LMFDB - Embedded newform 546.2.bu.a.323.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			323.9
Character	$\chi$	$=$	546.323
Dual form			546.2.bu.a.71.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.39783 - 1.02278i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.04268 - 2.04268i) q^{5} +(-1.08548 - 1.34972i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.907836 + 2.85934i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.39783 - 1.02278i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.04268 - 2.04268i) q^{5} +(-1.08548 - 1.34972i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.907836 + 2.85934i) q^{9} +(2.50176 - 1.44439i) q^{10} +(-0.446430 + 1.66610i) q^{11} +(-0.699162 - 1.58467i) q^{12} +(3.02199 - 1.96661i) q^{13} -1.00000i q^{14} +(-4.94452 + 0.766095i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.47565 - 6.02001i) q^{17} +(0.136851 + 2.99688i) q^{18} +(-5.79151 + 1.55183i) q^{19} +(2.79035 - 0.747671i) q^{20} +(-0.626147 + 1.61491i) q^{21} +(-0.862436 + 1.49378i) q^{22} +(-3.94076 - 6.82559i) q^{23} +(-0.265197 - 1.71163i) q^{24} -3.34505i q^{25} +(3.42802 - 1.11745i) q^{26} +(1.65548 - 4.92538i) q^{27} +(0.258819 - 0.965926i) q^{28} +(2.64980 - 1.52986i) q^{29} +(-4.97432 - 0.539744i) q^{30} +(5.66232 + 5.66232i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.32809 - 1.87232i) q^{33} +(4.91531 - 4.91531i) q^{34} +(-2.50176 - 1.44439i) q^{35} +(-0.643461 + 2.93018i) q^{36} +(-5.75540 - 1.54215i) q^{37} -5.99581 q^{38} +(-6.23563 - 0.341854i) q^{39} +2.88878 q^{40} +(-3.05005 - 0.817259i) q^{41} +(-1.02278 + 1.39783i) q^{42} +(9.94067 + 5.73925i) q^{43} +(-1.21967 + 1.21967i) q^{44} +(7.69512 + 3.98629i) q^{45} +(-2.03989 - 7.61296i) q^{46} +(2.12290 + 2.12290i) q^{47} +(0.186842 - 1.72194i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.865763 - 3.23107i) q^{50} +(-11.0155 + 4.86009i) q^{51} +(3.60043 - 0.192141i) q^{52} +1.27079i q^{53} +(2.87386 - 4.32908i) q^{54} +(2.49139 + 4.31521i) q^{55} +(0.500000 - 0.866025i) q^{56} +(9.68270 + 3.75426i) q^{57} +(2.95546 - 0.791914i) q^{58} +(2.54856 - 0.682885i) q^{59} +(-4.66513 - 1.80880i) q^{60} +(-2.57403 + 4.45834i) q^{61} +(4.00386 + 6.93490i) q^{62} +(2.52695 - 1.61695i) q^{63} +1.00000i q^{64} +(2.15580 - 10.1901i) q^{65} +(2.73335 - 1.20597i) q^{66} +(0.346835 - 1.29441i) q^{67} +(6.02001 - 3.47565i) q^{68} +(-1.47259 + 13.5715i) q^{69} +(-2.04268 - 2.04268i) q^{70} +(2.86989 + 10.7106i) q^{71} +(-1.37992 + 2.66380i) q^{72} +(-6.64934 + 6.64934i) q^{73} +(-5.16015 - 2.97921i) q^{74} +(-3.42126 + 4.67580i) q^{75} +(-5.79151 - 1.55183i) q^{76} +1.72487 q^{77} +(-5.93468 - 1.94411i) q^{78} -8.40565 q^{79} +(2.79035 + 0.747671i) q^{80} +(-7.35167 + 5.19163i) q^{81} +(-2.73460 - 1.57882i) q^{82} +(10.1535 - 10.1535i) q^{83} +(-1.34972 + 1.08548i) q^{84} +(-5.19729 - 19.3966i) q^{85} +(8.11652 + 8.11652i) q^{86} +(-5.26867 - 0.571683i) q^{87} +(-1.49378 + 0.862436i) q^{88} +(-0.857755 + 3.20119i) q^{89} +(6.40119 + 5.84211i) q^{90} +(-2.68175 - 2.41002i) q^{91} -7.88152i q^{92} +(-2.12362 - 13.7063i) q^{93} +(1.50112 + 2.60001i) q^{94} +(-8.66029 + 15.0001i) q^{95} +(0.626147 - 1.61491i) q^{96} +(-8.03620 + 2.15329i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-5.16923 + 0.236050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) $ 56 * q - 8 * q^6 + 24 * q^9	$ 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) $ 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.39783	−	1.02278i	−0.807035	−	0.590503i
$3$	−1.39783	−	1.02278i	−0.807035	−	0.590503i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	2.04268	−	2.04268i	0.913513	−	0.913513i	−0.0830341	−	0.996547i	$-0.526461\pi$
$5$	2.04268	−	2.04268i	0.913513	−	0.913513i	0.996547	+	0.0830341i	$0.0264611\pi$
$6$	−1.08548	−	1.34972i	−0.443146	−	0.551019i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$7$	−0.258819	−	0.965926i	−0.0978244	−	0.365086i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.907836	+	2.85934i	0.302612	+	0.953114i
$10$	2.50176	−	1.44439i	0.791125	−	0.456756i
$11$	−0.446430	+	1.66610i	−0.134604	+	0.502348i	0.865396	+	0.501089i	$0.167067\pi$
$11$	−0.446430	+	1.66610i	−0.134604	+	0.502348i	−0.999999	+	0.00125826i	$0.999599\pi$
$12$	−0.699162	−	1.58467i	−0.201831	−	0.457454i
$13$	3.02199	−	1.96661i	0.838150	−	0.545440i
$13$	3.02199	−	1.96661i	0.838150	−	0.545440i
$14$		−	1.00000i		−	0.267261i
$15$	−4.94452	+	0.766095i	−1.27667	+	0.197805i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.47565	−	6.02001i	0.842969	−	1.46007i	−0.0444037	−	0.999014i	$-0.514139\pi$
$17$	3.47565	−	6.02001i	0.842969	−	1.46007i	0.887373	−	0.461052i	$-0.152528\pi$
$18$	0.136851	+	2.99688i	0.0322560	+	0.706371i
$19$	−5.79151	+	1.55183i	−1.32866	+	0.356014i	−0.852216	−	0.523190i	$-0.824742\pi$
$19$	−5.79151	+	1.55183i	−1.32866	+	0.356014i	−0.476446	+	0.879204i	$0.658075\pi$
$20$	2.79035	−	0.747671i	0.623941	−	0.167184i
$21$	−0.626147	+	1.61491i	−0.136636	+	0.352403i
$22$	−0.862436	+	1.49378i	−0.183872	+	0.318476i
$23$	−3.94076	−	6.82559i	−0.821705	−	1.42323i	−0.904412	−	0.426661i	$-0.859690\pi$
$23$	−3.94076	−	6.82559i	−0.821705	−	1.42323i	0.0827070	−	0.996574i	$-0.473643\pi$
$24$	−0.265197	−	1.71163i	−0.0541331	−	0.349385i
$25$		−	3.34505i		−	0.669010i
$26$	3.42802	−	1.11745i	0.672289	−	0.219151i
$27$	1.65548	−	4.92538i	0.318598	−	0.947890i
$28$	0.258819	−	0.965926i	0.0489122	−	0.182543i
$29$	2.64980	−	1.52986i	0.492055	−	0.284088i	−0.233372	−	0.972388i	$-0.574976\pi$
$29$	2.64980	−	1.52986i	0.492055	−	0.284088i	0.725427	+	0.688300i	$0.241643\pi$
$30$	−4.97432	−	0.539744i	−0.908182	−	0.0985434i
$31$	5.66232	+	5.66232i	1.01698	+	1.01698i	0.999853	+	0.0171293i	$0.00545269\pi$
$31$	5.66232	+	5.66232i	1.01698	+	1.01698i	0.0171293	+	0.999853i	$0.494547\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	2.32809	−	1.87232i	0.405268	−	0.325928i
$34$	4.91531	−	4.91531i	0.842969	−	0.842969i
$35$	−2.50176	−	1.44439i	−0.422874	−	0.244146i
$36$	−0.643461	+	2.93018i	−0.107244	+	0.488363i
$37$	−5.75540	−	1.54215i	−0.946182	−	0.253529i	−0.247440	−	0.968903i	$-0.579589\pi$
$37$	−5.75540	−	1.54215i	−0.946182	−	0.253529i	−0.698741	+	0.715375i	$0.746256\pi$
$38$	−5.99581			−0.972648
$39$	−6.23563	−	0.341854i	−0.998501	−	0.0547404i
$40$	2.88878			0.456756
$41$	−3.05005	−	0.817259i	−0.476338	−	0.127634i	0.0126588	−	0.999920i	$-0.495970\pi$
$41$	−3.05005	−	0.817259i	−0.476338	−	0.127634i	−0.488997	+	0.872285i	$0.662637\pi$
$42$	−1.02278	+	1.39783i	−0.157819	+	0.215689i
$43$	9.94067	+	5.73925i	1.51594	+	0.875227i	0.999825	+	0.0187068i	$0.00595491\pi$
$43$	9.94067	+	5.73925i	1.51594	+	0.875227i	0.516113	+	0.856520i	$0.327378\pi$
$44$	−1.21967	+	1.21967i	−0.183872	+	0.183872i
$45$	7.69512	+	3.98629i	1.14712	+	0.594241i
$46$	−2.03989	−	7.61296i	−0.300765	−	1.12247i
$47$	2.12290	+	2.12290i	0.309657	+	0.309657i	0.844776	−	0.535120i	$-0.179733\pi$
$47$	2.12290	+	2.12290i	0.309657	+	0.309657i	−0.535120	+	0.844776i	$0.679733\pi$
$48$	0.186842	−	1.72194i	0.0269683	−	0.248541i
$49$	−0.866025	+	0.500000i	−0.123718	+	0.0714286i
$50$	0.865763	−	3.23107i	0.122437	−	0.456943i
$51$	−11.0155	+	4.86009i	−1.54248	+	0.680549i
$52$	3.60043	−	0.192141i	0.499290	−	0.0266452i
$53$			1.27079i			0.174557i	0.996184	+	0.0872783i	$0.0278169\pi$
$53$			1.27079i			0.174557i	−0.996184	+	0.0872783i	$0.972183\pi$
$54$	2.87386	−	4.32908i	0.391082	−	0.589113i
$55$	2.49139	+	4.31521i	0.335939	+	0.581863i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$	9.68270	+	3.75426i	1.28251	+	0.497263i
$58$	2.95546	−	0.791914i	0.388072	−	0.103983i
$59$	2.54856	−	0.682885i	0.331795	−	0.0889041i	−0.0890758	−	0.996025i	$-0.528391\pi$
$59$	2.54856	−	0.682885i	0.331795	−	0.0889041i	0.420871	+	0.907121i	$0.361725\pi$
$60$	−4.66513	−	1.80880i	−0.602265	−	0.233515i
$61$	−2.57403	+	4.45834i	−0.329570	+	0.570833i	−0.982427	−	0.186649i	$-0.940237\pi$
$61$	−2.57403	+	4.45834i	−0.329570	+	0.570833i	0.652856	+	0.757482i	$0.273571\pi$
$62$	4.00386	+	6.93490i	0.508491	+	0.880733i
$63$	2.52695	−	1.61695i	0.318365	−	0.203717i
$64$			1.00000i			0.125000i
$65$	2.15580	−	10.1901i	0.267394	−	1.26393i
$66$	2.73335	−	1.20597i	0.336452	−	0.148444i
$67$	0.346835	−	1.29441i	0.0423727	−	0.158137i	−0.941498	−	0.337019i	$-0.890581\pi$
$67$	0.346835	−	1.29441i	0.0423727	−	0.158137i	0.983871	+	0.178882i	$0.0572480\pi$
$68$	6.02001	−	3.47565i	0.730033	−	0.421485i
$69$	−1.47259	+	13.5715i	−0.177280	+	1.63382i
$70$	−2.04268	−	2.04268i	−0.244146	−	0.244146i
$71$	2.86989	+	10.7106i	0.340593	+	1.27111i	0.897677	+	0.440654i	$0.145253\pi$
$71$	2.86989	+	10.7106i	0.340593	+	1.27111i	−0.557084	+	0.830456i	$0.688080\pi$
$72$	−1.37992	+	2.66380i	−0.162625	+	0.313931i
$73$	−6.64934	+	6.64934i	−0.778246	+	0.778246i	−0.979532	−	0.201286i	$-0.935488\pi$
$73$	−6.64934	+	6.64934i	−0.778246	+	0.778246i	0.201286	+	0.979532i	$0.435488\pi$
$74$	−5.16015	−	2.97921i	−0.599855	−	0.346327i
$75$	−3.42126	+	4.67580i	−0.395053	+	0.539915i
$76$	−5.79151	−	1.55183i	−0.664331	−	0.178007i
$77$	1.72487			0.196567
$78$	−5.93468	−	1.94411i	−0.671970	−	0.220127i
$79$	−8.40565			−0.945710			−0.472855	−	0.881140i	$-0.656777\pi$
$79$	−8.40565			−0.945710			−0.472855	+	0.881140i	$0.656777\pi$
$80$	2.79035	+	0.747671i	0.311970	+	0.0835922i
