.762251	+	0.647282i	$0.775906\pi$
$758$	3.05587	−	7.37752i	0.110994	−	0.267964i
$759$	−4.66088	+	1.93060i	−0.169179	+	0.0700763i
$760$	4.96808	+	11.9940i	0.180211	+	0.435068i
$761$	12.8356	−	30.9880i	0.465291	−	1.12331i	−0.500904	−	0.865503i	$-0.666999\pi$
$761$	12.8356	−	30.9880i	0.465291	−	1.12331i	0.966196	−	0.257810i	$-0.0830009\pi$
$762$	12.5194	+	30.2244i	0.453529	+	1.09492i
$763$	8.99146	+	21.7073i	0.325513	+	0.785857i
$764$	−2.08168			−0.0753127
$765$	4.69989	−	1.94676i	0.169925	−	0.0703852i
$766$	7.43871	−	7.43871i	0.268771	−	0.268771i
$767$			21.1984i			0.765430i
$768$	−12.2841	+	29.6565i	−0.443265	+	1.07014i
$769$	49.8010	+	20.6283i	1.79587	+	0.743874i	0.987988	+	0.154531i	$0.0493865\pi$
$769$	49.8010	+	20.6283i	1.79587	+	0.743874i	0.807883	+	0.589343i	$0.200613\pi$
$770$	−3.08138			−0.111045
$771$	−23.2434	+	23.2434i	−0.837091	+	0.837091i
$772$	−9.57060	+	23.1055i	−0.344453	+	0.831584i
$773$	9.55224	−	23.0611i	0.343570	−	0.829452i	−0.653779	−	0.756686i	$-0.726817\pi$
$773$	9.55224	−	23.0611i	0.343570	−	0.829452i	0.997349	−	0.0727662i	$-0.0231827\pi$
$774$		−	0.427352i		−	0.0153608i
$775$	6.57052	+	15.8626i	0.236020	+	0.569803i
$776$			5.11700i			0.183690i
$777$	23.2715	+	56.1823i	0.834860	+	2.01553i
$778$	−3.87825	+	3.87825i	−0.139042	+	0.139042i
$779$		−	11.6066i		−	0.415850i
$780$	−10.5912	−	25.5693i	−0.379224	−	0.915528i
$781$	0.394382	−	0.163359i	0.0141121	−	0.00584543i
$782$	20.0198	−	20.0198i	0.715906	−	0.715906i
$783$	1.32128	+	3.18984i	0.0472186	+	0.113996i
$784$	−4.31951	+	4.31951i	−0.154268	+	0.154268i
$785$	3.38829	−	1.40348i	0.120933	−	0.0500922i
$786$	38.1465	+	15.8008i	1.36064	+	0.563596i
$787$		−	16.3566i		−	0.583049i	−0.956563	−	0.291525i	$-0.905837\pi$
$787$		−	16.3566i		−	0.583049i	0.956563	−	0.291525i	$-0.0941626\pi$
$788$	−3.91885	−	3.91885i	−0.139603	−	0.139603i
$789$		−	11.1918i		−	0.398437i
$790$			38.6448i			1.37492i
$791$	−22.6837	+	54.7633i	−0.806540	+	1.94716i
$792$	−0.360790	−	0.360790i	−0.0128201	−	0.0128201i
$793$	46.5025	+	19.2620i	1.65135	+	0.684013i
$794$	−30.1737			−1.07082
$795$	−0.154495	+	0.372985i	−0.00547939	+	0.0132284i
$796$	−15.8210	+	6.55326i	−0.560760	+	0.232274i
$797$		−	22.9809i		−	0.814025i	−0.913423	−	0.407013i	$-0.866571\pi$
$797$		−	22.9809i		−	0.814025i	0.913423	−	0.407013i	$-0.133429\pi$
$798$	−7.42366	+	7.42366i	−0.262795	+	0.262795i
$799$	26.7722	−	26.7722i	0.947133	−	0.947133i
$800$	10.4521	−	10.4521i	0.369539	−	0.369539i