$81$	−7.35167	+	5.19163i	−0.816852	+	0.576848i
$82$	−2.73460	−	1.57882i	−0.301986	−	0.174352i
$83$	10.1535	−	10.1535i	1.11449	−	1.11449i	0.121957	−	0.992535i	$-0.461083\pi$
$83$	10.1535	−	10.1535i	1.11449	−	1.11449i	0.992535	−	0.121957i	$-0.0389171\pi$
$84$	−1.34972	+	1.08548i	−0.147266	+	0.118436i
$85$	−5.19729	−	19.3966i	−0.563725	−	2.10385i
$86$	8.11652	+	8.11652i	0.875227	+	0.875227i
$87$	−5.26867	−	0.571683i	−0.564861	−	0.0612909i
$88$	−1.49378	+	0.862436i	−0.159238	+	0.0919360i
$89$	−0.857755	+	3.20119i	−0.0909219	+	0.339325i	−0.996370	−	0.0851326i	$-0.972869\pi$
$89$	−0.857755	+	3.20119i	−0.0909219	+	0.339325i	0.905448	+	0.424458i	$0.139535\pi$
$90$	6.40119	+	5.84211i	0.674745	+	0.615812i
$91$	−2.68175	−	2.41002i	−0.281124	−	0.252639i
$92$		−	7.88152i		−	0.821705i
$93$	−2.12362	−	13.7063i	−0.220210	−	1.42127i
$94$	1.50112	+	2.60001i	0.154828	+	0.268170i
$95$	−8.66029	+	15.0001i	−0.888527	+	1.53897i
$96$	0.626147	−	1.61491i	0.0639059	−	0.164821i
$97$	−8.03620	+	2.15329i	−0.815952	+	0.218634i	−0.642576	−	0.766222i	$-0.722134\pi$
$97$	−8.03620	+	2.15329i	−0.815952	+	0.218634i	−0.173376	+	0.984856i	$0.555468\pi$
$98$	−0.965926	+	0.258819i	−0.0975732	+	0.0261447i
$99$	−5.16923	+	0.236050i	−0.519527	+	0.0237239i
$100$	1.67253	−	2.89690i	0.167253	−	0.289690i
$101$	3.11520	+	5.39568i	0.309974	+	0.536890i	0.978356	−	0.206928i	$-0.0663464\pi$
$101$	3.11520	+	5.39568i	0.309974	+	0.536890i	−0.668383	+	0.743818i	$0.733013\pi$
$102$	−11.8980	+	1.84346i	−1.17808	+	0.182530i
$103$			14.8902i			1.46718i	0.679594	+	0.733588i	$0.262156\pi$
$103$			14.8902i			1.46718i	−0.679594	+	0.733588i	$0.737844\pi$
$104$	3.52748	+	0.746265i	0.345897	+	0.0731773i
$105$	2.01973	+	4.57776i	0.197105	+	0.446743i
$106$	−0.328905	+	1.22749i	−0.0319461	+	0.119224i
$107$	−13.3846	+	7.72758i	−1.29393	+	0.747053i	−0.979349	−	0.202176i	$-0.935199\pi$
$107$	−13.3846	+	7.72758i	−1.29393	+	0.747053i	−0.314585	+	0.949229i	$0.601865\pi$
$108$	3.89638	−	3.43776i	0.374929	−	0.330799i
$109$	6.00151	+	6.00151i	0.574840	+	0.574840i	0.933477	−	0.358637i	$-0.116758\pi$
$109$	6.00151	+	6.00151i	0.574840	+	0.574840i	−0.358637	+	0.933477i	$0.616758\pi$
$110$	1.28964	+	4.81299i	0.122962	+	0.458901i
$111$	6.46776	+	8.04218i	0.613893	+	0.763330i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	9.12535	+	5.26853i	0.858441	+	0.495621i	0.863490	−	0.504366i	$-0.168274\pi$
$113$	9.12535	+	5.26853i	0.858441	+	0.495621i	−0.00504883	+	0.999987i	$0.501607\pi$
$114$	8.38110	+	6.13240i	0.784962	+	0.574352i
$115$	−21.9922	−	5.89278i	−2.05078	−	0.549505i
$116$	3.05972			0.284088
$117$	8.36669	+	6.85554i	0.773501	+	0.633795i
$118$	2.63847			0.242891
$119$	−6.71444	−	1.79913i	−0.615512	−	0.164926i
$120$	−4.03801	−	2.95459i	−0.368618	−	0.269716i
$121$	6.94970	+	4.01241i	0.631790	+	0.364764i
$122$	−3.64022	+	3.64022i	−0.329570	+	0.329570i
$123$	3.42757	+	4.26193i	0.309053	+	0.384285i
$124$	2.07255	+	7.73487i	0.186121	+	0.694612i
$125$	3.38052	+	3.38052i	0.302363	+	0.302363i
$126$	2.85934	−	0.907836i	0.254730	−	0.0808765i
$127$	−18.1226	+	10.4631i	−1.60812	+	0.928448i	−0.618329	+	0.785920i	$0.712190\pi$
$127$	−18.1226	+	10.4631i	−1.60812	+	0.928448i	−0.989791	+	0.142528i	$0.954477\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	−8.02533	−	18.1896i	−0.706591	−	1.60151i
$130$	4.71973	−	9.28492i	0.413948	−	0.814342i
$131$		−	7.19779i		−	0.628874i	−0.949278	−	0.314437i	$-0.898184\pi$
$131$		−	7.19779i		−	0.628874i	0.949278	−	0.314437i	$-0.101816\pi$
$132$	2.95234	−	0.457430i	0.256968	−	0.0398142i
$133$	2.99790	+	5.19252i	0.259951	+	0.450249i
$134$	0.670034	−	1.16053i	0.0578821	−	0.100255i
$135$	−6.67934	−	13.4426i	−0.574866	−	1.15695i
$136$	6.71444	−	1.79913i	0.575759	−	0.154274i
$137$	−1.74850	+	0.468509i	−0.149384	+	0.0400274i	−0.332736	−	0.943020i	$-0.607972\pi$
$137$	−1.74850	+	0.468509i	−0.149384	+	0.0400274i	0.183352	+	0.983047i	$0.441305\pi$
$138$	−4.93499	+	12.7280i	−0.420094	+	1.08348i
$139$	7.89222	−	13.6697i	0.669409	−	1.15945i	−0.308660	−	0.951172i	$-0.599881\pi$
$139$	7.89222	−	13.6697i	0.669409	−	1.15945i	0.978070	−	0.208278i	$-0.0667860\pi$
$140$	−1.44439	−	2.50176i	−0.122073	−	0.211437i
$141$	−0.796182	−	5.13870i	−0.0670506	−	0.432757i
$142$			11.0884i			0.930517i
$143$	1.92746	+	5.91289i	0.161183	+	0.494461i
$144$	−2.02234	+	2.21588i	−0.168529	+	0.184657i
$145$	2.28767	−	8.53769i	0.189980	−	0.709016i
$146$	−8.14374	+	4.70179i	−0.673981	+	0.389123i
$147$	1.72194	+	0.186842i	0.142024	+	0.0154104i
$148$	−4.21324	−	4.21324i	−0.346327	−	0.346327i
$149$	5.03455	+	18.7892i	0.412446	+	1.53927i	0.789897	+	0.613240i	$0.210134\pi$
$149$	5.03455	+	18.7892i	0.412446	+	1.53927i	−0.377451	+	0.926030i	$0.623199\pi$
$150$	−4.51487	+	3.63099i	−0.368637	+	0.296469i
$151$	5.01991	−	5.01991i	0.408514	−	0.408514i	−0.472706	−	0.881220i	$-0.656723\pi$
$151$	5.01991	−	5.01991i	0.408514	−	0.408514i	0.881220	+	0.472706i	$0.156723\pi$
$152$	−5.19252	−	2.99790i	−0.421169	−	0.243162i
$153$	20.3686	+	4.47290i	1.64670	+	0.361612i
$154$	1.66610	+	0.446430i	0.134258	+	0.0359743i
$155$	23.1326			1.85805
$156$	−5.22929	−	3.41387i	−0.418678	−	0.273328i
$157$	7.53131			0.601064			0.300532	−	0.953772i	$-0.402836\pi$
$157$	7.53131			0.601064			0.300532	+	0.953772i	$0.402836\pi$
$158$	−8.11924	−	2.17554i	−0.645932	−	0.173077i
$159$	1.29974	−	1.77635i	0.103076	−	0.140873i
$160$	2.50176	+	1.44439i	0.197781	+	0.114189i
$161$	−5.57307	+	5.57307i	−0.439220	+	0.439220i
$162$	−8.44486	+	3.11198i	−0.663491	+	0.244500i
$163$	−0.397736	−	1.48437i	−0.0311531	−	0.116265i	0.948598	−	0.316482i	$-0.102502\pi$
$163$	−0.397736	−	1.48437i	−0.0311531	−	0.116265i	−0.979751	+	0.200217i	$0.935835\pi$
$164$	−2.23279	−	2.23279i	−0.174352	−	0.174352i
$165$	0.930990	−	8.58006i	0.0724774	−	0.667957i
$166$	12.4355	−	7.17962i	0.965179	−	0.557246i
$167$	1.88138	−	7.02139i	0.145585	−	0.543331i	−0.854143	−	0.520037i	$-0.825918\pi$
$167$	1.88138	−	7.02139i	0.145585	−	0.543331i	0.999729	−	0.0232939i	$-0.00741536\pi$
$168$	−1.58467	+	0.699162i	−0.122260	+	0.0539415i
$169$	5.26487	−	11.8862i	0.404990	−	0.914321i
$170$		−	20.0808i		−	1.54013i
$171$	−9.69495	−	15.1511i	−0.741391	−	1.15863i
$172$	5.73925	+	9.94067i	0.437614	+	0.757969i
$173$	7.09523	−	12.2893i	0.539440	−	0.934338i	−0.459494	−	0.888181i	$-0.651969\pi$
$173$	7.09523	−	12.2893i	0.539440	−	0.934338i	0.998934	−	0.0461571i	$-0.0146975\pi$
$174$	−4.94118	−	1.91584i	−0.374590	−	0.145239i
$175$	−3.23107	+	0.865763i	−0.244246	+	0.0654455i
$176$	−1.66610	+	0.446430i	−0.125587	+	0.0336509i
$177$	−4.26089	−	1.65207i	−0.320268	−	0.124177i
$178$	−1.65706	+	2.87011i	−0.124202	+	0.215124i
$179$	−2.69411	−	4.66633i	−0.201367	−	0.348778i	0.747602	−	0.664147i	$-0.231205\pi$
$179$	−2.69411	−	4.66633i	−0.201367	−	0.348778i	−0.948969	+	0.315369i	$0.897872\pi$
$180$	4.67103	+	7.29979i	0.348158	+	0.544094i
$181$		−	14.2323i		−	1.05788i	−0.848659	−	0.528940i	$-0.822590\pi$
$181$		−	14.2323i		−	1.05788i	0.848659	−	0.528940i	$-0.177410\pi$
$182$	−1.96661	−	3.02199i	−0.145775	−	0.224005i
$183$	8.15795	−	3.59932i	0.603053	−	0.266070i
$184$	2.03989	−	7.61296i	0.150382	−	0.561235i
$185$	−14.9065	+	8.60629i	−1.09595	+	0.632747i
$186$	1.49618	−	13.7889i	0.109705	−	1.01105i
$187$	8.47829	+	8.47829i	0.619994	+	0.619994i
$188$	0.777035	+	2.89993i	0.0566711	+	0.211499i
$189$	−5.18602	−	0.324292i	−0.377228	−	0.0235888i
$190$	−12.2475	+	12.2475i	−0.888527	+	0.888527i
$191$	0.744908	+	0.430073i	0.0538996	+	0.0311190i	0.526708	−	0.850046i	$-0.323426\pi$
$191$	0.744908	+	0.430073i	0.0538996	+	0.0311190i	−0.472808	+	0.881165i	$0.656760\pi$
$192$	1.02278	−	1.39783i	0.0738129	−	0.100879i
$193$	1.78606	+	0.478574i	0.128564	+	0.0344485i	0.322527	−	0.946560i	$-0.395468\pi$
$193$	1.78606	+	0.478574i	0.128564	+	0.0344485i	−0.193963	+	0.981009i	$0.562134\pi$
$194$	−8.31968			−0.597318
$195$	−13.4357	+	12.0391i	−0.962149	+	0.862137i
$196$	−1.00000			−0.0714286
$197$	12.9669	+	3.47446i	0.923852	+	0.247545i	0.689231	−	0.724542i	$-0.257949\pi$
$197$	12.9669	+	3.47446i	0.923852	+	0.247545i	0.234621	+	0.972087i	$0.424615\pi$
$198$	−5.05419	−	1.10989i	−0.359185	−	0.0788763i
$199$	−20.7346	−	11.9711i	−1.46984	−	0.848610i	−0.470408	−	0.882449i	$-0.655893\pi$
$199$	−20.7346	−	11.9711i	−1.46984	−	0.848610i	−0.999427	+	0.0338395i	$0.989226\pi$
$200$	2.36531	−	2.36531i	0.167253	−	0.167253i
$201$	−1.80871	+	1.45462i	−0.127577	+	0.102601i
$202$	1.61254	+	6.01810i	0.113458	+	0.423432i
$203$	−2.16355	−	2.16355i	−0.151851	−	0.151851i
$204$	−11.9698	−	1.29879i	−0.838050	−	0.0909337i
$205$	−7.89967	+	4.56088i	−0.551737	+	0.318545i
$206$	−3.85387	+	14.3828i	−0.268512	+	1.00210i
$207$	15.9391	−	17.4645i	1.10785	−	1.21387i
$208$	3.21413	+	1.63382i	0.222860	+	0.113285i
$209$		−	10.3420i		−	0.715371i
$210$	0.766095	+	4.94452i	0.0528656	+	0.341204i
$211$	−1.46282	−	2.53368i	−0.100705	−	0.174426i	0.811270	−	0.584671i	$-0.198776\pi$
$211$	−1.46282	−	2.53368i	−0.100705	−	0.174426i	−0.911975	+	0.410245i	$0.865443\pi$
$212$	−0.635396	+	1.10054i	−0.0436391	+	0.0755852i
$213$	6.94296	−	17.9068i	0.475724	−	1.22695i
$214$	−14.9285	+	4.00009i	−1.02049	+	0.273441i
$215$	32.0290	−	8.58214i	2.18436	−	0.585297i
$216$	4.65337	−	2.31217i	0.316622	−	0.157323i
$217$	4.00386	−	6.93490i	0.271800	−	0.470771i