$801$	−1.02833	+	0.425947i	−0.0363341	+	0.0150501i
$802$	6.83222	+	2.83000i	0.241254	+	0.0999307i
$803$	−1.14480			−0.0403990
$804$	2.74072	+	2.74072i	0.0966576	+	0.0966576i
$805$	64.0701	−	64.0701i	2.25817	−	2.25817i
$806$	21.3209	+	21.3209i	0.750996	+	0.750996i
$807$	−2.49510	−	1.03350i	−0.0878315	−	0.0363810i
$808$	19.2907	−	46.5718i	0.678644	−	1.63839i
$809$	−17.4413	+	7.22440i	−0.613202	+	0.253996i	−0.667597	−	0.744523i	$-0.732677\pi$
$809$	−17.4413	+	7.22440i	−0.613202	+	0.253996i	0.0543950	+	0.998519i	$0.482677\pi$
$810$	27.0077	+	11.1870i	0.948954	+	0.393070i
$811$	19.1892	−	46.3268i	0.673824	−	1.62675i	−0.101233	−	0.994863i	$-0.532279\pi$
$811$	19.1892	−	46.3268i	0.673824	−	1.62675i	0.775057	−	0.631892i	$-0.217721\pi$
$812$	1.04346	+	2.51913i	0.0366182	+	0.0884043i
$813$	26.2819	−	10.8863i	0.921745	−	0.381799i
$814$	−2.47316	+	1.02442i	−0.0866841	+	0.0359057i
$815$			31.5954i			1.10674i
$816$	5.54197	+	2.29556i	0.194008	+	0.0803606i
$817$			1.16370i			0.0407128i
$818$	−20.1749	+	8.35672i	−0.705399	+	0.292186i
$819$	7.50669	−	7.50669i	0.262305	−	0.262305i
$820$	−19.7333	+	8.17379i	−0.689116	+	0.285441i
$821$	−3.58150	+	1.48351i	−0.124995	+	0.0517748i	−0.444304	−	0.895876i	$-0.646549\pi$
$821$	−3.58150	+	1.48351i	−0.124995	+	0.0517748i	0.319309	+	0.947651i	$0.396549\pi$
$822$			12.8534i			0.448312i
$823$	−36.4659	+	15.1047i	−1.27112	+	0.526516i	−0.913305	−	0.407277i	$-0.866479\pi$
$823$	−36.4659	+	15.1047i	−1.27112	+	0.526516i	−0.357816	+	0.933792i	$0.616479\pi$
$824$	−3.71815	−	8.97640i	−0.129528	−	0.312708i
$825$	0.643401	+	1.55331i	0.0224004	+	0.0540793i
$826$	−10.4640	−	10.4640i	−0.364088	−	0.364088i
$827$	−4.83237			−0.168038			−0.0840190	−	0.996464i	$-0.526776\pi$
$827$	−4.83237			−0.168038			−0.0840190	+	0.996464i	$0.526776\pi$
$828$	5.00648			0.173987
$829$	−11.1225	−	26.8520i	−0.386299	−	0.932608i	−0.990717	−	0.135940i	$-0.956594\pi$
$829$	−11.1225	−	26.8520i	−0.386299	−	0.932608i	0.604418	−	0.796667i	$-0.293406\pi$
$830$	−28.7501	−	11.9087i	−0.997930	−	0.413356i
$831$	−1.51677	−	3.66181i	−0.0526162	−	0.127027i
$832$	13.8809	−	33.5116i	0.481235	−	1.16180i
$833$	−13.9009	−	13.9009i	−0.481638	−	0.481638i
$834$			8.49807i			0.294264i
$835$	−8.63381	−	20.8439i	−0.298785	−	0.721331i
$836$	0.327830	+	0.327830i	0.0113383	+	0.0113383i
$837$	26.7378			0.924193
$838$	−36.0612	−	14.9371i	−1.24571	−	0.515992i
$839$	−11.1009	+	26.7998i	−0.383244	+	0.925233i	0.608090	+	0.793868i	$0.291936\pi$
$839$	−11.1009	+	26.7998i	−0.383244	+	0.925233i	−0.991334	+	0.131365i	$0.958064\pi$
$840$	53.4921	+	22.1571i	1.84565	+	0.764494i
$841$	28.4363			0.980562
$842$	28.8953			0.995798
$843$	−14.3384	−	34.6161i	−0.493842	−	1.19224i
$844$	−21.2209	+	8.79000i	−0.730455	+	0.302564i
$845$	15.0407	+	36.3114i	0.517415	+	1.24915i
$846$	−6.67388			−0.229453
$847$	36.5450	−	15.1374i	1.25570	−	0.520129i
$848$	−0.0696116	+	0.0288341i	−0.00239047	+	0.000990165i
$849$	−45.2308	−	18.7352i	−1.55232	−	0.642991i
$850$	−6.67189	−	6.67189i	−0.228844	−	0.228844i
$851$	30.1232	−	72.7238i	1.03261	−	2.49294i
$852$	−2.67651			−0.0916956
$853$	2.52308	+	6.09126i	0.0863887	+	0.208561i	0.961170	−	0.275958i	$-0.0889949\pi$
$853$	2.52308	+	6.09126i	0.0863887	+	0.208561i	−0.874781	+	0.484518i	$0.838995\pi$
$854$	−32.4627	+	13.4465i	−1.11085	+	0.460130i
$855$	2.25592	+	0.934432i	0.0771508	+	0.0319569i
$856$	8.78941	+	21.2195i	0.300416	+	0.725268i
$857$	5.57461	−	13.4583i	0.190425	−	0.459726i	−0.799615	−	0.600513i	$-0.794963\pi$
$857$	5.57461	−	13.4583i	0.190425	−	0.459726i	0.990040	+	0.140786i	$0.0449631\pi$
$858$	2.08779	+	2.08779i	0.0712760	+	0.0712760i
$859$	12.1056	−	12.1056i	0.413039	−	0.413039i	−0.469757	−	0.882796i	$-0.655658\pi$
$859$	12.1056	−	12.1056i	0.413039	−	0.413039i	0.882796	+	0.469757i	$0.155658\pi$
$860$	1.97850	−	0.819521i	0.0674663	−	0.0279454i
$861$	−36.6029	−	36.6029i	−1.24742	−	1.24742i
$862$	−3.96251	−	3.96251i	−0.134964	−	0.134964i
$863$	0.514214	−	0.514214i	0.0175040	−	0.0175040i	−0.698301	−	0.715805i	$-0.746060\pi$
$863$	0.514214	−	0.514214i	0.0175040	−	0.0175040i	0.715805	+	0.698301i	$0.246060\pi$
$864$	−8.80896	−	21.2667i	−0.299687	−	0.723508i
$865$		−	16.0458i		−	0.545573i
$866$	0.0402914	−	0.0972721i	0.00136916	−	0.00330544i
$867$	4.89436	−	11.8160i	0.166221	−	0.401294i
$868$	21.1158			0.716717
$869$	1.58273	+	3.82106i	0.0536905	+	0.129620i
$870$	−2.82425	+	2.82425i	−0.0957510	+	0.0957510i
$871$	−7.52267	−	7.52267i	−0.254896	−	0.254896i
$872$	19.4344			0.658131
$873$	0.680550	+	0.680550i	0.0230331	+	0.0230331i
$874$	13.5897			0.459678
$875$	14.8009	+	14.8009i	0.500362	+	0.500362i
$876$	6.63146	+	2.74684i	0.224056	+	0.0928072i
$877$	−15.7156			−0.530678			−0.265339	−	0.964155i	$-0.585484\pi$
$877$	−15.7156			−0.530678			−0.265339	+	0.964155i	$0.585484\pi$
$878$	−18.4171	+	18.4171i	−0.621547	+	0.621547i
$879$	−5.99100	−	14.4636i	−0.202072	−	0.487844i
$880$	−0.323397	+	0.780751i	−0.0109017	+	0.0263191i
$881$	−38.5070	−	15.9501i	−1.29733	−	0.537373i	−0.376170	−	0.926551i	$-0.622759\pi$