$218$	4.24371	+	7.35032i	0.287420	+	0.497826i
$219$	16.0954	−	2.49380i	1.08763	−	0.168515i
$220$			4.98278i			0.335939i
$221$	−1.33563	−	25.0277i	−0.0898442	−	1.68354i
$222$	4.16591	+	9.44213i	0.279597	+	0.633714i
$223$	−4.11651	+	15.3630i	−0.275662	+	1.02878i	0.679735	+	0.733458i	$0.262095\pi$
$223$	−4.11651	+	15.3630i	−0.275662	+	1.02878i	−0.955397	+	0.295325i	$0.904572\pi$
$224$	0.866025	−	0.500000i	0.0578638	−	0.0334077i
$225$	9.56465	−	3.03676i	0.637643	−	0.202451i
$226$	7.45082	+	7.45082i	0.495621	+	0.495621i
$227$	−3.35272	−	12.5125i	−0.222528	−	0.830484i	−0.983380	−	0.181559i	$-0.941886\pi$
$227$	−3.35272	−	12.5125i	−0.222528	−	0.830484i	0.760852	−	0.648925i	$-0.224781\pi$
$228$	6.50834	+	8.09263i	0.431025	+	0.535948i
$229$	−9.74834	+	9.74834i	−0.644189	+	0.644189i	−0.951582	−	0.307394i	$-0.900543\pi$
$229$	−9.74834	+	9.74834i	−0.644189	+	0.644189i	0.307394	+	0.951582i	$0.400543\pi$
$230$	−19.7176	−	11.3840i	−1.30014	−	0.750638i
$231$	−2.41107	−	1.76417i	−0.158637	−	0.116074i
$232$	2.95546	+	0.791914i	0.194036	+	0.0519917i
$233$	−17.7198			−1.16086			−0.580430	−	0.814310i	$-0.697115\pi$
$233$	−17.7198			−1.16086			−0.580430	+	0.814310i	$0.697115\pi$
$234$	6.30726	+	8.78741i	0.412318	+	0.574451i
$235$	8.67279			0.565750
$236$	2.54856	+	0.682885i	0.165897	+	0.0444521i
$237$	11.7496	+	8.59714i	0.763221	+	0.558445i
$238$	−6.02001	−	3.47565i	−0.390219	−	0.225293i
$239$	−3.93333	+	3.93333i	−0.254426	+	0.254426i	−0.822782	−	0.568357i	$-0.807579\pi$
$239$	−3.93333	+	3.93333i	−0.254426	+	0.254426i	0.568357	+	0.822782i	$0.307579\pi$
$240$	−3.13572	−	3.89903i	−0.202410	−	0.251681i
$241$	2.28012	+	8.50951i	0.146875	+	0.548146i	0.999665	+	0.0258910i	$0.00824227\pi$
$241$	2.28012	+	8.50951i	0.146875	+	0.548146i	−0.852790	+	0.522255i	$0.825091\pi$
$242$	5.67440	+	5.67440i	0.364764	+	0.364764i
$243$	15.5863	+	0.262154i	0.999859	+	0.0168172i
$244$	−4.45834	+	2.57403i	−0.285416	+	0.164785i
$245$	−0.747671	+	2.79035i	−0.0477670	+	0.178269i
$246$	2.20771	+	5.00382i	0.140758	+	0.319032i
$247$	−14.4500	+	16.0793i	−0.919434	+	1.02310i
$248$			8.00773i			0.508491i
$249$	−24.5777	+	3.80802i	−1.55755	+	0.241324i
$250$	2.39039	+	4.14028i	0.151182	+	0.261854i
$251$	1.15656	−	2.00322i	0.0730013	−	0.126442i	−0.827214	−	0.561887i	$-0.810076\pi$
$251$	1.15656	−	2.00322i	0.0730013	−	0.126442i	0.900215	+	0.435445i	$0.143409\pi$
$252$	2.99688	−	0.136851i	0.188786	−	0.00862078i
$253$	13.1314	−	3.51854i	0.825563	−	0.221209i
$254$	−20.2131	+	5.41609i	−1.26828	+	0.339836i
$255$	−12.5735	+	32.4287i	−0.787385	+	2.03076i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.19256	+	7.26172i	0.261525	+	0.452974i	0.966647	−	0.256112i	$-0.0824414\pi$
$257$	4.19256	+	7.26172i	0.261525	+	0.452974i	−0.705123	+	0.709085i	$0.749108\pi$
$258$	−3.04406	−	19.6469i	−0.189515	−	1.22316i
$259$			5.95843i			0.370239i
$260$	6.96203	−	7.74699i	0.431767	−	0.480448i
$261$	6.77998	+	6.18781i	0.419670	+	0.383016i
$262$	1.86293	−	6.95253i	0.115092	−	0.429529i
$263$	1.44442	−	0.833937i	0.0890669	−	0.0514228i	−0.454805	−	0.890591i	$-0.650291\pi$
$263$	1.44442	−	0.833937i	0.0890669	−	0.0514228i	0.543872	+	0.839168i	$0.316958\pi$
$264$	2.97013	+	0.322278i	0.182799	+	0.0198348i
$265$	2.59581	+	2.59581i	0.159460	+	0.159460i
$266$	1.55183	+	5.79151i	0.0951488	+	0.355100i
$267$	4.47311	−	3.59741i	0.273750	−	0.220158i
$268$	0.947571	−	0.947571i	0.0578821	−	0.0578821i
$269$	−17.3350	−	10.0084i	−1.05693	−	0.610222i	−0.132352	−	0.991203i	$-0.542253\pi$
$269$	−17.3350	−	10.0084i	−1.05693	−	0.610222i	−0.924583	+	0.380981i	$0.875586\pi$
$270$	−2.97255	−	14.7133i	−0.180904	−	0.895421i
$271$	19.9354	+	5.34166i	1.21099	+	0.324483i	0.807149	−	0.590348i	$-0.201009\pi$
$271$	19.9354	+	5.34166i	1.21099	+	0.324483i	0.403838	+	0.914831i	$0.367676\pi$
$272$	6.95130			0.421485
$273$	1.28370	+	6.11164i	0.0776928	+	0.369893i
$274$	−1.81018			−0.109357
$275$	5.57319	+	1.49333i	0.336076	+	0.0900512i
$276$	−8.06107	+	11.0170i	−0.485219	+	0.663145i
$277$	6.91279	+	3.99110i	0.415349	+	0.239802i	0.693086	−	0.720855i	$-0.256251\pi$
$277$	6.91279	+	3.99110i	0.415349	+	0.239802i	−0.277736	+	0.960657i	$0.589584\pi$
$278$	11.1613	−	11.1613i	0.669409	−	0.669409i
$279$	−11.0500	+	21.3310i	−0.661549	+	1.27705i
$280$	−0.747671	−	2.79035i	−0.0446819	−	0.166755i
$281$	−11.4207	−	11.4207i	−0.681299	−	0.681299i	0.278994	−	0.960293i	$-0.409999\pi$
$281$	−11.4207	−	11.4207i	−0.681299	−	0.681299i	−0.960293	+	0.278994i	$0.909999\pi$
$282$	0.560942	−	5.16967i	0.0334036	−	0.307850i
$283$	7.14047	−	4.12255i	0.424457	−	0.245060i	−0.272525	−	0.962149i	$-0.587859\pi$
$283$	7.14047	−	4.12255i	0.424457	−	0.245060i	0.696982	+	0.717088i	$0.254526\pi$
$284$	−2.86989	+	10.7106i	−0.170296	+	0.635555i
$285$	27.4474	−	12.1099i	1.62584	−	0.717328i
$286$	0.331419	+	6.21028i	0.0195972	+	0.367221i
$287$			3.15765i			0.186390i
$288$	−2.52695	+	1.61695i	−0.148902	+	0.0952800i
$289$	−15.6603	−	27.1245i	−0.921195	−	1.59556i
$290$	4.41943	−	7.65468i	0.259518	−	0.449498i
$291$	13.4356	+	5.20934i	0.787606	+	0.305377i
$292$	−9.08317	+	2.43383i	−0.531552	+	0.142429i
$293$	−14.2375	+	3.81492i	−0.831763	+	0.222870i	−0.649483	−	0.760376i	$-0.725015\pi$
$293$	−14.2375	+	3.81492i	−0.831763	+	0.222870i	−0.182280	+	0.983247i	$0.558348\pi$
$294$	1.61491	+	0.626147i	0.0941836	+	0.0365176i
$295$	3.81098	−	6.60080i	0.221884	−	0.384314i
$296$	−2.97921	−	5.16015i	−0.173163	−	0.299928i
$297$	7.46711	+	4.95703i	0.433286	+	0.287636i
$298$			19.4520i			1.12682i
$299$	−25.3322	−	12.8769i	−1.46500	−	0.744693i
$300$	−5.30080	+	2.33873i	−0.306042	+	0.135027i
$301$	2.97085	−	11.0874i	0.171237	−	0.639066i
$302$	6.14811	−	3.54961i	0.353784	−	0.204257i
$303$	1.16410	−	10.7284i	0.0668756	−	0.616330i
$304$	−4.23968	−	4.23968i	−0.243162	−	0.243162i
$305$	3.84905	+	14.3649i	0.220396	+	0.822529i
$306$	18.5169	+	9.59226i	1.05854	+	0.548353i
$307$	7.53860	−	7.53860i	0.430250	−	0.430250i	−0.458463	−	0.888713i	$-0.651600\pi$
$307$	7.53860	−	7.53860i	0.430250	−	0.430250i	0.888713	+	0.458463i	$0.151600\pi$
$308$	1.49378	+	0.862436i	0.0851162	+	0.0491418i
$309$	15.2294	−	20.8139i	0.866372	−	1.18406i
$310$	22.3443	+	5.98715i	1.26907	+	0.340047i
$311$	13.1987			0.748432			0.374216	−	0.927342i	$-0.377912\pi$
$311$	13.1987			0.748432			0.374216	+	0.927342i	$0.377912\pi$
$312$	−4.16753	−	4.65099i	−0.235940	−	0.263310i
$313$	−19.2373			−1.08736			−0.543679	−	0.839293i	$-0.682969\pi$
$313$	−19.2373			−1.08736			−0.543679	+	0.839293i	$0.682969\pi$
$314$	7.27469	+	1.94925i	0.410534	+	0.110002i
$315$	1.85882	−	8.46465i	0.104733	−	0.476929i
$316$	−7.27951	−	4.20283i	−0.409504	−	0.236427i
$317$	−4.57322	+	4.57322i	−0.256858	+	0.256858i	−0.823775	−	0.566917i	$-0.808136\pi$
$317$	−4.57322	+	4.57322i	−0.256858	+	0.256858i	0.566917	+	0.823775i	$0.308136\pi$
$318$	1.71521	−	1.37942i	0.0961840	−	0.0773540i
$319$	1.36595	+	5.09780i	0.0764786	+	0.285422i
$320$	2.04268	+	2.04268i	0.114189	+	0.114189i
$321$	26.6129	+	2.88767i	1.48539	+	0.161174i
$322$	−6.82559	+	3.94076i	−0.380375	+	0.219610i
$323$	−10.7872	+	40.2585i	−0.600218	+	2.24004i
$324$	−8.96254	+	0.820249i	−0.497919	+	0.0455694i
$325$	−6.57842	−	10.1087i	−0.364905	−	0.560731i
$326$		−	1.53673i		−	0.0851118i
$327$	−2.25083	−	14.5273i	−0.124471	−	0.803361i
$328$	−1.57882	−	2.73460i	−0.0871760	−	0.150993i
$329$	1.50112	−	2.60001i	0.0827592	−	0.143343i
$330$	3.11995	−	8.04674i	0.171748	−	0.442959i
$331$	22.8621	−	6.12587i	1.25661	−	0.336708i	0.431725	−	0.902005i	$-0.357905\pi$
$331$	22.8621	−	6.12587i	1.25661	−	0.336708i	0.824888	+	0.565297i	$0.191238\pi$
$332$	13.8700	−	3.71644i	0.761213	−	0.203966i
$333$	−0.815414	−	17.8567i	−0.0446844	−	0.978540i
$334$	3.63454	−	6.29521i	0.198873	−	0.344458i
$335$	−1.93558	−	3.35253i	−0.105752	−	0.183168i
$336$	−1.71163	+	0.265197i	−0.0933770	+	0.0144677i
$337$			29.0006i			1.57976i	0.613260	+	0.789881i	$0.289858\pi$
$337$			29.0006i			1.57976i	−0.613260	+	0.789881i	$0.710142\pi$
$338$	8.16184	−	10.1185i	0.443946	−	0.550375i
$339$	−7.36711	−	16.6977i	−0.400126	−	0.906896i
$340$	5.19729	−	19.3966i	0.281863	−	1.05193i
$341$	−11.9618	+	6.90615i	−0.647768	+	0.373989i
$342$	−5.44321	−	17.1441i	−0.294335	−	0.927045i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	2.97085	+	11.0874i	0.160178	+	0.597791i
$345$	24.7142	+	30.7303i	1.33057	+	1.65446i
$346$	10.0342	−	10.0342i	0.539440	−	0.539440i
$347$	−10.5525	−	6.09249i	−0.566488	−	0.327062i	0.189257	−	0.981928i	$-0.439392\pi$
$347$	−10.5525	−	6.09249i	−0.566488	−	0.327062i	−0.755745	+	0.654865i	$0.772725\pi$
$348$	−4.27696	−	3.12943i	−0.229269	−	0.167755i
$349$	−28.0558	−	7.51754i	−1.50179	−	0.402404i	−0.588094	−	0.808793i	$-0.700121\pi$
$349$	−28.0558	−	7.51754i	−1.50179	−	0.402404i	−0.913700	+	0.406388i	$0.866788\pi$
$350$	−3.34505			−0.178801
$351$	−4.68346	−	18.1402i	−0.249985	−	0.968250i
$352$	−1.72487			−0.0919360
$353$	−8.58425	−	2.30014i	−0.456894	−	0.122424i	0.0230296	−	0.999735i	$-0.492669\pi$
$353$	−8.58425	−	2.30014i	−0.456894	−	0.122424i	−0.479923	+	0.877310i	$0.659335\pi$
$354$	−3.68812	−	2.69857i	−0.196021	−	0.143428i
$355$	27.7405	+	16.0160i	1.47231	+	0.850039i
$356$	−2.34343	+	2.34343i	−0.124202	+	0.124202i
$357$	7.54551	+	9.38228i	0.399351	+	0.496563i