$881$	−38.5070	−	15.9501i	−1.29733	−	0.537373i	−0.921163	+	0.389178i	$0.872759\pi$
$882$			3.46527i			0.116682i
$883$		−	29.1314i		−	0.980349i	−0.871624	−	0.490175i	$-0.836933\pi$
$883$		−	29.1314i		−	0.980349i	0.871624	−	0.490175i	$-0.163067\pi$
$884$	15.3574	+	6.36125i	0.516526	+	0.213952i
$885$	−8.32170	+	20.0904i	−0.279731	+	0.675330i
$886$	−6.26753	−	15.1312i	−0.210562	−	0.508341i
$887$	−2.22335	+	2.22335i	−0.0746526	+	0.0746526i	−0.743447	−	0.668795i	$-0.766811\pi$
$887$	−2.22335	+	2.22335i	−0.0746526	+	0.0746526i	0.668795	+	0.743447i	$0.266811\pi$
$888$	50.2996			1.68794
$889$	−58.0969	−	24.0645i	−1.94851	−	0.807099i
$890$	3.93149	+	3.93149i	0.131784	+	0.131784i
$891$	3.12860			0.104812
$892$	0.849643	+	0.849643i	0.0284482	+	0.0284482i
$893$	18.1733			0.608148
$894$	20.4520	+	20.4520i	0.684017	+	0.684017i
$895$	−42.7563	+	42.7563i	−1.42919	+	1.42919i
$896$	−4.20136	−	10.1430i	−0.140358	−	0.338854i
$897$	−86.8213			−2.89888
$898$	0.161182	−	0.389128i	0.00537872	−	0.0129854i
$899$	−1.67052	+	4.03300i	−0.0557151	+	0.134508i
$900$		−	1.66848i		−	0.0556161i
$901$	−0.0927929	−	0.224022i	−0.00309138	−	0.00746325i
$902$	1.61127	−	1.61127i	0.0536493	−	0.0536493i
$903$	3.66988	+	3.66988i	0.122126	+	0.122126i
$904$	34.6688	+	34.6688i	1.15307	+	1.15307i
$905$	61.7858	−	25.5925i	2.05383	−	0.850724i
$906$	−11.3664	+	11.3664i	−0.377622	+	0.377622i
$907$	−30.6885	−	30.6885i	−1.01900	−	1.01900i	−0.999816	−	0.0191799i	$-0.993894\pi$
$907$	−30.6885	−	30.6885i	−1.01900	−	1.01900i	−0.0191799	−	0.999816i	$-0.506106\pi$
$908$	−5.44543	+	13.1464i	−0.180713	+	0.436280i
$909$	−3.62833	−	8.75956i	−0.120344	−	0.290536i
$910$	−48.9931	−	20.2936i	−1.62411	−	0.672727i
$911$	−20.6097	+	8.53680i	−0.682828	+	0.282837i	−0.697009	−	0.717063i	$-0.745486\pi$
$911$	−20.6097	+	8.53680i	−0.682828	+	0.282837i	0.0141803	+	0.999899i	$0.495486\pi$
$912$	1.10185	+	2.66011i	0.0364860	+	0.0880850i
$913$	−3.33044			−0.110221
$914$	8.37136	−	20.2103i	0.276900	−	0.668496i
$915$	36.5103	+	36.5103i	1.20699	+	1.20699i
$916$	−8.07794	−	3.34599i	−0.266903	−	0.110555i
$917$	−73.3247	+	30.3721i	−2.42140	+	1.00297i
$918$	−13.5751	+	5.62301i	−0.448046	+	0.185587i
$919$	37.7428			1.24502			0.622510	−	0.782612i	$-0.286113\pi$
$919$	37.7428			1.24502			0.622510	+	0.782612i	$0.286113\pi$
$920$	−28.6807	−	69.2414i	−0.945575	−	2.28282i
$921$	39.3551	−	16.3014i	1.29680	−	0.537150i
$922$	5.97267	+	14.4193i	0.196700	+	0.474875i
$923$	7.34643			0.241811
$924$	2.06771			0.0680226
$925$	−24.2363	−	10.0390i	−0.796884	−	0.330080i
$926$	3.10439	−	7.49466i	0.102017	−	0.246290i
$927$	−1.68835	−	0.699336i	−0.0554525	−	0.0229692i
$928$	3.75814			0.123367
$929$	22.3354	+	22.3354i	0.732802	+	0.732802i	0.971174	−	0.238372i	$-0.0766137\pi$
$929$	22.3354	+	22.3354i	0.732802	+	0.732802i	−0.238372	+	0.971174i	$0.576614\pi$
$930$	11.8367	+	28.5762i	0.388139	+	0.937051i
$931$		−	9.43612i		−	0.309256i
$932$	7.83581	+	7.83581i	0.256670	+	0.256670i
$933$	10.1162	−	24.4227i	0.331190	−	0.799562i
$934$	−9.71392	−	23.4515i	−0.317849	−	0.767356i
$935$	−2.51259	−	1.04075i	−0.0821704	−	0.0340361i
$936$	−3.36034	−	8.11258i	−0.109836	−	0.265168i
$937$	53.8715			1.75991			0.879953	−	0.475060i	$-0.157574\pi$
$937$	53.8715			1.75991			0.879953	+	0.475060i	$0.157574\pi$
$938$	7.42669			0.242490
$939$	−22.1863	−	22.1863i	−0.724024	−	0.724024i
$940$	−12.7983	−	30.8979i	−0.417436	−	1.00778i
$941$	8.54098	+	20.6198i	0.278428	+	0.672185i	0.999792	−	0.0203708i	$-0.00648469\pi$
$941$	8.54098	+	20.6198i	0.278428	+	0.672185i	−0.721364	+	0.692556i	$0.756485\pi$
$942$	2.26645	−	0.938792i	0.0738448	−	0.0305875i
$943$			67.0049i			2.18198i
$944$	−3.74954	+	1.55311i	−0.122037	+	0.0505494i
$945$	−43.4451	+	17.9955i	−1.41327	+	0.585395i
$946$	−0.161549	+	0.161549i	−0.00525241	+	0.00525241i
$947$	−12.4514	+	5.15755i	−0.404617	+	0.167598i	−0.575704	−	0.817658i	$-0.695272\pi$
$947$	−12.4514	+	5.15755i	−0.404617	+	0.167598i	0.171087	+	0.985256i	$0.445272\pi$
$948$		−	25.9319i		−	0.842228i
$949$	−18.2019	−	7.53948i	−0.590859	−	0.244742i
$950$		−	4.52897i		−	0.146939i
$951$	37.2988	−	15.4497i	1.20950	−	0.500990i
$952$	−32.1283	+	13.3080i	−1.04129	+	0.431315i
$953$	3.86117	+	9.32168i	0.125075	+	0.301959i	0.973997	−	0.226559i	$-0.0727478\pi$
$953$	3.86117	+	9.32168i	0.125075	+	0.301959i	−0.848922	+	0.528518i	$0.822748\pi$
$954$	−0.0163566	+	0.0394884i	−0.000529565	+	0.00127848i
$955$	5.41511	+	2.24301i	0.175229	+	0.0725822i
$956$	−24.7531	+	10.2531i	−0.800573	+	0.331608i
$957$	−0.163582	+	0.394921i	−0.00528785	+	0.0127660i
$958$	−8.94175	−	3.70379i	−0.288895	−	0.119664i
$959$	−17.4702	−	17.4702i	−0.564141	−	0.564141i
$960$	26.3108	−	26.3108i	0.849177	−	0.849177i
$961$	1.98364	+	1.98364i	0.0639885	+	0.0639885i
$962$	−46.0692			−1.48533
$963$	3.99112	+	1.65317i	0.128612	+	0.0532728i
$964$	8.34580	−	3.45694i	0.268800	−	0.111341i
$965$	49.7922	−	49.7922i	1.60287	−	1.60287i
$966$	42.8568	−	42.8568i	1.37889	−	1.37889i