$358$	−1.39457	−	5.20462i	−0.0737055	−	0.275073i
$359$	−13.6176	−	13.6176i	−0.718709	−	0.718709i	0.249632	−	0.968341i	$-0.419690\pi$
$359$	−13.6176	−	13.6176i	−0.718709	−	0.718709i	−0.968341	+	0.249632i	$0.919690\pi$
$360$	2.62254	+	8.26001i	0.138220	+	0.435341i
$361$	14.6789	−	8.47486i	0.772573	−	0.446045i
$362$	3.68360	−	13.7474i	0.193606	−	0.722546i
$363$	−5.61065	−	12.7167i	−0.294483	−	0.667452i
$364$	−1.11745	−	3.42802i	−0.0585705	−	0.179677i
$365$			27.1649i			1.42188i
$366$	8.81155	−	1.36525i	0.460587	−	0.0713626i
$367$	−9.81631	−	17.0024i	−0.512407	−	0.887516i	−0.999897	−	0.0143866i	$-0.995420\pi$
$367$	−9.81631	−	17.0024i	−0.512407	−	0.887516i	0.487489	−	0.873129i	$-0.337913\pi$
$368$	3.94076	−	6.82559i	0.205426	−	0.355809i
$369$	−0.432126	−	9.46308i	−0.0224956	−	0.492628i
$370$	−16.6261	+	4.45494i	−0.864349	+	0.231602i
$371$	1.22749	−	0.328905i	0.0637281	−	0.0170759i
$372$	5.01401	−	12.9318i	0.259965	−	0.670481i
$373$	7.66469	−	13.2756i	0.396863	−	0.687386i	−0.596474	−	0.802632i	$-0.703432\pi$
$373$	7.66469	−	13.2756i	0.396863	−	0.687386i	0.993337	+	0.115246i	$0.0367656\pi$
$374$	5.99505	+	10.3837i	0.309997	+	0.536930i
$375$	−1.26785	−	8.18292i	−0.0654714	−	0.422564i
$376$			3.00223i			0.154828i
$377$	4.99902	−	9.83435i	0.257463	−	0.506495i
$378$	−4.92538	−	1.65548i	−0.253334	−	0.0851489i
$379$	−2.11146	+	7.88009i	−0.108459	+	0.404773i	−0.998715	−	0.0506876i	$-0.983859\pi$
$379$	−2.11146	+	7.88009i	−0.108459	+	0.404773i	0.890256	+	0.455461i	$0.150525\pi$
$380$	−15.0001	+	8.66029i	−0.769487	+	0.444263i
$381$	36.0337	+	3.90988i	1.84606	+	0.200309i
$382$	0.608215	+	0.608215i	0.0311190	+	0.0311190i
$383$	−6.84818	−	25.5578i	−0.349926	−	1.30594i	−0.886751	−	0.462247i	$-0.847043\pi$
$383$	−6.84818	−	25.5578i	−0.349926	−	1.30594i	0.536826	−	0.843693i	$-0.319623\pi$
$384$	1.34972	−	1.08548i	0.0688774	−	0.0553932i
$385$	3.52335	−	3.52335i	0.179567	−	0.179567i
$386$	1.60134	+	0.924534i	0.0815060	+	0.0470575i
$387$	−7.38597	+	33.6341i	−0.375450	+	1.70972i
$388$	−8.03620	−	2.15329i	−0.407976	−	0.109317i
$389$	15.4625			0.783981			0.391990	−	0.919969i	$-0.371787\pi$
$389$	15.4625			0.783981			0.391990	+	0.919969i	$0.371787\pi$
$390$	−16.0938	+	8.15145i	−0.814942	+	0.412765i
$391$	−54.7868			−2.77069
$392$	−0.965926	−	0.258819i	−0.0487866	−	0.0130723i
$393$	−7.36177	+	10.0613i	−0.371352	+	0.507524i
$394$	11.6258	+	6.71215i	0.585698	+	0.338153i
$395$	−17.1700	+	17.1700i	−0.863918	+	0.863918i
$396$	−4.59471	−	2.38019i	−0.230893	−	0.119609i
$397$	−6.10106	−	22.7694i	−0.306203	−	1.14277i	−0.931905	−	0.362703i	$-0.881854\pi$
$397$	−6.10106	−	22.7694i	−0.306203	−	1.14277i	0.625701	−	0.780063i	$-0.284813\pi$
$398$	−16.9297	−	16.9297i	−0.848610	−	0.848610i
$399$	1.12027	−	10.3244i	0.0560835	−	0.516869i
$400$	2.89690	−	1.67253i	0.144845	−	0.0836263i
$401$	2.88110	−	10.7524i	0.143875	−	0.536949i	−0.855928	−	0.517095i	$-0.827013\pi$
$401$	2.88110	−	10.7524i	0.143875	−	0.536949i	0.999803	−	0.0198538i	$-0.00632007\pi$
$402$	−2.12356	+	0.936925i	−0.105914	+	0.0467296i
$403$	28.2471	+	5.97589i	1.40709	+	0.297680i
$404$			6.23039i			0.309974i
$405$	−4.41226	+	25.6219i	−0.219247	+	1.27316i
$406$	−1.52986	−	2.64980i	−0.0759257	−	0.131507i
$407$	5.13876	−	8.90060i	0.254719	−	0.441186i
$408$	−11.2257	−	4.35254i	−0.555757	−	0.215483i
$409$	−18.5711	+	4.97612i	−0.918283	+	0.246053i	−0.686851	−	0.726798i	$-0.741008\pi$
$409$	−18.5711	+	4.97612i	−0.918283	+	0.246053i	−0.231432	+	0.972851i	$0.574341\pi$
$410$	−8.81094	+	2.36088i	−0.435141	+	0.116596i
$411$	2.92328	+	1.13344i	0.144195	+	0.0559084i
$412$	−7.44511	+	12.8953i	−0.366794	+	0.635306i
$413$	−1.31923	−	2.28498i	−0.0649152	−	0.112436i
$414$	19.9162	−	12.7441i	0.978826	−	0.626336i
$415$		−	41.4807i		−	2.03621i
$416$	2.68175	+	2.41002i	0.131484	+	0.118161i
$417$	−25.0131	+	11.0359i	−1.22490	+	0.540430i
$418$	2.67671	−	9.98961i	0.130922	−	0.488608i
$419$	−15.9960	+	9.23531i	−0.781457	+	0.451174i	−0.836946	−	0.547285i	$-0.815661\pi$
$419$	−15.9960	+	9.23531i	−0.781457	+	0.451174i	0.0554894	+	0.998459i	$0.482328\pi$
$420$	−0.539744	+	4.97432i	−0.0263368	+	0.242722i
$421$	20.9699	+	20.9699i	1.02201	+	1.02201i	0.999752	+	0.0222576i	$0.00708540\pi$
$421$	20.9699	+	20.9699i	1.02201	+	1.02201i	0.0222576	+	0.999752i	$0.492915\pi$
$422$	−0.757212	−	2.82595i	−0.0368605	−	0.137565i
$423$	−4.14285	+	7.99734i	−0.201432	+	0.388844i
$424$	−0.898585	+	0.898585i	−0.0436391	+	0.0436391i
$425$	−20.1372	−	11.6262i	−0.976799	−	0.563955i
$426$	11.3410	−	15.4996i	0.549473	−	0.750960i
$427$	4.97264	+	1.33241i	0.240643	+	0.0644800i
$428$	−15.4552			−0.747053
$429$	3.35333	−	10.2366i	0.161901	−	0.494226i
$430$	33.1589			1.59906
$431$	−9.63530	−	2.58177i	−0.464116	−	0.124360i	0.0191808	−	0.999816i	$-0.493894\pi$
$431$	−9.63530	−	2.58177i	−0.464116	−	0.124360i	−0.483297	+	0.875456i	$0.660561\pi$
$432$	5.09325	−	1.02900i	0.245049	−	0.0495078i
$433$	22.5884	+	13.0414i	1.08553	+	0.626731i	0.932383	−	0.361472i	$-0.117726\pi$
$433$	22.5884	+	13.0414i	1.08553	+	0.626731i	0.153148	+	0.988203i	$0.451059\pi$
$434$	5.66232	−	5.66232i	0.271800	−	0.271800i
$435$	−11.9300	+	9.59442i	−0.571997	+	0.460017i
$436$	2.19670	+	8.19821i	0.105203	+	0.392623i
$437$	33.4151	+	33.4151i	1.59846	+	1.59846i
$438$	16.1924	+	1.75698i	0.773705	+	0.0839518i
$439$	13.7683	−	7.94912i	0.657125	−	0.379391i	−0.134056	−	0.990974i	$-0.542800\pi$
$439$	13.7683	−	7.94912i	0.657125	−	0.379391i	0.791180	+	0.611583i	$0.209467\pi$
$440$	−1.28964	+	4.81299i	−0.0614810	+	0.229450i
$441$	−2.21588	−	2.02234i	−0.105518	−	0.0963021i
$442$	5.18752	−	24.5206i	0.246745	−	1.16632i
$443$		−	5.40463i		−	0.256782i	−0.991724	−	0.128391i	$-0.959019\pi$
$443$		−	5.40463i		−	0.256782i	0.991724	−	0.128391i	$-0.0409812\pi$
$444$	1.58016	+	10.1986i	0.0749909	+	0.484005i
$445$	4.78687	+	8.29111i	0.226919	+	0.393036i
$446$	−7.95248	+	13.7741i	−0.376561	+	0.652222i
$447$	12.1798	−	31.4133i	0.576085	−	1.48580i
$448$	0.965926	−	0.258819i	0.0456357	−	0.0122281i
$449$	16.3882	−	4.39121i	0.773407	−	0.207234i	0.149531	−	0.988757i	$-0.452224\pi$
$449$	16.3882	−	4.39121i	0.773407	−	0.207234i	0.623876	+	0.781523i	$0.285557\pi$
$450$	10.0247	−	0.457772i	0.472569	−	0.0215796i
$451$	2.72327	−	4.71684i	0.128234	−	0.222107i
$452$	5.26853	+	9.12535i	0.247811	+	0.429221i
$453$	−12.1512	+	1.88269i	−0.570915	+	0.0884566i
$454$		−	12.9539i		−	0.607957i
$455$	−10.4008	+	0.555053i	−0.487599	+	0.0260213i
$456$	4.19204	+	9.50136i	0.196310	+	0.444942i
$457$	0.0705509	−	0.263300i	0.00330023	−	0.0123166i	−0.964256	−	0.264972i	$-0.914637\pi$
$457$	0.0705509	−	0.263300i	0.00330023	−	0.0123166i	0.967556	+	0.252655i	$0.0813039\pi$
$458$	−11.9392	+	6.89312i	−0.557884	+	0.322094i
$459$	−23.8969	−	27.0849i	−1.11541	−	1.26422i
$460$	−16.0994	−	16.0994i	−0.750638	−	0.750638i
$461$	5.91669	+	22.0814i	0.275568	+	1.02843i	0.955460	+	0.295121i	$0.0953600\pi$
$461$	5.91669	+	22.0814i	0.275568	+	1.02843i	−0.679892	+	0.733312i	$0.737973\pi$
$462$	−1.87232	−	2.32809i	−0.0871080	−	0.108312i
$463$	−4.23145	+	4.23145i	−0.196652	+	0.196652i	−0.798563	−	0.601911i	$-0.794406\pi$
$463$	−4.23145	+	4.23145i	−0.196652	+	0.196652i	0.601911	+	0.798563i	$0.294406\pi$
$464$	2.64980	+	1.52986i	0.123014	+	0.0710220i
$465$	−32.3353	−	23.6596i	−1.49951	−	1.09719i
$466$	−17.1160	−	4.58621i	−0.792882	−	0.212452i
$467$	−11.2748			−0.521735			−0.260868	−	0.965375i	$-0.584009\pi$
$467$	−11.2748			−0.521735			−0.260868	+	0.965375i	$0.584009\pi$
$468$	3.81800	+	10.1204i	0.176487	+	0.467817i
$469$	−1.34007			−0.0618786
$470$	8.37727	+	2.24468i	0.386415	+	0.103539i
$471$	−10.5275	−	7.70288i	−0.485080	−	0.354930i
$472$	2.28498	+	1.31923i	0.105175	+	0.0607226i
$473$	−14.0000	+	14.0000i	−0.643719	+	0.643719i
$474$	9.12418	+	11.3452i	0.419087	+	0.521104i
$475$	5.19095	+	19.3729i	0.238177	+	0.888889i
$476$	−4.91531	−	4.91531i	−0.225293	−	0.225293i
$477$	−3.63363	+	1.15367i	−0.166372	+	0.0528229i
$478$	−4.81732	+	2.78128i	−0.220339	+	0.127213i
$479$	−0.236062	+	0.880996i	−0.0107860	+	0.0402538i	−0.971109	−	0.238636i	$-0.923300\pi$
$479$	−0.236062	+	0.880996i	−0.0107860	+	0.0402538i	0.960323	+	0.278890i	$0.0899664\pi$
$480$	−2.01973	−	4.57776i	−0.0921875	−	0.208945i
$481$	−20.4256	+	6.65826i	−0.931327	+	0.303591i
$482$			8.80969i			0.401270i
$483$	13.4902	−	2.09015i	0.613826	−	0.0951052i
$484$	4.01241	+	6.94970i	0.182382	+	0.315895i
$485$	−12.0169	+	20.8138i	−0.545658	+	0.945107i
$486$	14.9873	+	4.28724i	0.679838	+	0.194473i
$487$	−7.04569	+	1.88789i	−0.319271	+	0.0855483i	−0.414895	−	0.909869i	$-0.636182\pi$
$487$	−7.04569	+	1.88789i	−0.319271	+	0.0855483i	0.0956247	+	0.995417i	$0.469515\pi$
$488$	−4.97264	+	1.33241i	−0.225101	+	0.0603156i
$489$	−0.962221	+	2.48169i	−0.0435131	+	0.112226i
$490$	−1.44439	+	2.50176i	−0.0652509	+	0.113018i
$491$	16.7764	+	29.0576i	0.757109	+	1.31135i	0.944319	+	0.329032i	$0.106722\pi$
$491$	16.7764	+	29.0576i	0.757109	+	1.31135i	−0.187209	+	0.982320i	$0.559944\pi$
$492$	0.837398	+	5.40472i	0.0377528	+	0.243664i
$493$		−	21.2691i		−	0.957910i
$494$	−18.1193	+	11.7914i	−0.815225	+	0.530522i
$495$	−10.0769	+	11.0412i	−0.452922	+	0.496267i
$496$	−2.07255	+	7.73487i	−0.0930604	+	0.347306i
$497$	9.60283	−	5.54420i	0.430746	−	0.248691i
$498$	−24.7258	−	2.68290i	−1.10799	−	0.120224i
$499$	4.17983	+	4.17983i	0.187115	+	0.187115i	0.794448	−	0.607333i	$-0.207760\pi$
$499$	4.17983	+	4.17983i	0.187115	+	0.187115i	−0.607333	+	0.794448i	$0.707760\pi$
$500$	1.23736	+	4.61788i	0.0553363	+	0.206518i
$501$	−9.81118	+	7.89045i	−0.438331	+	0.352519i
$502$	1.63562	−	1.63562i	0.0730013	−	0.0730013i
$503$	−34.3630	−	19.8395i	−1.53217	−	0.884599i	−0.999261	−	0.0384265i	$-0.987765\pi$
$503$	−34.3630	−	19.8395i	−1.53217	−	0.884599i	−0.532909	−	0.846173i	$-0.678901\pi$
$504$	2.93018	+	0.643461i	0.130521	+	0.0286620i
$505$	17.3850	+	4.65829i	0.773621	+	0.207291i
$506$	13.5946			0.604354
$507$	−19.5163	+	11.2300i	−0.866751	+	0.498742i
$508$	−20.9262			−0.928448
$509$	7.78615	+	2.08629i	0.345115	+	0.0924733i	0.427213	−	0.904151i	$-0.359495\pi$
$509$	7.78615	+	2.08629i	0.345115	+	0.0924733i	−0.0820981	+	0.996624i	$0.526162\pi$
$510$	−20.5383	+	28.0695i	−0.909449	+	1.24294i
$511$	8.14374	+	4.70179i	0.360258	+	0.207995i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−1.94439	+	31.0944i	−0.0858471	+	1.37285i
$514$	2.17023	+	8.09940i	0.0957246	+	0.357249i
$515$	30.4159	+	30.4159i	1.34028	+	1.34028i
$516$	2.14466	−	19.7653i	0.0944134	−	0.870120i
$517$	−4.48468	+	2.58923i	−0.197236	+	0.113874i
$518$	−1.54215	+	5.75540i	−0.0677584	+	0.252878i
$519$	−22.4872	+	9.92143i	−0.987077	+	0.435503i
$520$	8.72987	−	5.68111i	0.382830	−	0.249133i
$521$		−	14.4268i		−	0.632049i	−0.948751	−	0.316024i	$-0.897652\pi$
$521$		−	14.4268i		−	0.632049i	0.948751	−	0.316024i	$-0.102348\pi$
$522$	4.94743	+	7.73175i	0.216543	+	0.338410i
$523$	−3.76733	−	6.52521i	−0.164734	−	0.285328i	0.771827	−	0.635833i	$-0.219343\pi$
$523$	−3.76733	−	6.52521i	−0.164734	−	0.285328i	−0.936561	+	0.350505i	$0.886010\pi$
$524$	3.59890	−	6.23347i	0.157219	−	0.272310i
$525$	5.40196	+	2.09449i	0.235761	+	0.0914112i
$526$	1.61104	−	0.431678i	0.0702448	−	0.0188220i
$527$	53.7674	−	14.4069i	2.34215	−	0.627576i
$528$	2.78552	+	1.08002i	0.121224	+	0.0470020i
$529$	−19.5591	+	33.8774i	−0.850398	+	1.47293i
$530$	1.83552	+	3.17921i	0.0797298	+	0.138096i
$531$	4.26628	+	6.66726i	0.185141	+	0.289335i
$532$			5.99581i			0.259951i
$533$	−10.8245	+	3.52852i	−0.468860	+	0.152837i
$534$	5.25177	−	2.31710i	0.227266	−	0.100271i
$535$	−11.5554	+	43.1253i	−0.499583	+	1.86447i
$536$	1.16053	−	0.670034i	0.0501274	−	0.0289411i
$537$	−1.00674	+	9.27821i	−0.0434442	+	0.400384i
$538$	−14.1540	−	14.1540i	−0.610222	−	0.610222i
$539$	−0.446430	−	1.66610i	−0.0192291	−	0.0717639i
$540$	0.936809	−	14.9813i	0.0403138	−	0.644692i
$541$	−11.0227	+	11.0227i	−0.473903	+	0.473903i	−0.903175	−	0.429272i	$-0.858770\pi$
$541$	−11.0227	+	11.0227i	−0.473903	+	0.473903i	0.429272	+	0.903175i	$0.358770\pi$
$542$	17.8736	+	10.3193i	0.767735	+	0.443252i
$543$	−14.5566	+	19.8943i	−0.624682	+	0.853747i
$544$	6.71444	+	1.79913i	0.287879	+	0.0771371i
$545$	24.5183			1.05025
$546$	−0.341854	+	6.23563i	−0.0146300	+	0.266861i
$547$	21.0958			0.901990			0.450995	−	0.892527i	$-0.351069\pi$
$547$	21.0958			0.901990			0.450995	+	0.892527i	$0.351069\pi$
$548$	−1.74850	−	0.468509i	−0.0746922	−	0.0200137i
$549$	−15.0847	−	3.31257i	−0.643800	−	0.141377i
$550$	4.99678	+	2.88489i	0.213063	+	0.123012i
$551$	−12.9722	+	12.9722i	−0.552636	+	0.552636i
$552$	−10.6378	+	8.55524i	−0.452775	+	0.364135i
$553$	2.17554	+	8.11924i	0.0925135	+	0.345265i
$554$	5.64427	+	5.64427i	0.239802	+	0.239802i
$555$	29.6391	+	3.21603i	1.25811	+	0.136513i
$556$	13.6697	−	7.89222i	0.579725	−	0.334705i
$557$	5.57264	−	20.7974i	0.236120	−	0.881213i	−0.741520	−	0.670931i	$-0.765895\pi$
$557$	5.57264	−	20.7974i	0.236120	−	0.881213i	0.977641	−	0.210283i	$-0.0674385\pi$
$558$	−16.1944	+	17.7442i	−0.685563	+	0.751170i
$559$	41.3275	−	2.20549i	1.74797	−	0.0932823i
$560$		−	2.88878i		−	0.122073i
$561$	−3.17974	−	20.5226i	−0.134249	−	0.866465i
$562$	−8.07562	−	13.9874i	−0.340650	−	0.590022i
$563$	12.5256	−	21.6950i	0.527891	−	0.914333i	−0.471581	−	0.881823i	$-0.656316\pi$
$563$	12.5256	−	21.6950i	0.527891	−	0.914333i	0.999471	−	0.0325105i	$-0.0103502\pi$
$564$	1.87984	−	4.84834i	0.0791555	−	0.204152i
$565$	29.4020	−	7.87825i	1.23695	−	0.331441i
$566$	7.96416	−	2.13399i	0.334759	−	0.0896983i
$567$	6.91748	+	5.75747i	0.290507	+	0.241791i
$568$	−5.54420	+	9.60283i	−0.232629	+	0.402926i
$569$	−11.3432	−	19.6469i	−0.475530	−	0.823642i	0.524077	−	0.851671i	$-0.324410\pi$
$569$	−11.3432	−	19.6469i	−0.475530	−	0.823642i	−0.999607	+	0.0280285i	$0.991077\pi$
$570$	29.6464	−	4.59336i	1.24175	−	0.192395i
$571$			7.57683i			0.317080i	0.987353	+	0.158540i	$0.0506787\pi$
$571$			7.57683i			0.317080i	−0.987353	+	0.158540i	$0.949321\pi$
$572$	−1.28721	+	6.08444i	−0.0538210	+	0.254403i
$573$	−0.601381	−	1.36304i	−0.0251231	−	0.0569420i
$574$	−0.817259	+	3.05005i	−0.0341118	+	0.127307i
$575$	−22.8320	+	13.1820i	−0.952159	+	0.549729i
$576$	−2.85934	+	0.907836i	−0.119139	+	0.0378265i
$577$	5.29010	+	5.29010i	0.220230	+	0.220230i	0.808595	−	0.588366i	$-0.200228\pi$
$577$	5.29010	+	5.29010i	0.220230	+	0.220230i	−0.588366	+	0.808595i	$0.700228\pi$
$578$	−8.10637	−	30.2534i	−0.337181	−	1.25838i
$579$	−2.00713	−	2.49571i	−0.0834134	−	0.103718i
$580$	6.25002	−	6.25002i	0.259518	−	0.259518i
$581$	−12.4355	−	7.17962i	−0.515910	−	0.297861i
$582$	11.6295	+	8.50922i	0.482057	+	0.352718i
$583$	−2.11726	−	0.567319i	−0.0876881	−	0.0234959i
$584$	−9.40359			−0.389123
$585$	31.0941	−	3.08679i	1.28558	−	0.127623i
$586$	−14.7397			−0.608893
$587$	−6.00016	−	1.60774i	−0.247653	−	0.0663585i	0.132857	−	0.991135i	$-0.457585\pi$
$587$	−6.00016	−	1.60774i	−0.247653	−	0.0663585i	−0.380510	+	0.924777i	$0.624252\pi$
$588$	1.39783	+	1.02278i	0.0576454	+	0.0421788i
$589$	−41.5803	−	24.0064i	−1.71329	−	0.989167i
$590$	5.38953	−	5.38953i	0.221884	−	0.221884i
$591$	−14.5718	−	18.1190i	−0.599405	−	0.745315i
$592$	−1.54215	−	5.75540i	−0.0633822	−	0.236545i
$593$	30.4769	+	30.4769i	1.25154	+	1.25154i	0.955032	+	0.296504i	$0.0958208\pi$
$593$	30.4769	+	30.4769i	1.25154	+	1.25154i	0.296504	+	0.955032i	$0.404179\pi$
$594$	5.92970	+	6.72076i	0.243299	+	0.275756i
$595$	−17.3905	+	10.0404i	−0.712940	+	0.411616i
$596$	−5.03455	+	18.7892i	−0.206223	+	0.769635i
$597$	16.7395	+	37.9405i	0.685102	+	1.55280i
$598$	−21.1363	−	18.9946i	−0.864326	−	0.776748i
$599$			16.8196i			0.687229i	0.939111	+	0.343614i	$0.111651\pi$
$599$			16.8196i			0.687229i	−0.939111	+	0.343614i	$0.888349\pi$
$600$	−5.72548	+	0.887097i	−0.233742	+	0.0362156i
$601$	−18.5605	−	32.1476i	−0.757097	−	1.31133i	−0.944325	−	0.329013i	$-0.893284\pi$
$601$	−18.5605	−	32.1476i	−0.757097	−	1.31133i	0.187229	−	0.982316i	$-0.440049\pi$
$602$	5.73925	−	9.94067i	0.233914	−	0.405151i
$603$	4.01602	−	0.183389i	0.163545	−	0.00746818i
$604$	6.85732	−	1.83741i	0.279021	−	0.0747633i
$605$	22.3920	−	5.99993i	0.910365	−	0.243932i
$606$	3.90114	−	10.0615i	0.158473	−	0.408722i
$607$	−6.76372	+	11.7151i	−0.274531	+	0.475502i	−0.970017	−	0.243038i	$-0.921856\pi$
$607$	−6.76372	+	11.7151i	−0.274531	+	0.475502i	0.695486	+	0.718540i	$0.255189\pi$
$608$	−2.99790	−	5.19252i	−0.121581	−	0.210585i
$609$	0.811428	+	5.23711i	0.0328807	+	0.212218i
$610$			14.8716i			0.602133i
$611$	10.5903	+	2.24046i	0.428438	+	0.0906394i
$612$	15.4033	+	14.0579i	0.622640	+	0.568258i
$613$	−6.63090	+	24.7468i	−0.267819	+	0.999515i	0.692683	+	0.721242i	$0.256429\pi$
$613$	−6.63090	+	24.7468i	−0.267819	+	0.999515i	−0.960502	+	0.278273i	$0.910238\pi$
$614$	9.23286	−	5.33059i	0.372608	−	0.215125i
$615$	15.7071	+	1.70432i	0.633373	+	0.0687249i
$616$	1.21967	+	1.21967i	0.0491418	+	0.0491418i
$617$	−3.63391	−	13.5620i	−0.146296	−	0.545984i	−0.999694	−	0.0247245i	$-0.992129\pi$
$617$	−3.63391	−	13.5620i	−0.146296	−	0.545984i	0.853398	−	0.521259i	$-0.174538\pi$
$618$	20.0975	−	16.1630i	0.808442	−	0.650173i
$619$	−2.26075	+	2.26075i	−0.0908673	+	0.0908673i	−0.751079	−	0.660212i	$-0.770466\pi$
$619$	−2.26075	+	2.26075i	−0.0908673	+	0.0908673i	0.660212	+	0.751079i	$0.270466\pi$
$620$	20.0334	+	11.5663i	0.804560	+	0.464513i
$621$	−40.1425	+	8.11007i	−1.61086	+	0.325446i
$622$	12.7490	+	3.41609i	0.511188	+	0.136973i
$623$	3.31411			0.132777
$624$	−2.82176	−	5.57114i	−0.112961	−	0.223024i
$625$	30.5359			1.22144
$626$	−18.5818	−	4.97899i	−0.742679	−	0.199000i
$627$	−10.5776	+	14.4563i	−0.422429	+	0.577330i
$628$	6.52231	+	3.76566i	0.260268	+	0.150266i
$629$	−29.2875	+	29.2875i	−1.16777	+	1.16777i
$630$	3.98629	−	7.69512i	0.158818	−	0.306581i
$631$	−5.21129	−	19.4488i	−0.207458	−	0.774245i	−0.988686	−	0.149999i	$-0.952073\pi$
$631$	−5.21129	−	19.4488i	−0.207458	−	0.774245i	0.781228	−	0.624246i	$-0.214594\pi$
$632$	−5.94369	−	5.94369i	−0.236427	−	0.236427i
$633$	−0.546632	+	5.03779i	−0.0217267	+	0.200234i
$634$	−5.60103	+	3.23376i	−0.222445	+	0.128429i
$635$	−15.6459	+	58.3913i	−0.620888	+	2.31719i
$636$	2.01378	−	0.888489i	0.0798516	−	0.0352309i
$637$	−1.63382	+	3.21413i	−0.0647341	+	0.127349i
$638$			5.27763i			0.208943i
$639$	−28.0198	+	17.9294i	−1.10844	+	0.709277i
$640$	1.44439	+	2.50176i	0.0570945	+	0.0988906i
$641$	−6.54052	+	11.3285i	−0.258335	+	0.447449i	−0.965796	−	0.259303i	$-0.916507\pi$
$641$	−6.54052	+	11.3285i	−0.258335	+	0.447449i	0.707461	+	0.706752i	$0.249841\pi$
$642$	24.9587	+	9.67720i	0.985042	+	0.381929i
$643$	37.5442	−	10.0599i	1.48060	−	0.396726i	0.574049	−	0.818821i	$-0.305372\pi$