$967$	−1.82224	+	1.82224i	−0.0585994	+	0.0585994i	−0.735799	−	0.677200i	$-0.763193\pi$
$967$	−1.82224	+	1.82224i	−0.0585994	+	0.0585994i	0.677200	+	0.735799i	$0.263193\pi$
$968$		−	32.7185i		−	1.05161i
$969$	−8.56069	+	3.54595i	−0.275009	+	0.113912i
$970$	1.83980	−	4.44167i	0.0590724	−	0.142613i
$971$	21.7472			0.697901			0.348950	−	0.937141i	$-0.386538\pi$
$971$	21.7472			0.697901			0.348950	+	0.937141i	$0.386538\pi$
$972$	−5.35693	−	2.21891i	−0.171823	−	0.0711716i
$973$	−11.5505	−	11.5505i	−0.370292	−	0.370292i
$974$	7.82858	−	18.8999i	0.250844	−	0.605590i
$975$			28.9345i			0.926646i
$976$			9.63653i			0.308458i
$977$	2.11108	+	2.11108i	0.0675396	+	0.0675396i	0.740070	−	0.672530i	$-0.234792\pi$
$977$	2.11108	+	2.11108i	0.0675396	+	0.0675396i	−0.672530	+	0.740070i	$0.734792\pi$
$978$			21.1343i			0.675802i
$979$	0.549749	+	0.227714i	0.0175701	+	0.00727776i
$980$	−16.0431	+	6.64526i	−0.512477	+	0.212275i
$981$	2.58473	−	2.58473i	0.0825240	−	0.0825240i
$982$	−2.13421	−	5.15244i	−0.0681054	−	0.164421i
$983$	11.7604	−	11.7604i	0.375098	−	0.375098i	−0.494232	−	0.869330i	$-0.664551\pi$
$983$	11.7604	−	11.7604i	0.375098	−	0.375098i	0.869330	+	0.494232i	$0.164551\pi$
$984$	−39.5572	+	16.3851i	−1.26104	+	0.522339i
$985$	5.97160	+	14.4167i	0.190271	+	0.459355i
$986$		−	2.39893i		−	0.0763974i
$987$	57.3119	−	57.3119i	1.82426	−	1.82426i
$988$	3.05336	+	7.37146i	0.0971403	+	0.234517i
$989$		−	6.71805i		−	0.213622i
$990$	0.183453	+	0.442895i	0.00583052	+	0.0140761i
$991$			39.9840i			1.27013i	0.772458	+	0.635066i	$0.219027\pi$
$991$			39.9840i			1.27013i	−0.772458	+	0.635066i	$0.780973\pi$
$992$	11.1374	−	26.8881i	0.353613	−	0.853697i
$993$	5.80487	−	14.0142i	0.184212	−	0.444727i
$994$	−3.62635	+	3.62635i	−0.115021	+	0.115021i
$995$	48.2165			1.52856
$996$	19.2922	+	7.99111i	0.611298	+	0.253208i
$997$	8.52338	−	20.5773i	0.269938	−	0.651688i	−0.729542	−	0.683936i	$-0.760267\pi$
$997$	8.52338	−	20.5773i	0.269938	−	0.651688i	0.999480	+	0.0322479i	$0.0102666\pi$
$998$			41.4550i			1.31223i
$999$	−28.8869	+	28.8869i	−0.913941	+	0.913941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	353.2.d.a.70.11	✓	112
353.116	even	8	inner	353.2.d.a.116.18	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
353.2.d.a.70.11	✓	112	1.1	even	1	trivial