$643$	37.5442	−	10.0599i	1.48060	−	0.396726i	0.906551	+	0.422096i	$0.138705\pi$
$644$	−7.61296	+	2.03989i	−0.299993	+	0.0803828i
$645$	−53.5486	−	20.7623i	−2.10848	−	0.817515i
$646$	−20.8393	+	36.0948i	−0.819913	+	1.42013i
$647$	−14.4953	−	25.1065i	−0.569868	−	0.987040i	−0.996578	−	0.0826520i	$-0.973661\pi$
$647$	−14.4953	−	25.1065i	−0.569868	−	0.987040i	0.426711	−	0.904388i	$-0.359672\pi$
$648$	−8.86945	−	1.52738i	−0.348425	−	0.0600011i
$649$			4.55102i			0.178643i
$650$	−3.73794	−	11.4669i	−0.146614	−	0.449769i
$651$	−12.6896	+	5.59870i	−0.497344	+	0.219430i
$652$	0.397736	−	1.48437i	0.0155765	−	0.0581324i
$653$	−34.2471	+	19.7726i	−1.34019	+	0.773761i	−0.986835	−	0.161728i	$-0.948293\pi$
$653$	−34.2471	+	19.7726i	−1.34019	+	0.773761i	−0.353358	+	0.935488i	$0.614960\pi$
$654$	1.58580	−	14.6149i	0.0620098	−	0.571486i
$655$	−14.7028	−	14.7028i	−0.574484	−	0.574484i
$656$	−0.817259	−	3.05005i	−0.0319086	−	0.119085i
$657$	−25.0492	−	12.9762i	−0.977264	−	0.506250i
$658$	2.12290	−	2.12290i	0.0827592	−	0.0827592i
$659$	−43.6509	−	25.2019i	−1.70040	−	0.981726i	−0.945350	−	0.326059i	$-0.894279\pi$
$659$	−43.6509	−	25.2019i	−1.70040	−	0.981726i	−0.755050	−	0.655667i	$-0.772387\pi$
$660$	5.09629	−	6.96506i	0.198373	−	0.271114i
$661$	−31.1518	−	8.34711i	−1.21167	−	0.324665i	−0.404250	−	0.914648i	$-0.632468\pi$
$661$	−31.1518	−	8.34711i	−1.21167	−	0.324665i	−0.807415	+	0.589984i	$0.799134\pi$
$662$	23.6686			0.919905
$663$	−23.7309	+	36.3504i	−0.921630	+	1.41173i
$664$	14.3592			0.557246
$665$	16.7304	+	4.48289i	0.648777	+	0.173839i
$666$	3.83402	−	17.4593i	0.148565	−	0.676533i
$667$	−20.8844	−	12.0576i	−0.808648	−	0.466873i
$668$	5.14001	−	5.14001i	0.198873	−	0.198873i
$669$	21.4672	−	17.2645i	0.829968	−	0.667485i
$670$	−1.00193	−	3.73926i	−0.0387080	−	0.144460i
$671$	−6.27892	−	6.27892i	−0.242395	−	0.242395i
$672$	−1.72194	−	0.186842i	−0.0664254	−	0.00720757i
$673$	−14.3618	+	8.29182i	−0.553609	+	0.319626i	−0.750576	−	0.660784i	$-0.770224\pi$
$673$	−14.3618	+	8.29182i	−0.553609	+	0.319626i	0.196968	+	0.980410i	$0.436891\pi$
$674$	−7.50590	+	28.0124i	−0.289117	+	1.07900i
$675$	−16.4757	−	5.53768i	−0.634148	−	0.213145i
$676$	10.5026	−	7.66130i	0.403946	−	0.294665i
$677$		−	43.7323i		−	1.68077i	−0.541991	−	0.840384i	$-0.682329\pi$
$677$		−	43.7323i		−	1.68077i	0.541991	−	0.840384i	$-0.317671\pi$
$678$	−2.79439	−	18.0355i	−0.107318	−	0.692650i
$679$	4.15984	+	7.20506i	0.159640	+	0.276505i
$680$	10.0404	−	17.3905i	0.385032	−	0.666894i
$681$	−8.11104	+	20.9194i	−0.310816	+	0.801633i
$682$	−13.3417	+	3.57489i	−0.510879	+	0.136890i
$683$	4.92584	−	1.31987i	0.188482	−	0.0505036i	−0.163343	−	0.986569i	$-0.552228\pi$
$683$	4.92584	−	1.31987i	0.188482	−	0.0505036i	0.351825	+	0.936066i	$0.385561\pi$
$684$	−0.820530	−	17.9687i	−0.0313737	−	0.687050i
$685$	−2.61461	+	4.52863i	−0.0998990	+	0.173030i
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	23.5969	−	3.65607i	0.900278	−	0.139488i
$688$			11.4785i			0.437614i
$689$	2.49915	+	3.84032i	0.0952102	+	0.146305i
$690$	15.9185	+	36.0797i	0.606007	+	1.37353i
$691$	−0.776008	+	2.89610i	−0.0295207	+	0.110173i	−0.979114	−	0.203311i	$-0.934830\pi$
$691$	−0.776008	+	2.89610i	−0.0295207	+	0.110173i	0.949593	+	0.313484i	$0.101496\pi$
$692$	12.2893	−	7.09523i	0.467169	−	0.269720i
$693$	1.56590	+	4.93200i	0.0594837	+	0.187351i
$694$	−8.61608	−	8.61608i	−0.327062	−	0.327062i
$695$	−11.8016	−	44.0441i	−0.447659	−	1.67069i
$696$	−3.32127	−	4.12975i	−0.125892	−	0.156538i
$697$	−15.5208	+	15.5208i	−0.587893	+	0.587893i
$698$	−25.1542	−	14.5228i	−0.952099	−	0.549695i
$699$	24.7691	+	18.1234i	0.936855	+	0.685491i
$700$	−3.23107	−	0.865763i	−0.122123	−	0.0327228i
$701$	24.6775			0.932055			0.466027	−	0.884770i	$-0.345685\pi$
$701$	24.6775			0.932055			0.466027	+	0.884770i	$0.345685\pi$
$702$	0.171143	−	18.7342i	0.00645939	−	0.707077i
$703$	35.7256			1.34742
$704$	−1.66610	−	0.446430i	−0.0627934	−	0.0168255i
$705$	−12.1231	−	8.87037i	−0.456581	−	0.334077i
$706$	−7.69643	−	4.44354i	−0.289659	−	0.167235i
$707$	4.40555	−	4.40555i	0.165688	−	0.165688i
$708$	−2.86401	−	3.56118i	−0.107636	−	0.133837i
$709$	−5.45655	−	20.3641i	−0.204925	−	0.764791i	−0.989472	−	0.144722i	$-0.953771\pi$
$709$	−5.45655	−	20.3641i	−0.204925	−	0.764791i	0.784547	−	0.620069i	$-0.212895\pi$
$710$	22.6500	+	22.6500i	0.850039	+	0.850039i
$711$	−7.63096	−	24.0346i	−0.286183	−	0.901369i
$712$	−2.87011	+	1.65706i	−0.107562	+	0.0621008i
$713$	16.3349	−	60.9625i	0.611745	−	2.28306i
$714$	4.86009	+	11.0155i	0.181884	+	0.412245i
$715$	16.0153	+	8.14093i	0.598938	+	0.304454i
$716$		−	5.38822i		−	0.201367i
$717$	9.52105	−	1.47517i	0.355570	−	0.0550914i
$718$	−9.62909	−	16.6781i	−0.359355	−	0.622420i
$719$	−4.85123	+	8.40257i	−0.180920	+	0.313363i	−0.942194	−	0.335067i	$-0.891241\pi$
$719$	−4.85123	+	8.40257i	−0.180920	+	0.313363i	0.761274	+	0.648430i	$0.224574\pi$
$720$	0.395331	+	8.65732i	0.0147331	+	0.322639i
$721$	14.3828	−	3.85387i	0.535645	−	0.143526i
$722$	16.3722	−	4.38691i	0.609309	−	0.163264i
$723$	5.51616	−	14.2269i	0.205148	−	0.529103i
$724$	7.11616	−	12.3256i	0.264470	−	0.458076i
$725$	−5.11747	−	8.86371i	−0.190058	−	0.329190i
$726$	−2.12816	−	13.7355i	−0.0789832	−	0.509772i
$727$			7.28473i			0.270176i	0.990834	+	0.135088i	$0.0431316\pi$
$727$			7.28473i			0.270176i	−0.990834	+	0.135088i	$0.956868\pi$
$728$	−0.192141	−	3.60043i	−0.00712122	−	0.133441i
$729$	−21.5187	−	16.3078i	−0.796991	−	0.603992i
$730$	−7.03079	+	26.2393i	−0.260221	+	0.971159i
$731$	69.1006	−	39.8953i	2.55578	−	1.47558i
$732$	8.86466	+	0.961870i	0.327647	+	0.0355517i
$733$	−24.5636	−	24.5636i	−0.907278	−	0.907278i	0.0887735	−	0.996052i	$-0.471705\pi$
$733$	−24.5636	−	24.5636i	−0.907278	−	0.907278i	−0.996052	+	0.0887735i	$0.971705\pi$
$734$	−5.08130	−	18.9637i	−0.187554	−	0.699962i
$735$	3.89903	−	3.13572i	0.143818	−	0.115663i
$736$	5.57307	−	5.57307i	0.205426	−	0.205426i
$737$	2.00177	+	1.15572i	0.0737362	+	0.0425716i
$738$	2.03182	−	9.25248i	0.0747925	−	0.340588i
$739$	7.84445	+	2.10191i	0.288563	+	0.0773201i	0.400197	−	0.916429i	$-0.368942\pi$
$739$	7.84445	+	2.10191i	0.288563	+	0.0773201i	−0.111634	+	0.993749i	$0.535608\pi$
$740$	−17.2126			−0.632747
$741$	36.6442	−	7.69679i	1.34616	−	0.282749i
$742$	1.27079			0.0466522
$743$	34.2598	+	9.17990i	1.25687	+	0.336778i	0.824987	−	0.565151i	$-0.191182\pi$
$743$	34.2598	+	9.17990i	1.25687	+	0.336778i	0.431884	+	0.901929i	$0.357849\pi$
$744$	8.19016	−	11.1934i	0.300266	−	0.410370i
$745$	48.6642	+	28.0963i	1.78292	+	1.02937i
$746$	10.8395	−	10.8395i	0.396863	−	0.396863i
$747$	38.2501	+	19.8146i	1.39950	+	0.724979i
$748$	3.10327	+	11.5816i	0.113467	+	0.423464i
$749$	10.9284	+	10.9284i	0.399317	+	0.399317i
$750$	0.893249	−	8.23224i	0.0326168	−	0.300599i
$751$	−12.5690	+	7.25670i	−0.458648	+	0.264801i	−0.711476	−	0.702711i	$-0.751973\pi$
$751$	−12.5690	+	7.25670i	−0.458648	+	0.264801i	0.252827	+	0.967511i	$0.418640\pi$
$752$	−0.777035	+	2.89993i	−0.0283355	+	0.105750i
$753$	−3.66552	+	1.61724i	−0.133579	+	0.0589356i
$754$	7.37400	−	8.20541i	0.268545	−	0.298824i
$755$		−	20.5081i		−	0.746366i
$756$	−4.32908	−	2.87386i	−0.157447	−	0.104521i
$757$	−22.5379	−	39.0368i	−0.819155	−	1.41882i	−0.906306	−	0.422623i	$-0.861110\pi$
$757$	−22.5379	−	39.0368i	−0.819155	−	1.41882i	0.0871511	−	0.996195i	$-0.472224\pi$
$758$	−4.07903	+	7.06509i	−0.148157	+	0.256616i
$759$	−21.9541	−	8.51222i	−0.796883	−	0.308974i
$760$	−16.7304	+	4.48289i	−0.606875	+	0.162612i
$761$	−46.9700	+	12.5856i	−1.70266	+	0.456227i	−0.973608	−	0.228229i	$-0.926707\pi$
$761$	−46.9700	+	12.5856i	−1.70266	+	0.456227i	−0.729055	+	0.684455i	$0.760040\pi$
$762$	33.7939	+	13.1028i	1.22422	+	0.474666i
$763$	4.24371	−	7.35032i	0.153633	−	0.266099i
$764$	0.430073	+	0.744908i	0.0155595	+	0.0269498i
$765$	50.7431	−	32.4697i	1.83462	−	1.17395i
$766$		−	26.4593i		−	0.956015i
$767$	6.35877	−	7.07571i	0.229602	−	0.255489i
$768$	1.58467	−	0.699162i	0.0571818	−	0.0252288i
$769$	1.71215	−	6.38984i	0.0617418	−	0.230423i	−0.928159	−	0.372183i	$-0.878609\pi$
$769$	1.71215	−	6.38984i	0.0617418	−	0.230423i	0.989901	+	0.141760i	$0.0452760\pi$
$770$	4.31521	−	2.49139i	0.155509	−	0.0897834i
$771$	1.56669	−	14.4387i	0.0564229	−	0.519997i
$772$	1.30749	+	1.30749i	0.0470575	+	0.0470575i
$773$	11.4518	+	42.7389i	0.411894	+	1.53721i	0.790976	+	0.611847i	$0.209573\pi$
$773$	11.4518	+	42.7389i	0.411894	+	1.53721i	−0.379082	+	0.925363i	$0.623760\pi$
$774$	−15.8394	+	30.5764i	−0.569337	+	1.09905i
$775$	18.9408	−	18.9408i	0.680372	−	0.680372i
$776$	−7.20506	−	4.15984i	−0.258646	−	0.149330i
$777$	6.09417	−	8.32885i	0.218627	−	0.298796i
$778$	14.9356	+	4.00199i	0.535469	+	0.143478i
$779$	18.9327			0.678333
$780$	−17.6552	+	3.70831i	−0.632157	+	0.132779i
$781$	−19.1261			−0.684384
$782$	−52.9200	−	14.1799i	−1.89242	−	0.507071i
$783$	−3.14845	−	15.5839i	−0.112517	−	0.556924i
$784$	−0.866025	−	0.500000i	−0.0309295	−	0.0178571i
$785$	15.3840	−	15.3840i	0.549080	−	0.549080i
$786$	−9.71497	+	7.81307i	−0.346521	+	0.278683i
$787$	12.1111	+	45.1994i	0.431716	+	1.61119i	0.748806	+	0.662790i	$0.230628\pi$
$787$	12.1111	+	45.1994i	0.431716	+	1.61119i	−0.317090	+	0.948396i	$0.602706\pi$
$788$	9.49241	+	9.49241i	0.338153	+	0.338153i
$789$	−2.87199	−	0.311628i	−0.102245	−	0.0110943i
$790$	−21.0289	+	12.1410i	−0.748175	+	0.431959i
$791$	2.72719	−	10.1780i	0.0969677	−	0.361888i
$792$	−3.82211	−	3.48828i	−0.135813	−	0.123951i
$793$	0.989152	+	18.5352i	0.0351258	+	0.658204i
$794$		−	23.5727i		−	0.836563i
$795$	−0.973547	−	6.28345i	−0.0345281	−	0.222851i
$796$	−11.9711	−	20.7346i	−0.424305	−	0.734918i
$797$	−6.21149	+	10.7586i	−0.220022	+	0.381090i	−0.954815	−	0.297202i	$-0.903946\pi$
$797$	−6.21149	+	10.7586i	−0.220022	+	0.381090i	0.734792	+	0.678292i	$0.237280\pi$
$798$	3.75426	−	9.68270i	0.132899	−	0.342764i
$799$	20.1583	−	5.40140i	0.713150	−	0.191088i
$800$	3.23107	−	0.865763i	0.114236	−	0.0306093i
$801$	−9.93199	+	0.453538i	−0.350930	+	0.0160250i
$802$	5.56585	−	9.64034i	0.196537	−	0.340412i
$803$	−8.10999	−	14.0469i	−0.286195	−	0.495705i
$804$	−2.29370	+	0.355382i	−0.0808925	+	0.0125333i
$805$			22.7680i			0.802465i
$806$	25.7379	+	13.0831i	0.906579	+	0.460834i
$807$	13.9950	+	31.7199i	0.492646	+	1.11659i
$808$	−1.61254	+	6.01810i	−0.0567291	+	0.211716i
$809$	45.1620	−	26.0743i	1.58781	−	0.916723i	0.594144	−	0.804359i	$-0.297491\pi$
$809$	45.1620	−	26.0743i	1.58781	−	0.916723i	0.993667	−	0.112364i	$-0.0358424\pi$
$810$	−10.8933	+	23.6069i	−0.382753	+	0.829461i
$811$	23.1215	+	23.1215i	0.811905	+	0.811905i	0.984919	−	0.173014i	$-0.0553507\pi$
$811$	23.1215	+	23.1215i	0.811905	+	0.811905i	−0.173014	+	0.984919i	$0.555351\pi$
$812$	−0.791914	−	2.95546i	−0.0277907	−	0.103716i
$813$	−22.4028	−	27.8562i	−0.785701	−	0.976961i
$814$	7.26731	−	7.26731i	0.254719	−	0.254719i
$815$	−3.84453	−	2.21964i	−0.134668	−	0.0777507i
$816$	−9.71671	−	7.10966i	−0.340153	−	0.248888i
$817$	−66.4778	−	17.8127i	−2.32576	−	0.623186i
$818$	−19.2262			−0.672230
$819$	4.45649	−	9.85595i	0.155722	−	0.344395i
$820$	−9.12175			−0.318545
$821$	49.9173	+	13.3753i	1.74213	+	0.466802i	0.982918	−	0.184045i	$-0.0589192\pi$
$821$	49.9173	+	13.3753i	1.74213	+	0.466802i	0.759209	+	0.650846i	$0.225586\pi$
$822$	2.53032	+	1.85142i	0.0882550	+	0.0645757i
$823$	−3.26283	−	1.88380i	−0.113735	−	0.0656650i	0.442053	−	0.896989i	$-0.354250\pi$
$823$	−3.26283	−	1.88380i	−0.113735	−	0.0656650i	−0.555788	+	0.831324i	$0.687584\pi$
$824$	−10.5290	+	10.5290i	−0.366794	+	0.366794i
$825$	−6.26299	−	7.78757i	−0.218049	−	0.271128i
$826$	−0.682885	−	2.54856i	−0.0237606	−	0.0886759i
$827$	4.95114	+	4.95114i	0.172168	+	0.172168i	0.787931	−	0.615763i	$-0.211152\pi$
$827$	4.95114	+	4.95114i	0.172168	+	0.172168i	−0.615763	+	0.787931i	$0.711152\pi$
$828$	22.5359	−	7.15513i	0.783178	−	0.248658i
$829$	8.77230	−	5.06469i	0.304675	−	0.175904i	−0.339866	−	0.940474i	$-0.610382\pi$
$829$	8.77230	−	5.06469i	0.304675	−	0.175904i	0.644541	+	0.764570i	$0.277048\pi$
$830$	10.7360	−	40.0673i	0.372652	−	1.39075i
$831$	−5.58086	−	12.6491i	−0.193598	−	0.438794i
$832$	1.96661	+	3.02199i	0.0681800	+	0.104769i
$833$			6.95130i			0.240848i
$834$	−27.0171	+	4.18598i	−0.935525	+	0.144949i
$835$	−10.4994	−	18.1855i	−0.363346	−	0.629334i
$836$	5.17100	−	8.95643i	0.178843	−	0.309765i
$837$	37.2630	−	18.5152i	1.28800	−	0.639979i
$838$	−17.8412	+	4.78055i	−0.616316	+	0.165141i
$839$	−33.0855	+	8.86523i	−1.14224	+	0.306062i	−0.779850	−	0.625966i	$-0.784705\pi$
$839$	−33.0855	+	8.86523i	−1.14224	+	0.306062i	−0.362387	+	0.932028i	$0.618038\pi$
$840$	−1.80880	+	4.66513i	−0.0624096	+	0.160962i
$841$	−9.81905	+	17.0071i	−0.338588	+	0.586451i
$842$	14.8280	+	25.6828i	0.511005	+	0.885087i
$843$	4.28326	+	27.6449i	0.147523	+	0.952142i
$844$		−	2.92564i		−	0.100705i
$845$	−13.5252	−	35.0340i	−0.465281	−	1.20521i
$846$	−6.07155	+	6.65259i	−0.208744	+	0.228721i
$847$	2.07698	−	7.75138i	0.0713657	−	0.266340i
$848$	−1.10054	+	0.635396i	−0.0377926	+	0.0218196i
$849$	−14.1976	−	1.54053i	−0.487261	−	0.0528708i
$850$	−16.4420	−	16.4420i	−0.563955	−	0.563955i
$851$	12.1545	+	45.3613i	0.416651	+	1.55496i
$852$	14.9662	−	12.0362i	0.512732	−	0.412355i
$853$	23.2961	−	23.2961i	0.797644	−	0.797644i	−0.185080	−	0.982723i	$-0.559254\pi$
$853$	23.2961	−	23.2961i	0.797644	−	0.797644i	0.982723	+	0.185080i	$0.0592544\pi$
$854$	4.45834	+	2.57403i	0.152561	+	0.0880814i
$855$	−50.7524	−	11.1451i	−1.73570	−	0.381155i
$856$	−14.9285	−	4.00009i	−0.510247	−	0.136720i
$857$	−3.90760			−0.133481			−0.0667405	−	0.997770i	$-0.521260\pi$
$857$	−3.90760			−0.133481			−0.0667405	+	0.997770i	$0.521260\pi$
$858$	5.88849	−	9.01986i	0.201030	−	0.307933i
$859$	46.2425			1.57777			0.788887	−	0.614539i	$-0.210658\pi$
$859$	46.2425			1.57777			0.788887	+	0.614539i	$0.210658\pi$
$860$	32.0290	+	8.58214i	1.09218	+	0.292649i
$861$	3.22958	−	4.41384i	0.110064	−	0.150423i
$862$	−8.63877	−	4.98760i	−0.294238	−	0.169878i
$863$	−8.38383	+	8.38383i	−0.285389	+	0.285389i	−0.835254	−	0.549865i	$-0.814679\pi$
$863$	−8.38383	+	8.38383i	−0.285389	+	0.285389i	0.549865	+	0.835254i	$0.314679\pi$
$864$	5.18602	+	0.324292i	0.176432	+	0.0110326i
$865$	−10.6098	−	39.5963i	−0.360744	−	1.34632i
$866$	18.4434	+	18.4434i	0.626731	+	0.626731i
$867$	−5.85199	+	53.9323i	−0.198744	+	1.83164i
$868$	6.93490	−	4.00386i	0.235386	−	0.135900i
$869$	3.75253	−	14.0046i	0.127296	−	0.475075i
$870$	−14.0067	+	6.17980i	−0.474870	+	0.209515i
$871$	−1.49746	−	4.59378i	−0.0507396	−	0.155654i
$872$			8.48742i			0.287420i
$873$	−13.4526	−	21.0234i	−0.455300	−	0.711534i
$874$	23.6280	+	40.9249i	0.799230	+	1.38431i
$875$	2.39039	−	4.14028i	0.0808100	−	0.139967i
$876$	15.1860	+	5.88803i	0.513086	+	0.198938i
$877$	3.63895	−	0.975054i	0.122879	−	0.0329252i	−0.196856	−	0.980432i	$-0.563073\pi$
$877$	3.63895	−	0.975054i	0.122879	−	0.0329252i	0.319734	+	0.947507i	$0.396406\pi$
$878$	15.3565	−	4.11477i	0.518258	−	0.138867i
$879$	23.8034	+	9.22924i	0.802868	+	0.311295i
$880$	−2.49139	+	4.31521i	−0.0839847	+	0.145466i
$881$	11.6281	+	20.1405i	0.391762	+	0.678552i	0.992682	−	0.120757i	$-0.0385323\pi$
$881$	11.6281	+	20.1405i	0.391762	+	0.678552i	−0.600920	+	0.799309i	$0.705199\pi$
$882$	−1.61695	−	2.52695i	−0.0544457	−	0.0850867i
$883$		−	52.4326i		−	1.76450i	−0.470784	−	0.882248i	$-0.656029\pi$
$883$		−	52.4326i		−	1.76450i	0.470784	−	0.882248i	$-0.343971\pi$
$884$	11.3571	−	22.3424i	0.381982	−	0.751457i
$885$	−12.0783	+	5.32898i	−0.406006	+	0.179132i
$886$	1.39882	−	5.22047i	0.0469943	−	0.175385i
$887$	15.8997	−	9.17967i	0.533858	−	0.308223i	−0.208728	−	0.977974i	$-0.566932\pi$
$887$	15.8997	−	9.17967i	0.533858	−	0.308223i	0.742586	+	0.669750i	$0.233599\pi$
$888$	−1.11328	+	10.2601i	−0.0373593	+	0.344306i
$889$	14.7970	+	14.7970i	0.496276	+	0.496276i
$890$	2.47787	+	9.24753i	0.0830583	+	0.309978i
$891$	−5.36776	−	14.5663i	−0.179827	−	0.487989i
$892$	−11.2465	+	11.2465i	−0.376561	+	0.376561i
$893$	−15.5892	−	9.00040i	−0.521671	−	0.301187i
$894$	19.8951	−	27.1905i	0.665393	−	0.909387i
$895$	−15.0350	−	4.02862i	−0.502565	−	0.134662i
$896$	1.00000			0.0334077
$897$	22.2398	+	43.9091i	0.742564	+	1.46608i
$898$	16.9663			0.566173
$899$	23.6666	+	6.34144i	0.789324	+	0.211499i
$900$	9.80161	+	2.15241i	0.326720	+	0.0717471i
$901$	7.65017	+	4.41683i	0.254864	+	0.147146i
$902$	3.85128	−	3.85128i	0.128234	−	0.128234i
$903$	−15.4927	+	12.4597i	−0.515565	+	0.414633i
$904$	2.72719	+	10.1780i	0.0907050	+	0.338516i
$905$	−29.0720	−	29.0720i	−0.966387	−	0.966387i
$906$	−12.2245	−	1.32643i	−0.406131	−	0.0440677i
$907$	29.7986	−	17.2042i	0.989445	−	0.571256i	0.0843368	−	0.996437i	$-0.473123\pi$
$907$	29.7986	−	17.2042i	0.989445	−	0.571256i	0.905108	+	0.425181i	$0.139789\pi$
$908$	3.35272	−	12.5125i	0.111264	−	0.415242i
$909$	−12.6000	+	13.8058i	−0.417916	+	0.457910i
$910$	−10.1901	−	2.15580i	−0.337799	−	0.0714640i
$911$			4.55472i			0.150905i	0.997149	+	0.0754523i	$0.0240401\pi$
$911$			4.55472i			0.150905i	−0.997149	+	0.0754523i	$0.975960\pi$
$912$	1.59007	+	10.2626i	0.0526524	+	0.339828i
$913$	12.3839	+	21.4496i	0.409848	+	0.709877i
$914$	0.136294	−	0.236068i	0.00450820	−	0.00780844i
$915$	9.31180	−	24.0163i	0.307839	−	0.793955i
$916$	−13.3165	+	3.56814i	−0.439989	+	0.117895i
$917$	−6.95253	+	1.86293i	−0.229593	+	0.0615192i
$918$	−16.0726	−	32.3470i	−0.530474	−	1.06761i
$919$	−12.8663	+	22.2851i	−0.424420	+	0.735117i	−0.996366	−	0.0851740i	$-0.972855\pi$
$919$	−12.8663	+	22.2851i	−0.424420	+	0.735117i	0.571946	+	0.820291i	$0.306189\pi$
$920$	−11.3840	−	19.7176i	−0.375319	−	0.650071i
$921$	−18.2480	+	2.82731i	−0.601292	+	0.0931631i
$922$			22.8604i			0.752866i
$923$	29.7363	+	26.7233i	0.978782	+	0.879607i
$924$	−1.20597	−	2.73335i	−0.0396734	−	0.0899206i
$925$	−5.15859	+	19.2521i	−0.169613	+	0.633005i
$926$	−5.18245	+	2.99209i	−0.170306	+	0.0983261i
$927$	−42.5762	+	13.5179i	−1.39839	+	0.443985i
$928$	2.16355	+	2.16355i	0.0710220	+	0.0710220i
$929$	−12.4325	−	46.3989i	−0.407899	−	1.52230i	−0.798647	−	0.601800i	$-0.794450\pi$
$929$	−12.4325	−	46.3989i	−0.407899	−	1.52230i	0.390748	−	0.920498i	$-0.372216\pi$
$930$	−25.1100	−	31.2224i	−0.823388	−	1.02382i
$931$	4.23968	−	4.23968i	0.138950	−	0.138950i
$932$	−15.3458	−	8.85988i	−0.502667	−	0.290215i
$933$	−18.4495	−	13.4994i	−0.604011	−	0.441951i
$934$	−10.8906	−	2.91813i	−0.356352	−	0.0954842i
$935$	34.6368			1.13274
$936$	1.06854	+	10.7637i	0.0349264	+	0.351824i
$937$	34.8238			1.13764			0.568822	−	0.822461i	$-0.307399\pi$