353.2.d.a.116.18	yes	112	353.116	even	8	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:	\( N \)	\(=\)	\( 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	353.d (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.999206i q^{2} +(0.722463 - 1.74418i) q^{3} +1.00159 q^{4} +(-2.60544 - 1.07921i) q^{5} +(-1.74279 - 0.721889i) q^{6} +(3.34997 - 1.38760i) q^{7} -2.99920i q^{8} +(-0.398887 - 0.398887i) q^{9} +O(q^{10})\)	\(q-0.999206i q^{2} +(0.722463 - 1.74418i) q^{3} +1.00159 q^{4} +(-2.60544 - 1.07921i) q^{5} +(-1.74279 - 0.721889i) q^{6} +(3.34997 - 1.38760i) q^{7} -2.99920i q^{8} +(-0.398887 - 0.398887i) q^{9} +(-1.07835 + 2.60337i) q^{10} +0.301577i q^{11} +(0.723610 - 1.74695i) q^{12} +(-1.98615 + 4.79499i) q^{13} +(-1.38650 - 3.34731i) q^{14} +(-3.76467 + 3.76467i) q^{15} -0.993646 q^{16} -3.19772i q^{17} +(-0.398570 + 0.398570i) q^{18} +(1.08533 - 1.08533i) q^{19} +(-2.60958 - 1.08092i) q^{20} -6.84544i q^{21} +0.301338 q^{22} +(-6.26561 + 6.26561i) q^{23} +(-5.23115 - 2.16681i) q^{24} +(2.08811 + 2.08811i) q^{25} +(4.79118 + 1.98457i) q^{26} +(4.24862 - 1.75984i) q^{27} +(3.35529 - 1.38981i) q^{28} +0.750794i q^{29} +(3.76168 + 3.76168i) q^{30} +(5.37165 + 2.22501i) q^{31} -5.00555i q^{32} +(0.526005 + 0.217878i) q^{33} -3.19518 q^{34} -10.2257 q^{35} +(-0.399520 - 0.399520i) q^{36} +(-8.20726 + 3.39956i) q^{37} +(-1.08447 - 1.08447i) q^{38} +(6.92841 + 6.92841i) q^{39} +(-3.23677 + 7.81426i) q^{40} +(5.34704 - 5.34704i) q^{41} -6.84001 q^{42} +(-0.536106 + 0.536106i) q^{43} +0.302056i q^{44} +(0.608795 + 1.46976i) q^{45} +(6.26063 + 6.26063i) q^{46} +(8.37227 + 8.37227i) q^{47} +(-0.717872 + 1.73310i) q^{48} +(4.34713 - 4.34713i) q^{49} +(2.08645 - 2.08645i) q^{50} +(-5.57740 - 2.31024i) q^{51} +(-1.98930 + 4.80261i) q^{52} +(0.0700567 - 0.0290184i) q^{53} +(-1.75844 - 4.24525i) q^{54} +(0.325465 - 0.785743i) q^{55} +(-4.16171 - 10.0473i) q^{56} +(-1.10890 - 2.67712i) q^{57} +0.750198 q^{58} +(3.77351 - 1.56304i) q^{59} +(-3.77065 + 3.77065i) q^{60} -9.69814i q^{61} +(2.22324 - 5.36738i) q^{62} +(-1.88976 - 0.782764i) q^{63} -6.98887 q^{64} +(10.3496 - 10.3496i) q^{65} +(0.217705 - 0.525587i) q^{66} +(-0.784430 + 1.89378i) q^{67} -3.20280i q^{68} +(6.40167 + 15.4550i) q^{69} +10.2176i q^{70} +(-0.541680 - 1.30773i) q^{71} +(-1.19634 + 1.19634i) q^{72} +3.79603i q^{73} +(3.39686 + 8.20074i) q^{74} +(5.15061 - 2.13345i) q^{75} +(1.08705 - 1.08705i) q^{76} +(0.418470 + 1.01028i) q^{77} +(6.92290 - 6.92290i) q^{78} +(12.6702 - 5.24818i) q^{79} +(2.58889 + 1.07235i) q^{80} -10.3741i q^{81} +(-5.34280 - 5.34280i) q^{82} +11.0434i q^{83} -6.85631i q^{84} +(-3.45102 + 8.33149i) q^{85} +(0.535680 + 0.535680i) q^{86} +(1.30952 + 0.542421i) q^{87} +0.904492 q^{88} +(0.755075 - 1.82291i) q^{89} +(1.46859 - 0.608311i) q^{90} +18.8191i q^{91} +(-6.27555 + 6.27555i) q^{92} +(7.76163 - 7.76163i) q^{93} +(8.36562 - 8.36562i) q^{94} +(-3.99906 + 1.65647i) q^{95} +(-8.73057 - 3.61632i) q^{96} -1.70612 q^{97} +(-4.34367 - 4.34367i) q^{98} +(0.120295 - 0.120295i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 112 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 112 * q - 112 * q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 + 4 * q^9	\( 112 q - 112 q^{4} - 4 q^{5} + 8 q^{6} - 4 q^{7} + 4 q^{9} - 4 q^{10} - 16 q^{12} + 16 q^{13} + 24 q^{14} + 96 q^{16} - 12 q^{18} - 4 q^{19} - 24 q^{22} - 24 q^{23} - 20 q^{24} - 44 q^{25} + 8 q^{26} + 24 q^{27} - 44 q^{28} + 44 q^{30} + 4 q^{31} - 36 q^{33} + 24 q^{35} + 20 q^{36} - 4 q^{37} + 32 q^{38} + 8 q^{39} - 32 q^{40} - 32 q^{41} + 56 q^{42} - 48 q^{43} - 104 q^{45} + 76 q^{46} - 44 q^{47} + 4 q^{48} + 8 q^{49} + 20 q^{50} - 32 q^{51} - 72 q^{52} + 20 q^{53} + 64 q^{54} + 16 q^{55} - 24 q^{56} - 20 q^{57} - 64 q^{58} + 60 q^{59} - 176 q^{60} - 12 q^{62} + 28 q^{63} - 104 q^{64} + 4 q^{65} + 64 q^{66} + 8 q^{67} - 48 q^{69} + 8 q^{71} + 56 q^{72} + 4 q^{74} + 92 q^{75} - 20 q^{77} + 72 q^{78} + 24 q^{79} - 36 q^{80} - 72 q^{82} - 4 q^{85} - 44 q^{86} + 24 q^{87} + 344 q^{88} + 16 q^{89} - 44 q^{90} + 44 q^{92} + 76 q^{93} + 148 q^{94} - 20 q^{95} + 4 q^{96} + 72 q^{97} - 64 q^{98} + 56 q^{99}+O(q^{100}) \) 112 * q - 112 * q^4 - 4 * q^5 + 8 * q^6 - 4 * q^7 + 4 * q^9 - 4 * q^10 - 16 * q^12 + 16 * q^13 + 24 * q^14 + 96 * q^16 - 12 * q^18 - 4 * q^19 - 24 * q^22 - 24 * q^23 - 20 * q^24 - 44 * q^25 + 8 * q^26 + 24 * q^27 - 44 * q^28 + 44 * q^30 + 4 * q^31 - 36 * q^33 + 24 * q^35 + 20 * q^36 - 4 * q^37 + 32 * q^38 + 8 * q^39 - 32 * q^40 - 32 * q^41 + 56 * q^42 - 48 * q^43 - 104 * q^45 + 76 * q^46 - 44 * q^47 + 4 * q^48 + 8 * q^49 + 20 * q^50 - 32 * q^51 - 72 * q^52 + 20 * q^53 + 64 * q^54 + 16 * q^55 - 24 * q^56 - 20 * q^57 - 64 * q^58 + 60 * q^59 - 176 * q^60 - 12 * q^62 + 28 * q^63 - 104 * q^64 + 4 * q^65 + 64 * q^66 + 8 * q^67 - 48 * q^69 + 8 * q^71 + 56 * q^72 + 4 * q^74 + 92 * q^75 - 20 * q^77 + 72 * q^78 + 24 * q^79 - 36 * q^80 - 72 * q^82 - 4 * q^85 - 44 * q^86 + 24 * q^87 + 344 * q^88 + 16 * q^89 - 44 * q^90 + 44 * q^92 + 76 * q^93 + 148 * q^94 - 20 * q^95 + 4 * q^96 + 72 * q^97 - 64 * q^98 + 56 * q^99

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