$937$	34.8238			1.13764			0.568822	+	0.822461i	$0.307399\pi$
$938$	−1.29441	−	0.346835i	−0.0422639	−	0.0113246i
$939$	26.8904	+	19.6756i	0.877537	+	0.642088i
$940$	7.51085	+	4.33639i	0.244977	+	0.141438i
$941$	−32.2919	+	32.2919i	−1.05269	+	1.05269i	−0.0541537	+	0.998533i	$0.517246\pi$
$941$	−32.2919	+	32.2919i	−1.05269	+	1.05269i	−0.998533	+	0.0541537i	$0.982754\pi$
$942$	−8.17510	−	10.1651i	−0.266359	−	0.331198i
$943$	6.44124	+	24.0390i	0.209756	+	0.782819i
$944$	1.86568	+	1.86568i	0.0607226	+	0.0607226i
$945$	−11.2558	+	9.93094i	−0.366151	+	0.323054i
$946$	−17.1464	+	9.89947i	−0.557477	+	0.321860i
$947$	5.80669	−	21.6709i	0.188692	−	0.704209i	−0.805118	−	0.593115i	$-0.797898\pi$
$947$	5.80669	−	21.6709i	0.188692	−	0.704209i	0.993810	−	0.111094i	$-0.0354354\pi$
$948$	5.87692	+	13.3202i	0.190873	+	0.432619i
$949$	−7.01757	+	33.1709i	−0.227800	+	1.07677i
$950$			20.0563i			0.650712i
$951$	11.0700	−	1.71516i	0.358969	−	0.0556180i
$952$	−3.47565	−	6.02001i	−0.112647	−	0.195109i
$953$	−3.04642	+	5.27655i	−0.0986832	+	0.170924i	−0.911140	−	0.412097i	$-0.864796\pi$
$953$	−3.04642	+	5.27655i	−0.0986832	+	0.170924i	0.812457	+	0.583022i	$0.198130\pi$
$954$	−3.80840	+	0.173908i	−0.123302	+	0.00563050i
$955$	2.40010	−	0.643106i	0.0776656	−	0.0208104i
$956$	−5.37303	+	1.43970i	−0.173776	+	0.0465632i
$957$	3.30457	−	8.52291i	0.106822	−	0.275506i
$958$	−0.456037	+	0.789880i	−0.0147339	+	0.0255199i
$959$	0.905090	+	1.56766i	0.0292269	+	0.0506225i
$960$	−0.766095	−	4.94452i	−0.0247256	−	0.159584i
$961$			33.1237i			1.06851i
$962$	−21.4529	+	1.14486i	−0.691669	+	0.0369117i
$963$	−34.2468	−	31.2557i	−1.10359	−	1.00720i
$964$	−2.28012	+	8.50951i	−0.0734376	+	0.274073i
$965$	4.62592	−	2.67078i	0.148914	−	0.0859753i
$966$	13.5715	+	1.47259i	0.436657	+	0.0473800i
$967$	29.9904	+	29.9904i	0.964426	+	0.964426i	0.999389	−	0.0349622i	$-0.0111311\pi$
$967$	29.9904	+	29.9904i	0.964426	+	0.964426i	−0.0349622	+	0.999389i	$0.511131\pi$
$968$	2.07698	+	7.75138i	0.0667565	+	0.249139i
$969$	56.2543	−	45.2414i	1.80715	−	1.45336i
$970$	−16.9944	+	16.9944i	−0.545658	+	0.545658i
$971$	25.8769	+	14.9401i	0.830431	+	0.479449i	0.854000	−	0.520273i	$-0.174170\pi$
$971$	25.8769	+	14.9401i	0.830431	+	0.479449i	−0.0235694	+	0.999722i	$0.507503\pi$
$972$	13.3670	+	8.02016i	0.428747	+	0.257247i
$973$	−15.2466	−	4.08531i	−0.488783	−	0.130969i
$974$	−7.29423			−0.233722
$975$	−1.14352	+	20.8585i	−0.0366219	+	0.668007i
$976$	−5.14805			−0.164785
$977$	−2.46578	−	0.660703i	−0.0788871	−	0.0211377i	0.219160	−	0.975689i	$-0.429668\pi$
$977$	−2.46578	−	0.660703i	−0.0788871	−	0.0211377i	−0.298047	+	0.954551i	$0.596335\pi$
$978$	−1.57174	+	2.14809i	−0.0502588	+	0.0686882i
$979$	−4.95056	−	2.85821i	−0.158221	−	0.0913488i
$980$	−2.04268	+	2.04268i	−0.0652509	+	0.0652509i
$981$	−11.7120	+	22.6088i	−0.373935	+	0.721842i
$982$	8.68412	+	32.4096i	0.277121	+	1.03423i
$983$	3.28424	+	3.28424i	0.104751	+	0.104751i	0.757540	−	0.652789i	$-0.226401\pi$
$983$	3.28424	+	3.28424i	0.104751	+	0.104751i	−0.652789	+	0.757540i	$0.726401\pi$
$984$	−0.589980	+	5.43729i	−0.0188079	+	0.173335i
$985$	33.5843	−	19.3899i	1.07009	−	0.617814i
$986$	5.50484	−	20.5443i	0.175310	−	0.654265i
$987$	−4.75754	+	2.09905i	−0.151434	+	0.0668134i
$988$	−20.5537	+	6.70003i	−0.653901	+	0.213157i
$989$		−	90.4680i		−	2.87671i
$990$	−12.5912	+	8.05692i	−0.400175	+	0.256066i
$991$	4.50317	+	7.79972i	0.143048	+	0.247766i	0.928643	−	0.370975i	$-0.120976\pi$
$991$	4.50317	+	7.79972i	0.143048	+	0.247766i	−0.785595	+	0.618741i	$0.787643\pi$
$992$	−4.00386	+	6.93490i	−0.127123	+	0.220183i
$993$	−38.2226	−	14.8200i	−1.21296	−	0.470298i
$994$	10.7106	−	2.86989i	0.339718	−	0.0910273i
$995$	−66.8071	+	17.9009i	−2.11793	+	0.567497i
$996$	−23.1889	−	8.99099i	−0.734768	−	0.284890i
$997$	−8.44727	+	14.6311i	−0.267528	+	0.463372i	−0.968223	−	0.250089i	$-0.919540\pi$
$997$	−8.44727	+	14.6311i	−0.267528	+	0.463372i	0.700695	+	0.713461i	$0.252873\pi$
$998$	2.95559	+	5.11923i	0.0935575	+	0.162046i
$999$	−17.1237	+	25.7945i	−0.541769	+	0.816102i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.a.323.9	yes	56
3.2	odd	2		546.2.bu.b.323.4	yes	56
13.6	odd	12		546.2.bu.b.71.4	yes	56
39.32	even	12	inner	546.2.bu.a.71.9	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.9	✓	56	39.32	even	12	inner
546.2.bu.a.323.9	yes	56	1.1	even	1	trivial
546.2.bu.b.71.4	yes	56	13.6	odd	12
546.2.bu.b.323.4	yes	56	3.2	odd	2

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

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.39783 - 1.02278i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.04268 - 2.04268i) q^{5} +(-1.08548 - 1.34972i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.907836 + 2.85934i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.39783 - 1.02278i) q^{3} +(0.866025 + 0.500000i) q^{4} +(2.04268 - 2.04268i) q^{5} +(-1.08548 - 1.34972i) q^{6} +(-0.258819 - 0.965926i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.907836 + 2.85934i) q^{9} +(2.50176 - 1.44439i) q^{10} +(-0.446430 + 1.66610i) q^{11} +(-0.699162 - 1.58467i) q^{12} +(3.02199 - 1.96661i) q^{13} -1.00000i q^{14} +(-4.94452 + 0.766095i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.47565 - 6.02001i) q^{17} +(0.136851 + 2.99688i) q^{18} +(-5.79151 + 1.55183i) q^{19} +(2.79035 - 0.747671i) q^{20} +(-0.626147 + 1.61491i) q^{21} +(-0.862436 + 1.49378i) q^{22} +(-3.94076 - 6.82559i) q^{23} +(-0.265197 - 1.71163i) q^{24} -3.34505i q^{25} +(3.42802 - 1.11745i) q^{26} +(1.65548 - 4.92538i) q^{27} +(0.258819 - 0.965926i) q^{28} +(2.64980 - 1.52986i) q^{29} +(-4.97432 - 0.539744i) q^{30} +(5.66232 + 5.66232i) q^{31} +(0.258819 + 0.965926i) q^{32} +(2.32809 - 1.87232i) q^{33} +(4.91531 - 4.91531i) q^{34} +(-2.50176 - 1.44439i) q^{35} +(-0.643461 + 2.93018i) q^{36} +(-5.75540 - 1.54215i) q^{37} -5.99581 q^{38} +(-6.23563 - 0.341854i) q^{39} +2.88878 q^{40} +(-3.05005 - 0.817259i) q^{41} +(-1.02278 + 1.39783i) q^{42} +(9.94067 + 5.73925i) q^{43} +(-1.21967 + 1.21967i) q^{44} +(7.69512 + 3.98629i) q^{45} +(-2.03989 - 7.61296i) q^{46} +(2.12290 + 2.12290i) q^{47} +(0.186842 - 1.72194i) q^{48} +(-0.866025 + 0.500000i) q^{49} +(0.865763 - 3.23107i) q^{50} +(-11.0155 + 4.86009i) q^{51} +(3.60043 - 0.192141i) q^{52} +1.27079i q^{53} +(2.87386 - 4.32908i) q^{54} +(2.49139 + 4.31521i) q^{55} +(0.500000 - 0.866025i) q^{56} +(9.68270 + 3.75426i) q^{57} +(2.95546 - 0.791914i) q^{58} +(2.54856 - 0.682885i) q^{59} +(-4.66513 - 1.80880i) q^{60} +(-2.57403 + 4.45834i) q^{61} +(4.00386 + 6.93490i) q^{62} +(2.52695 - 1.61695i) q^{63} +1.00000i q^{64} +(2.15580 - 10.1901i) q^{65} +(2.73335 - 1.20597i) q^{66} +(0.346835 - 1.29441i) q^{67} +(6.02001 - 3.47565i) q^{68} +(-1.47259 + 13.5715i) q^{69} +(-2.04268 - 2.04268i) q^{70} +(2.86989 + 10.7106i) q^{71} +(-1.37992 + 2.66380i) q^{72} +(-6.64934 + 6.64934i) q^{73} +(-5.16015 - 2.97921i) q^{74} +(-3.42126 + 4.67580i) q^{75} +(-5.79151 - 1.55183i) q^{76} +1.72487 q^{77} +(-5.93468 - 1.94411i) q^{78} -8.40565 q^{79} +(2.79035 + 0.747671i) q^{80} +(-7.35167 + 5.19163i) q^{81} +(-2.73460 - 1.57882i) q^{82} +(10.1535 - 10.1535i) q^{83} +(-1.34972 + 1.08548i) q^{84} +(-5.19729 - 19.3966i) q^{85} +(8.11652 + 8.11652i) q^{86} +(-5.26867 - 0.571683i) q^{87} +(-1.49378 + 0.862436i) q^{88} +(-0.857755 + 3.20119i) q^{89} +(6.40119 + 5.84211i) q^{90} +(-2.68175 - 2.41002i) q^{91} -7.88152i q^{92} +(-2.12362 - 13.7063i) q^{93} +(1.50112 + 2.60001i) q^{94} +(-8.66029 + 15.0001i) q^{95} +(0.626147 - 1.61491i) q^{96} +(-8.03620 + 2.15329i) q^{97} +(-0.965926 + 0.258819i) q^{98} +(-5.16923 + 0.236050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 8 q^{6} + 24 q^{9}+O(q^{10}) \) 56 * q - 8 * q^6 + 24 * q^9	\( 56 q - 8 q^{6} + 24 q^{9} + 24 q^{10} - 8 q^{11} + 24 q^{13} - 4 q^{15} + 28 q^{16} + 4 q^{17} + 8 q^{19} + 4 q^{21} + 8 q^{23} + 8 q^{24} + 4 q^{26} - 24 q^{27} - 16 q^{30} - 8 q^{31} - 32 q^{33} - 24 q^{34} - 24 q^{35} - 12 q^{36} - 8 q^{37} - 60 q^{39} + 28 q^{41} - 8 q^{44} - 40 q^{45} - 20 q^{46} - 64 q^{50} + 8 q^{54} + 8 q^{55} + 28 q^{56} + 40 q^{57} + 4 q^{58} + 8 q^{59} + 4 q^{60} + 8 q^{61} + 32 q^{62} + 24 q^{65} + 32 q^{66} - 56 q^{69} + 112 q^{71} + 16 q^{72} + 8 q^{73} - 48 q^{74} - 40 q^{75} + 8 q^{76} - 8 q^{78} + 16 q^{79} + 12 q^{81} + 4 q^{83} - 4 q^{84} + 32 q^{85} + 16 q^{86} + 144 q^{87} - 88 q^{89} + 8 q^{90} - 8 q^{91} - 76 q^{93} - 8 q^{94} + 48 q^{95} - 4 q^{96} - 64 q^{97} - 40 q^{99}+O(q^{100}) \) 56 * q - 8 * q^6 + 24 * q^9 + 24 * q^10 - 8 * q^11 + 24 * q^13 - 4 * q^15 + 28 * q^16 + 4 * q^17 + 8 * q^19 + 4 * q^21 + 8 * q^23 + 8 * q^24 + 4 * q^26 - 24 * q^27 - 16 * q^30 - 8 * q^31 - 32 * q^33 - 24 * q^34 - 24 * q^35 - 12 * q^36 - 8 * q^37 - 60 * q^39 + 28 * q^41 - 8 * q^44 - 40 * q^45 - 20 * q^46 - 64 * q^50 + 8 * q^54 + 8 * q^55 + 28 * q^56 + 40 * q^57 + 4 * q^58 + 8 * q^59 + 4 * q^60 + 8 * q^61 + 32 * q^62 + 24 * q^65 + 32 * q^66 - 56 * q^69 + 112 * q^71 + 16 * q^72 + 8 * q^73 - 48 * q^74 - 40 * q^75 + 8 * q^76 - 8 * q^78 + 16 * q^79 + 12 * q^81 + 4 * q^83 - 4 * q^84 + 32 * q^85 + 16 * q^86 + 144 * q^87 - 88 * q^89 + 8 * q^90 - 8 * q^91 - 76 * q^93 - 8 * q^94 + 48 * q^95 - 4 * q^96 - 64 * q^97 - 40 * q^99

Introduction

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